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UNIVERSITY OF CALIFORNIA
Santa Barbara
Polarization control of long-wavelength vertical cavity surface emitting laser
(VCSEL) fabricated by orientation-mismatched wafer bonding
A Dissertation submitted in partial satisfaction of the
requirements for the degree Doctor of Philosophy
in Electrical and Computer Engineering
by
Yae Okuno
Committee in charge:
Professor John E. Bowers, Chair
Professor Larry Coldren
Professor Steve DenBaars
Professor Evelyn Hu
September 2004
UMI Number: 3143802
________________________________________________________ UMI Microform 3143802
Copyright 2004 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
____________________________________________________________
ProQuest Information and Learning Company 300 North Zeeb Road
PO Box 1346 Ann Arbor, MI 48106-1346
The dissertation of Yae Okuno is approved.
____________________________________________Evelyn Hu
____________________________________________Steve DenBaars
____________________________________________Larry Coldren
____________________________________________John E. Bowers, Committee Chair
August 2004
iii
Polarization control of long-wavelength vertical cavity surface emitting laser
(VCSEL) fabricated by orientation-mismatched wafer bonding
Copyright © 2004
by
Yae Okuno
iv
To my family: husband Jon L., mother Toshiko, and father Teruo
for their endless support and love
v
ACKNOWLEDGEMENTS
I am very grateful for the fact that I have been able to receive tremendous help
and support from so many people to accomplish what I have wanted.
First, I would like to thank my committee, Prof. Bowers, Prof. Coldren, Prof.
DenBaars, and Prof. Hu, for their precious input on this thesis work. My advisor,
Prof. John Bowers has provided me with great opportunity to pursue this research and
to obtain variety of experience and knowledge. Prof. Steve DenBaars, as MOCVD
lab principal, provided me with the superb environment for MOCVD research. I also
like to thank Prof. Speck for his input on crystal defect discussion, and Prof.
Blumenthal for providing me NSF funding. This research was also funded by Walsin
Corporation.
Next, I would like to thank to the people who have been directly involved in
this thesis work. Dr. Jon Geske has been a great help on every aspect of this
research, and provided me with a lot of input throughout the past 5 years. Kian-Giap
Gan has been not only helpful on this research, but also a great brain on helping me
through the course works and screening exam. Hsu-Feng (Hubert) Chou, Prof. Yi-jen
Chiu, Chad. Wang, Dr. Andrew Jackson, Shaomin Wu, and Dr. Staffan Björlin are all
thanked for their time and help for my work. I would like to put a special note for Dr.
Kohl Gill for his help on low-temperature PL measurement.
vi
The members of Bowers group have been great help, not just on research but
also on private time. Of all, I am indebted to Dr. Patrick Abraham for his continuous
help on MOCVD issues even after he left UCSB 3 months after I joined the group.
Dr. Alexis Black, Dr. Vijay Jayaraman, Manish Metha, Dr. Toshio Kimura, Dr.
Gehong Zeng, Dr. Thomas Liljeberg, Dr. Daniel Lasaosa, Dr. Donato Pasquariello,
Dr. Chris LaBounty, Dr. Bin Liu, Dr. Maura Raburn, Emily. Burmeister, Qi Chen,
Brian Koch, Raja Jindal, Garrett Cole, Dr. Satoshi Kodama: Thank you all. And
special big thank you for the ladies who have helped me so much: Kate Ferrian,
Hillary, Michelle, Christina (hope to see you again at Motorhead show!).
MOCVD lab has been a big part of my work. Among the group, my first and
biggest thank you goes to Brian Carralejo for his help on everything in the lab, and
especially for helping me on weekend mornings as I used to grow on weekends, and
it seemed problems always happen when nobody else is around. Dr. Stacia Keller has
been a great lab leader and I also appreciate her help on my research. Mike Iza, Dr.
Paul Fini, Dr. Hugues Marchand, Dr. Brendan Moran, Dr. Mike Ceaven, Dr. Tom
Katona, Dr. Erik. Skogen, Dr. Jon Barton, James Raring, Jeff Hennes, Bilge Imar:
Thank you for keeping the machine I/III working, and for helping me when I had
problem with the machine. Users of the other machine, Dr. Ilan , Dr. Sten Heikman,
Dr. Tal Margalith, Dr. Andreas Stonas, Pablo Cantu, Dr. Gia Parish, Dr. Monica
Hansen, Dr. Huili Xing, Dr. Lee MaCarthy: Thank you for your help on the lab issues
and the fun time in the lab working together.
vii
I am very indebted to Coldren lab for letting me using test equipments as they
were inevitable for my research. Dr. Dan Cohen has been very helpful on those
equipments, and I appreciate for his generous help. Also, people in the lab other than
already mentioned: Rintaro Koda, Dr. Shigeru Nakagawa, Dr. Milan Masanovic:
Thank you for everything.
The Cleanroom (Nanofab) is the greatest one of all the labs I have seen so far,
and it is supported by great personnel such as Jack Whaley, Bob Hill, Dr. Brian
Thibeault (also thank you for a help on mask order), Don Freeborn, Neil Baker, Luis
Zuzunaga. Also, Martin Vandenbroek is thanked for maintaining the teaching lab
clean and safe place.
I believe evrybody knows how great is Ms. Valerie DeVeyra. Thank you for
your help throughout these 5 years.
Outside of UCSB, I would like to express my appreciation to the people I met
at UC Berkeley. I am very indebted to Prof. C. J. Chang-Hasnain for all she did for
me: letting me come to the US and join her group, and for giving me a great insight
of VCSELs. Without her, I won’t be who I am now. I had a great and wonderful
time with people: Dr. Jacob Hernandez, Dr. Sui Lim, Dr. Melissa Li, Steven Chase,
Dr. Chih-Hao Chang, Darren Hsiung, Kevin Lascola, Dr. Wupen Yuen: Thank you
very much for helping me at the time when, as a foreigner, I was having a lot of
difficulty living in the US. I was very fortunate to be around you for the first 2 years
of my US life. And late Gabriel Li, I send my thank you and a prayer to you.
viii
I have had great friends who supported me to the great extent. Mike&Koko
Larson, Sumiko Fujisaki, Sonoko Migitaka, Naoko Asai, I hope we will be friends
hereafter for long, too.
Back in Japan, people at Hitachi Central Research Laboratory taught me the
basics of semiconductors: Dr. N. Chinone, T. Tsuchiya, T. Kawano, M. Aoki, and Dr.
Diego Olego from Philips, thank you for giving me precious knowledge.
In the last but not least, the greatest support came from my family. My
husband Jon for his continuous love, and my parents for their mental and financial
help, and for bringing me up to be who I am.
And, some great music that helped me getting through the graduate school:
Deep Purple, Rob Halford, Uli Jon Roth, Megadeth, Rammstein, AC/DC,,,, the list
goes on.
ix
VITA OF YAE OKUNO
September 2004
EDUCATION
1986 - 1990 Kyoto University, Japan
Bachelor of Science in Nuclear Engineering, March 1990
1997 - 1999 University of California, Berkeley,
Master of Science in Electrical Engineering, May 1999
1999 - 2004 University of California, Santa Barbara
Doctor of Philosophy in Electrical and Computer Engineering,
September 2004 (expected)
PROFESSIONAL EMPLOYMENT
1990 - 1997 Central Research Laboratory, Hitachi Ltd, Tokyo, Japan
Researcher, Opto-electronics Department
1997 - 1999 University of California, Berkeley,
Graduate student researcher
1999 - 2004 University of California, Santa Barbara
Graduate student researcher
x
PUBLICATIONS
A) First-authored
[1] Y. Okuno, T. Kawano, T. Tsuchiya, and T. Taniwatari, "Threading dislocation
reduction in InP on GaAs by thin strained interlayer and its application to the
fabrication of 1.3 µm wavelength laser on GaAs", Jpn. J. Appl. Phys. 32, pp.614-7,
1993.
[2] Y. Okuno, T. Kawano, T. Tsuchiya, and T. Taniwatari, "Threading dislocation
reduction in InP/GaAs by thin strained interlayer and its application to the fabrication
of 1.3 µm wavelength laser on GaAs", Extended Abstracts of the 1992 International
Conference on Solid State Devices and Materials, Tokyo, Japan, pp.610-2, 1992.
[3] Y. Okuno, T. Kawano, M. Koguchi, K. Nakamura, and H. Kakibayashi,
"Dislocation reduction in InP layers grown on sawtooth-patterned GaAs substrates”,
J. Cryst. Growth 137, pp.313-8, 1994.
[4] Y. Okuno and T. Kawano, "Study of threading dislocation reduction by strained
interlayer in InP layers grown on GaAs substrates", J. Cryst. Growth 145, pp.338-44,
1994.
[5] Y. Okuno, K. Uomi, M. Aoki, T. Taniwatari, M. Suzuki, and M. Kondow, "Anti-
phase direct bonding and its application to the fabrication of InP-based 1.55 µm
wavelength lasers on GaAs substrates", Appl. Phys. Lett. 66, pp.451-3, 1995.
xi
[6] Y. Okuno, M. Aoki, T. Tsuchiya, and K. Uomi, "Free-orientation integration by
direct bonding: fabrication of (001) InP-based 1.55 µm-wavelength lasers on (110)
GaAs substrate", Proc. 7th Int. Conf. Indium Phosphide and Related Materials, NY,
USA, pp.785-8, 1995.
[7] Y. Okuno, M. Aoki, T. Tsuchiya, and K. Uomi, "Fabrication of (001) InP-based
1.55-µm wavelength lasers on a (110) GaAs substrate by direct bonding (a prospect
for free-orientation integration)", Appl. Phys. Lett. 67, pp.810-2, 1995.
[8] Y. Okuno, "Investigation on direct bonding of III-V semiconductor wafers with
lattice mismatch and orientation mismatch", Appl. Phys. Lett. 68, pp.2855-7, 1996.
[9] Y. Okuno and K. Uomi, "Direct bonding of lattice-mismatched and orientation-
mismatched III-V semiconductor wafers: A step toward establishing 'free-orientation
integration'", Inst. Phys. Conf. Ser. No. 145, pp.301-6, 1996.
[10] Y. Okuno and M. Tamura, "Direct water bonding of a (001) InP-based strained
multiple quantum well on a (110) Si substrate with a GaAs buffer layer, aligning
cleavage planes of InP and Si", Jpn. J. Appl. Phys. 35, pp.L1652-4, 1996.
[11] Y. Okuno, K. Uomi, M. Aoki, and T. Tsuchiya, "Direct wafer bonding of III-V
compound semiconductors for free-material and free-orientation integration", IEEE J.
Quantum. Electron. 33, pp.959-69, 1997.
[12] Y. Okuno, K. Uomi, M. Aoki, and T. Tsuchiya, "Direct wafer bonding aiming
for free-material and free-orientation integration of semiconductor materials ", IEICE
Trans. Electron. E80-C, pp.682-8, 1997.
xii
[13]Y. Okuno, T. Tsuchiya, and M. Okai, "Crystal growth and fabrication of a 1.3-
µm-wavelength multiple-quantum-well laser on a (211)A InP substrate", Proc. 9th
Int. Conf. Indium Phosphide and Related Materials, NY, USA, pp.567-70, 1997.
[14] Y. Okuno, T. Tsuchiya, and M. Okai, "Fabrication of a 1.3-µm-wavelength
multiple-quantum-well laser on a (211)A InP substrate", Appl. Phys. Lett. 71,
pp.1918-20, 1997.
[15] Y. L. Okuno, J. Geske, Y.-J. Chiu, S. P. DenBaars, and J. E. Bowers,
"Polarization control of 1.3 µm-wavelength vertical cavity surface emitting laser
(VCSEL) fabricated by orientation-mismatched wafer bonding", IEEE 18th Int.
Semiconductor Laser Conference, NJ, USA, pp.17-18, 2002.
[16] Y. L. Okuno, J. Geske, Y.-J. Chiu, S. P. DenBaars, and J. E. Bowers,
"Orientation-mismatched wafer bonding for polarization control of 1.3 µm-
wavelength vertical cavity surface emitting laser (VCSEL)", Proc. 29th Int. Symp.
Compound Semiconductors, pp.367-70, 2002.
[17] Y. L. Okuno, J. Geske, K.-G. Gan, Y.-J. Chiu, S. P. DenBaars, and J. E. Bowers,
"1.3 µm-wavelength vertical cavity surface emitting laser fabricated by orientation-
mismatched wafer bonding: a prospect for polarization control", Appl. Phys. Lett. 82,
pp.2377-9, 2003.
[18] Y. L. Okuno, S. P. DenBaars, and J. E. Bowers, “High doping incorporation on
(311)B InP/InGaAs by metalorganic chemical vapour deposition and its application
to tunnel junction fabrication”, Appl. Phys. Lett. 84, pp.3483-5, 2004.
xiii
[19] Y. L. Okuno, S. P. DenBaars, and J. E. Bowers, “An InP/InGaAs tunnel junction
fabricated on (311)B InP substrate by MOCVD”, Proc. 16th Int. Conf. Indium
Phosphide and Related Materials, NY, USA, pp.114-117, 2004.
[20] Y. L. Okuno and J. E. Bowers “Electrical properties of orientation-mismatched
interface of (311)B InP/(100) GaAs, and the effect of surface preparation methods”,
Proc. 16th Int. Conf. Indium Phosphide and Related Materials, NY, USA, pp.314-
317, 2004.
B) Co-authored
[1] D. J. Olego, M. Tamura, Y. Okuno, T. Kawano, and A. Hashimoto,
"Heteroepitaxial InP layers grown by metalorganic chemical vapor deposition on
novel GaAs on Si buffers obtained by molecular beam epitaxy", J. Appl. Phys. 71,
pp.4329-32, 1992.
[2] D. J. Olego, Y. Okuno, T. Kawano, and M. Tamura, "Structural and
optoelectronic properties and their relationship with strain relaxation in
heteroepitaxial InP layers grown on GaAs substrates", J. Appl. Phys. 71, pp.4492-
501, 1992.
[3] D. J. Olego, Y. Okuno, T. Kawano, and M. Tamura, "Heteroepitaxial GaAs layers
on InP substrates: radiative recombinations, strain relaxation, structural properties,
and comparison with InP layers on GaAs", J. Appl. Phys. 71, pp.4502-8, 1992.
[4] M. Tamura, D. J. Olego, Y. Okuno, and T. Kawano, "Threading dislocations in
GaAs/InP and InP/GaAs heterostructures", Proc. Gallium Arsenide and Related
Compounds, Bristol, UK, pp.151-6, 1992.
xiv
[5] M. Aoki, N. Kikuchi, K. Sekine, S. Sasaki, M. Suzuki, T. Taniwatari, Y. Okuno,
A. Takai, and T. Kawano, "Low drive voltage and extremely low chirp integrated
electroabsorption modulator DFB laser for 2.5 Bbits/s 200 km normal fiber
transmission", Electron. Lett. 29, pp.1983-4, 1993.
[6] M. Aoki, M. Suzuki, and Y. Okuno, "Multi-wavelength DFB laser arrays grown
by in-plane thickness control epitaxy", Proc. 7th Int. Conf. Indium Phosphide and
Related Materials, NY, USA. pp.53-6, 1995
[7] T. Tsuchiya, Y. Okuno, A. Niwa, and M. Okai, "1.3-µm InGaAsP multiple
quantum well laser on (211) InP substrate", Tech. Digest. 2nd Optoelectronics and
Communications Conference, Seoul, South Korea, pp.170-1, 1997.
[8] M. Raburn, B. Liu, Y. Okuno, and J. E. Bowers, "InP/InGaAsP wafer-bonded
vertically coupled X-crossing multiple channel optical add-drop multiplexer", Proc.
13th Int. Conf. Indium Phosphide and Related Materials, NJ, USA, pp.166-9, 2001
[9] M. Raburn, B. Liu, Y. Okuno, and J. E. Bowers, "InP-InGaAsP wafer-bonded
vertically coupled X-crossing multiple channel optical add-drop multiplexer", IEEE
Photon. Tech. Lett. 13, pp.579-581, 2001.
[10] C. LaBounty, A. Karim, X. Fan, G. Zeng, P. Abraham, Y. Okuno, and J. E.
Bowers, "Wafer-fused thin film cooler semiconductor laser structures", Proc. Int.
Conf. Thermoelectrics, NJ, USA, pp.397-400, 2001.
[11] J. Geske, Y. L. Okuno, J. E. Bowers, and V. Jayaraman, "Vertical and lateral
heterogeneous integration", Appl. Phys. Lett. 79, pp.1760-2, 2001.
xv
[12] J. Geske, V. Jayaraman, Y. L. Okuno, and J. E. Bowers, "Vertical and lateral
heterogeneous integration", 14th Annual Meeting of the IEEE Lasers and Electro-
Optics, vol. 2, NJ, USA, pp.881-2, 2001.
[13] M. Raburn, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, "Optimization
and assessment of shape, alignment, and structure of InP/InGaAsP waveguide
vertically coupled optical add-drop multiplexers", Proc. 14th Int. Conf. Indium
Phosphide and Related Materials, NJ, USA, pp.131-4, 2002.
[14] M. Raburn, K. Rauscher, Y. Okuno, N. Dagli, and J. E. Bowers, "3-D photonic
circuit technology", IEEE J. Selected Topics Quantum Electron. 8, pp.935-42, 2002.
[15] J. Geske, Y. L. Okuno, and J. E. Bowers, "Dual-wavelength vertical-cavity
surface-emitting laser arrays fabricated by nonplanar wafer bonding", IEEE 18th Int.
Semiconductor Laser Conference, NJ, USA, pp.141-2, 2002.
[16] J. Geske, Y. L. Okuno, J. E. Bowers, and D. Leonard, "Long-wavelength, two-
dimensional, WDM vertical-cavity surface-emitting laser arrays fabricated by
nonplanar wafer bonding", Proc. 29th Int. Symp. Compound Semiconductors,
pp.351-4, 2002.
[17] J. Geske, Y. L. Okuno, D. Leonard, and J. E. Bowers, "Long-wavelength two-
dimensional WDM vertical cavity surface-emitting laser arrays fabricated by
nonplanar wafer bonding", IEEE Photon. Tech. Lett. 15, pp.179-181, 2003.
[18] J. Piprek, D. Pasquariello, D. Lasaosa, Y. Okuno, and J. E. Bowers, "1.55 µm
Traveling-Wave Amplification Photodetector", Proc. 15th Int. Conf. Indium
Phosphide and Related Materials, NJ, USA, pp.499-501, 2003.
xvi
[19] Y. Dong, Y. L. Okuno, and U. K. Mishra, "Selective area growth of InP through
narrow openings by MOCVD and its application to InP HBT", Proc. 15th Int. Conf.
Indium Phosphide and Related Materials, NJ, USA, pp.389-92, 2003.
[20] M. Mehta, V. Jayaraman, A. W. Jackson, S. Wu, Y. Okuno, J. Piprek, and J. E.
Bowers, "134°C Continuous-Wave Operation of a 1.33-µm Wafer-Bonded VCSEL",
Tech. Digest Conf. Lasers and Electro-Optics, 2003.
[21] M. Mehta, V. Jayaraman, A. W. Jackson, S. Wu, Y. Okuno, J. Piprek, and J. E.
Bowers, "Wafer-Bonded VCSELs with Tunnel Junctions", SPIE Proc. XX,
(ITCOM’03), 2003.
[22] J. Geske, D. Leonard, M. MacDoughal, Y. L. Okuno, J. Piprek, and J. E.
Bowers, "Long-Wavelength WDM Vertical-Cavity Surface-Emitting Laser Arrays
Spanning 140 nm", Proc. 29th European Conf. Optical Communication (ECOC´03),
2003.
[23] V. Jayaraman, M. Mehta, A. W. Jackson, Y. Okuno, J. Piprek, and J. E. Bowers,
"High-Power 1320-nm Wafer-Bonded VCSELs With Tunnel Junctions", IEEE
Photon. Tech. Lett. 15, pp.1495-7, 2003.
[24] Y. Dong, Y. L. Okuno, and U. K. Mishra, "MOCVD selective growth of InP
through narrow openings and its application to InP HBT extrinsic base regrowth", J.
Cryst. Growth 260, pp.316-21, 2004.
xvii
ABSTRACT
Polarization control of long-wavelength vertical cavity surface emitting laser
(VCSEL) fabricated by orientation-mismatched wafer bonding
by
Yae Okuno
This thesis explores fabrication and investigation of controlling polarization
of light output of a long-wavelength VCSEL. The conventional VCSELs are
fabricated on symmetric (001) crystal plane which does not have fundamental
polarization selection rule. Unstable polarization of the VCSEL limits its use as a
transmitter and application to other polarization-sensitive scheme.
In order to achieve a polarization-controlled VCSEL, we fabricated its active
region on (113)B plane. The (113) and other planes of (11n) family are asymmetric,
which leads to asymmetric stress and anisotropic optical gain. A large dichroism
such as anisotropic gain is expected to be most effective in stabilizing polarization.
The active region for 1.3-µm wavelength VCSEL was grown on (113)B InP
substrate by metal-organic chemical vapor deposition (MOCVD). Since this plane is
asymmetric, it is more difficult to grow on than (001) plane. The growth condition
was optimized to low-migration condition in order to achieve flat surface
xviii
morphology and good crystalline quality. We also observed that the doping
efficiency of both n-type and p-type impurities was higher than that on (001) surface.
To complete the VCSEL, the active region on (113)B InP was integrated to
(001) GaAs-based distributed Bragg reflectors (DBRs) by wafer bonding technique.
Only by this technique, we can integrate such materials with different
crystallographic orientations without degrading material qualities significantly. The
VCSEL had maximum output power polarized at [33−2 ] axis, while minimum power
was orthogonal at [−110] axis. An index-guiding mesa structure was fabricated in an
asymmetric shape. Depending on its orientation of asymmetry, the index-guiding
either enhanced or distracted the polarization originating from gain anisotropy.
Statistical data showed that with appropriate index-guiding structure, the VCSEL
polarization can be stabilized with high yield over a wide operation range. We also
performed high-speed modulation on the VCSEL. The bit error rate (BER) was the
same on 2 types of the measurement links with and without having a polarization-
sensitive part. This result is a strong proof that the polarization of this VCSEL is
stable under practical operation.
xix
Contents
Chapter 1 Introduction 1
1.01 Polarization control of VCSEL 2
[1] Overview of polarization characteristics 2
[2] Approaches of polarization control 5
1.02 Long-wavelength VCSEL 10
1.03 Scope of this thesis 12
[1] Polarization control technique 12
[2] Choice of VCSEL wavelength 15
[3] Contents 16
References 18
Chapter 2 Theoretical analysis 27
2.01 Polarization characteristics of VCSEL 28
[1] SFM model 28
[2] Mechanism of polarization switching 32
[3] Birefringence by electro-optic effect 36
2.02 Properties of strained materials on (11n) substrate 38
[1] Strain/stress notations and strain energy density 38
[2] Strain/stress on (11n) coordinate 44
[3] Strain-induced piezoelectric effect and polarization 49
2.03 Optical gain on (11n) plane 55
[1] 4×4 Hamiltonian and effective mass 55
[2] Optical matrix element 58
[3] Optical gain anisotropy 64
[4] Anisotropy on (001) plane 65
xx
2.04 Defects and stress in bonded structure 67
[1] Defect classification 68
[2] Stress by misfit dislocations 71
[3] Cross hatch 75
[4] Stress by thermal expansion mismatch 77
2.05 Summary 79
References 80
Chapter 3 Experimental 86
3.01 MOCVD 86
[1] System and growth overview 86
[2] Growth calibration 87
[3] Problem with the system 89
3.02 Wafer bonding 91
[1] Bonding procedure summary 91
[2] Advantage/disadvantage of each procedure 93
[3] Pre- and post-bonding procedures 94
3.03 Material characterization methods 97
[1] PL measurement 97
[2] X-ray diffraction measurement 100
[3] Other characterization 102
References 103
Chapter 4 MOCVD growth on (113)B InP 105
4.01 Introduction 105
4.02 Optimizing growth condition 106
[1] Low-migration condition 106
[2] Solid-phase incorporation on (113)B surface 109
xxi
4.03 MQW growth 113
[1] PL and X-ray results 112
[2] Notes on MQW growth 115
[3] Piezoelectric effect 116
4.04 Doping characteristics 117
4.05 Tunnel junction 121
[1] I-V characteristics 121
[2] Theoretical calculation 124
[3] Annealing problem 127
[4] Tunnel junction grown by MBE 129
4.06 Summary 130
References 132
Chapter 5 Wafer bonding of (113)B InP to (001) GaAs 138
5.01 Introduction 138
5.02 MQW qualities after bonding 138
[1] Problem of PL deterioration 138
[2] Possible solution for annealing problem 143
[3] Annealing experiment – MQW design 146
[4] Annealing experiment – temperature and time 149
5.03 I-V characteristics of bonded interface 150
[1] VCSEL design consideration 150
[2] I-V test procedure and results 152
[3] Thermioic emission theory 154
[4] Discussion 158
5.04 Summary 159
References 161
xxii
Chapter 6 Optically pumped VCSEL with no guiding 164
6.01 Introduction 164
6.02 Fabrication 165
6.03 Polarization characteristics 168
[1] Measurement setup 168
[2] Results and analysis on unstrained MQW VCSEL 171
[3] Results of unstable polarization 175
[4] Results on strained MQW VCSEL 177
6.04 Summary 178
References 181
Chapter 7 Optically pumped VCSEL with index guiding 183
7.01 Introduction 183
7.02 Structure design and fabrication 183
7.03 Polarization performance 188
[1] CW measurement 188
[2] Statistical data 192
[3] Spectra observation 197
[4] Stability over transmission 203
7.04 Summary 208
References 209
Chapter 8 Conclusion and future work 211
8.01 Summary of this work 211
8.02 Electrically pumped VCSEL 214
8.03 Future work and conclusion 215
xxiii
Appendix A Material parameters 216
Appendix B Rotation matrix operation 217
[1] Strain and Stress 217
[2] Luttinger-Kohn 4×4 Hamiltonian 220
Appendix C Calculation of strain and polarization by various methods 224
Appendix D Poisson Ratio on (11n) plane 227
Appendix E MOCVD growth on (111) InP 229
[1] Effect of substrate misorientation 230
[2] Optimizing growth condition and MQW growth 236
[3] Problem of using (111) substrate 241
[4] Summary 244
References 245
Notations
VCSEL: Vertical-cavity surface-emitting laser
DBR: Distributed Bragg reflector
MOCVD: Metal-organic chemical vapor deposition
MBE: Molecular beam epitaxy
CBE: Chemical beam epitaxy
RIN: Relative intensity noise
BER: Bit error rate
TE mode: Transverse electric mode
TM mode: Transverse magnetic mode
CW: Continuous wave
FP: Fabri-Perot
1.3Q: InGaAsP which has a band-edge transition energy
corresponding to 1.3 µm
1
Chapter 1 Introduction
It has been ten years since the first report of an electrically-pumped long-
wavelength vertical-cavity surface-emitting laser (LW-VCSEL) fabricated by wafer
bonding technique [1]. This report was made by my predecessor from our group, and
led to a success of the first above-room-temperature operation of the LW-VCSEL,
and also led to some start-up companies in the last decade. A number of performance
requirements are important, including high temperature, high power, and high-speed
operation.
This thesis investigates another important aspect, polarization control.
Polarization control has been investigated actively in short-wavelength VCSELs, but
little has been done with LW-VCSELs. This work is one of the first to deliberately
investigate and achieve the polarization control on an LW-VCSEL.
In this chapter, as an introduction, I would like to begin with reviewing the
existing techniques for the polarization control and those for fabrication of LW-
VCSELs, followed by an explanation of the VCSEL investigated in this thesis.
2
1.01 Polarization control of VCSEL
[1] Overview of polarization characteristics
The polarization we discuss here is specifically the direction of the electric
field (E-field) of the output light from a laser. The polarization-uncontrolled laser has
problems such as increased RIN as I will explain later, while polarization
insensitiveness is a virtue for some other devices such as an optical amplifier.
Another similar aspect of the laser is a number of operating modes, which is not a
focus in this thesis. It is a common sense that a single-mode operation is desirable for
a laser to achieve better performance as a transmitter, but the VCSEL we aim can be
either multi-mode or single-mode. The polarization will be discussed by total power
from all modes at each polarization axis, unless otherwise stated.
Polarization control is usually not a problem on edge-emitting lasers. Figure
1-1 compares edge-emitting laser (EEL) and VCSEL by macroscopic and
microscopic structures. Both lasers are fabricated on conventional (001) substrates.
The EEL on the left side has a gain region of a narrow stripe buried by some method.
Its light-emitting surface is yz-plane which is (110) plane in this case: it can be either
(110) or (−110) plane, and the discussion hereafter is relevant in both cases. As the
light travels in the gain medium which is a rectangular waveguide, the light is either
TE or TM mode. TE mode is defined to have the E-field along y-axis which is
±[−110], and TM mode has its E-field along the z-axis which is ±[001]. If we compare
atomic structures in [−110] and [001] axes, we can see that these two axes are totally
3
Figure 1-1 Comparison of edge-emitting laser and VCSEL
different. By this structural asymmetry and by the physics, we can fix the
polarization of EEL by choosing strain in the gain medium. If the medium is
compressively-strained we get TE mode operation, and if the medium has tensile
strain larger than certain amount, we get TM mode operation. Around the boundary
of these two conditions, that is, with the gain medium having a small tensile strain,
both TE and TM mode can co-exist in the EEL.
In contrast, a VCSEL has a very different geometry, which affects not only
the polarization behavior but also other characteristics such as single longitudinal
mode operation. Since the VCSEL on the right side of Fig. 1-1 is fabricated on (001)
Edge-emitting laser
TE
TM
[001]
[110][110]
VCSEL
random
[001]
[110]
[110]
z=[001]
x=[110]
y=[110]
4
substrate and therefore, its light-emitting surface is (001) plane which is also the xy-
plane. As can be seen on atomic structure, this (001) plane has 4-fold symmetry so
that any two axes with 90° crossing angle (such as [110] x-axis and [−110] y-axis) are
equivalent. Adding strain in the gain medium does not change this symmetry as long
as it is a conventional biaxial strain (*refer to Fig. 2-3). Therefore, we cannot choose
one particular axis which is different from the others. Another aspect is that a typical
VCSEL is fabricated in a symmetric circular shape, and this is another reason why the
most VCSELs do not have controlled polarization output. In reality, VCSELs have
two possible polarization axes orthogonal to each other, and the lasing modes are
commonly TEMl,m modes whose E-field can be expressed as:
ysy
myxs
x
lx
ml eyHEexHEyxE
2
0
2
0, )()(),(−−
= 1-(1)
where Hl(x) is a lth order Hermite polynomial function and E0 is a constant. Since
H0(x) =1, the fundamental TEM0,0 mode is a symmetric Gaussian mode.
total power
power at axis #1
power at axis #2
IthPump current (arb. unit)
Ligh
t out
put p
ower
(arb
. uni
t)
Isw
Figure 1-2
An example of L-I curve of a
polarization-unstable VCSEL, showing
polarization switch at Isw.
5
To illustrate unstable polarization and its effect, I show a sketch of Light
output power - Pump current (L-I) curves of a polarization-unstable device in Figure
1-2. The curves are for total output power, power at polarization axis #1, and power
at another polarization axis #2. The VCSEL starts to lase with #1 polarization right
above threshold current Ith, but around the current Isw, #2 polarization starts to lase
and the lasing mode switches from #1 to #2 polarization. The switching can occur
more than 1 time between these 2 axes as pumping power increases. As explained
above, these two equivalent axes are at 90° crossing angle, and they are generally
[110] and [−110] axes if the VCSEL is on (001) substrate. These two polarization
states usually have slightly different lasing wavelength, which results in jitter and eye
closure after transmission through a fiber with dispersion. An early work clearly
showed that when polarization was switching or unstable, the RIN increased [2,3],
leading to a deterioration of BER [4,5]. Also, there are many applications of lasers
which are polarization sensitive, such as external modulated systems, polarization-
coherent transmission and magneto-optic disks, and it is obvious that the polarization-
unstable VCSELs cannot be used for such applications. There are numerous
publications on unstable polarization behavior [6-9].
[2] Approaches for polarization control
The definition of “polarization control” is, in fact, not consistent. There are
many publications from the past which didn’t even specify at what pumping level the
polarization data was taken. . Some would claim “complete polarization control” by
6
data taken at low pump power (Ith < I < Isw in Fig. 1-2), which is not accurate.
However, what matters is that the polarization is fixed during practical operation.
Hence, if the Isw is well beyond the practical usage range, the author may be entitled
to claim “complete polarization control”. Therefore in this section, I am not going
into detail of results but just explain the ideas behind each approach.
As stated before, the main cause of unstable polarization of the VCSEL is its
macroscopic and microscopic symmetry. Therefore, the basic idea of various
approaches suggested for control of polarization is to break that symmetry. Table 1-1
summarizes the major approaches reported in the past. The case (a) is most easy and
common approach [11-15]. By introducing macroscopic asymmetry in the VCSEL
transverse geometry, anisotropic loss and anisotropic effective index are introduced.
For a rectangular-shape VCSEL, an axis ratio of 6:5 was sufficient to control
polarization axis parallel to the longer perimeter at 100%, however, increasing the
asymmetry lead to increasing threshold current density [16]. It was also theoretically
shown that the optical gain decreases as the asymmetry increases [17]. The approach
of (b) is similar to (a): the tilted pillar results in the asymmetric resonant cavity.
On the other hand, the approach (c) is about breaking microscopic symmetry.
That is, if the strained gain medium is on asymmetric plane, the optical gain becomes
anisotropic. As shown on Fig. 1-1, (001) plane is symmetric, but the other plane
expressed as (11n) or tilted plane have asymmetric lattice structure (except (111)
plane). There have been both theoretical [18,19] and experimental papers on this
approach. It was reported that VCSELs on (113) GaAs substrate had successful
7
stable polarization control [20,21]. Also, it was shown that a small tilt of 2° from
(001) plane was able to control polarization to a good extent [22].
A major disadvantage of this technique is that it is difficult to perform crystal
growth on largely tilted substrate. In fact, the growth on (001) plane is the easiest
because it is symmetric. Therefore, by breaking the crystallographic symmetry
drastically with this approach, we have to sacrifice the ease of crystal growth.
Another disadvantage is that non-(001) substrates are still uncommon, which results
in higher prices. The detailed polarization control mechanism of this approach is
explained in Chapter 2.
Table 1-1 List of polarization control approaches
Anisotropic gain
Crystalline ordering
Asymmetric stress
Anisotropic transverse cavity
Fabricate on (11n) substrate
Tilted substrate/ growth condition
Add external asymmetric stress
Fabricate in elliptic/rectangle shape
Asymmetric current injection One-dimensional injection
Tilted pillar Fabricate pillar in tilted way
Quantum dot Asymmetric shape by nature
Photonic crystal Asymmetric air holes
(a)
Anisotropic loss Grating-like polarizer on DBR
birefringence
dichroism
dichroism
dichroism
dichroismbirefringence
birefringence
birefringence
dichroism
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Scheme Method Mechanism
dichroism
8
The approach (d) is about creating anisotropic loss. A grating of dielectric
material was formed on top of the DBR, so that the reflectivity becomes different
between direction parallel to the grating and perpendicular to the grating [23].
Spontaneous crystalline ordering of (e) is a well-known phenomenon which is
mostly observed in InGaP alloys grown on slightly misoriented GaAs substrates.
What occurs in an ordered InGaP alloy is that the group-III atoms, In and Ga, don’t
mix randomly, and (111) planes become alternately enriched by In and Ga, resulting
in periodic order of lattice planes such as In/P/Ga/P/In/P··· in [111] direction. When
the substrate is tilted toward (110), the ordering happens in (111)B planes ((1−11) and
(−111) planes) [24]. This will break the symmetry in the emitting surface of the
VCSEL, enhancing character of [110] direction since it is orthogonal to both (111)B
planes. As a result, the optical gain becomes anisotropic and hence, it leads to a
polarization control. There are both theoretical [25] and experimental [26] papers on
the VCSEL with ordered material. A problem on this approach is that the degree of
ordering is the highest on alloys with equal number of group-III atoms, such as
In0.5Ga0.5P and In0.5Ga0.5As. Therefore, to achieve strong ordering, there is little
freedom of material choice. Also, the degree of ordering is sensitive to growth
conditions, so that it may be difficult to control the ordering precisely and with
reproducibility.
Another common and easy method is to add an external asymmetric stress,
shown as (f). The asymmetric stress creates birefringence due to photoelastic effect
and anisotropic gain. It was reported that a pressure applied unintentionally by a
9
measurement probe tip affected the polarization characteristics [27]. There have been
experiments to add uniaxial stress by depositing a SiN strip in one direction [28] or
by applying mechanical stress using screws on specially designed VCSEL holder
[29]. On the other hand, the idea behind approach (g) is that by injecting current in
one direction, a birefringence is generated by the electro-optic effect [30]. However,
this could result in non-uniform pumping of the VCSEL.
The last two approaches on the Table 1-1 are related to new techniques. The
quantum dot (QD) of (h) has become a solid candidate for next generation laser
material, due to its characteristics associated to one-dimentional confinement. For
VCSEL, the QD gained attention as a material for LW-VCSEL which can be
fabricated on GaAs substrate. It was reported that the QD grows in a uniform
asymmetric shape on (001) substrate [31], resulting in anisotropic gain. Hence, the
VCSEL with such QD gain medium will have polarization preference. The research
on photonic crystal (PC) of (i) has been active in recent years due to development of
nano-processing technology. For a VCSEL, the PC is used to create transverse
confinement. That is, an area surrounded by nano-holes has higher refractive index.
The polarization control on PC-VCSEL was reported by making these holes in an
asymmetric shape [32].
Even though the importance of polarization control has been pointed out for a
long time, in reality, no particular technology has been implemented in commercial
VCSEL fabrication. This is because most VCSELs end up having accidental
asymmetry by various reasons. For example, a slight error in fabrication process
10
results in cavity asymmetry. On a VCSEL with an AlAs oxidation layer, it is
reported that the oxidation proceeds in an asymmetric way, resulting in an
asymmetric aperture shape [33]. Also, it is usual to have contact metal pads in an
asymmetric shape, and even though those pads may be away from the VCSEL cavity,
an asymmetric pressure from a probing needle can influence the polarization. In
electrically-pumped VCSELs, there is a birefringence generation due to an internal
vertical E-field, which I will explain in Chapter 2. These asymmetries are small for
complete polarization control, but enough to make a polarization selection close to
threshold.
1.02 Long-wavelength VCSEL
The various fabrication techniques of LW-VCSEL are well documented
[34,35], so here I just make a brief summary and give an update for recent trends.
Figure 1-3 summarizes the material systems for LW-VCSELs. The techniques on
GaAs substrate have been successful for fabricating 1.3 µm-wavelength VCSEL, but
it has been difficult to push the wavelength limit beyond 1.3 µm and up to 1.55 µm
wavelength. On InGaNAs material, it was shown that adding a small amount of Sb
improves material quality, since Sb works as a surfactant [36]. The QD VCSEL has
received attention not only as a LW material, but also for 1D properties and
polarization control, as mentioned earlier. Still, the InP approaches have been more
successful so far. There have been several start-up companies on VCSEL based on
InP techniques [37-39].
11
Figure 1-3 Summary of material systems for LW-VCSEL on InP and GaAs
A recent trend in LW-VCSELs is tunable devices. In fact, all the start-up
companies mentioned above are in the tunable VCSEL business. This is not
surprising since the market trend of LW devices has been shifting toward wavelength-
division-multiplexed (WDM) communication systems. All the devices employ the
same tuning technology of altering cavity resonant wavelength by moving a micro-
mechanical membrane. This trend coincides with the advance of MEMS technology.
Another new aspect in LW-VCSEL is the use of tunnel junction (TJ). There
are many benefits of incorporating the TJ in a VCSEL structure. Firstly, we can
reduce the amount of free-carrier absorption by p-doped material. Also for InP-based
LW-VCSELs, it is very useful since we can pattern the TJ to create carrier
InP substrate
GaAs substrate
Waferbonding
InGaNAs(Sb)GaAsSb
In(Ga)As quantum dot (QD)
InGaAsPInGaAlAs
AlGaAs/GaAs
AlGaAs/GaAs metamorphic growth
dielectric, metalInGaAlAs/InAlAs/InP
AlGaAsSb/InP
Gain media
Gain media
DBRDBR
Air-gap/InP
12
confinement structure. That is, GaAs-based VCSELs can use AlAs oxidation layer
for carrier confinement, but there is no material on InP which can be oxidized easily.
In fact, most of the recently reported LW-VCSELs with high performance have a TJ
in their structure [38-40]. The detail of the TJ will be discussed in Chapter 4.
1.03 Scope of this thesis
[1] Polarization control technique
As mentioned earlier, goal of this thesis is to investigate and demonstrate LW-
VCSELs with controlled polarization. The main focus is how to add polarization
control function to a wafer-bonded VCSEL. Referring to Table 1-1, those techniques
are distinguished by the two polarization selection mechanisms: birefringence and
dichroism. Dichroism means strength of anisotropic gain/loss on the VCSEL
polarization discussion. The details will be explained in next chapter, but the bottom
line is that dichroism works more efficiently than birefringence.
Among the techniques with the dichroism, approach (a) produce anisotropic
scattering loss as large as 1% [15,17]. However, to produce such a large dichroism,
the cavity shape has to be largely asymmetric, which will lead to threshold increase
and beam shape distortion. Also, the shape asymmetry has different influence on
different modes [14]. It was already implemented on LW-VCSEL by other
researchers (although their publication came out after this thesis research started)
[41]. The approaches (d) and (f) produce only small dichroism. The QD of (h) is
attractive not only from research point of view, but also for developing next
13
generation device, however, this technique is based on GaAs and does not have any
merit from wafer bonding.
Fabricating on a (11n) substrate of (c) is most promising, because it is
expected to give the best performance. This technique produces dichroism as large as
4%, which is most efficient for polarization selection. Also, this is the only technique
that has shown stable polarization under high-speed modulation of the VCSEL, which
is the most important aspect for practical application [42,43]. Hence, the purpose of
this thesis is to implement this technique on InP-based VCSEL for the first time, and
to investigate the performance of the VCSEL fabricated by this technique combined
with the wafer bonding technique.
Figure 1-4 shows a sketch of our VCSEL design and fabrication process. The
double-bonded VCSEL is basically the same as that has been fabricated previously,
except that its InP active region has its crystallographic orientation of (11n). The
fabrication starts from growing this active region on a (11n) InP substrate, which will
be done by MOCVD. As I wrote earlier, crystal growth on (11n) substrate is more
difficult than that on (001) substrate. However, the major advantage of our approach
is that we only need to grow a thin layer of active region on (11n) substrate. It is
much more diffulcult to grow a thick layer, because, if the growth condition is not
perfect, growth problems will become more prominent as the layer thickness
increases. One DBR is as thick as 5-7 µm, while the active region is around 1 µm or
less, so that the total VCSEL structure thickness is as much as 15 µm. With our
approach, we can grow the DBRs conventionally on (001) GaAs substrates by MBE.
14
The rest of fabrication process is to wafer-bond this (11n)-InP active region twice to
(001)-GaAs DBRs, in the same way as an ordinary wafer-bonded VCSEL.
Figure 1-4 Structure of VCSEL to be fabricated in this thesis and its fabrication process
⇒
MQWs
InP
InP
InGaAs etch stop
(11n) InPsubstrate
GaAs DBR
(001) GaAssubstrate
MQWs
InP
InP
GaAs DBR
(001) GaAssubstrate
(11n) InPsubstrate
etchoff
bondinterface
[11n]
[001]
[001]GaAs DBR
MQWs
InP
InP
GaAs DBR
(001) GaAssubstrate
⇒
(1) MOCVD growth on (11n) InP substrate (MBE growth on (001) GaAs substrate)
(2) 1st Wafer bonding of (11n) InP/(001) GaAs
(3) 2nd wafer bonding to DBR Complete of VCSEL structure
15
[2] Choice of VCSEL wavelength
The choice of lasing wavelength is not critical to this thesis: it can be 1.3 or
1.55 µm, both of which are commercially important and ideas presented here can be
applied to either wavelength range. We chose to fabricate in 1.3 µm range based on a
prospect that the materials for 1.3 µm-wavelength VCSEL are easier to grow than the
others. This prospect is from miscibility gap consideration of the material. Figure 1-
5 is a diagram of InGaAsP systems showing miscibility gap range for different
temperature, together with bandgap/lattice constant, after Ref. 44. A straight line
from InP means that materials on this line are lattice-matched to InP. There is also a
Figure 1-5 Diagram of miscibility gap for InGaAsP compounds
InP
InAs
GaP
GaAs
700 °C600 °C
500 °C400 °C
1.55 µmwell
Lattice-match to GaAs
Lattice-match to InP
1.3 µmwell
0.5 eV
2.0 eV
1.5 eV
1.0 eV
16
line for GaAs. The dotted lines show bandgaps of 2.0, 1,5, 1.0, and 0.5 eV. The
elliptic miscibility- gap lines are obtained from Enthalpy calculation, and they mean
that the materials inside the ellipses are unstable above the temperature designated for
each curve, so that the materials could cause phase separation. However, the absolute
value of the temperature is irrelevant here. That is, it seems most of InGaAsP
compounds are unstable over 400 °C from these curves, but that does not mean that
such compounds cannot be grown at temperature around 400 °C. It does tell that in
relativistic scale, if one material is in inner ellipse than another material, the inner
material is less stable. There are marks for quantum well materials for 1.3-µm and
1.55-µm MQW. Both have lattice-mismatch of about +8000 ppm with InP, and well
thickness is 50 Å for both MQWs. We see that the well for 1.55-µm is at inner
ellipse than the 1.3-µm well. This means that to obtain good material quality, 1.55-
µm well needs to be grown at higher temperature than 1.3-µm well. On our particular
case, the MQW was grown on (113)B InP substrate at relatively low-temperature, as
it will be explained in following chapters. Therefore, it is predicted that 1.3-µm
MQW is safer to grow at low temperature on (113)B substrate.
[3] Contents
We have many new issues to develop and investigate to accomplish our
approach. The majority of this thesis work is spent on developing growth technique
on (11n) InP substrate, and wafer bonding of (11n) InP and (001) GaAs wafers. In
this Chapter 1, I have reviewed polarization problems for VCSELs and approaches
17
for polarization control, and explained the approach investigated in this thesis. Next
in Chapter 2, I will summarize the physics of various aspects related to this thesis,
beginning with theoretical analysis of VCSEL polarization. The rest of Chapter 2 is
spent to describe properties of (11n)-oriented materials and defects. In Chapter 3, I
summarize experimental procedures used in this thesis work, mostly MOCVD and
wafer bonding. Our initial research was conducted on (111) InP substrates, however,
since the (111) InP has inherent difficulties, this is described in Appendix E. Chapter
4 summarizes all MOCVD growth work on (113)B InP substrates. Then in Chapter
5, I show the results related to wafer bonding of (113)B InP and (001) GaAs wafers.
The next 2 chapters are on results on 2 generations of VCSEL. Chapter 6 is about the
primary results from the 1st generation devices. Chapter 7 is the core part of this
thesis, which is the summary of results from 2nd generation VCSEL with statistical
data and high-speed modulation. Chapter 8 summarizes this thesis, then it concludes
with future work.
18
References
[1] J. J. Dudley, D. I. Babic, R. Mirin, L. Yang, B. I. Miller, R. J. Ram, T. Reynolds,
E. L. Hu, and J. E. Bowers, “Low threshold, wafer fused long wavelength vertical
cavity lasers”, Appl. Phys. Lett. 64, pp.1463-5, 1994.
[2] D. V. Kuksenkov, H. Temkin, and S. Swirhun, "Polarization instability and
relative intensity noise in vertical-cavity surface-emitting lasers”, Appl. Phys. Lett.
67, pp.2141-3, 1995.
[3] T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga, “Excess
intensity noise originated from polarization fluctuation in vertical-cavity surface-
emitting lasers”, IEEE Photon. Tech. Lett. 7, pp.1113-5, 1995.
[4] D. V. Kuksenkov, H. Temkin, and S. Swirhun, “"Polarization instability and
performance of free-space optical links based on vertical-cavity surface-emitting
lasers”, IEEE Photon. Tech. Lett. 8, pp.703-5, 1996.
[5] D. V. Kuksenkov and H. Temkin, “Polarization related properties of vertical-
cavity surface-emitting lasers”, IEEE J. Select. Topics Quantum Electron. 3, pp.390-
5, 1997.
19
[6] C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez,
and N. G. Stoffel, “Dynamic polarization and transverse mode characteristics of
vertical cavity surface emitting lasers”, IEEE J. Quantum Electron. 27, pp.1402-9,
1991.
[7] F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of
GaAlAs-GaAs surface emitting lasers”, ”, IEEE J. Quantum Electron. 27, pp.1410-6,
1991.
[8] K. D. Choquette, R. P. Chneider, Jr., K. L. Lear, and R. E. Leibenguth, “Gain-
dependent polarization properties of vertical cavity surface emitting lasers”, IEEE J.
Select. Topics Quantum Electron. 1, pp.661-6, 1995.
[9] C. Degen, B. Krauskopf, G, Jennemann, I. Fischer, and W. Elsäβer, "Polarization
selective symmetry breaking in near-fields of vertical cavity surface emitting lasers ",
J. Opt. B: Quantum Semiclass Opt. 2, pp.517-25, 2000.
[10] T. Mukaihara, F. Koyama, and K. Iga, “Engineered polarization control of
GaAs/GaAlAs surface-emitting lasers by anisotropic stress from elliptical etched
substrate hole”, IEEE Photon. Tech. Lett. 5, pp.133-5, 1993.
20
[11] K. D. Choquette and R. E. Leibenguth, “Control of vertical-cavity laser
polarization with anisotropic transverse cavity geometries”, IEEE Photon. Tech. Lett.
6, pp.40-2, 1994
[12] B. Weigl, M. Grabherr, C. Jung, R. Jäger, G. Reiner, R. Michalzik, D. Sowada,
and and K. J. Ebeling, “High-performance oxide-confined GaAs VCSEL’s”, IEEE J.
Select. Topics Quantum Electron. 3, pp.409-15, 1997.
[13] N. Ueki, H. Nakayama, J. Sakurai, A. Murakami, H. Otoma, Y. Miyamoto, M.
Yamamoto, R. Ishii, M. Yoshikaea, and T. Nakamura, “Complete polarization control
of 12 × 8-bit matrix-addressed oxide-confined vertical-cavity surface-emitting laser
array”, Jpn. J. Appl. Phys. 40, L33-5, 2001.
[14] P. Debermardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsäβer, “Influence of
anisotropies on transverse modes in oxide-confined VCSELs”, IEEE J. Quantum
Electron. 38, pp.73-84, 2002.
[15] P. Debermardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J.
Ebeling, “Single-mode, single-polarization VCSELs via elliptical surface etching:
Experiments and theory”, IEEE J. Select. Topics Quantum Electron. 9, pp.1394-1404,
2003.
21
[16] T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y.
Sugimoto, and K. Kasahara, “Polarization-controlled single-mode VCSEL”, IEEE J.
Quantum Electron. 34, pp.1009-15, 1998.
[17] G. P. Bava, P. Debermardi, and L. Fratta, “Three-dimentional model for
vectorial fields in vertical-cavity surface-emitting lasers”, Phys. Rev. A 63, pp.23816-
28, 2001.
[18] T. Ohtoshi, T. Kuroda, A. Niwa, and S. Tsuji, “Dependence of optical gain on
crystal orientation in surface-emittimg lasers with strained quantum wells”, Appl.
Phys. Lett. 65, pp.1886-7, 1995.
[19] R. H. Henderson and E. Towe, “Strain and crystallographic orientation effects on
interband optical matrix elements and band gaps of [11l]-oriented III-V epilayers”, J.
Appl. Phys. 78, pp.2447-55, 1995.
[20] M. Takahashi, N. Egami, T. Mukaihara, F. Koyama, and K. Iga, “Lasing
characteristics of GaAs (311)A substrate based InGaAs-GaAs vertical-cavity surface-
emitting lasers”, IEEE J. Select. Topics Quantum Electron. 3, pp.372-8, 1997.
22
[21] A. Mizutani, N. Hatori, N. Nishiyama, F. Koyama, and K. Iga, "A low-threshold
polarization-controlled GaAs vertical-cavity surface-emitting laser grown on GaAs
(311)B substrate", IEEE Photon. Tech. Lett. 10, pp.633-2, 1998
[22] T. Numai, K. Kurihara, K. Kühn, H. Kosaka, I. Ogura, M. Kajita, H. Saito, and
K. Kasahara, “Control of light-output polarization for surface-emitting-laser type
device by strained active layer grown on misoriented substrate”, IEEE J. Quantum
Electron. 31, pp.636-41, 1995.
[23] T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga,
“Polarization control of vertical-cavity surface-emitting lasers using a birefringent
metal/dielectric polarizer loaded on top distributed Bragg reflector”, IEEE J. Select.
Topics Quantum Electron. 1, pp.667-73, 1995.
[24] O. Ueda, M. Hoshino, M. Takeuchi, M. Ozeki, T. Kato, and T. Matsumoto,
“Comparative study of atomic ordering and alloy clustering in InGaP crystals grown
by metalorganic vapor phase epitaxy, chloride-vapor phase epitaxy, and liquid phase
epitaxy”, J. Appl. Phys. 68, 4268-71, 1990.
[25] A. T. Meney, E. P. O’Reilly, and K. J. Ebeling, “Polarisation selectivity in
ordered GaInP2 vertical cavity surface-emitting lasers”, Electron. Lett. 31, pp.461-2,
1995.
23
[26] Y. H. Chen, C. I. Wilkinson, J. Woodhead, J. P. R. David, C. C. Button, and P.
N. Robson, “Polarisation characteristics of visible VCSELs”, J. Cryst. Growth 170,
pp.392-8, 1997
[27] T. Mukaihara, F. Koyama, and K. Iga, “Stress effect for polarisation control of
surface emitting lasers”, Electron. Lett. 28, pp.555-6, 1992.
[28] A. K. Dutta and K. Kasahara, “Polarization control in vertical-cavity surface
emitting laser using uniaxial stress”, Solid-State Electron. 42, pp.907-10, 1998.
[29] K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J.
Danckaert, and I. Veretennicoff, ”Impact of in-plane anisotropic strain on polarization
behavior of vertical-cavity surface-smitting lasers”, Appl. Phys. Lett. 77, pp.1590-2,
2000.
[30] B. S. Ryvkin, E. A. Avrutin, and A. C. Walker, “Current-directionality-induced
giant absorption dischroism in III-V semiconductors and its potential for polarization
control in vertical cavity surface-emitting lasers”, J. Appl. Phys. 91, pp.3516-21,
2002.
24
[31] H. Saito, K. Nishi, S. Sugou, and Y. Sugimoto, “Controlling polarization of
quantum-dot surface-emittig lasers by using structurally anisotropic self-assembled
quantum dots”, Appl. Phys. Lett. 71, pp.590-2, 1997.
[32] D.-S. Song, Y.-J. Lee, H.-W. Choi, and Y.-H. Lee, “Polarization-controlled,
single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers”,
Appl. Phys. Lett. 82, pp.3182-4, 2003.
[33] A. C. Alonzo, X.-C. Cheng, and T. C. Macgill, “Strain in wet thermally oxidized
square and circular mesas”, J. Appl. Phys. 87, pp.4594-9, 2000
[34] K. A. Black, “Fused long-wavelength vertical cavity lasers”, Ph.D. Dissertation
in Materials, University of California, Santa Barbara, 2000.
[35] A. M. Karim, “Wafer bonded 1.55 µm vertical cavity laser arrays for wavelength
division multiplexing”, Ph.D. Dissertation in Electrical and Computer Engineering,
University of California, Santa Barbara, 2001.
[36] H. Shimizu, C. Setiagung, M. Ariga, Y. Ikenaga, K. Kumada, T. Hama, N. Ueda,
N. Iwai, and A. Kasukawa, “1.3-µm-range GaInNAsSb-GaAs VCSELs”, IEEE J.
Select. Topics Quantum Electron. 9, pp.1214-9, 2003.
25
[37] W. Yuen, G. S. Li, R. F. Nabiev, J. Boucart, P. Kner, R. J. Stone, D. Zhang, M.
Beaudoin, T. Zheng, C. He, K. Yu, M. Jansen, D. P. Worland, and C. J. Chang-
Hasnain, “High-performance 1.6µm single-epitaxy top-emitting VCSEL”, Electron.
Lett. 36, pp.1121-3, 2000
[38] A. Syrbu, A. Mereuta, A. Mircea, A. Caliman, V. Iakovlev, C.-A. Berseth, G.
Suruceanu, A. Rudra, E. Deichsel, and E. Kapon, “1550 nm-band VCSEL 0.76 mW
singlemode output power in 20-80ºC temperature range” Electron. Lett. 40, pp.306-7,
2004
[39] M. Maute, F. Riemenschneider, G. Böhm, H. Halbritter, M. Ortsiefer, R. Shau,
P. Meissner, and M.-C. Amann, “Micro-mechanically tunable long wavelength
VCSEL with buried tunnel junction”, Electron. Lett. 40, pp.430-1, 2004.
[40] V. Jayaraman, M. Mehta, A. W. Jackson, Y. Okuno, J. Piprek, J. E. Bowers,
"High-Power 1320-nm Wafer-Bonded VCSELs With Tunnel Junctions", IEEE
Photon. Tech. Lett., 15, pp.1495-7, 2003.
[41] M. Ortsiefer, R. Shau, M. Zigldrum, G. Böhm, F. Köhler, and M.-C. Amann,
“Submilliamp long-wavelegth InP-based vertical-cavity surface-emitting laser with
stable linear polarization”, Electron. Lett. 36, pp.1124-6, 2000.
26
[42] N. Nishiyama, A. Mizutani, N. Hatori, M. Arai, F. Koyama, and K. Iga, "Lasing
characteristics of InGaAs-GaAs polarization-controlled vertical-cavity surface-
emitting laser grown on GaAs (311)B substrate”, IEEE J. Select. Topics Quantum
Electron. 5, pp.530-6, 1999.
[43] H. Uenohara, K. Tateno, T. Kagawa, Y. Ohiso, H. Tsuda, T. Kurokawa, and C.
Amano, “Polarization-controlled 850-nm-wavelength vertical-cavity surface-emitting
lasers grown on GaAs (311)B substrates by metal-organic chemical vapor
deposition”, IEEE J. Select. Topics Quantum Electron. 5, pp.537-45, 1999.
[44] H. Nagai, S. Adachi, and T. Fukui, “III-V mixed crystals”, Chapter 3, Corona
Publishing Co., Ltd., Tokyo, Japan, 1988.
27
Chapter 2 Theoretical analysis
In this chapter, I would like to go through various theoretical aspects of
VCSEL polarization and material properties related to this thesis work. This chapter
is to help understanding the experimental results explained later in this thesis. Also, I
believe that the contents of this chapter are new to the most of the readers, and I hope
that this chapter will be a good reference to other researchers.
In the first section, I will show how the VCSEL polarization is affected by
properties such as birefringence, and how the dichroism is effective to control the
polarization. I will also mention the electro-optic effect as a polarization control
mechanism on (001)-based VCSEL. In the second section, I will summarize various
stress, strain, and other related characteristics of (11n)-oriented materials. This
section is very useful throughout this thesis. The third section is about optical gain on
(11n)-oriented materials, and I will show how the gain is expected to be anisotropic
on such materials. Lastly on fourth section, I will cover properties of defects, and
then investigate stress in wafer bonded structure from defects and thermal expansion
mismatch.
28
2.01 Polarization characteristics of VCSEL
[1] SFM model
In 1995, a group from University of Arizona published a paper which
introduced a four-level model describing VCSEL polarization [1]. This model was
named as SFM model after the initials of 3 authors, and was extended by the original
author and a group of Dr. M. P. van Exter from Leiden University in Netherlands.
Here I am going to summarize their works and show the physical insight of VCSEL
polarization [2-8].
The different polarizations of light are associated with different spin sublevels
of the lasing transitions between conduction and valence bands. Figure 2-1 depicts
the band structure of compressively strained material near its band gap. Among the
valence bands, we neglect light-hole and split-off states as they can be disregarded in
such case. Near the band gap, the electron states of the conduction band have z-
direction angular momentum quantum number Jz=±1/2, and heavy hole state has
21=ZJ 2
1−=ZJ
23=ZJ 2
3−=ZJ
CB
VB-hh
E+E-
γs
γ γ
fast
Figure 2-1
Band structure with conduction
band (CB) and heavy-hole valence
band (VB-hh)
29
Jz=±3/2. For light emission with transverse electric field in xy-plane of Fig. 1-1, the
quantum allowed transitions are to have ∆Jz=±1. Then there are 2 possible transitions
with opposite spin values: from Jz=1/2 to Jz=3/2 which is associated with left
circularly polarized light having E-field of E-, and from Jz=-1/2 to Jz=-3/2 for right
circularly polarized light with E+. These fields satisfy Maxwell-Bloch equations, and
rate equations developed are:
EiENNi
dtdE
pad )()1)(1( γγακ −−−±+= ±± 2-(1)
])()()[( 22−+ −+++−−= ENNENNN
dtdN
ddµγ 2-(2)
])()[( 22−+ −−+−−= ENNENNN
dtdN
dddsd γγ 2-(3)
N: normalized total carrier number
Nd: difference in the carrier numbers of the 2 magnetic sublevels
(2
−+ += NNN 2
−+ −= NNNd )
κ: field decay rate α: linewidth enhancement factor
µ: injection current normalized to threshold
γ : decay rate of the total carrier population
γs: decay rate of the total carrier population difference through
spin-flop relaxation process
γa: dichroism
γp: birefringence
30
The 2 orthogonal linear polarization modes Ex and Ey can be written in terms of the 2
circular modes E±:
2_EE
Ex
+= +
2_EE
iEy
−−= + 2-(4)
And the Eq. (1)-(3) can be written as
xaxpydxx EEiEiNNEi
dtdE
)()())(1( γκγκαακ +−−−++= 2-(5)
yaypxdyy EEiEiNNEi
dtdE
)()())(1( γκγκαακ −−+−−+= 2-(6)
)]()1([ **22yxxydyx EEEEiNEEN
dtdN −+−++−= µγ 2-(7)
)]()([ **22yxxyyxdds
d EEEEiNEENNdt
dN−++−−= γγ 2-(8)
The 2 terms, γa and γp, contribute to the polarization selection, and they are both in s-1
unit. The birefringence reflects difference of refractive index, and it corresponds to
half of a frequency splitting between 2 linearly polarized modes. It is set in a way
that x-polarized mode has higher frequency if γp is positive. The dichroism represents
strength of anisotropy in gain, loss, and/or confinement factor, and is expressed by a
difference of FWHM of FP spectra from 2 polarization modes, i.e. [9],
)()(22 yxa FWHMFWHM −= πγ 2-(9)
Also, it can be put to a difference of gain/loss ∆a as [9]
gr
a
Va
γ2=∆ Vgr: group velocity in the gain medium 2-(10)
31
The axes for birefringence and dichroism can be different, and in that case, we get
elliptically polarized light emission. If the axes coincide, which is the case for most
of real-life VCSELs, we get linearly polarized emission.
An arbitrary steady state solution of Eq. 2-(1)~(3) can be expressed as
)( ϕω ±±±± = tieQE 0NN = 0
dd NN = 2-(11)
where ϕ is a relative phase angle, 0N and 0dN are the values at threshold, and ω± is
frequency difference from cavity resonance. If we don’t have any anisotropy, i.e., γa
= γp= 0, we get steady-state solution as
2
1−=±µQ 0=±ω 10 =N 00 =dN
∴ ϕµ cos1−=xE ϕµ sin1−=xE 2-(12)
Hence, Ex and Ey are equal in amplitude and frequency but just π/2 out of phase. If
γa, γp≠ 0, the x- and y-polarized modes have different threshold conditions:
txi
x
xx e
NN
E ωµ0
0−= (ϕ=0) apx αγγω += 2-(13)
tyi
y
yy e
N
NE ωµ
0
0−= (ϕ=π/2) )( apy αγγω +−= 2-(14)
κγa
xN +=10
κγa
yN −=10 000 == dydx NN 2-(15)
Hence, if both γa and γp are positive, the x-polarized mode has higher threshold carrier
density and higher frequency than the y-polarized mode. While the threshold
32
condition is affected by the dichroism only, both birefringence and dichroism
(together with α) influence the frequency splitting between 2 polarization modes.
This model, however, is not appropriate for a system with large γa orγp, such
as the VCSEL in (11n) substrate [10]. From Ref. 11, anisotropic gain of a strained
MQW on (112) InP substrate was calculated to be about 200 cm-1 at high injection
carrier level (we later obtain similar estimate on (113) substrate). Using Eq. 2-(10)
and with ngr =3 for simplicity, this gain difference corresponds to a dichroism:
GHz 1000 210200
2
10=×=
∆= gr
aaV
γ 2-(16)
By Eq. 2-(13) and Eq. 2-(14), 2αγa should contribute to the frequency difference
between 2 polarization modes. For 1.3-µm wavelength and with α =3, this dichroism
corresponds to a wavelength difference of 5.4 nm, which is too large. Also from Eq.
2-(15), normalized threshold current is changed by ±γa/κ. The value for κ is about
250-300 ns-1, then this amount of change becomes as big as ±4, which is too large for
a change from 1. Nonetheless, the model gives an idea of how birefringence and
dichroism affect polarization behavior when their values are small.
[2] Mechanism of polarization switching
On the outcome of Eq. 2-(13)~(15), the lower frequency of y-polarized mode
means the mode has higher effective index and hence, it is better confined than x-
polarized mode. Together with lower threshold carrier density, the model predicts
that the y-polarized mode is the stronger lasing mode, while x-polarized mode is
33
weaker non-lasing mode. However, this model does not include frequency
dependence of material gain. In real device, a frequency shift accompanies a change
in optical gain, and the gain-cavity mode offset varies not only between devices, but
also as the operating temperature changes. Hence in real cases, polarization stability
is affected by various factors, and I would like to show some examples next.
Figure 2-2 illustrates possible relation between material gain and mode
frequencies for 3 different cases (after Ref. 12). All cases are to have frequency
splitting between 2 modes, with y-polarized mode always having lower frequency.
Also, they are set for a typical design in which, at the room temperature, the cavity
mode ω0 is set at lower frequency (=longer wavelength) side than material gain peak.
This is a well-known design rule to achieve the best gain-cavity mode overlap over a
wide range of operating temperature. As the device temperature increases, both
material gain and cavity mode shift to lower frequency, however, the material gain
shifts much larger by temperature (0.5 nm/°C) than the cavity mode (0.1 nm/°C). The
graphs at left side of Fig. 2-2 are at temperature T1 which can be around room
temperature, and right side ones are at T2 which is higher than T1.
The case (a) is that the material gain is the same between x-polarized and y-
polarized modes, which is the case for most of VCSELs on (001) substrates. In this
case, x-polarized mode which has higher frequency can be the lasing mode at T1, if its
gain is larger enough than that of y-polarized mode. As temperature increases, the
cavity mode moves to higher frequency relative to the material gain curve.
34
Figure 2-2 Example of relation between material gain and mode frequencies for 3 different
cases (after Ref. 12). Closed marks indicate lasing modes.
Frequency
Mat
eria
l gai
n
ω0
xy
Frequencyω0
xyat T1 at T2
Frequency
Mat
eria
l gai
n
ω0
xy
Frequencyω0
xyat T1 at T2
(b) Small gain difference (y>x)
(c) Large gain difference (y>>x)
Frequency
Mat
eria
l gai
nWavelength
ω0
xy
Frequency
Wavelength
ω0
xyat T1 at T2
T1 < T2
(a) No gain difference
35
At T2, y-polarized mode has higher gain so that it is the lasing mode. The switching
from x- to y-polarized mode happens at a temperature lower than T2, depending on
gain and confinement conditions. The case (b) is that the material gain is slightly
different between 2 modes: In this particular case, y-polarized mode has higher gain.
This can be the case equivalent for the scheme (a) of Table 1-1, a VCSEL with
asymmetric cavity shape, on which the optical loss is anisotropic. As can be seen, the
polarization switching can occur in the same way as the case (a) with no gain
difference. Hence, a small amount of gain/loss difference is not necessary enough for
stable polarization. The case (c) has a large difference between material gains of 2
modes, which can be a case for the scheme (c) of Table 1-1, i.e., a VCSEL on (11n)
substrate. In this case, the polarization can be stable for a wide range of operating
temperature.
Of course, these depictions do not apply to all the VCSELs. For example on
case (b), if the x-polarized mode has higher gain, the polarization can be stable at x-
polarized mode up to T2 (but will become unstable somewhere above T2). Also, the
graphs are not in scale. In real cases, frequency splitting is on the order of 50 GHz.
Nonetheless, the bottom line from the depiction of Fig. 2-2 is that dichroism is much
more effective than birefringence, if we want to ensure stable polarization over a wide
range of operation power and temperature. Also, by the same analogy as Fig. 2-2,
one can easily see that if there is only the dichroism but no birefringence, the
polarization will be stable for entire range. Therefore, as stated in Chapter 1, we have
employed the scheme of fabricating on (11n), since we can expect large dichroism
36
with it. It was shown that when the dichroism γa is present, an intensity ratio between
2 polarization modes can be expressed as [7]
DI
IM a
eglanon
egla γ==
−−
−
modsin
modsin 2- (17)
κnumber)photon (
factor)emission us(spontaneo=D
where D corresponds to the noise strength.
[3] Birefringence by electro-optic effect
On electrically-pumped VCSEL, birefringence γp is generated due to electro-
optic effect of z-direction E-field, Ez. The refractive indices are given by [13]:
12 010100410
001010100 =+++
nnErn
nnnz 2-(18)
where nklm: refractive index in [klm] axis
n0: optical index without electric field
r41: electro-optic coefficient
By performing rotation of coordinates by 45° about the z-axis, we can rewrite the
equation as:
1)1()1()1( 22
0
2412
0
2412
0
=+++− zyzxz nn
nErn
nErn
2-(19)
where notations are modified as: nx: n110 ny: n1-10 nz: n001
37
The r41 value for InGaAsP compound is reported to be about 1.2×10-12 m/V [14], and
Ez is estimated to be on the order of 10 V/µm = 107 V/m. Since n0 is about 3.5, we
can use an approximation of r41Ez << 1/n02, and we obtain:
zx Ern
nn 41
30
0 2−≈ zy Er
nnn 41
30
0 2+≈ 0nnz = 2-(20)
Therefore, we have a birefringence expressed as:
zxy Ernnn 413
0=− 2-(21)
Thus, the index is maximum in [1−10] direction and minimum in [110], and their
difference is about 4×10-4 with n0 ≈ 3.5. In order to obtain frequency splitting due to
this birefringence in an approximate order, we simplify the situation by neglecting
material variation on refractive index and r41, and resulting equation is [15]:
zgr
yxyx En
rn 413
0
00=
−=
−ν
ννω
ωω2-(22)
where ngr is group refractive index, and the brankets mean spatial averaging in the
longitudinal direction. To get an order of the difference, we simplify by ngr = n0 and
use values noted earlier, then for 0.85 µm wavelength, we obtain
GHz 5010102.15.31085.0
103 71226
8≈××××
××=− −
−yx νν 2-(23)
As mentioned earlier, this is close to the values observed on real VCSELs [13,15].
This value is much smaller than the dichroism on (11n) plane from Eq. 2-(16), but for
a general VCSEL on (001) substrate, the dichroism is about 1GHz [7,9], and this
birefringence will be an important source of polarization.
38
2.02 Properties of strained materials on (11n) substrate
Nowadays almost all semiconductor optical devices could have strained layers
in their structure. Since the semiconductor devices are generally made on (001)
substrate, strain/stress effects on (001)-oriented semiconductor crystal have been well
investigated and documented. However, as the research on non-(001) crystals are
minorities, works on strain/stress on such misoriented crystals are few and not well
summarized. So my goal here is make this section a good summary of strain/stress
associated properties of non-(001)-oriented III-V semiconductors. However, I don’t
treat any arbitrary crystal orientations, but only treat orientations that can be
expressed as (11n), where n is a real number between 0 to ∞. Thus I cover
orientations such as (111) and (113) which I actually worked on in this thesis, and I
also include (001) (n=∞) so that I can make comparison of (11n) crystals with the
common (001) case. To be precise, the (11n) planes should be distinguished by
(11n)A and (11n)B planes, however in this chapter, the difference of A/B planes does
not affect on properties we investigate. Hence, for example, properties of the (111)
plane we discuss in this chapter apply to all 111 planes. They are (111), (1−1
−1),
(−11
−1), (
−1
−11) which are A planes, and B planes are (
−111), (1
−11), (11
−1), (
−1
−1
−1).
[1] Strain/stress notations and strain energy density
We consider a case that a layer is epitaxially grown on a substrate with a small
mismatch of lattice constants between them. The substrate has its surface plane
39
orientation (11n), and the epilayer retains the same crystal orientation as substrate’s
[16]. The epilayer thickness is thin enough that there is no dislocation generation due
to the lattice mismatch (means it is less than a critical thickness), and the substrate is
much thicker that the stress/strain in the substrate can be neglected. This is a case so-
called biaxial strain, which means that the stress is applied only on two faces of
crystal cube (x and y) and there is no stress applied to the z face (Fig. 2-3, middle).
The epilayer has to plastically deform in all dimensions to accommodate the lattice
mismatch. Due to the atomic structure, the amount of such 3-dimentional
deformation depends on which crystal plane the epilayer is grown on. So we are to
summarize dependence of stress and strain components on (11n) plane.
Figure 2-3 Classification of strain/stress
σx x y
zσx
σy
σy
σx x y
zσx
σy
σy
σx x y
zσx
σz
σz
⇓ ⇓ ⇓
uniaxial strain biaxial strain uniform pressure
40
To begin with, we first take a look of strain and stress in the epilayer on (11n)
plane, but using a normal (001) coordinate, and we also look at energy associated
with strain. We define strain and stress notation as follows. α11 is strain/stress in
[100] direction, α22 is in [010], and α33 is in [001], and other αij (i≠j) are off-diagonal
shear components between these axes as shown in Figure 2-4. Due to the symmetry,
relation αij = αji holds for all off-diagonal components. Stress σij and strain εij are
related by the Hook’s law, which can be expressed by a matrix form [17]:
|
222
|||||
31
23
12
33
22
11
666564636261
565554535251
464544434241
363534333231
262524232221
161514131211
31
23
12
33
22
11
εεε
εεε
σσσσσσ
•=
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
222
||
000000000000000000000000
|
31
23
12
33
22
11
44
44
44
111212
121112
121211
εεε
εεε
•=
CC
CCCCCCCCCC
2-(24)
where Cij are elastic constants of the epilayer. Due to symmetry of Zinc-Blende
crystals, Cij matrix becomes such simple.
To calculate εij in an (11n)-oriented epilayer, we copy formula from work by
Caridi and Stark [17,18]. Their work were originally done for (kkn)-oriented crystals,
so we set k=1 and summarize outcome here:
41
Figure 2-4 Identification of strain/stress components
])21(4)1(2)1([144
212
211
222211 CnCnCnn
D++−+−== δεε
])21(4)1(2)1(2[144
212
411
233 CnCnCn
D++−−−−= δε
)2)(2(11211
212 CCn
D++−= δε 2-(25)
1212112
3123 )2)(2(1 εδεε nCCnnD
=++−==
442
122
114 )21(4)21(2)2( CnCnCnD +++++=
where δ is the lattice-constant mismatch (ae-as)/ae when as is the lattice constant of
the substrate and ae is that of the epilayer. Using Eq. 2-(24) and the symmetry of
strain as in Eq. 2-(25), stress components are expressed as
33121112112211 )( εεσσ CCC ++== 3311111233 2 εεσ CC +=
124412 2 εσ C= 124423443123 22 εεσσ nCC === 2-(26)
e1
e2
e3
α11
α12
α13
α21
α22
α23
α31 α32
α33
42
The strain energy density is expressed as
31
23
12
33
22
11
312312332211
222
|][21
εεε
εεε
σσσσσσ ••=U | 2-(27)
With Eq. 2-(25) and 2-(26), U can be explicitly rewritten and calculated as
)()(21
113333222211122
332
222
1111 εεεεεεεεε +++++= CCU
)(2 231
223
21244 εεε +++ C
212
244331112
23311
2111211 )21(22
21)( εεεεε nCCCCC +++++=
])21(4)1(2)2()2[()1( 312
221211
2212
211
211
4222
2
CnCCnCCnCnnUD +−−−+++−=δ
4412111211222 ))(2)(21()1(8 CCCCCnn −++−+
2441211
2244
21211
222 )2()21(24)2)(21()2(2 CCCnCCCnn +++++++
DCnCCnCC ])21(6)()1)[(2( 442
121122
1211 ++−−+=
44
222
211
444
21211
22
12112 )21(4)21(2)2()21(6)()1(
)2(CnCnCn
CnCCnCCU+++++
++−−+=∴
δ
BCnCnCn
CCnCC =+++++
++−+= ]
)21(4)21(2)2()2()2(
3)[2(21
442
222
114
121122
1211
2-(28)
43
The constant B is plotted for InP as a function of angle between (11n) and (001)
planes (=θ as defined in Fig. 2-6) in Figure 2-5. As seen on the plot, the B is
minimum on (001) plane and becomes maximum on (111), meaning that a strained
layer accumulates least energy on (100) plane. This is one reason that epitaxial
growth of strained material is easy on (001) plane, but not on the other (11n) planes.
However, the largest optical gain is predicted on (111) plane [11], which may be
related to the largest strain energy on this plane.
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
14
12
10
Stra
in e
nerg
y co
nsta
nt B
(101
0 N/m
2 )
Figure 2-5
Orientation dependence
of energy constant B
for InP from Eq. 2-(28)
44
Figure 2-6 Configuration of coordinate systems
[2] Strain/stress on (11n) coordinate
Next we find out the strain/stress in the growth plane and in growth direction.
We define the notations in a new coordinate system in the similar manner as we
defined αij (i,j = 1,2,3) previously: parameters αij (k,l = x,y,z) are along xyz-
coordinates where z-axis is taken in [11n] direction as shown in Figure 2-6. These
two different coordinate systems are related by a rotation matrix R as [19]
||||
3
2
1
ααα
ααα
•= R
z
y
x
2-(29)
where
[100]
[010]
[001]
[110]
z=[11n]
x=[nn2]
y=[110]
ϕ=45°
θ
45
|
cos0sin
sin2
12
1cos2
1
sin2
12
1cos2
1
||cos0sin
sinsincoscossinsincossincoscos
|
θθ
θθ
θθ
θθθϕϕθϕθϕϕθϕ
−
−
=−
−=R
2-(30)
where ϕ and θ are angles between two coordinate systems, and ϕ=45° by the way we
defined. The θ is a tilt angle of (11n) from (001) plane, so that it is easily found to be
as a function of n as
222sinn+
=θ22
cosn
n+
=θ 2-(31)
Therefore the matrix R can be rewritten as
|2022)2(2)2(
|)2(2
1 2
2
2n
nnnn
nR
−++−
+= 2-(32)
We already know strain components on (1,2,3) coordinate as shown by Eq. 2-(25).
To obtain strain in (x,y,z) coordinate, we perform rotation as shown in Appendix B
and result comes down as simple as follows:
|00
0000
|||||
333231
232221
131211
zz
T
zzzyzx
yzyyyx
xzxyxx
RRε
δδ
εεεεεεεεε
εεεεεεεεε
=••= 2-(33)
where
])21(2)23()21([244
222
4211
2 CnCnnCnDzz ++++−+−= δε 2-(34)
46
This result is a confirmation that the epilayer is under a biaxial strain, i.e., the lattice-
constant mismatch δ exists along x- and y-axes on (11n) plane, resulting in plastic
deformation along [11n] axis, and there is no shear strain in the epilayer. The z-axis
strain -εzz/δ for InP is plotted as a function of θ in Figure 2-7. It shows that the -εzz
becomes minimum when grown on (111) plane. On (001), the εzz becomes a familiar
expression:
11
122CC
zz δε −= 2-(35)
In the same manner, stress components in xyz-coordinates are obtained by
performing rotation matrix treatment:
1.2
1.0
0.8
0.6
z-ax
is s
train
-εzz
/δ
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
Figure 2-7
Orientation dependence
of z-axis strain for InP
from Eq. 2-(34)
47
RRT
zzzyzx
yzyyyx
xzxyxx
••= ||||
333231
232221
131211
σσσσσσσσσ
σσσσσσσσσ
2-(36)
Performing this rotation as shown in Appendix B, plugging in results of Eq. 2-(25)
and 2-(26), and after tedious calculations, we obtain
]6)21(4))(2)(1)[(2(144
244
21211
221211 CnCnCCnnCC
Dxx +++−−−+= δσ
])2(2)21(4))(1()[2(144
244
21211
221211 CnCnCCnnCC
Dyy ++++−−+= δσ
0=zzσ
0== yzxy σσ 2-(37)
)2)(2)(1(214412111211
2 CCCCCnnDzx −−+−= δσ
This result is another beautiful confirmation of the fact that the stress is only applied
on x- and y- planes, and no stress is applied on (11n) plane as it should be by the
nature of biaxial strain. Also, note that the stress along x- and y-directions are not the
same. The difference is
)2)(2)(1(24412111211
2 CCCCCnDyyxx −−+−−=− δσσ 2-(38)
This difference, reformed as (σxx-σyy)/δ, is plotted for InP as a function of θ in Figure
2-8. It becomes zero only when n=1 or ∞, which means the in-plane stress becomes
symmetric only on (111) and (001) planes. Otherwise, the in-plane stress is
asymmetric, resulting in in-plane gain anisotropy and polarization field. The
48
existence of shear stress σzx also reflects the fact of asymmetric stress. In fact, σzx
can be related as
)(tan
1)(2 yyxxyyxxzx
n σσθ
σσσ −−=−−= 2-(39)
σzz/δ is also plotted in Fig. 2-8. On the other hand, if we take average of σxx and σyy,
δδσσ
BCnCCnCCD
yyxx =++−−+=+
])21(6)()1)[(2(12 44
21211
221211
2-(40)
by using Eq. 2-(28). Therefore, the strain energy U can be also expressed as
22 yyxxBU
σσδδ
+== 2-(41)
This, by using Eq. 2-(33) and 2-(37), agrees with Eq. AB-(13).
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
5
0
-5
(101
0 N/m
2 )
Figure 2-8
Stress difference from
Eq. 2-(38), diagonal stress
σσσσxz from Eq. 2-(39), and
their sum σσσσa from
Eq. 2-(46), for InP
σxx-σyy
σxz
σa
49
[3] Strain-induced piezoelectric effect and polarization
Since III-V semiconductors consist of negative-charged group-III and
positive-charged group-V atoms, there is a polarization field induced by the
piezoelectric effect in a layer when it is under strain. This polarization field has not
just in-plane component but also longitudinal component. The longitudinal
component generates an internal electric field depending on the direction that the
strain is added to. Figure 2-9 depicts cases for 3 orientations. If a layer is strained in
[001] direction as shown on the left side, amount of displacement of group-III and
group-V atoms are equal so that there is no field generated. However, if strained in
[111] direction, the displacement amount becomes different for group-III and group-
V, thus the net charge does not cancel out and there is an electric field generated. If
we take a look at [110] orientation on the right side, we see that the net charge cancels
Figure 2-9 Schematic drawing of generation of longitudinal piezo-electric field on (111)-
oriented crystal (center), whereas no field is generated on other crystals.
[112][110]
[111][001]
[110][110]
E
[110]
[110]
[001]
50
out so that there is no field generation. Thus, the longitudinal field generation exists
in a layer of orientations other than [001] and [110] as shown later, and it can affect
on optical properties of the layer. That is, this piezoelectric field brings so-called
quantum-confined Stark effect (QCSE) so that the band structure of the material
becomes biased as shown in Figure 2-10.
Figure 2-10 Change of band structure of MQW due to QCSE in electric field
The in-plane component of polarization, on the other hand, does not generate
electric fields as I show later, but leads to birefringence of light. It is, of course, the
main source of VCSEL polarization control which is the title of this thesis. It is also
closely related to the asymmetry of in-plane stress we showed in the previous section.
But first in this section, we derive the polarization field in transverse and longitudinal
direction following textbook methods.
The polarization field P is generated by off-diagonal strain and is given by
||2 14 jki eP ε= 2-(42)
Ec1
Eg
Eh1
Ec1
Eg
Eh1
(a) no electric field (b) under electric field
wellbarrier barrier
51
where e14 is the piezoelectric constant of the material, (i,j,k) = (1,2,3) and i≠j≠k.
Therefore, using Eq. 2-(25), P can be expressed as
P= |1
|2|| 1214
3
2
1
nn
ePPP
ε−= 2-(43)
A minus sign is added to adjust the sign of polarization. In order to find out
transverse and longitudinal components we perform vector cross-section. As shown
in Fig. 2-6, (x,y,z) vectors of (11n)-oriented crystal we set are
]2,,[−
= nnx ]0,1,1[−
=y 2-(44)
and obviously, z = [1,1,n]. By taking vector cross-sections, we find
)2)(1(22224
)1(22 121122
142
2
1214 CCnnD
en
nePx +−+=+
−−= δε
0=yP 2-(45)
)2(232232 1211
21421214 CCn
Dne
nnePz ++=+
−= δε
Hence, Px represents the in-plane (transverse) component.
These results are plotted in Figure 2-11 for InP. As it was schematically
shown in Fig. 2-9, there is no longitudinal polarization on [001]- and [110]-oriented
layers. Otherwise, we have longitudinal polarization component which becomes
maximum on [111] oriented layer. As for in-plane polarization, the result agrees with
the findings from previous stress observation. There is no in-plane polarization on
(001) and (111) planes as the stress is symmetric on these planes.
52
Let us look back the stress components now. If we see Eq. 2-(39), we realize
that the σxz and (σxx-σyy) share tangential components of something, which we put
here as σa (this is already plotted in Fig. 2-8). It is expressed as
)2)(2)(1(224412111211
22 CCCCCnnDa −−+−+= δσ 2-(46)
and θσσσ sinayyxx −=− θσσ cosaxz =
Hence we find a relation
)2(2
441211
14
CCCeP ax −−
= σ 2-(47)
Thus, we can see that the in-plane polarization is closely related to the asymmetric
stress. Note that the sign of denominator of Eq. 2-(47) is minus.
1
0
-1
Pola
rizat
ion
field
P/2
e 14δ
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
Figure 2-11
Orientation dependence
of in-plane polarization
Px and longitudinal
polarization Pz from
Eq. 2-(45) for InP
Px
Pz
53
Now we find out strength of actual fields generated by such polarization. We
go back to basic electromagnetics. A displacement field D and an electric field E
generated are
D = є0E + PT PT = є0χeE + P
∴ D = є0E + є0χeE + P = є0єrE + P 2-(48)
where є0 is the permittivity of free space, єr is the low frequency relative dielectric
constant, χe is the electric susceptibility, PT is a total polarization field, and P is the
strain-induced polarization field we derived. We recall basic equations
∇ × E = 0 ∇ • D = ρe = 0 2-(49)
where ρe is external charge density which is zero in our case.
The results of P we derived do not contain any position-dependent terms,
hence, one may think curl and divergence of P would be zero. However, there is one
thing we have neglected: interface of epilayer and substrate, at which P changes
abruptly [20]. Therefore, there are non-zero terms of curl and divergence associated
with the interface. By splitting P into Px and Pz (while Py = 0), we can organize as
follows:
∇ • P = ∇ • Px + ∇ • Pz = ∇ • Pz
∇ × P = ∇ × Px + ∇ × Pz = ∇ × Px 2-(50)
Using Eq. 2-(48)~(50), we obtain
∇ • D = 0 = ∇ • є0єrE + ∇ • P = ∇ • є0єrEz + ∇ • Pz
∴ є0єrEz = -Pz Ex = 0 2-(51)
∇ × є0єrE = ∇ × D - ∇ × P =0 ∇ × Dx = ∇ × Px
54
∴ Dx = Px Dz = 0 2-(52)
Using results shown in Fig. 2-11 and material parameters listed in Appendix A, we
can calculate how much are these fields in real material. We calculate for a thin InP
layer under +1% of lattice mismatch strain (which is not realistic, but we just like to
get an order of magnitude). From Fig. 2-11 we see that we get a maximum value of
Px/2e14δ on (110) plane, which is about 0.8634, then the Dx value is -6.04×10-4 C/m2.
For Pz, the maximum is at (111), and resulting Ez becomes 5.98×106 V/m.
Let us take a look at how such an electric field will affect band gap as shown
in Fig. 2-10. An energy shift of the ground state ∆E1 is expressed as [21]
2
4221 *
LFemCE pert−=∆ Cpert = 2.19488×10-3 2-(53)
where m* is an effective mass of electron/hole, e is an electron charge, F is an electric
field, and L is a width of quantum wells. Again we assume the unrealistic InP well
under +1% strain with L = 100Å, and use Ez = 5.98×106 V/m = F, then we obtain
∆Ec1 = 0.793 ×10-3 eV ∆Ehh
1 = 6.28 ×10-3 eV 2-(54)
Altogether, an energy shift of about 7 meV is expected for the ground transition
energy. And if the piezo-free transition is at 1240nm wavelength, this energy shift
corresponds to a wavelength shift of about 9 nm. These shift amounts are fairly small
compared to other material system such as GaAs or GaN, due to a very small e14
value of InP.
55
2.03 Optical gain on (11n) plane
The optical gain for semiconductor has been well investigated by now. I
believe the calculation method of gain is familiar to many readers and there are
commercial softwares for such calculation, but only for (001)-oriented materials. On
the other hand, there are not many publications on the optical gain on (11n) plane.
Hence, I would like to give an overview for (11n) gain calculation and a summary of
publications.
[1] 4×4 Hamiltonian and effective mass
We start with effective-mass theory on quantum wells using the Luttinger-
Kohn 4×4 Hamiltonian matrix, including the effect of biaxial strain [22]. First, we
recall the valence band equation for a quantum well on (001)-oriented crystal is:
)()()]([ 0 rErrVHH ψψε =++ 2-(55)
where
−−
=
hh
lh
lh
hh
PSRSPRRPS
RSP
H
**
*
*
0
00
00
−
−
=
−
−
23,2
32
1,23
21,2
32
3,23
)(
)(
)(
)(
)(
23
21
21
23
rF
rF
rF
rF
rψ
2-(56)
:)(rFi envelope function
][2
])2()[(2
23
//
2//
22
3212
//210
2
⊥+=−++=hhhh
hhmk
mk
kkm
P γγγγ
56
][2
])2()[(2
23
//
2//
22
3212
//210
2
⊥+=++−=lhlh
lhmk
mk
kkm
P γγγγ
]2)([32 212
22
213
0
2kkikk
mR γγ +−−=
32130
2)(32
2kikk
mS −= γ
where ki are set as k1 = [100], k2 = [010], k3 = [001], and
22
21
2// kkk +=
zik∂∂−⇔3 2-(57)
And mhh⊥ is an effective mass of heavy-hole band in k3 direction, mlh
// is the mass of
light-hole band in k// plane. Also the strain Hamiltonian is
4332211v
**
*
*
)(a
00
00
I
ASRSARRAS
RSA
H εεε
εε
εε
εε
εε
ε +++
−−−−
= 2-(58)
a31a v = )2(b
21
332211 εεε −+−=A
]d)(b3[21
122211 εεεε iR −−= )(d3 2313 εεε iS −−=
On the other hand, conduction band equation is much simpler:
)(a)(2 332211c
23
22
21
2εεε +++++= kkk
mH
cc
2-(59)
a32a c =
57
To obtain the Hamiltonian matrix on (11n)-oriented crystal, we perform rotation on
matrix and variables: ki are rotated by Eq. 2-(29), and rotation of strain εij are already
done by Eq. 2-(33). For H0 and Hε, their rotation can be done by [23]
)()()()( ** ϕθϕθ RRHRRH iti = 2-(60)
The explicit expression of these rotation matrices and resulting Hamiltonians are
summarized in Appendix B. Using the outcome, when strain is zero, the eigenvalues
of the Hamiltonian on (11n) can be determined, and we can obtain energy dispersion
along kz direction by setting kx = ky = 0 [24]:
])2(
)12(3)1([2
2)( 2
1
22
23
222
22
10
22
nnn
mkzE z
+++−
±=γγγ
2-(61)
The effective mass of the valence band in z-direction can be obtained by taking the
curvature of E(z):
])2(
)12(3)1([2/ 2
1
22
23
222
22
10 nnn
mmm
lh
hh
+++−
=⊥
⊥ γγγ 2-(62)
Both masses for InP are plotted on Figure 2-12. It can be seen that the heavy-hole
mass mhh⊥ is minimum on (001) plane and maximum on (111), whereas the light-hole
mass mlh⊥ is maximum on (001) and minimum on (111). The effect of surface
orientation can be discussed by the difference (mhh⊥ - mlh
⊥ ). The 2 masses are
conveniently plotted on Fig. 2-12 in the way that they are at the same point on (001),
so that it is easy to see that the difference increases as the misorientation from (001)
plane increases, and becomes maximum on (111). The larger difference means less
mixing between heavy- and light-hole bands.
58
Figure 2-12 Orientation dependence of z-effective mass from Eq. 2-(62) for InP
[2] Optical matrix element
The optical gain is expressed as [25]:
22
2200
202
)/()(/
)sin)2(
)(
τωτ
θθφχµ
πϖω ππ
+−×
−⋅⋅⋅∫⋅∫∫ ⋅⋅= ∞
E
ffMkddkdg vc
2-(63)
where E is transition energy from conduction to valence band, ω is photon frequency,
µ is permeability, χ is dielectric constant, τ is intraband relaxation time, fc and fv are
Fermi distribution functions for conduction and valence band states. M is the optical
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
1.5
0
mhh⊥ mlh
⊥
mxhh
/ m0
1.2
0.9
0.6
0.3
mx lh/ m
00.13
0.08
0.12
0.11
0.10
0.09
59
dipole matrix element, on which we can attribute most of the gain anisotropy,
expressed as:
lhhh
pecM^^⋅= 2-(64)
where e^
is the polarization vector and p^
is the momentum vector, and hh and lh
denote heavy- and light-hole states. The basis states for (001)-oriented crystal are:
++ == sc21,
21 −− =−= sc
21,
21 2-(65)
++ +−== )(2
123,
23 yixhh 2-(66)
−− −=−= )(2
123,
23 yixhh 2-(67)
+−+ ++−== )32)(
61
21,
23 zyixlh 2-(68)
−+− +−=−= )32)(
61
21,
23 zyixlh 2-(69)
The superscript + and - denotes spin states. Because of symmetry considerations, all
the inner products are zero except [26]:
0Pzpsypsxps zyx === eV 25.72 20
0=P
m2-(70)
For (11n)-oriented crystals, the conduction band wave functions are unchanged, while
those for valence band are calculated to be as follows [27]:
60
21,
23)1(
21
23,
23)1(
21 2
121
11 ⋅Λ
−−±⋅Λ
+=±tt
nPPhh
])1(3
1)1[(])1(3
1)1([21 2
121
21
21
±±
Λ−−
Λ+−
Λ−
Λ+= yPPixPP tttt
zPt21
)1(3
1Λ
−+ 2-(71)
21,
23)1(
21
23,
23)1(
21 2
121
11 ±⋅Λ
++⋅Λ
−=±tt
nPPlh
])1(3
1)1[(])1(3
1)1([21 2
121
21
21
yPPixPP tttt
Λ++
Λ−−
Λ+
Λ−±=
±
Λ++ zPt
21
)1(3
1 2-(72)
222 ttt PSR ++=Λ 2-(73)
where Pt, Rt, St, are rotated Hamiltonian components for kz2. By setting kx = ky =0 on
Eq. AB-(18)-(20), we can obtain explicit expression of the matrix elements for (11n)-
oriented crystals for no-strain case:
Λ+−+=2
312 tt
b
hhx RP
MM
Λ−−+=2
312
tt
b
hhy RP
MM
Λ
+=t
b
hhz P
MM 1
2
2-(74)
Λ+−−=2
312 tt
b
lhx RP
MM
Λ−−−=2
312
tt
b
lhy RP
MM
Λ
−=t
b
lhz P
MM 1
2
2-(75)
61
They are normalized by Mb which is defined by Kane as [28]:
20
2
31 PM b = 2-(76)
This result shows the anisotropy of optical matrix elements clearly. For heavy-hole
state, the coupling is higher for x-direction, i.e., [nn−2 ], by ΛtR3 , while for light-
hole state, y-polarized light couples more by the same difference. The sign of Rt is
minus for n<1, so that the description above becomes opposite. For in-plane
polarization, heavy-hole state is dominant over light-hole, whereas for z-direction
coupling, light-hole state is dominant (note that the sign of Pt is minus). Hence,
VCSEL with tensile-strained gain media will not work well since the light-hole has
higher energy, and we only need to consider compressive-strained materials with
0.25
0
-0.25
(|Mxhh|2 -
|Mxlh|2
)/ |M
b|2
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
Figure 2-13
Matrix element difference
from Eq. 2-(76) for InP
62
transition to the heavy-hole state. In Figure 2-13, we plot the difference between x-
oriented and y-oriented matrix elements for the heavy-hole state:
23
222
2223
2
22
22
)12(3)1(
))(1()2(
33
γγ
γγ
++−
−−+
=Λ
=−
nn
nn
RM
MM t
b
hhy
hhx
2-(77)
An impressive fact is that this figure shows the very same curve as that of (σxx-σyy)/δ
in Fig. 2-8, the stress anisotropy, even though these curves were obtained from
different approach.
It is not proved why the heavy-hole matrix elements and the stress show such
an angle dependence as seen on Fig. 2-13 and Fig. 2-8, i.e., x-axis properties being
larger for 1<n<∞ and y-axis properties being larger for n<1. However, it is likely to
be related to an asymmetry of lattice geometry. Figure 2-14 shows lattice order of
each orientation. Upper part shows in-plane lattice order and lower part is cross-
sectional view. (001) plane is 4-fold and (111) is 3-fold symmetric. On (113) plane,
the lattice spacing in [nn−2 ] direction is larger than that in [
−110] direction, and matrix
element/stress larger for x-axis which is [nn−2 ]. While on (110) plane, we can see
that the lattice spacing is larger in [−110] direction, and matrix element/stress are
larger for the y-axis of [1−10]. Therefore, it can be explained that under compressive
strain, the axis in which the lattice spacing is larger is the dominant polarization axis.
63
Figure 2-14 In-plane (upper) and cross-sectional (lower) atomic order for each orientations
[11n]
[110]
[nn2]
[11n]
[110]
[11n]
[110]
[nn2]
[11n]
[110]
(a) n=∞: (001) (b) n=3: (113)
(c) n=1: (111) (d) n=0: (110)
64
[3] Optical gain anisotropy
These matrix elements were calculated without taking strain into account.
With strain added, the elements change and the anisotropy increases. Nonetheless, to
get the idea of anisotropic gain without going into complicated calculation, we can
use the results above to estimate the anisotropy. We can easily calculate a ratio of
matrix element:
tt
tt
hhy
hhx
RPRP
MM
3)2(3)2(
2
−−Λ+−Λ= = 1.0379 for (113) 2-(78)
The material gain of 1.3-µm wavelength MQW on (001) plane was calculated using
the Crosslight commercial software. Figure 2-15 shows a result for the MQW with 5
50-Å InGaAsP well with +6000 ppm strain sandwiched by unstrained 1.1Q InGaAsP
barriers. At the maximum injection carrier of 5×1018 /cm3, the peak gain is about
5000 cm-1. To make a modest estimate, we use the peak gain value of 2000 cm-1 at
2.5×1018 /cm3 as the gain for y-polarization, the gain for x-polarization is
2000×1.0379 = 2076 cm-1, hence the gain difference is 76 cm-1. At 5×1018 /cm3, the
difference is 190 cm-1. This value is fairly close to the value rigidly calculated on
1.55-µm strained MQW on (112) plane at the same injection level [11].
65
Figure 2-15 Material gain curves for 1.3-µµµµm MQW with injection level
0.25 →→→→ 5××××1018 /cm3
[4] Anisotropy on (001) plane
The (001) plane has 4-fold symmetry so that any two axes with 90° crossing
angle are equivalent. However, the axes at 45° crossing angle are not necessary
equivalent. Constant energy contours on kxky-plane were calculated for valence-band
states [29,30]. While the contour for the light-hole state shows almost a circular
shape, the contour for the heavy-hole state has an asymmetry between in-plane axes
⟨100⟩ and ⟨110⟩. The asymmetry can be also seen on a plot of energy dependence on
in-plane vector k// toward ⟨100⟩ and ⟨110⟩, that the energy is higher (means closer to
the conduction band) for k//=⟨110⟩ [30]. On (001), the polarization axes generally
6000
0
-6000
Mat
eria
l gai
n (/c
m)
Wavelength (µm)
1.24 1.30 1.36
5×1018 (/cm3)
2.5×1017 (/cm3)
66
switches between two ⟨110⟩ axes, and it is likely because the higher energy at ⟨110⟩
axes. However, the asymmetry is small near band-edge, and also it is small on the
band structure of strained MQW.
The calculation of optical matrix element does not reflect in-plane asymmetry,
since the basis states are expressed by the combination of 2 orthogonal in-plane
components x and y , as seen on Eq. 2-(66)~(69). Hence, it does not count the 45°
asymmetry and results show no variation of gain on (001) [11].
On the other hand, the in-plane stress does not show any 45° asymmetry. By
setting n=∞, the stress in [100] direction σ11 from Eq. 2-(26) and the stress in [110]
direction σxx from Eq. 2-(37) are the same as:
))(2(2)( 121112111111
212
121111 CCCCCC
CCCxx −+=−+== δδδσσ
2-(79)
Therefore, it is not clear if the optical gain is different between ⟨100⟩ and ⟨110⟩
directions, or the stress asymmetry may not be representing the gain anisotropy.
67
2.04 Defects and stress in bonded structure
Integration of materials with different properties such as lattice constant or
bandgap is, of course, very useful for every devices and circuits. A problem is that it
is difficult to integrate dissimilar materials. More specifically, it is difficult to
integrate materials with large geometry mismatches, such as lattice constants and
thermal expansion coefficient. A typical example is an epitaxial growth of III-V
semiconductor on a Si substrate, which has been tried for decades without major
success. One successful example is GaN growth on sapphire substrates. Even though
GaN and sapphire have large lattice and thermal mismatches, GaN has been
successfully grown on sapphire and devices fabricated. However, GaN is
exceptional. In general, it is difficult to epitaxially integrate lattice/thermal
mismatched materials, and this is because there are defects generated due to the
geometry mismatch and such defects affect device properties severely. Wafer
bonding has been a successful technique to integrate dissimilar materials, and it is
because the wafer bonding generates defects confined to the bonded interface, rather
than propagating into active regions and hence, they don’t affect device properties
severely.
In this section I will go through defects and stress existing in wafer-bonded
materials. Followed by defect characterization, we estimate stress associated with
defects and that from mismatch of thermal expansion coefficients.
68
[1] Defect classification
Crystal defects include any kind of structural irregularity in crystalline order.
We can sort them into point defects, line defects, and plane defects. The line defects
are usually mentioned as dislocations, and the plane defects include stacking fault,
twin, or anti-phase boundaries. Dislocations can be sorted in three kinds: edge (also
known as 90º or Lomer) dislocation, screw dislocation, and mixed dislocation.
Basically, they are lines of atoms with broken bonds, and characterized by their
Burgers vector which is a shortest path of atomic displacement (and a direction of
dislocation slipping). For the edge dislocation, its line is perpendicular to Burgers
vector. Screw dislocation has its line and Burgers vector parallel. Mixed dislocation
could have line and Burgers vector at any angle between 0 and 90º, and they are
characterized by this angle.
For epitaxially grown III-V semiconductors, most commonly seen
dislocations are edge and 60º dislocations. They are illustrated in Figure 2-16. The
edge dislocation relieves geometry mismatch more efficiently, however, it is
energetically easier to introduce 60º dislocation in III-V materials. Hence, there are
Figure 2-16 Illustration of (a) edge dislocation and (b) 60º dislocations
(a) 90° (edge) dislocation (b) 60° (mixed) dislocation
69
mostly 60º dislocations present in a layer grown under a large lattice mismatch, such
as a GaAs layer on Si. This 60º dislocation also has low energy to propagate and slip,
therefore, once it is generated at a lattice-mismatched interface, it threads microns
throughout the epilayer as growth proceeds. This is a reason why heteroepitaxy of
III-V on Si has never been successful, since it is difficult to eliminate or terminate
60º-dislocation propagation.
In the case of wafer bonding, on the other hand, it brings two perfect materials
[31] into contact abruptly. Hence, dislocation formation mechanism are very
different (and much simple). In the case of InP vs GaAs, their lattice mismatch at
room temperature is 3.7% (It is 3.6% at 600 °C. Since the difference is small, we
neglect the effect of thermal expansion for simplicity. We will discuss thermal
mismatch in later section). This means that every 26 atoms of InP would match with
every 27 atoms of GaAs if they are placed with the same orientation. Figure 2-17
Figure 2-17 High-resolution TEM image of bonded interface of (001) InP
and (001) GaAs [32]
(001) GaAs
(001) InP
5 nm
70
shows a high-resolution transmission electron microscope (TEM) image of such
bonded interface [32]. As the two materials are put in contact and brought to an
elevated temperature, high enough that atomic bonding can be cut and reformed,
atoms on their surfaces would rearrange themselves to form atomic bonds with each
other. Among 27 of GaAs atoms, 26 atoms will find their InP mates but the
remaining 1 will not. Hence, this leftover 1 atom forms a defect as shown in Fig. 2-
16 (a), i.e., an edge dislocation if defects are formed on a line penetrating the paper
plane. The edge dislocation has a slip plane parallel to the interface, so it could move
left or right, but it can hardly climb up into InP or GaAs layer as it is energetically
difficult. Hence, the dislocations are confined at the interface and do not affect
crystalline quality of layers away from it.
What happens if their surface orientations of materials bonded are different?
As we saw before, the geometry mismatch at the interface is now largely affected by
orientation relation of the two, and the mismatch becomes different depending on
which cross-section of the interface you are looking at. Figure 2-18 is an example of
wafer bonding of orientation-mismatched (001) GaP and (110) InP [32]. As they are
aligned by their [1−10] direction, the geometry mismatch in this direction is the same
as the lattice mismatch of GaP and InP, which is 7.7%, so that there must be 1 defect
per every 13 atoms. Whereas on the other cross-section, the mismatch is so large that
they are approximately 3 atoms of InP lined up with 4 atoms of GaP. In such a case
the lattice alignment is called “misfit vernier” and there is little lattice deformation.
71
Figure 18 High-resolution TEM image of bonded interface of orientation-mismatched
(001) GaP and (110) InP [32]
In this way, the linear dislocation density is very different depending on which cross-
section to observe.
In real samples, there is another source of dislocation: tilt between InP and
GaAs. The tilt exists both in vertical and horizontal orientations. The vertical tilt is
from surface misorientation of commercial substrates, and horizontal tilt is from
misalignment of two wafers when we place them together. This issue of tilt is already
discussed elsewhere [33], and since the effect of the tilt is minor compared to lattice-
and thermal mismatch, we do not need to discuss it here.
[2] Stress by misfit dislocations
Let us look at the case of our subject, a bonded interface of (113)B InP and
(001) GaAs. In Figure 2-19 we show free-standing atomic order of each materials at
the bonded interface: (a) top view, (b) side view at (−110) cross section, (c) side view
(001) GaP
(110) InP
[001]
[110]
[110]
[110]
[001]
[110]
[110]
[110]
5 nm
72
at cross section orthogonal to (b). It is a complex interface, and there may not be
dislocation lines since atom positions are 50% off between neighboring atomic
planes. Our purpose here is to obtain an order of stress magnitude by interface
defects, so we employ a very simple model and calculate stress from 1-dimentional
Figure 2-19 Atomic order of (113) InP and (001) GaAs: (a) top view, (b)(c) side view
6.8818Å
4.14
99Å
[001]
[110]
[113]
[110]
3.99
75Å
[113]
[110]
InP
[332] Ga As
In P
(a)
(b) (c)
In P
[001]
[110]
[113]
[110]
(1st layer)
(2nd layer)
3.9975Å
73
misfit dislocation array. From the theory of J. W. Matthews, force by an edge
dislocation FED is expressed as [34]
)1(ln)1(4
2
+−
=bRGbFED νπ
2-(80)
where b is Burgers vector length, ν is Poisson ratio, G is shear modulus, and R is a
height of the edge dislocation. By dividing FED by an area that an edge dislocation
affects, we can obtain dislocation stress σED as
)/(11ε
σbR
FSR
F EDEDED =•
=InP
GaAsInP
lll −
=ε
R
GbbR ε
νπ)1(ln
)1(41 +−
= 2-(81)
where S is a spacing between dislocations, which can be expressed by b and a
geometry mismatch ε. The parameters G and ν are orientation-dependent, but we use
values for (001) here since we just want to get an order of magnitude. (Orientation-
dependence of ν is discussed in Appendix D). As for R, in Fig. 2-18, the number of
monolayers deformed at the interface is about 5-6, so we can assume R = 10Å. Also,
b = 3.9975Å. The only orientation-dependent term is ε, which is
4191.08818.6
9975.38818.6 =−=ε for [33−2 ] direction
0367.01499.4
9975.31499.4 =−=ε for [−110] direction 2-(82)
By substituting these numbers and numbers from Appendix A into Eq. 2-(81), we get
74
8109.8 ×=EDσ N/m2 for [33−2 ] direction
7108.7 ×=EDσ N/m2 for [−110] direction 2-(83)
To get an idea of how much large or small these stress values are, let us compare
these values with the stress in strained material such as strained MQW. From
previous section Eq. 2-(41), average in-plane stress is
δσσ
Byyxx =+2
From Fig. 2-5, B on (311)B is 12.427 1010 N/m2. If we set δ = +1%, we get the
average stress = 1.2 109 N/m2. Hence, dislocation stress for [33−2 ] direction is
comparable to this, but for the other [−110] direction, it is an order of magnitude
smaller.
These dislocation stress values are at the interface. If we look at how they
affect the active region, it seems that the effect is insignificant. This is because the
stress is expected to decay as we go further from the interface, such that [35]
)/exp()( 0 Shh hEDED −∝ =σσ 2-(84)
where h is a distance from the interface with dislocations. Since S is on the order of
R=10Å, the stress decays quickly as we see further away from interface and becomes
much smaller than the stress in strained material. Since in our VCSEL, the gain
medium sits around 3000Å away from two interfaces, this model tells that the
contribution from dislocation at the interface to polarization is negligible.
75
[3] Cross hatch
Aside from crystal defects, we also have surface defects on semiconductor
materials. The definition of surface varies, but basically we call whatever is wrong
with a surface as “surface defects”. Those could include pits due to non-optimized
growth conditions, precipitates, pits due to grown-in dust particles, and cross hatch.
The cross hatch is the result of a plane defect terminated at the layer surface,
and it appears as a line. Plane defects are usually formed on a 111 plane, hence on
(001) surface, the cross hatches are formed along [110] or [−110] directions as these
are intersecting line directions between 111 and (001) planes, and they form
rectangular patterns. On a (113)B surface, we can observe cross-hatch patterns
formed in different way as shown in Fig. 2-20. They are formed along [−2
−11],
[−1
−2 1], and [
−110] as these are intersections between 111 and (113)B planes.
Cross hatch has been observed on wafer-bonded surface by others and was
attributed to mismatch in thermal expansion between the two bonded materials during
Figure 2-20 Normalski picture of surface of wafer-bonded (113) InP layer
[110]
[110]
[113]
(111)
[211]
[121]
(111)
(111)200 µm
76
cooling stage of bonding [33]. However, mechanism of such cross-hatch generation
was not fully explained and is doubtful. That is, the mismatch between the two
materials exists only at the bonded interface no matter what is the source of the
mismatch, so that it is difficult to think that thermal mismatch would create volume
dislocations in the bulk layers. Rather, the source of such cross hatch patterns can be
attributed to the following reasons. One is the surface roughness of the materials
before bonding. It is very common for the pre-bonding surface to have bumpy point
defect, or it is highly possible to have dust particles trapped between two surfaces.
Having such bumps at the interface, two materials are brought up to a high
temperature under high pressure, then the bumps could push surrounding materials
and cause slipping of crystal planes along 111. It is indeed very noticeable on Fig.
2-20 picture that point defects seem to be cores of cross hatches. Another possible
reason is that strain in the etch-stop layer might generate cross hatches at the interface
with the InP layer, and that they were transferred to the InP layer surface. That is, the
etch-stop layer is of InGaAs(P) designed to be lattice-matched to InP, but it is
difficult to grow perfectly lattice-matched material by MOCVD, hence, the layer
could be strained due to a small lattice-mismatch up to 0.2%. And even if the
mismatch is small, the layer is as thick as 200 nm and it could be close to a critical
thickness. Under such conditions, it is highly possible that plane defects are created
in the etch-stop layer during the heat treatment.
It is very likely that in sample like Fig. 2-20, there are many plain defects
penetrating through the InP active region layer, then they will be source of non-
77
radiative recombination. More importantly to us, if the formation of such defects are
asymmetric, they could generate asymmetric stress in gain medium and affect
polarization behavior. However, it is difficult to model plain defect generation by
above-mentioned mechanism since the conditions would vary from sample to sample.
Indeed, the bonding temperature seemed to matter the defect formation significantly.
The sample of Fig. 2-20 was bonded at 650 °C, whereas samples bonded at lower
temperature such as 575 °C had much less cross-hatch. This may be because of lower
migration speed of In atoms at lower temperature. We need further investigation to
verify the mechanism of plain defect generation.
[4] Stress by thermal expansion mismatch
Another source of stress in bonded structure would be thermal expansion
mismatch between the two bonded materials. That is, during cooling down the
sample from bonding temperature, the two materials would shrink at different rates,
so that mismatch would be generated. And at low temperatures, such mismatch
cannot be relieved by creating any dislocation. The thermal expansion constants at
the room temperature are listed in Appendix A. Their temperature dependence is
negligible here since we want to find the order of magnitude of the strain. The
thermal expansion/deflation should occur in a symmetric way no matter what
orientation the materials are, so it should generate symmetric mismatch strain. If we
set the bonding temperature to be 575°C, the amount of strain generated in InP/GaAs
bonded structure during cooling down to room temperature (25°C) is
78
%1.01010)56.44.6()25575( 36 =≈×−×− −− 2-(85)
Since GaAs shrinks more than InP, it generates about 0.1% compressive strain in InP
side or 0.1% tensile strain in GaAs side. Right after the bonding, both InP and GaAs
sides are equally thick (3~400 µm), so the strain is almost evenly split between them.
As we etch off the InP substrate, the strain will be concentrated onto InP side, i.e., the
InP active region will be under biaxial 0.1% compressive strain, and generate
asymmetric stress in accordance to Eq. 2-(37) with δ = 0.1%.
For more precise estimation, the temperature range we have to consider is not
necessarily 575-25°C. It is said that a threshold temperature at which atomic bonding
of InP can be rearranged is about 400ºC, based on various observations. It is also the
temperature at which dislocations become “frozen”, i.e., dislocations can be still
generated and re-arranged when a temperature is being brought down from bonding
temperature until around 400ºC. Hence, we may have to change the temperature
difference in Eq. 2-(85) to (400-25) and the result becomes about 0.07%.
As a conclusion on thermal mismatch stress, it would be insignificant if the
gain medium is a strained MQW, to which strain of about 1% is intentionally added.
However, if the strain in the gain medium is small, this thermal mismatch strain could
become significant and the main source of asymmetric stress, thus affecting the
polarization. Aside from affecting the properties of gain medium, the thermal stress
would cause wafer bowing which would be an obstacle for a large-scale wafer
bonding. We can eliminate this problem by thinning the substrates or employing thin
film transfer technology.
79
2.05 Summary
I have shown various physical aspects of polarization, strain/stress, optical
gain, and defects in this chapter. The mechanism of VCSEL polarization was
explained based on spin sublevel model. I also showed the effectiveness of dichroism
on polarization control. I have summarized strain/stress on (11n) materials, and the
results indicated why we have in-plane anisotropy on (11n) plane but not on (001)
and (111) plane. The anisotropy of optical gain on (11n) plane was shown by the
anisotropy of optical matrix element. An impressive result was that anisotropy of
stress and heavy-hole matrix element showed the exact same trend. Other aspects
such as piezoelectric effect and effective masses were also shown for (11n) materials.
Then I organized defects associated with lattice-mismatched wafer-bonded structure.
It was concluded that the effect of defects on polarization is minor, but it may worth
to investigate experimentally. Thermal expansion mismatch was also examined, and
it can be a source of polarization for our VCSEL.
80
References
[1] M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in
surface-emitting semiconductor lasers”, Phys. Rev. A 52, pp.1728-39, 1995.
[2] M. Travagnin, M. P. van Exter, A. K. Jansen van doorn, and J. P. Woerdman,
“Role of optical anisotropies in the polarization properties of surface-emitting
semiconductor lasers”, Phys. Rev. A 54, pp.1647-60, 1996; ibid 55, pp.4641, 1997.
[3] M. Travagnin, M. P. van Exter, and J. P. Woerdman, “Influence of carrier
dynamics on the polarization stability and noise-induced polarization hopping in
surface-emitting semiconductor lasers”, Phys. Rev. A 56, pp.1497-1507, 1997.
[4] J. Martin-Regalado, S. balle, M. San Miguel, A. Valle, and L. Pasquera,
“Polarization and transverse-mode selection in quantum-well vertical-cavity surface-
emitting lasers: index- and gain-guided devices”, Quantum. Sem. Opt. 9, pp.713-36,
1997.
[5] J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization
properties of vertical-cavity surface-emitting lasers”, IEEE J. Quantum Electron. 33,
pp.765-83, 1997.
81
[6] M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, “Physical insight into
the polarization dynamics of semiconductor vertical-cavity lasers”, Phys. Rev. A 57,
pp.2080-90, 1998.
[7] M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, “Polarization fluctuations
in vertical-cavity semiconductor lasers”, Phys. Rev. A 58, pp.4191-4205, 1998.
[8] J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux,
“Minimal rate equations describing polarization switching in vertical-cavity surface-
emitting lasers”, Opt. Com. 201, pp.129-137, 2002.
[9] M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, “Polarization modal
noise and dichroism in vertical-cavity semiconductor lasers”, Appl. Phys. Lett. 74,
pp.2274-6, 1999.
[10] T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable
reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting
lasers”, Phys. Rev. A 59, pp.4660-7, 1999.
[11] T. Ohtoshi, T. Kuroda, A. Niwa, and S. Tsuji, “Dependence of optical gain on
crystal orientation in surface-emittimg lasers with strained quantum wells”, Appl.
Phys. Lett. 65, pp.1886-7, 1995.
82
[12] K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B.
Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity
surface-emitting lasers: Experiments, models and applications”, Nanoscale Linear and
Nonlinear Optics, Am. Inst. Phys. Conf. Proc. 560, pp.403-17, 2000.
[13] C. Degen, B. Krauskopf, G, Jennemann, I. Fischer, and W. Elsäβer,
"Polarization selective symmetry breaking in near-fields of vertical cavity surface
emitting lasers ", J. Opt. B: Quantum Semiclass Opt. 2, pp.517-25, 2000.
[14] H. Nagai, S. Adachi, and T. Fukui, “III-V mixed crystals”, Chapter 2, Corona
Publishing Co., Ltd., Tokyo, Japan, 1988.
[15] M. P. van Exter, A. K. Jansen van doorn, and J. P. Woerdman, “Electro-optic
effect and birefringence in semiconductor vertical-cavity lasers”, Phys. Rev. A 56,
pp.845-53, 1997.
[16] The remark “epilayer retains the same crystal orientation as substrate’s” may
sound nothing odd. Indeed, one may think that epilayer should always retain the
same orientation as substrate, which is correct to say in general. However, when the
epilayer is lattice-mismatched and grown on the substrate slightly misoriented from
(001), in some cases, the epilayer tries to relax the lattice-mismatch by misorienting
itself slightly from the substrate orientation. Thus the epilayer doesn’t necessary
83
retain the exact same orientation as the substrate. The degree of epilayer
misorientation is less than 1 degree in general, so normally it is not large enough to be
recognized.
[17] E. A. Caridi and J. B. Stark, “Strain tensor elements for misfit-strained [hhk]-
oriented cubic crystals”, Appl. Phys. Lett. 60, pp.1441-3, 1992.
[18] There are a few different methods of calculating εij published by other authors.
They are shown in Appendix C.
[19] D. Sun and E. Towe, “Strain-generated internal fields in pseudomorphic (In,
Ga)AsGaAs quantum well structures on (11l) GaAs substrates”, Jpn. J. Appl. Phys.
33, pp.702-8, 1994.
[20] D. L. Smith and C. Mailhiot, “Piezoelectric effects in strained-layer
superlattice”, J. Appl. Phys. 63, pp.2717-9, 1988.
[21] G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Variational calculations
on a quantum well in an electric field”, Phys. Rev. B 28, pp.3241-45, 1983.
[22] S. L. Chuang, “Efficient band-structure calculations of strained quantum wells”,
Phys. Rev. B 43, pp.9649-61, 1991.
84
[23] A. Niwa, T. Ohtoshi, and T. Kuroda, “Orientation dependence o optical
properties in long-wavelength strained quantum-well lasers”, IEEE J. Select. Topics
Quantum Electron. 1, pp.211-7, 1995.
[24] R. H. Henderson and E. Towe, “Effective mass theory for III-V semiconductors
on arbitrary (hkl) surfaces”, J. Appl. Phys. 79, pp.2029-37, 1996.
[25] T. C. Chong and C. G. Fonstad, “Theoretical gain of strained-layer
semiconductor lasers in the large strain regime”, IEEE J. Quantum Electron. 25,
pp.171-83, 1989.
[26] J. P. Loehr and J. Singh, “Theoretical studies of the effect of strain on the
performance of strained quantum well lasers based on GaAs and InP technology”,
IEEE J. Quantum Electron. 27, pp.708-16, 1991.
[27] R. H. Henderson and E. Towe, “Strain and crystallographic orientation effects on
interband optical matrix elements and band gaps of [11l]-oriented III-V epilayers”, J.
Appl. Phys. 78, pp.2447-55, 1995.
[28] E. O. Kane, “Semiconductors and semimetals”, Vol. 1, Academic Press, New
York, 1966.
85
[29] D. A. Broido and L. J. Sham, “Effective masses of holes at GaAs-AlGaAs
heterojunctions”, Phys. Rev. B 31, pp.888-92, 1985.
[30] L. A. Coldren and S. W. Corzine, “Diode lasers and photonic integral circuits”,
Appendix 8, Wiley, New York, 1995.
[31] By “perfect material” I mean materials with good quality in today’s technology
standard. For III-V semiconductor, a dislocation density of ≤103 /cm2 is current
standard level.
[32] Y. Okuno, K. Uomi, M. Aoki, and T. Tsuchiya, “Direct wafer bonding of III-V
compound semiconductors for free-material and free-orientation integration”, IEEE J.
Quantum Electron. 33, pp.959-69, 1997.
[33] K. A. Black, “Fused long-wavelength vertical cavity lasers”, Ph.D. Dissertation
in Materials, University of California, Santa Barbara, 2000.
[34] J. W. Matthews, “Epitaxial growth”, Chapter 8, Academic Press, New York,
1975.
[35] J. S. Speck, private communication.
86
Chapter 3 Experimental
3.01 MOCVD
[1] System and growth overview
The UCSB MOCVD system for InP-based materials has a horizontal quartz
reactor made by Thomas Swan. Inside the reactor is a graphite susceptor, on which is
a 2-inch wafer holder that can be rotated by H2 flow. The susceptor is heated by
infrared lamps, and its temperature is monitored by a thermocouple which is put
inside the susceptor block. The actual temperature of the wafer which sits on the
wafer holder is not the same as the thermocouple reading: the temperature is likely to
be lower by 20-30 ºC at the wafer due to the H2 flow for rotation. The carrier gas has
been H2 so far for the InP reactor, but I like to note that N2 has been widely used as
carrier gas these days, thanks to development of a compact purifier. The N2 carrier
gas has not only a safety benefit, but also a benefit of improving growth uniformity
across the wafer. There is another reactor for GaN-based materials attached to the
system, and we can switch the gas flow between the two reactors. Metal-organic
sources installed in the system are trimethylindium (TMIn), trimethylgallium
(TMGa), tertiarybutylarsine (TBAs), and tertiarybutylphosphine (TBP),
trimethylaluminum (TMAl), diethylzinc (DEZn). A gas source disilane (Si2H6) is
shared with another MOCVD system. We also have aluminum source (TMAl)
installed, but it was practically impossible to grow Al-compounds. It was because
TMAl and TBP seemed to form adduct which clogs the exhaust line. Hence, the
87
material worked on this MOCVD was limited to InGaAsP compounds. The system
has the Epison equipment which reads mol concentration of gas flow of either TMIn,
TMGa, TBAs, or TBP. More details of the machine can be found elsewhere [1].
A standard growth condition on (001) substrate is as follows: growth
temperature (Tg) of 615 ºC, the V/III ratio of 50 for InP, reactor pressure of 350 torr,
and total gas flow inside the reactor of 16L. The TMIn flow was kept at 1 mol/min,
and the TBP flow was at 50 mol/min. This condition gave about 27 nm/min of
growth rate for InP. For growth of InGaAsP compound, TMGa and TBAs flow was
added and their flows were adjusted to obtain target compositions. Due to the
mechanism of MOCVD growth, composition ratio (Ga/In and As/P) is not the same
between gas-phase and solid-phase, hence, the V/III ratio differs from 50 for
InGaAsP growth. For InGaAs lattice-matched to InP, V/III ratio was set about 5.
Such a low ratio compared to InP is due to the fact that Ga is less mobile than In atom
so that we need to enhance group-III migration by having low group-V flow.
[2] Growth calibration
To grow one wafer for device fabrication, we need to do some calibration
growths to determine the growth rate and the gas flow for each material in the device
structure. That is, a device structure typically consists of InGaAsP layers with 2 or
more different compositions, and we have to find how much TMGa and TBAs flow
needed to grow each InGaAsP layers. We also need to calibrate dopant flows to grow
doped materials, however, doping specification is not tight for most devices and the
88
system doping characteristics were stable enough over a long time. Therefore, doping
calibration was done in every 2-3 months or before growing device structures with
critical doping. On the other hand, it is very critical to control composition and
thickness of InGaAsP layers since those parameters determine device performance,
hence calibrations were needed each time to grow one device structure.
For lattice-matched materials, a bulk layer of the material was grown with gas
flows based on previous or similar growth data, and its composition, and thickness
were obtained by methods described later in material characterization section. For
lattice-mismatched materials, we have a thickness limit to grow without relaxation by
dislocations. We can grow such material thicker than its critical thickness and have it
intentionally relaxed, but if the mismatch is around 1%, the grown layer is likely to be
partially relaxed even if it is grown over 1µm [2]. It will be difficult to find out how
much it is relaxed by using simple X-ray diffraction method. Therefore, a MQW
structure which consists of the InGaAsP material to calibrate and InP barrier was
grown. The X-ray tells net strain and total thickness of 1 pair InGaAs/InP, hence, if
we know the growth rate of InP, we can obtain growth rate of the InGaAsP, and by
the thickness ratio we can calculate strain in the InGaAsP layer.
Dr. G. Fish and Dr. P. Abraham wrote a very useful program for calibration.
It calculates material composition from measured strain and photoluminescence (PL)
data, and vice versa. It also calculates PL wavelength from MQW by specifying
material composition and thickness, hence, we can find out composition of the
89
InGaAsP in above-mentioned calibration MQW. Once the composition of the grown
material is found, the program calculates segregation coefficients for Ga/In and As/P.
The meaning of the segregation coefficient is well explained elsewhere [1]: it is
basically a parameter which correlates solid-phase composition ratio (Ga/In or As/P
of grown layer) to gas-phase composition ratio (TMGa/TMIn or TBAs/TBP)
determined by gas flow rate and Epison reading. Hence, with the segregation
coefficients we can estimate gas flow rate needed to obtain particular solid-phase
composition. The calibration is mostly about refining the segregation coefficients.
[3] Problem with the system
I like to address a few problems on this MOCVD system. First, the run-to-run
variations of composition (or segregation coefficients) and growth rate are not small.
For growing VCSEL active region, it is very important to control the growth rate
since the thickness of the active region determines the lasing wavelength. However,
it seemed the growth rate was affected by factors such as which reactor to use (we
usually had 2-3 identical reactors and used them alternatively), how much pre-
deposition inside the reactor, or even what time of the day the growth was performed.
Also, the wafers sit on the wafer holder which can be rotated by flowing H2 from
beneath, and without the rotation, the growth rate/composition distributions across the
wafer become significant. However, it is easy to lose the rotation by a slight
misalignment of H2 flow path. Once the material growth occurs, the inside of the
90
reactor gets quickly covered by black deposited materials and we can’t see inside
anymore, hence, there is no mean to make sure that the rotation is happening.
For these problems, I used the same reactor for series of calibration growth
and real sample growth. And for crucial calibration and real sample growth, I cleaned
the reactor each time, so that the growth conditions are as close as possible, and that I
could see inside the reactor to make sure that the wafer tray was rotating at the
beginning of the growth. The outcome was not spectacular, but at least, we were able
to grow materials with better property control than before.
Nowadays, it is typical for a commercially available MOCVD machine to
have in-situ monitoring system of growth rate and other properties of grown
materials. However, our system has horizontal reactor and it is difficult to implement
such monitoring system. Indeed, the horizontal reactor is now a minority (over 90%
of MOCVD machines sold have vertical reactors). The vertical reactor is more
suitable for in-situ monitoring and better uniformity, while it has a disadvantage of
having larger gas consumption rate.
91
3.02 Wafer bonding
[1] Bonding procedure summary
I have tried roughly two types of bonding procedure for this research. One is
HF-based cleaning/high-temperature bonding procedure which was used for earlier
work, and the other is NH4OH-based cleaning/low-temperature bonding combination
used for later work.
Table 3-1 summarizes procedures tried. All the methods basically consist of
cleaning wafer surface by organic solvents, cap layer etching, dip in chemical
solution (BHF or NH4OH) for oxide removal and surface activation, putting two
wafers together face to face, putting the attached wafers in the bonding fixture, and
finally the annealing treatment. It was done for 30 minutes throughout this work. A
pressure of about 1~2 MPa was applied during the annealing, and the value varied
depending on the size of wafers to bond. Though it is not mentioned in the table,
there was always 2-3 minutes of DI rinse following any chemical treatment.
For all InP materials, they were MOCVD-grown with InGaAs(P) cap layer,
which was selectively etched off so that I always got a fresh non-oxidized surface just
before the bonding. On DBR wafers, I also etched off 1 pair of GaAs/AlGaAs layers
selectively, but the etching was not performed if I could not get smooth surface
morphology after the etching. It seemed that due to the highly reactive nature of
AlGaAs, it gets oxidized gradually in the clean room, so that the selective etching of
GaAs/AlGaAs becomes difficult on old DBR wafers, especially if the Al content is
high.
92
Table 3-1 Variation of surface treatment and handling m
ethods of wafer bonding sam
ples
Isopropanol squirt cleaning → U
ltra-sound bath in Acetone →
Cap layer/surface layers etching
Buffered H
F dip
N2 blow
dry→
put wafers together
→ put in fixture
Fixture (dry)D
I wafer
NH
4 OH
N2 blow
dry→
put wafers together
→ put in fixture
N2 blow
dry→
put wafers together
→ put in fixture
put wafers together
in Methanol
→ put in fixture
Methanol
escape channel etching (on InP or GaA
s)
650ºC650ºC
575ºC575ºC
pre-bonding
1) comm
on cleaning
2)3)4) Eng. II → Eng. I
5)6)7) typical bond temp.
bad surface morphology
problems
BH
F/dry transferB
HF/D
I/dryN
H4 O
H/dry
NH
4 OH
/wet
93
[2] Advantage/disadvantage of each procedure
A problem on our wafer bonding procedure was that we had to carry wafers
from the research cleanroom in Engineering II building to the teaching cleanroom in
Engineering I building where the bonder was in. That is, the wafers were exposed to
the air for about 10 minutes before the bonding. To prevent contamination, we had to
carry wafers in some solutions, or put wafers together in Eng. II and carry in fixture.
The latter procedure, noted in the table as ”BHF/dry transfer”, worked well in terms
of bonding two wafers, but the surface of transferred InP layer had very bad
morphology as shown in Figure 3-1. In this procedure, wafers were put together right
after the surface treatment so that they were attached by strong Van der Waals force.
However, they were then handled in room temperature for 10 minutes until put in the
bonding furnace, and during that 10 minutes the surface traction might have lost and
resulted in bad bonding. The next procedure noted as ”BHF/DI/dry” worked well and
had no problem, except that I could not obtain good bonding yield at lower heating
temperature than 650 ºC. On this procedure, it seemed that after the 10-min transfer
Figure 3-1
Surface morphology of
(001) InP bonded to
(001) GaAs by
“BHF/dry transfer”
94
in DI wafer, the surface was not so ”active” any more and I could not get strong Van
der Waals traction.
On the other hand, transferring in NH4OH seemed to work very well, and I
was able to bond wafers at much lower temperature. This can be attributed to the fact
the wafers were immersed in the NH4OH solution until right before the bonding so
that the wafer surface had kept active. Lower bonding temperature was good for
reducing the amount of cross-hatch formed on the surface of the transferred layer, as
mentioned in the last chapter. On the other hand, NH4OH etches GaAs surface
slowly and we should not immerse wafers for too long.
With ”NH4OH/dry” procedure, wafers had strong Van der Waals traction.
”NH4OH/wet” also worked well, indeed, placing in wet surface is easier. That is,
with dry surface, wafers could attach in unwanted way due to the Van deer Walls
traction, so I have to place them very carefully or I have to detach them by immersing
in liquid. But with wet surface, we can take time in aligning wafers together, or
actually they align themselves due to the liquid surface tension force. However, there
was a problem on electrical conduction at the bonded interface, as I will show later.
[3] Pre- and post-bonding procedures
For the wet bonding, it is necessary to have escape channels on surface of
either wafer. The channels were to let liquid escape from the bond interface so that
no liquid would be trapped at the interface [3,4]. After crystal growth, stripes of 10
µm-width and 250 µm-apart were formed by photo-lithography, and the wafer surface
95
was wet-etched by appropriate chemical. If there is cap layer on top, the layer is
selectively etched off, then the subsequent material was etched to a few 1000-Å deep.
The photo-resist mask can be stripped off by acetone, but to ensure complete removal
of organic materials, the wafer should be further cleaned by HF solution.
One very important fact in achieving good bonding is to avoid any roughness
on surfaces of 2 wafers and the bonding fixture, so that the bonding pressure can be
applied to the wafers uniformly. After crystal growth, wafers could have some
roughness on surface due to inhomogeneous growth or grown-in dusts. A technique
to remove surface defects was developed by Dr. J. Geske. This technique was not
used in this work, however, it will improve bonding yield. As shown in Table 1,
Isopropanol squirt cleaning was done to remove any removable dusts on wafer
surface as much as possible. As for bonding fixture, surfaces of its parts were
mechanically polished each time before bonding.
Once the heat treatment was done and the wafers are bonded, the InP substrate
was selectively etched off by HCl solution, and then InGaAs etch stop layer were
etched off by a mixture of 3H3PO4+1H2O2+50H2O. The process of InP substrate
etching depends on its crystallographic orientation and conduction type. For
example, the HCl solution etches n-type InP fast but does p-type very slowly. For
(001) n-InP, it typically takes 40 min to etch off a substrate of about 350 µm-thick by
a mixture of 3HCl+H3PO4. On the other hand, it takes about 3 hours to etch off
(113)B substrate of similar thickness by the same mixture. For the most cases, the
etching of (113)B substrate was done by leaving the sample in the etching solution for
96
hours until the substrate is completely gone. However, to speed up the process, it is
also possible to thin the InP substrate mechanically and then use selective wet etching
for complete removal. This method was used on later works. Also after the second
bonding of VCSEL process, the GaAs substrate was etched off by a mixture of stirred
NH4OH+30H2O2. It takes about 3 hour to etch off 400 µm-thick substrate by this
method, but we again can speed up the process by mechanically thinning the
substrate. The etching slows down at AlGaAs layer, so the etching was stopped as
soon as the substrate is gone. The AlGaAs layer was etched off either by BHF or by
a mixture of 1HCl+2H2O.
97
3.03 Material characterization
[1] PL measurement
To determine composition of quaternary compound layers, we need to
measure lattice parameter by X-ray diffraction and bandgap by PL. The PL is also
used to investigate material quality by comparing peak intensity and FWHM. During
this research I used two different PL setups in this research: I name them “old setup”
and “new setup”. The old setup is a basic setup with 780-nm pump laser. The new
setup has much-improved features, such as a microscope, automated mapping
function, micron-step motion stage [5]. Its pump laser is switchable between 780-nm
and 980-nm, and pump power is also variable. Figure 3-2 compares PL results taken
Figure 3-2 PL peaks from the same sample measured by new setup and old setup
1200 1300 1400
8000
6000
4000
2000
0
new setup old setup
0.0004
0.0003
0.0002
0.0001
0
Wavelength (nm)
PL in
tens
ity: n
ew s
etup
(arb
. uni
t)
PL in
tens
ity: o
ld s
etup
(arb
. uni
t)
98
by two setups on the same MQW. The setups use very different intensity unit, and
the new setup gave narrower FWHM of the peak. It should be noted that the PL
intensity is in arbitrary unit for both setups, since the intensity depends on conditions
and sensitive alignments of the setup. To make a rigid comparison of PL intensity
between 2 or more samples, all samples should be measured at one time. Yet, the
intensity had an error of about ±5%, so that small difference should not be counted.
The difference of pump laser wavelength should not give any fundamental
difference on measuring the materials of our interest, which emit at around 1.3 µm.
One major difference is that the 980-nm light is transparent for InP, GaAs, and
AlGaAs, while these materials absorb 780-nm light. Hence, 980-nm laser can be
used to measure PL from an actual VCSEL structure and find out its cavity
wavelength. The 780-nm laser can be useful on some occasion, such as measuring on
an as-grown VCSEL active region with an InGaAs etch-stop layer beneath (but
without cap layer). Theoretically, the pump light should be mostly absorbed by the
MQWs in the active region above the InGaAs layer, and we should see the PL
emission from the MQWs clearly. However with the 980-nm pump light, the PL
peak from InGaAs layer was considerably strong and sometimes made the peak of
MQW emission unclear. On the other hand, with 780-nm pump light, the InGaAs
peak was less strong. This is probably because the 780-nm light was absorbed not
only by the MQWs but also by the thick InP cladding layer, so a small portion of the
light reached to the InGaAs layer. Meanwhile, the 980-nm light was only absorbed
by the thin MQWs, allowing a large portion of the light to reach the InGaAs layer.
99
Since the pump laser is an edge-emitting laser, its polarization may affect the
PL results from the material with anisotropic gain and absorption. I did a series of
experiment using the new setup on such anisotropic material. The pump laser was
linearly polarized, and PL was measured aligning maximum gain axis or minimum
gain axis of the material to the polarization axis of the pump laser. The PL intensity
from these 2 cases seemed to be slightly different, by about 5%, the value close to the
PL anisotropy reported on a similar material [6,7]. However, such a difference t is
too small to attribute to the anisotropy with our setup. Nonetheless, in order to avoid
any effect from the pump laser polarization, PL measurement on anisotropic material
was done by mis-aligning the polarization axes of pump laser and sample.
The measured PL emission wavelength can be converted to energy by using a
relation: E (eV) = 1240/λ (nm). However, the E obtained by this relation is not
exactly the bandgap of the material measured. Due to the thermal energy of
electrons, the actual recombination occurs, not from the conduction bad edge to
valence band edge (either heavy hole or light hole), but from slightly above the
conduction band edge. Therefore, the E obtained above is E = Eg + ∆E where Eg is
the real bandgap of the material. The ∆E is estimated to be kT/2 = 13 meV [1]. This
number is counted in the calibration program mentioned earlier. The Eg we discuss
here is transition energy between conduction band-edge to valence band-edge under
as-grown situation. The valence band-edge can be either heavy-hole or light-hole
band-edge, depending on how the material is strained. The notation I use here such
as “1,1Q” means InGaAsP that has an Eg which corresponds to 1.1-µm wavelength.
100
[2] X-ray diffraction measurement
The X-ray diffraction was performed on MOCVD-grown layers. As
explained in Chapter 2, if a grown layer has a lattice mismatch with the substrate and
if the layer thickness is within the critical thickness [8], the layer should be deformed
by biaxial strain as shown in Fig. 2-3. Therefore, by measuring a mismatch of lattice
parameter in z-direction, εzz, we can obtain the lattice mismatch in free-space, δ, using
the Eq. 2-(34). The X-ray was not performed on wafer-bonded samples.
The well-known Bragg's diffraction condition is
2d·sinθ = n·λX 3-(1)
where d is a spacing between diffracting planes, θ is a diffraction angle, and λX is the
wavelength of X-ray which is 1.54056 Å for Kα1 emission from Cu. If the diffraction
plane is (001), d is equal to 1/4 of the lattice constant under deformation. We only
measured diffraction with n=1. Usually, the X-ray machine is not reliable to obtain
an absolute value of diffraction angle, hence, we use difference of θ of the epitaxial
layer from that of the substrate, ∆θB, to determine the lattice mismatch. From Eq. 3-
(1),
dX
2sin λθ = 3-(2)
22cos
ddXλθθ −=
∆∆ 3-(3)
Eq. 3-(3) is a derivative of Eq. 3-(2). By dividing Eq. 3-(3) by Eq. 3-(2), we obtain
dd∆−=∆
θθ
tan3-(4)
101
Therefore, if ∆θB is small, it can substitute ∆θ and we obtain a relation
zzSS
B
dd ε
θθ
2tan
−=∆−=∆
3-(5)
where θS and dS mean they are parameters of substrates. The factor “2” was added
since in real case, the vertical strain applies from top and bottom interfaces. When
measuring on (11n)-oriented materials, we need to know how much is the d relative
to the lattice constant, and I will show the value for each case in each chapter.
The X-ray also reveals thickness of periodical structure. An X-ray scan of a
wafer with periodic structure such as MQW shows satellite peaks. (The actual scan
data will be shown in later chapters.) The total thickness of 1 period, Λ, is expressed
as [9]:
nm
Xnm
θθ
λ
sinsin2)(
−
−=Λ 3-(6)
where m and n is the order of satellite peak, sin θm (θn) is the diffraction angle of mth
(nth) peak. If we take n=0 and θm = θ0 + dθm where dθm ≈ 0, we can rewrite Eq. 3-(6)
as follows:
0000 sinsincoscossinsinsin2
θθθθθθθλ −+=−=Λ mmm
X ddm
mdθθ sincos 0≈
m
X
dm
θθλsincos2 0
=Λ∴ 3-(7)
102
The diffraction intensity from the satellite peaks is strong if the lattice mismatch is
large between the materials which consist the period.
[3] Other characterization
On calibration for VCSEL active region growth, the most important one is a
calibration of its optical thickness. This was done as follows: after calibration of each
consisting material, a real active region structure was grown on top of an etch-stop
layer. The wafer was glued up side down onto a glass plate using transparent wax,
then the InP substrate and the etch-stop layer were etched off, leaving only the active
region on the glass plate. By measuring reflectivity of this sample, we can obtain
optical thickness of the active region.
For the doping calibration, the Hall measurement was used to obtain carrier
concentration. The secondary ion mass spectroscopy (SIMS) measurement was also
used but to obtain atomic concentration. The SIMS and TEM services were
purchased from outside labs.
103
References
[1] G. A. Fish, “InGaAsP/InP based photonic integrated circuits for optical
switching”, Ph.D. Dissertation in Electrical and Computer Engineering, University of
California, Santa Barbara, 1999.
[2] Y. Okuno, T. Kawano, "Study of threading dislocation reduction by strained
interlayer in InP layers grown on GaAs substrates", J. Cryst. Growth 145, pp.338-44,
1994.
[3] K. A. Black, “Fused long-wavelength vertical cavity lasers”, Ph.D. Dissertation in
Materials, University of California, Santa Barbara, 2000.
[4] R. H. Horng, W. C. Peng, D. S. Wuu, W. J. Ho, and Y. S. Huang, “Surface
treatment and electrical properties of directly wafer-bonded InP epilayer on GaAs
substrate”, Solid-State Electron. 46, pp.1103-8, 2002.
[5] J. C. Geske, “Ultra-Wideband WDM VCSEL Arrays by Lateral Heterogeneous
Integration”, Ph.D. Dissertation in Electrical and Computer Engineering, University
of California, Santa Barbara, 2004.
104
[6] N. Nishiyama, A. Mizutani, N. Hatori, M. Arai, F. Koyama, and K. Iga, “Lasing
characteristics of InGaAs-GaAs polarization controlled vertical-cavity surface-
emitting laser grown on GaAs (311)B substrate”, IEEE J. Select. Topics Quantum
Electron. 5, pp.530-6, 1999.
[7] T. Kagawa, O. Tadanaga, H. Uenohara, K. Tateno, and C. Amano, “Polarization
control of VCSEL on (311)B substrate and its effects on transmission characteristics”,
IEICE Trans. Electron. E84-C, pp.351-7, 2001.
[8] J. W. Matthews and A. E. Blakeslee, “Defects in epitaxial multilayers”, J. Crystal
Growth 27, pp.118-25, 1974.
[9] M. Sato, T. Kawaguchi, and S. Nishi, “Precise thickness measurement within a
few monolayers by X-ray diffraction from InGaAs/GaAs strained-layer
superlattices”, J. Crystal Growth 150, pp.508-12, 1995.
105
Chapter 4 MOCVD growth on (113)B InP
4.01 Introduction
To choose a substrate orientation of active region, there are several criteria.
First, it should produce large in-plane anisotropic gain. Second, it is preferable to be
easy to grow on. Third, it should be compatible for processes such as wafer bonding.
Fig. 2-11 shows that (110) plane has the highest in-plane polarization. However,
crystal growth on (110) surface is extremely difficult. It has an equal number of
group-III and -V dangling bonds, and a group-III bond and a group-V bond form a
strong dimer bonding. A VCSEL was fabricated on a (110) GaAs substrate, but
polarization performance was not as good as expected [1].
Among other (11n) substrates, orientations such as (112), (113), (114) have
been investigated well. I actually have an experience of MOCVD growth on (112)
substrates [2]. However, it was expected that we would need high V/III ratio to grow
on (112)A [2]. Also, it was found that etching (112)B substrate from its backside,
(112)A plane, is very slow, so that it is a problem on substrate removal after wafer
bonding. The (113) substrate, on the other hand, has probably been most explored for
growth among these 3 orientations. In fact there have been researches of VCSEL
fabrication on (113) GaAs substrate for polarization control [3-5]. We can see in Fig.
2-11 that the (113) plane has near-highest in-plane polarization for 1<n<∞. As for
choosing between (113)A and (113)B planes, it was reported that growing on (113)A
needs high V/III ratio [3], and it seems (113)B is easier to grow on. It was confirmed
106
that the (113)B substrate can be selectively etched from backside in about 3 hours
with HCl+H2O mixture. Hence, (113)B InP was chosen for the active region.
In this chapter, I summarize the MOCVD work on (113) InP wafers. It starts
with optimizing growth condition, and proceeds to MQW growth, the same as we did
on (111) substrate. Then I show growth results aimed at fabrication of an electrically-
pumped VCSEL, such as doping characteristics and fabrication of tunnel junction.
4.02 Optimizing growth condition
[1] Low-migration condition
The atomic structure of (113)B plane was shown in Chapter 2, and I have the
side view here again as Figure 4-1. The surface consists (001)-like group-III atoms
and (111)B-like group-V atoms. However, the surface does not necessary possess
properties somewhere in between (001) and (111)B. In fact, most prominent
character of this surface is that there are too many steps. They are more than enough
for MOCVD step-flow growth, so that we need to suppress group-III migration.
Another issue reported is that In atoms tend to desorb from the surface [3]. For these
issues, we can foresee that the ideal growth condition would be low temperature to
suppress In desorption and migration.
Figure 4-2 shows surface morphology of 1-µm InP grown at (a) standard
condition with Tg = 615 ºC and V/III = 50, and at (b) low-migration condition with
Tg = 550 ºC and V/III = 100. The improvement on (b) is clear and agrees with the
prediction above. The V/III was doubled to 100 since at the lower temperature,
107
Figure 4-1 Surface structure of (113)B plane, where αααα is a lattice constant
decomposition of TBP becomes less. Hence, an effective moler V/III ratio is not
exactly double of that of standard condition. Figure 4-3 shows PL peaks from MQWs
grown under these 2 growth conditions. For both conditions, growths were done on
(113)B and (001) substrates at the same time. All MQWs have small lattice
mismatches. With standard condition, the PL from (113)B sample has intensity half
of that from (001) sample, whereas with low-migration condition, the intensity is
comparable between MQWs on (113)B and (001) substrates. Hence, the low-
migration condition is effective in obtaining good material quality.
It might be possible to grow good material at 550 ºC with V/III less than 100,
however, due to the system configuration, it was not possible to reduce V/III for
growing InGaAsP compounds. That is, at lower temperature, incorporation of As
increases: More precisely, the As incorporation decreases at higher temperature since
(11/8)α
In P
α/√11[113]
[110]
[332]
(001) (111)B (001) (111)B
108
Figure 4-2 Surface morphology of InP grown on (113)B InP substrate by (a) high-migration
condition, and (b) low-migration condition
Figure 4-3 PL spectra from 1.3Q InGaAsP grown by high-migration and
low-migration condition, on (113)B and (001) substrate at the same time
(a) (b)200 µm
1200 1300 1400
0.0004
0.0003
0.0002
0.0001
0
550 ºC, V/III=100615 ºC, V/III=50
on (113)B on (001)
PL in
tens
ity (a
rb. u
nit)
Wavelength (nm)
109
As desorption increases, while the temperature affect is less on P incorporation and
desorption rate. Therefore, we need smaller flow rate of TBAs at lower temperature.
As explained in Chapter 3, we have fixed flow rates of TBP and TMIn that result in
V/III=100, and we add TBAs and TMGa needed to grow designed InGaAsP
composition. And at 550 ºC, TBAs flow rate needed to grow 1.1Q InGaAsP was
almost at the lowest limit of mass flow controller (MFC). One may think about
increasing TMIn flow rate, but it was not possible either since the TMGa flow rate
needed to grow InGaAs was almost at the highest limit of MFC. Hence, we could
grow at lower V/III if we changed size of MFCs, however, since the higher V/III is
effective in suppressing group-III migration and is not going to degrade material
quality, the V/III was set at 100 for InP throughout this work.
[2] Solid-phase incorporation on (113)B surface
As seen in Fig. 4-3 that the PL peaks from MQWs are different between on
(113)B and on (001) substrates, there seems to be a difference in incorporation ratio
of Ga/In and As/P between (113)B and (001) surfaces. To investigate the difference
in detail, several InGaAsP bulk layers were grown and their compositions were
determined from X-ray and PL results. Figure 4-4 shows (a) PL and (b) X-ray from
InGaAsP grown on (113)B and (001) substrates at the same time. As indicated by the
arrows, there are 2 sharp diffraction peaks from (113)B substrate. These were
observed from all (113) samples at the exact same separation between them, and they
are due to a slight difference in diffraction from In-plane and P-plane. The scanning
110
Figure 4-4 (a) PL and (b) X-ray from 1.4Q InGaAsP layer grown on (113)B
and (001) substrates at the same time
104
103
102
101
0 1000-1000
substrate
1.4Q peak(113)B
1.4Q peak(001)
1300 1400
0.0003
0.0002
0.0001
0
on (113)Bon (001)
Wavelength (nm)
PL in
tens
ity (a
rb. u
nit)
Diffraction angle (arcsec)
Diff
ract
ion
inte
nsity
(arb
. uni
t)(a) PL
(b) X-ray
111
angle ωθ was normalized such that ωθ = 0 at stronger peak of substrate. We need
values of dS to calculate θS for (113)B samples, and since the scan was measured by
(113) diffraction, dS is (1/√11)α from Fig. 4-1, where lattice constant α=5.8688Å
from Appendix A. The (001) sample measures (004) diffraction and dS = (1/4)α.
Using Eq. 3-(2), we get θS = 25.805º for (113)B and θS = 31.668º for (001) substrates.
The 1.4Q peak from (113)B appears about +470 arcsec, and using Eq. 3-(5) and Eq.
2-(34), its mismatch was calculated to be tensile 0.236%. A mismatch on (001)
sample can be calculated in the same manner.
Together with this mismatch and the PL peak wavelength, composition of
each layer on each substrate was obtained. Figure 4-5 shows incorporation relation of
(a) Ga and (b) As between on (001) and on (113)B substrates. The dashed lines are
for help of eyes, and it simply means that if a data point is on the line, the
incorporation is the same on (001) and (113)B surfaces. From data fitting, the
relations were formulated as shown above of the graphs. The Ga incorporation on
(113)B surface, Ga(113)B, is larger than that on (001) surface, Ga(001), up to 60% where
they are equal. This result agrees with the report that In tends to desorb from (113)B
surface, that way the Ga incorporation becomes more on (113)B surface. The relation
equation predicts that Ga(113)B will be less than Ga(001) beyond 60%, however, this
prediction may not be correct since Ga(113)B should be 100% when Ga(001) is 100%.
Data for Ga was taken up to 60% due to lattice-mismatch restriction. Whereas for
As, the data and equation show that its incorporation is less on (113)B for the entire
112
range. In and As are more volatile than Ga and P, hence, the result suggests that
bonding strength on (113)B surface is weaker than that on (001) surface.
These relations were very reliable for predicting composition on (113)B from
that on (001), as long as the growth condition was kept the same. Hence, I was able
to do InGaAsP calibration mostly on (001) substrates and obtain desired materials on
(113)B substrate, so that I didn’t have to use expensive (113)B substrates for
calibration.
Figure 4-5 Relation of Ga incorporation (left) and As incorporation (right) between
(113)B surface and (001) surface. Dashed lines are for help of eyes.
0 20 40 60 80 100
100
80
60
40
20
0
Ga on (001) substrate (%)
Ga
on (1
13)B
sub
stra
te (%
)
0 20 40 60 80 100
100
80
60
40
20
0
As on (001) substrate (%)
As o
n (1
13)B
sub
stra
te (%
)As (113)B = 0.5031 × (As (001)) 1.1492Ga (113)B = 1.8493 × (Ga (001)) 0.85043
113
4.03 MQW growth
[1] PL and X-ray results
Next I like to explain details of MQW growth on (113)B substrate. As
already shown in Fig. 4-3, for the most cases, a PL from an MQW grown on (113)B
substrate had its intensity similar to that from the MQW on (001) substrate grown at
the same time. Figure 4-6 shows PLs from an unstrained MQW and a strained
MQW, both grown on (113)B and (001) substrate at the same time. The unstrained
MQW in this figure and that in Fig. 4-3 consist of small-strained wells and barriers.
They are designed to be on (113)B as 5 50-Å +0.3% compressively-strained 1.47Q
wells sandwiched by 6 100-Å –0.15% tensile-strained 1.1Q barriers, so that net strain
Figure 4-6 PL spectra from unstrained MQW and strained MQW,
grown on (113)B and (001) substrates at the same time
1200 1300 1400
0.0003
0.0002
0.0001
0
Unstrained MQWStrained MQW
on (113)B on (001)
PL in
tens
ity (a
rb. u
nit)
Wavelength (nm)
114
(a) Unstrained MQW (b) Strained MQW
Figure 4-7 X-ray scan from (a) unstrained MQW and (b) strained MQW
grown on (113) substrate
will be ~0%. Figure 4-7 (a) shows an X-ray scan from this MQW on (113)B. We see
weak satellite peaks but no peak for the MQW net strain, which means the net strain
is very small as designed.
The structure of the strained MQW is the same as that of the unstrained
MQW, but materials for wells and barriers were designed to be on (113)B as +0.9%
compressively-strained 1.43Q for wells and –0.3% tensile-strained 1.1Q for barriers,
so that the net strain will be +0.1%. Its X-ray scan is shown on Fig. 4-7 (b). Now we
see the satellite peaks much stronger than those of unstrained MQWs due to a large
strain contrast between wells and barriers. A peak for the MQW net strain appears as
a shoulder of substrate peak, and it corresponds to about +0.1% compressive strain as
105
104
103
102
100
101
0-2000 1000-1000 0-4000 2000-2000
satellite+1satellite
-1
+1-1
satellite-2
-2
-3
MQW net strain
Diffraction angle (arcsec) Diffraction angle (arcsec)
Diff
ract
ion
inte
nsity
(arb
. uni
t)
115
designed. The thickness of 1 pair of well/barrier appears to be 153 Å for both MQWs
of Fig. 4-7, the value very close to the design.
[2] Notes on MQW growth
I would like to mention on design rules of InGaAsP/InGaAsP MQWs. For the
“unstrained” MQWs, it would be nice if we could really grow unstrained materials all
the time. However, it takes a lot of effort to calibrate and grow materials with precise
composition control. And even if we do so, the MOCVD system does not have good
run-to-run variation of composition. Hence, if we target 0% strain in both wells and
barriers, they could turn out to be both compressively-strained or both tensile-
strained. It is well known that compensating strain in well and barrier is effective in
reducing strain energy in the whole MQW structure. In another word, it is not
favorable to have strain of the same sign in both well and barrier, as the strain would
add up. Therefore, by designing the well and barrier slightly strained in the opposite
direction, there is less chance of growing well and barrier strained in the same
direction, even if the material composition goes off from the design. For the strained
MQW, we really have to make sure that the barriers will not turn out to have
compressive strain, and also for strain compensation, it is good to increase designed
amount of tensile strain in the barriers. The MQWs on (001) substrate were more
tolerant to such strain control. On some strained MQWs, the barrier material had
small compressive strain, but the PL properties were not deteriorated. However, it
seemed the strain control was important for the MQWs on (113)B.
116
It turned out that InGaAsP/InGaAsP MQWs have a problem of deteriorating
by annealing during the wafer-bonding process. For this problem, we tried several
different approaches on designing MQWs. This issue will be explained in detail in
next chapter.
[3] Piezoelectric effect
As explained in Chapter 2, the piezoelectric effect is expected in strained
materials grown on (11n) substrate. However, this effect is expected to be small on
our materials since the piezoelectric constant e14 is small on InP-based materials. The
strength of piezoelectric field can be calculated by Eq. 2-(45) and 2-(51), and we
already calculated the field Ez for (111) which was 5.98×106 V/m with +1% strain.
Since the orientation-dependent term of (113) is about half of that of (111), the field
is expected to be about 3×106 V/m on (113)B, and corresponding wavelength shift
would be half of that of (111), that is, 4.5 nm.
In order to confirm negligible piezo-effect on our material, a PL measurement
varying pump intensity was carried out at low-temperature. If the material is in the
piezoelectric field as shown in Fig. 2-10, we would see a shift of PL peak wavelength
by changing the pump intensity. That is, the electric field would be screened out by
the carriers generated by pumping, and the amount of screening would vary as pump
intensity [6]. Figure 4-8 shows results taken on strained MQW at 20K. We don’t see
any wavelength shift when pump power was varied, which confirms our expectation.
117
4.04 Doping characteristics
In order to realize electrically-pumped operation, we need to investigate
doping characteristics on (311)B InP. The doping incorporation depends heavily on
surface orientation due to the different configuration of the surface [7,8]. The most
common dopants for n-type is Si, and that of p-type is Zn. Recently C (Carbon) has
been actively investigated as an alternative of p-dopant, but it has a problem that it
dopes as n-type in InP [9]. In our MOCVD system we have Si2H6 as n-doping
source, and DEZn as p-doping source. Both Si and Zn are incorporated at group-III
sites, however, their incorporation behaviors are quite different. Zn simply sticks to a
group-III site, while Si precursor forms a complex with group-V precursor, such as
SiH3PH2 [10] and the complex sticks to a group-V site [8]. On (11n) surface, there
are group-III and group-V atoms mixed, so that the doping behavior depends on how
1150 1200 1250
PL in
tens
ity (a
rb.u
nit)
Wavelength (nm)
Figure 4-8
20K PL spectra from MQW
on (113)B substrate, with
pump intensity altered
from 0.4 to 15 dB
118
group-III/group-V atoms are situated on the surface and how many dangling bonds
are available. The doping dependence has been widely investigated in the past, and
one major finding is that typically, the Si-dope increases on (11n)B plane and the Zn-
dope increases on (11n)A plane. This is because B-plane has higher number of
group-V atoms and the opposite for A-plane.
We grew doped samples under a fixed growth condition, and measured the
doping incorporation by SIMS and Hall measurement. SIMS measures atomic
concentration of species physically, whereas the Hall measures carrier concentration
by electro-magnetic effect. These concentrations are not always the same because not
all the incorporated atoms are active as carrier as some dopant atoms may be
incorporated at interstitial sites other than at group-III sites. Graphs of Figure 4-9
show relations between dopant gas flow rates vs. dopant incorporations. Closed
marks are data from the layers grown on (113)B substrates, and open marks are those
on (001) substrates. The carrier concentration values are shown by triangle data
points, and the other data points are by SIMS. Data by these two different methods
are on the same line within a measurement error margin, which suggests that almost
all of the incorporated dopants were active. It was reported that Si could be
incorporated at group-V site and act as p-dopant under an extreme growth condition
on (113)B GaAs [11], but all the samples grown here showed n-type conduction.
On Fig. 4-9 left, we see that the Si incorporation on (113)B plane is about four
times larger than that on (001) plane. This result is as expected, and it quantitatively
agrees with the result reported by R. Bhat et al [7]. However, this is not the case on
119
Figure 4-9 Relation between dopant flow rate and incorporation of Si (left) and Zn (right)
on (113)B plane (closed marks) and on (001) plane (open marks)
Zn incorporation: Fig. 4-9 right shows that the incorporation on (113)B increased to
two times of that on (001), which is the opposite of the prediction. This may be
because we are using TBP/TBA, while the doping research works of the past were
done with gas sources such as phosphine and arsine. Figure 4-10 illustrates cross-
sectional atomic structure of (113)B plane. A group-III site b2 is considered as a
"weak absorption site", whereas a group-V site b3 is a "stable absorption site" [8].
However, if the layer is grown with sufficient group-V supply, a group-V site b3
would be quickly filled and the group-III site b2 could turn into a stable site for Zn to
stick. However with the gas sources, there is a large number of atomic hydrogen in
the growth environment as they are generated by decomposition of the gas sources.
Si2H6/TMIn mole flow ratio
Atom
con
cent
ratio
n (/c
m3 ) (113)B
(001)
10-310-410-5 10-21016
1017
1018
1019
1020
DEZn/TMIn mole flow ratio
10-110-210-31017
1018
1019
1020
InGaAs
InP
(113)B
(001)
(113)B
(001)
(113)B
(001)InP SIMS InP Hall InGaAs SIMS
120
Hydrogen is known to passivate Zn by nesting between Zn and group-V atoms [12].
That is, Hydrogen de-activates Zn and reduces p carrier concentration. Hence,
increasing gas group-V source supply may not result in an increase in Zn
incorporation and activation. On the other hand, it is said that metalorganic group-V
regents we used, TBA and TBP, generate much less hydrogen. If so, it can be
assumed that Zn was more efficiently incorporated and activated on (113)B plane in
our case than the cases with gas group-V sources.
It is a well-known phenomenon that the doing incorporation increases as the
number of atomic steps on the surface increases, since the steps provide absorption
sites for dopants. For GaAs-based short-wavelength lasers, it is common to use a
(001) substrate with a large misorientation angle such as 15°, not only for increasing
doping but also for a control of crystalline ordering [13]. However, it is important to
carefully consider direction of misorientation. For Si-doping, the incorporation
increases if the misorientation is to [111]B, but decreases if the misorientation is to
b2b3
[011]
[113]B[100] Group III
Group V
Figure 4-10
Cross-sectional atomic
structure of
(113)B-oriented material
121
[111]A [8]. An opposite behavior was observed for Zn-doping [14]. The doping
incorporation depends on absorption and desorption rate, and if the sites at steps are
weak-bonding sites, the misorientation will actually decrease the doping
incorporation.
The result that we can dope both n- and p-type for over 1019/cm3 under the
same growth condition is very beneficial since we don’t have to alter growth
condition to achieve desirable doping level when fabricating devices. We took
advantage of this high-doping property to fabricate a tunnel junction on (113)B InP
substrate which is shown next.
4.05 Tunnel junction
[1] I-V characteristics
In recent years, tunnel junctions (TJs) have been applied to fabrication of
devices such as solar cells [15-17] and VCSELs [18-21]. For solar cells, TJs are used
to integrate multiple PiN junctions to achieve higher efficiency. For VCSELs, a TJ is
beneficial since it reduces amount of p-type layer, resulting in reduced optical
absorption loss. It also enables us to avoid a combination of p-type metal contact and
p+-contact layer, as it can be replaced with a combination of low-resistive n-contact
with moderately-doped n-contact layer, so that we don’t have to deal with difficulty
of p+-doping.
A TJ consists of thin p+- and n+-layers, and each layer needs to be doped to
more than 1019 cm-3 carrier density in order to achieve tunneling effect at decent
122
reverse bias voltage. This requirement is not easy to achieve by MOCVD in general.
That is, p-dopants such as Zn and C incorporate higher at lower growth temperature,
while the n-dopant Si incorporates higher at higher growth temperature. Therefore, to
achieve high-doping concentration on both layers, one may have to alter growth
temperatures at a p+/n+ interface [22], which is not favorable for obtaining abrupt
interfaces. Also, the maximum doping level achievable is lower on MOCVD than
MBE, since the MOCVD growth relies on surface chemistry. In our case on (113)B
InP, we can dope up to 2×1019 cm-3 for n-type InP and 5×1019 cm-3 for p-type InGaAs
at the same growth condition. Figure 4-11 is a band diagram of interface of these
materials. There is a 0.150 eV offset at the interface which suggests that these doping
level is high enough to make a TJ. The InGaAs layer absorbs 1.3-µm light, but the
absorption can be minimized by placing it at a null of the internal electric field.
Figure 4-12 is a schematic of the layout of the TJ sample we grew. The TJ
consists of a 100Å p+-InGaAs doped 5×1019 cm-3 and a 200Å n+-InP doped 2×1019
cm-3. It also has PiN structure with 1.3-µm-wavelength MQW in order to observe
any effects of the TJ on the MQW quality. The structure is basically the same as that
of an actual VCSEL. There was only a 1-second H2 purge between gas switching at
the p+/n+ hetero interface. To test current conduction across the TJ, a 60-µm
diameter mesa was etched down beyond the TJ, and n-metal contacts were deposited
on top of the mesa and on the back of the substrate.
123
Figure 4-11 Band diagram of our TJ
Figure 4-12 Schematic structure of TJ test sample
p-InGaAs5×1019 /cm3
n-InP2 ×1019 /cm3
0.150 eV
Vi = 1.029 eV
(113)B n-InPsubstrate
n-InP
p-InPTunnel junction
n-InP
MQW
n+-InP
p+-InGaAs
N metal contact
N metal contact
60-µm φ
124
Figure 4-13 I-V characteristics of the TJ sample. Reverse voltage is applied to TJ.
Figure 4-13 shows reverse-biased current-voltage (I-V) characteristics of the
TJ. The I-V includes a voltage drop at the forward-biased PiN junction. Considering
this, it shows good conduction across the TJ. Hence, it can be said that on (113)B
InP, we can grow a TJ by MOCVD which is suitable for device application.
[2] Theoretical calculation
There is a theoretical analysis on TJ [23], and I would like to apply it on our
TJ. First, depletion region width at the interface can be calculated as:
d
a
apdn
ipnn N
NNNVeV
ed
εεεεε
+−
=)/(2 02
a
d
apdn
ipnp N
NNNVeV
ed
εεεεε
+−
=)/(2 02 4-(1)
0
1
2
3
0 1 2 3
Reverse voltage VR (V)
Cur
rent
den
sity
(kA/
cm2 ) measured
Eq. 4-(10) with
A’ = 2×107 kA/cm2/V7/4
125
where Vi is the Built-in potential which is equal to the voltage difference between
Fermi levels of the 2 materials, V is the applied forward bias voltage, dn(dp) is the
depletion region width on n-side(p-side), εn(εp) is the low-frequency relative
dielectric constant of n(p) material and ε0 is permittivity of free space, Nd(Na) is
donor(acceptor) concentration, and e is an electric charge. When V = 0, using Vi
=1.029 eV shown in Fig. 4-11 and material parameters in Appendix A, we obtain:
dn0 = 72 Å dp
0 = 29 Å 4-(2)
Hence, under no bias, the p+-InGaAs and n+-InP of our TJ are thick enough to be not
depleted, and the total depletion width is about 100 Å. Under a bias,
i
inn V
eVVdd
−= 0
i
ipp V
eVVdd
−= 0 4-(3)
By a simple triangle potential model, the tunneling probability across the interface
can be expressed as
)exp(23
EE
P gt
β−= 4-(4)
where E is an average electric field in the depletion region which can be expressed
as follows, as well as β:
810 1002.1
10101029.1)/(
×=×
=+
−= −
pn
i
ddVeV
E V/m when V = 0 4-(5)
qm*
324=β where )11(
211
***he mmm
+= 4-(6)
126
We apply me* of n-InP and mhh
* of p-InGaAs on (001) for simplicity, and for Eg we
take an average of these 2 materials. . Using Eq. 4-(3) and 4-(5), E can be re-
written as
)()/(/
)(
)/(00
00 pn
ii
i
ipn
i
ddVeVeV
VeVVdd
VeVE
+−
=−
+
−= 4-(7)
Applying these results to Eq. 4-(4), we get
1210))/(/
8.26exp( −≈−
−=VeVeV
Pii
t when V=0 4-(8)
The probability is small when there is no bias. The tunneling current is expressed as
tR PEAVI 23
= 4-(9)
where A is an constant and VR is the reverse applied voltage, hence, VR = -V.
Applying the results to Eq. 4-(8), we finally get
))/(/
8.26exp(])/[(' 43
RiiRiR VeVeV
VeVVAI+
−+= 4-(10)
where A’ includes all the constant parts. The result of this equation is already plotted
in Fig. 4-13 with A’ = 2×107 kA/cm2/V7/4. The measured I-V curve includes forward-
biased PiN junction and some resistance, therefore, it is difficult to fit the measured
curve. Considering this, it can be said that the calculation models the I-V trend well
enough.
127
[3] Annealing problem
Even though the TJ showed good conductivity, it had a problem of thermal
stability due to diffusion of Zn. After the growth of the layers in Fig. 4-12, pieces
from the grown wafer were annealed at 550 ºC or 575 ºC for 30 minutes in N2, and
then processed for I-V test. Figure 4-14 (a) compares I-V curves from those samples
with that of as-grown. Degradation of TJ by annealing is visible, which is not
surprising considering the diffusive nature of doped Zn in III-V semiconductors.
Still, it is a little surprising that the degradation is very visible even on the sample
annealed at 550 ºC, the same as growth temperature. The temperature may not be
exactly the same since we are talking about the temperature read by thermocouples.
Nonetheless, the result tells that it would be difficult to fabricate wafer bonded
VCSEL with this TJ, even if we perform bonding at 550 ºC, since we have to bond
twice.
Figure 4-14 (b) shows PL from the MQW of as-grown and annealed samples.
The intensity is not affected by annealing, however, it can be seen that the peak
becomes wider and the peak wavelength shifts shorter. These phenomena on MQW
PL are typical of Zn diffusion effect.
128
Figure 4-14 (a) I-V and (b) PL from the TJ samples annealed and as-grown
0
5000
10000
1100 1200 1300 1400
Wavelength (nm)
PL
inte
nsity
(arb
. uni
t)
0
1
2
3
0 1 2 3
Reverse voltage (V)
Cur
rent
den
sity
(kA/
cm2 )
As-grown
Annealed at 550°C
Annealed at 575°C
(a) I-V
(b) PL
129
[4] Tunnel junction grown by MBE
In this way, the TJ grown by MOCVD turned out to be not applicable to this
project due to its thermal instability. Hence, to fabricate electrically-pumped VCSEL,
we chose to grow an TJ by MBE(CBE) using C as p-dopant. Figure 4-15 shows I-V
curves of a sample with the same structure as Fig. 4-12, but only its TJ was grown by
MBE, and the TJ consists of a 100Å C-doped p+-InAlAs doped to about 1×1020 cm-3
and a 200Å Si-doped n+-InP about 5×1019 cm-3. These doping level numbers are
those targeted on (001) substrate, and the doping characteristics were not investigated
on (113)B by MBE. The figure also has a curve from an MOCVD-grown TJ sample.
These 2 samples were grown at the same time except the TJ part. The samples had
different thickness of n- and p-InP cladding layers from the samples in Fig. 4-13 and
4-14. Not only the MBE TJ sample has lower turn-on voltage, but also it has lower
resistance. The thermal stability of the MBE TJ was not investigated in this research,
but the same TJ was used to fabricate a wafer-bonded VCSEL on (001) with record
performance [24], and thermal stability of C is reported to be much better than that of
Zn. Hence, the MBE TJ is expected to show much better stability than the MOCVD
TJ with Zn-doping.
130
Figure 4-15 I-V curves of MOCVD-grown and MBE-grown TJs (as-grown)
4.06 Summary
I have summarized MOCVD crystal growth on (113)B InP substrate. The
growth condition is optimized to low-migration condition, and MQWs grown on
(113)B had qualities as good as those of MQWs on (001) substrate. It was also
shown that the InP (113)B plane can be doped higher than the (001) plane. With this
result, we fabricated TJ which consisted of p+-InGaAs/n+-InP on (113)B InP
substrates. The TJ showed good current-voltage characteristics, however, the
characteristics deteriorated by annealing due to Zn diffusion from p+-InGaAs.
The TJ growth and doping experiment did not contribute to the final result of
this thesis. However, results found in this chapter would be beneficial for future
development of our VCSEL and other devices. Currently, we opt to grow TJ by
0
1
2
3
0 1 2 3
Reverse voltage (V)
Cur
rent
den
sity
(kA/
cm2 )
MOCVD
MBE
131
MBE so that there are 3 growth stages, which makes the whole process a little
complicated, so it would have been nice if we could reduce number of stages. With
MOCVD, it is difficult to dope C highly enough for TJ, unless the growth
temperature is lowered to 500 °C or below. There are long-wavelength VCSELs with
TJ grown by MOCVD [25-27]: their growth conditions are not described in
publication, but presumably the TJs were grown by alternating growth temperature at
the p+/n+ interface. Also, most of their fabrication processes do not include high-
temperature annealing. For wafer-bonded VCSEL of our interest, at this point, a
good and easy way to grow its structure with TJ seems to grow the whole structure by
MBE(CBE).
132
References
[1] D. Sun, E. Towe, O. H. Ostdiek, J. W. Granthan, and G. J. Vansuch, “Polarization
control of vertical-cavity surface-emitting lasers through use of an anisotropic gain
distribution in [110]-oriented strained quantum-well structures”, IEEE J. Select.
Topics Quantum Electron. 1, pp.674-80, 1995.
[2] Y. Okuno, T. Tsuchiya, and M. Okai, “Crystal growth and fabrication of a 1.3-
µm-wavelength multiple-quantum-well laser on (211)A InP substrate”, Appl. Phys.
Lett. 71, pp.1918-20, 1997; unpublished data, 1997.
[3] M. Takahashi, P. O. Vacaro, T. Watanabe, T. Mukaihara, F. Koyama, and K. Iga,
“Growth and characteristics of vertical-cavity surface-emitting lasers grown on
(311)A-oriented GaAs substrates by molecular beam epitaxy”, Jpn. J. Appl. phys 35,
pp.6102-7, 1996.
[4] N. Nishiyama, M. Arai, S. Shinada, M. Azuchi, T. Miyamoto, F. Koyama, and K.
Iga, "Highly strained GaInAs-GaAs quantum-well vertical-cavity surface-emitting
laser on GaAs (311)B substrate for polarization operation”, IEEE J. Select. Topics
Quantum Electron. 7, pp.242-8, 2001.
133
[5] H. Uenohara, K. Tateno, T. Kagawa, Y. Ohiso, H. Tsuda, T. Kurokawa, and C.
Amano, “Polarization-controlled 850-nm-wavelength vertical-cavity surface-emitting
lasers grown on GaAs (311)B substrates by metal-organic chemical vapor
deposition”, IEEE J. Select. Topics Quantum Electron. 5, pp.537-45, 1999.
[6] T. Sauncy, M. Holtz, O. Brafman, D. Fekete, and Y. Finkelstein, “Excitation
intensity dependence of photoluminescence from narrow ⟨100⟩- and ⟨111⟩A-grown
InxGa1-xAs/GaAs single quantum wells, Phys. Rev. B 59, pp.5049-55, 1999.
[7] R. Bhat, C. Caneau, C. E. Zah, M. A. Koza, W. A. Bonner, D. M. Hwang, S. A.
Schwarz, S. G. Menocal, and F. G. Favire, “Orientation dependence of S, Zn, Si, Te,
and Sn doping in OMCVD growth of InP and GaAs: application to DH lasers and
lateral p-n junction arrays grown on non-planar substrate”, J. Crystal Growth 107,
pp.772-8, 1991.
[8] M. Kondo, C. Anayama, N. Okada, H. Sekiguchi, K. Domen, and T. Takahashi,
“Crystallographic orientation dependence of impurity incorporation into III-V
compound semiconductors grown by metalorganic vapor phase epitaxy”, J. Appl.
Phys. 76, pp.914-27, 1994.
134
[9] G. M. Cohen, J. L. Benchimol, G. Le Roux, P. Legay, and J. Sapriel, “p-and n-
type carbon doping of InxGa1-xAsyP1-y alloys lattice matched to InP”, Appl. Phys.
Lett. 68, pp.3793-5, 1996.
[10] Ch. Giesen, X. G. Xu, R. Hövel, M. Heuken, K. Heime, “Silicon doping of InP
grown by MOVPE using tertiarybutylphosphine”, Proc. 9th Int. Conf. Indium
Phosphide and Related Materials, NY, USA, pp.47-50, 1997.
[11] M. Takahashi, M. Hirai, K. Fujita, N. Egami, and K. Iga, “Growth and
fabrication of strained-layer InGaAs/GaAs quantum well lasers grown on
GaAs(311)A substrates using only a silicon dopant”, J. Appl. phys 82, pp.4551-7,
1997.
[12] B. Pajot, J. Chevallier, A. Jalil, and B. Rose, “Spectroscopic evidence for
hydrogen-phosphorus pairing in zinc-doped InP containing hydrogen”, Semicond.
Sci. Technol. 4, pp.91-4, 1989.
[13] K. Itaya, H. Sugawara, and G. Hatakoshi, “InGaAlP visible light laser diodes and
light-emitting diodes”, J. Crystal Growth 138, pp.768-75, 1994.
135
[14] J.-F. Lin, M.-J. Jou, C.-Y. Chen, and B.-J. Lee, “Effect of substrate
misorientation on optical properties and hole concentration of Ga0.5In0.5P and
(Al0.5Ga0.5)0.5In0.5P grown by low pressure metalorganic vapor phase epitaxy”, J.
Crystal Growth 124, pp.415-9, 1992.
[15] P. Basmaji, M. Guittard, A. Rudra, J. F. Carlin and P. Gibart, “GaAs tunnel
junction grown by metalorganic vapor-phase epitaxy for multigap cascade solar
cells”, J. Appl. Phys. 62, pp.2103-6, 1987.
[16] M. W. Wanlass, J. S. Ward, K. A. Emery and T. J. Coutts, “Monolithic, two-
terminal InP/Ga0.47In0.53As tandem solar cells” Proc. IEEE 5th Int. Conf. of InP and
Related Materials, NY, USA, pp.213-7, 1993.
[17] T. Takamoto, M. Yumaguchi, E. Ikeda, T. Agui, H. Kurita, and M. Al-Jassim,
“Mechanism of Zn and Si diffusion from a highly doped tunnel junction for
InGaP/GaAs tandem solar cells”, J. Appl. Phys. 85, 1481-6, 1999.
[18] J. Boucart, C. Starck, F. Gaborit, A. Plais, N. Bouche, E. Derouin, J. C. Remy, J.
Bonnet-Gamard, L. Goldstein, C. Fortin, D. Carpentier. P. Salet. F. Brillouet and J.
Jacquet, “Metamorphic DBR and tunnel-junction injection: A CW RT monolithic
long-wavelength VCSEL”, IEEE J. Select. Topics Quantum Electron. 5, 520-9, 1999.
136
[19] S. Sekiguchi, T. Kimura, T. Miyamoto, F. Koyama and K. Iga, “Long-
wavelength GaInAsP/InP laser with n-n contacts using AlAs/InP hole injecting tunnel
junction”, Jpn. J. Appl. Phys. 38, L443-5, 1999.
[20] M. Ortsiefer, R. Shau, G. Bohn, F. Kohler, G. Abstreiter and M-C Amann,
“Low-resistance InGa(Al)As tunnel junctions for long-wavelength vertical-cavity
surface-emitting lasers”, Jpn. J. Appl. Phys. 39, 1727-9, 2000.
[21] J. K. Kim, E. Hall, O. Sjölund, G. Almuneau and L. A. Coldren, “Room-
temperature electrically-pumped multiple-active-region VCSELs with high
differential efficiency at 1.55 µm”, Electron. Lett. 35, 1084-5, 1999.
[22] J.-H. Oh, N. Hayakawa and M. Konagai, “Carbon diffusion behavior in a GaAs
tunnel junction with heavily carbon doped p+-layer by metalorganic molecular beam
epitaxy”, Jpn. J. Appl. Phys. 36, 6300-1, 1997.
[23] M. S. Tyagi, “Introduction to semiconductor materials and devices”, Chapter 3,
John Wiley & Sons, Inc., USA, 1991.
[24] V. Jayaraman, M. Mehta, A. W. Jackson, Y. Okuno, J. Piprek, J. E. Bowers,
"High-Power 1320-nm Wafer-Bonded VCSELs With Tunnel Junctions", IEEE
Photon. Tech. Lett., 15, pp.1495-7, 2003.
137
[25] N. Nishiyama, C. Caneau, G. Guryanov, X. S. Liu, M. Hu, and C. E. Zah, “High
efficiency long wavelength VCSEL on InP grown by MOCVD”, Electron. Lett. 39,
pp.437-9, 2003.
[26] C.-K. Lin, D. P. Bour, J. Zhu, W. H. Perez, M. H. Leary, A. Tandon, S. W.
Corzine, and M. R. T. Tan, “High temperature continuous-wave operation of 1.3- and
1.55-µm VCSELs with InP/air-gap DBRs”, IEEE J. Select. Topics Quantum Electron.
9, pp.1415-21, 2003.
[27] A. Syrbu, A. Mereuta, A. Mircea, A. Caliman, V. Iakovlev, C.-A. Berseth, G.
Suruceanu, A. Rudra, E. Deichsel, and E. Kapon, “1550 nm-band VCSEL 0.76 mW
singlemode output power in 20-80ºC temperature range” Electron. Lett. 40, pp.306-7,
2004.
138
Chapter 5 Wafer bonding of (113)B InP to (001)
GaAs
5.01 Introduction
As we established growth technique on (113)B InP substrate, the next step
toward VCSEL fabrication is to investigate wafer bonding of (113)B InP and (001)
GaAs wafers. Generally, wafer bonding is possible between any wafers as long as
their surface is atomically flat, no matter what crystal orientation the wafers are.
However, as shown on Fig. 4-1, high-index surface such as (113) has microscopic
steps, and hence it is not necessary easy to bond (11n) wafers [1]. At UCSB, we
apply very high pressure during the bonding, which facilitated the bonding of (113)B
and (001) wafers.
Since the process of wafer bonding is already explained in Chapter 3, here I
would like to summarize optical and electrical properties of the bonded materials.
5.02 MQW qualities after bonding
[1] Problem of PL deterioration
After the active region including MQWs is grown by MOCVD, it goes
through wafer bonding process twice to fabricate a VCSEL. Therefore, it is
important to investigate any change of optical quality of the MQWs after the bonding
procedure. In the past on research of bonding of (001) InP/(001) GaAs, it was
139
reported that the PL from an MQW degrades after the bonding, and the degradation
was prevented by utilizing a superlattice which stops diffusion of point defects from
bonded interface [2,3]. Another report, however, shows that the MQW PL never
degraded after the bonding [4]. In this research, I did not see any degradation of PL
from MQWs on (001) InP after the bonding. If the defect consideration given in
Chapter 2 is correct, i.e., if the defects created by bonding are edge dislocations and
they don’t propagate, the quality of MQW should be unaffected by bonding, and the
PL degradation observed in Ref. 3 should be a result of point defects diffusion or
some other cause. I would like to leave any further discussion on the case of (001)
InP/(001) GaAs bonding, and limit to the case on (113)B InP/(001) GaAs hereafter.
A series of test was performed by bonding a (001) GaAs substrate and a
(113)B InP wafer with MQWs grown on. The as-grown structure of the InP wafer is
shown in Figure 5-1. It is the same as a VCSEL active region structure: it is a (5/2)λ
InGaAsetch stop
MQWs
(113)B InPsubstrate
InP
InP
InP
InP
Figure 5-1
Layer structure of the wafer
for bonding test5/2
cavi
ty
InGaAs cap layer(removed prior to bonding)
140
cavity and has 3 sets of identical MQW placed at peaks, (3/4)λ, (5/4)λ, and (7/4)λ.
Hence, it is symmetric from top and from bottom. Design detail of the MQW will be
described later. The InGaAs cap layer was about 20 nm-thick and was selectively
etched off prior to the bonding, but it was left for annealing test.
Figure 5-2 shows cross-sectional TEM pictures of a bonded sample, low-
magnification (left) and high-resolution atomic image (right). This cross-section
corresponds to the schematic atomic image shown on Fig. 2-18 (c). The thickness of
(5/2)λ-cavity InP is about 1 µm, which gives scale for low-magnification picture. We
don’t see any sign of defects in the picture. Compared to pictures in Fig. 2-16 and 2-
17, the interface is not clear in the high-resolution image. It may be due to inter-
diffusion between InP and GaAs at the interface, but it could also because of artifact
of TEM observation method.
Figure 5-2 Cross-sectional TEM pictures of a bonded (113)B InP/(001) GaAs interface: low-
magnification (left) and high-resolution atomic image (right).
5 nm
[001]
[110]
[110]
[113]
141
Figure 5-3 shows PLs from pieces from the same wafer: an as-grown piece, a
piece bonded onto GaAs substrate, and an annealed piece. Both bonding and
annealing was done at at 650 ºC for 30 minutes in N2. The 3 MQWs of the wafer of
(a) were unstrained, and one set consists of 5 50-Å +0.3% compressively-strained
1.47Q wells and 6 100-Å –0.15% tensile-strained 1.1Q barriers (the same as the one
showed in Fig. 4-6). The PL from bonded piece shows intensity degraded to 1/3 of
as-grown, and it also shows wavelength shift by about 20 nm. The annealed piece
shows the very same trend, which suggests that this PL degradation is due to
annealing, not due to any mismatch with GaAs substrate. Considering the fact that
the bonding was done at the temperature 100 ºC higher than the growth temperature,
it seems that some kind of change happened on the MQWs. However, the MQWs
(a) 1,1Q barrier (b) InP barrrier
Figure 5-3 PL spectra from as-grown, annealed, and wafer bonded samples.
Bonding and annealing were done at 650 °°°°C for 30 min.
PL in
tens
ity (a
rb. u
nit)
As-grown Bonded to GaAs sub. Annealed
0
4000
1200 1300 1400
Wavelength (nm)
3000
2000
1000
0
8000
12000
1200 1300 1400
Wavelength (nm)
10000
6000
4000
2000
142
grown on (001) substrates at the same time did not show any PL degradation or
wavelength shift by annealing under the same condition.
The degradation of MQWs on (113)B accompanies the wavelength shift,
which can be due to intermixing at well/barrier interface. The intermixing in
InGaAsP system is affected by factors such as diffusion of point defects and presence
of miscibility gap [5]. The point defects can be created either intentionally by ion
implant or by depositing dielectric cap layer, or unintentionally by evaporation of
group-V atoms from surface [6,7]. The source of point defects in our case may be the
group-V evaporation, however, this will not explain why the wavelength shift was not
observed on MQWs on (001) annealed in the same way. In fact, I also performed
annealing of similar (113)B MQW wafers in TBAs ambient, and observed the same
result as those annealed in N2. Hence, it is likely that the degradation is due to an
inherent problem of (113)B material. One possible explanation is that the point
defects are present in epitaxal layers on (113)B due to insufficient group-V supply
during the MOCVD growth. That is, even though we grew at the V/III ratio as high
as 100, the growth on (113)B may require even higher V/III ratio to obtain better
material. We did not perform any experiment to investigate this possibility. The
intermixing does not accompany PL degradation on the case of (001) material [6,7].
However, the epitaxial materials on (113)B seemed to be very sensitive to strain
balance. Therefore, it is possible that the intermixing caused a strain unbalance
between well and barrier, which resulted in PL degradation.
143
[2] Possible solution for annealing problem
To solve this problem, there are 2 approaches: to reduce the bonding
temperature to near growth temperature, or to design the MQW to be more resistive
to annealing. The bonding temperature matters to the yield. It is difficult to obtain
perfectly flat surface of the wafers to bond, and hence if there is some roughness on
their surface, bonding would occur only where the 2 wafers are in contact. If surface
atoms are mobile, they can fill the roughness and the bonding would occur in larger
area. As stated in Chapter 3, I was able to obtain very little bonding by
”BHF/DI/dry” cleaning method at heating temperature 600 ºC or lower. By using
NH4OH, I was able to bond at as low as 550 ºC. To gain larger bonding yield, the
bonding was typically performed at 575 ºC. I will also show results of annealing
experiments by different temperature later.
As for another approach of growing heat-resistive MQW, it was effective to
use InP as barrier, rather than InGaAsP. Fig. 5-3 (b) shows PL results of annealing
test on the wafer, which this time, had 3 sets of MQW and each consists of 5 50-Å
+0.6% compressively-strained 1.51Q wells and InP barriers. Even though the
annealed piece shows a modest intensity reduction, the bonded piece shows the peak
as good as that of as-grown. The peaks show wavelength shift, which suggests that
the intermixing was still happening, however since the barrier is InP, it didn’t result in
any strain unbalance.
This InP-barrier MQW is applicable for optically-pumped VCSELs, however,
it is expected to be not applicable for electrically-pumped VCSELs. Figure 5-4
144
Figure 5-4 Schematics of conduction band structure of MQW
shows a sketch of band structure of MQWs with InGaAsP barrier (left) and InP
barrier (right). The InGaAsP barrier must be designed such that its bandgap is in
between cladding and well materials, and that barrier and well make type-I lineup.
Provided that, InGaAsP-barrier MQW confines carrier effectively between 2 cladding
layers, so that the carrier will be consumed efficiently by recombination in 5 wells.
The InP-barrier MQW does not have this feature: carriers would be confined too deep
by each well. This results in each carrier localized in a well at the side that the carrier
is injected, that is, electrons localized on one side and holes on the other side. Hence,
carriers cannot recombine with their opposites efficiently. It is possible to fabricate
an edge emitting lasers with InP-barrier MQW since their gain volume is large, but
VCSELs need gain materials to be efficient due to its small gain volume. Therefore,
it is expected that InP-barrier MQW will not work for electrically pumped VCSEL.
There is another possibility to seek for heat-resistive MQW: to grow the
MQW at higher temperature, so that the bond temperature is not too far higher than
InGaAsP barrier InP barrier
wells wells
InPclad
InPclad
InPclad
InPclad
145
Figure 5-5 Surface morphology of bulk InGaAsP at 600°°°°C with increased III/V
the growth temperature. To remind the readers, our standard growth condition on
(113)B substrate is Tg = 550 ºC and V/III = 100 for InP. I grew a few bulk 1.3Q
InGaAsP at 600 ºC. Their PL results were good, however, there was a problem of
roughened surface morphology. Figure 5-5 shows morphology pictures of samples
grown with (a) V/III = 200 for InP, and at (b) V/III = 400 for InP. Increasing growth
temperature increases group-III migration, and we need to suppress the migration by
increasing the V/III ratio. On both samples we see pits which can be attributed to
group-V desorption. Even though we see a little change between (a) and (b), the
improvement of raising V/III is minor, and it seems to be difficult to suppress the
increased migration and higher desorption by just increasing the V/III. I also tried the
Tg = 575 ºC and didn’t see any improvement either. The surface morphology not
only indicates imperfect growth but also it is bad for obtaining good bonding. The
50 µm
(a) V/III=200 for InP (a) V/III=400 for InP
146
good PL results, on the other hand, could be a result of higher n-type impurity
incorporation due to the higher temperature, though this is not confirmed. As a
conclusion, the growth condition was not changed from the standard.
[3] Annealing experiment – MQW design
In order to fabricate electrically pumped VCSEL, we need to grow the
InGaAsP-barrier MQW which is heat-resistive. Also for higher gain, the MQW
should have strained wells. I ran a series of annealing test on various MQWs. As a
design rule, the well should be under compressive strain of about 0.7-0.8%, and its
thickness should be around 50 Å. The thickness can be altered to obtain the MQW
PL wavelength of around 1.3 µm. The barrier should have a bandgap around 1.1 µm
and thickness around 100 Å. The thickness can be adjusted to compensate strain.
Table 5-1 summarizes designs of MQWs tested. The “Constant III” design is
based on an idea that if the group-III composition is the same for well and barrier,
there will be no diffusion of group-III species between well and barrier, so that the
diffusion problem will be limited to group-V species. The “Constant V” design has
the same idea, however, this design has a disadvantage that the strain contrast is large
between well and barrier, in order to obtain the barrier with near-1.1Q bandgap: the
barrier material for this particular design is still 1.2Q bandgap. The last design,
“unstrained barrier”, is to investigate whether the deterioration by annealing can be
reduced if strain contrast between well and barrier is small.
147
Table 5-1 Design detail of MQWs tested for annealing
Table 5-2 Ratio of PL peak intensity between as-grown samples on (113)B and (001), and
between as-grown and annealed samples. Annealing was doe at 600 °°°°C.
Well : InGa0.20As0.66P +7400ppm 50Å
Barrier : InGa0.20As0.33P -3400ppm 100Å
Well : InGa0.18As0.63P +7800ppm 50Å
Barrier : InGa0.15As0.32P -240ppm 100Å
Well : InGa0.165As0.58P +7200ppm 40Å
Barrier : InGa0.352As0.58P -5860ppm 80Å
Constant-III
Constant-V
Unstrained barrier
composition strain thickness
-220ppm
-2000ppm
-2100ppm
net strain
as-grown intensityon (113)B/on (001)
on (113)Bannealed/as-grown
0.26
Constant-III
Constant-V 0.25
Unstrained barrier 0.10 1.04
0.46 0.58
148
Table 5-2 shows intensity of PL peaks by ratios: the intensity of as-grown
MQW on (113)B substrate by a ratio to that of the MQW grown on (001) substrate at
the same time, and the intensity of annealed MQW on (113)B by a ratio to that of as-
grown on (113)B. Annealing was done at 600 ºC for 30 min in N2. The MQWs on
(001) substrates have different compositions of well and barrier, so that the strains in
well and barrier differ from those listed in Table 5-1. Nonetheless, the PL intensities
from all MQWs on (001) were similar and as good as the intensity of a standard
MQW which would be applicable for a device. Also, there was no deterioration by
annealing on any of these MQWs on (001) substrates.
The table shows that the MQWs on (113)B show some PL deterioration by
annealing, except the unstrained-barrier MQW which has very bad as-grown PL. As
mentioned earlier, epitaxial materials on (113)B is very sensitive to strain balance. It
is highly likely that the strain compensation became unbalanced due to intermixing by
annealing, resulting in the intensity degradation. Between the constant-III MQW and
constant-V MQW, constant-III shows better intensity as-grown and annealed. This
may not be necessary due to difference of diffusivity between group-III and group-V
[8], but it is probably because the constant-V MQW has large net strain and large
well/barrier strain contrast. Overall, we can conclude that the constant-III MQW is
most suitable for electrically pumped VCSEL. Reason for the weak PL of as-grown
unstrained-barrier MQW is unclear: it may be because the growth did not result in as
designed and the barrier material turned to be slightly compressively-strained, or it
may mean that it is important to compensate strain between well and barrier.
149
[4] Annealing experiment – temperature and time
We also investigated the effect of annealing temperature and time on MQW
quality. We grew a wafer with constant-III MQW, and cleaved it into 8 pieces, and
performed annealing with different temperature and time for each piece.
Figure 5-6 PL intensity dependence on annealing temperature and time
Figure 5-6 shows the dependence of PL intensity on temperature and time of
annealing. The PL intensity is an average of mapping, and the mapping was done
before and after the annealing for each piece. On the figure, the PL intensity ratio of
the as-grown sample is 0.9, which may seem strange since nothing was done on this
sample. This is because the ratio is between the 2 mapping results taken before and
PL in
tens
ity ra
tio: (
as-g
row
n)/(a
nnea
led)
0
1.0
0 30 60
Annealing time (min.)
0.8
0.6
0.4
0.2
(as-grown)
600 °C
575 °C
550 °C
150
after performing the annealing test, and the PL intensity changed due to the condition
of PL measurement setup. We may normalize the whole results by dividing by 0.9.
The result tells that the effect of annealing on PL degradation is significant
even at 550 °C. Since we perform 30-min bonding 2 times, we see at 60 min that the
550 °C and 575 °C don’t make much difference on PL degradation. Therefore, as
mentioned before, we chose to bond at 575 °C to increase bonding yield.
5.03 I-V characteristics of bonded interface
[1] VCSEL design consideration
To realize electrically-pumped operation, it may be necessary to conduct
current across the bonded interface. Figure 5-7 compares 2 possible designs of an
electrically-pumped VCSEL with a tunnel junction. On the right side is an intracavity
structure which was already used to fabricate high-performance VCSEL [9]. With
this structure, we don’t have to use doped DBR at all, and we can minimize optical
absorption by doped layers. However, this structure has a problem of current
funneling, that is, the current runs shortest path so that there are little pumping current
through the center of the VCSEL. Since the fundamental mode of the VCSEL is a
Gaussian shape which has a maximum at the VCSEL center, this means that it is hard
to pump the fundamental mode. In order to pump the center area, the VCSEL size
has to be small. On the other hand, the left side is a half-intracavity structure on
which one contact is formed on the backside of the substrate. With this structure,
current funneling is expected to be much less than the other structure. Now the
151
Figure 5-7 2 possible design of electrically pumped VCSEL for this thesis
problem is that we have to pass current across the bonded interface: It is inevitable to
have voltage drop at the interface due to band discontinuity. However, current pass is
not patterned on this side, meaning the current can go through the whole bonded area
which is larger than 10 mm2. Also, n/n bonded interface typically shows good
conduction, while p/p interface is very hazardous [3,10]. As for the optical
absorption, n-type absorption is much less significant than p-type absorption.
For the purpose of this research, it is better if the VCSEL structure is simple
so that there are less structural anisotropy which may affect polarization behavior.
p-InP clad
n-metal contactn-metal contact
n-metal contact
Half intra-cavity structure Intra-cavity structure
GaAsundoped
DBRn-InP clad
GaAsundoped DBR
GaAsn-doped DBR
GaAsundopedsubstrate
GaAsn-dopedsubstrate
n-InP clad
MQW
n-metal contact
bondinterface
tunnel junctionbond interface
152
Hence, together with the consideration given above, the half-intracavity structure
seems to be better for this work. Even though the conduction area at bonded interface
is large, we should investigate the conduction across the orientation- and lattice-
mismatched bonded interface of (113)B InP/(001) GaAs. The current conductivity at
n-InP/n-GaAs bonded interface has been investigated by researchers including myself
in the past [10-13]. It was shown that the conductivity of (111)/(001) bonded
interface was as good as that of (001)/(001) bonded interface, whereas a (110)/(001)
interface had a large voltage drop [11]. Hence, the voltage drop does not necessary
increase simply due to an orientation mismatch, but it is likely to be related to
interface states, or surface states of the wafers before bonding.
[2] I-V test procedure and results
A 1 µm n-doped InP layer and an InGaAs etch-stop layer was grown on
(113)B substrate. No growth was performed on (001) n-GaAs substrate which was
doped around 3-4×1018 cm-3. Its surface was slightly etched prior to the bonding.
After the n-InP layer was bonded onto the GaAs substrate, a 50- or 60-µm-diameter
mesa was etched down to GaAs substrate, and n-contact metals were formed on top
of the mesa and the back of the substrate. Figure 5-8 is a simple sketch of test
N contactn-InP1 µm
n-GaAs(001) substrate
Figure 5-8
Simple schematic of the
bonded sample for I-V test
153
structure. The voltage was applied to the samples in a way such that the InP side was
positively biased. Figure 5-9 shows current- voltage (I-V) curves from bonded
samples, (113)B InP/(001) GaAs and (001) InP/(001) GaAs, both bonded at 650 ºC
and treated by HF/dry procedure explained in Chapter 3. We can see that the I-V
performance is worse for (113)B/(001) combination. Also, Figure 5-10 compares I-V
from samples with different treatments on (a) (113)B/(001) and (b) (001)/(001)
combinations. For samples on (a), bonding temperature was 575 ºC and their InP
layer was doped to 3.5×1018 cm-3, whereas samples on (b) were bonded at 650 ºC and
their InP was doped to 1×1018 cm-3.
Figure 5-9 I-V curves from bonded samples, (113)B InP/(001) GaAs and
(001) InP/(001) GaAs, bonded at 650 ºC and treated by HF/dry
2100
1
4
5
3
2
Voltage (V)
Cur
rent
den
sity
(kA/
cm2 )
Bond temp.:650°C (001) n-InP: 1×1018/cm3
(113)B n-InP: 3.5×1018/cm3
154
Figure 5-10 I-V curves from bonded samples: (a) (113)B InP/(001) GaAs and
(b) (001) InP/(001) GaAs, with different treatment
[3] Thermioic emission theory
These I-V relations can be expressed by the thermionic emission theory [10]:
−−−= )exp()exp()exp(2
nkTqV
nkTqV
kTqVbATI IG 5-(1)
IRVVV IG ++= 5-(2)
where I is the current density, A is the effective Richardson constant, T is the absolute
temperature, q is the electrical charge unit, n is an ideality factor, k is the Bolzmann’s
constant, V is the applied voltage, VG and VI are voltages applied to the GaAs and InP
parts, R is the resistance, and Vb is the barrier height at the bonded interface. If we
assume that VG/VI is not too far from 1, and if V is large enough that the second term
in the parenthesis of Eq. 5-(1) vanishes (or the first term vanishes when a negative
(a) (113)B InP/(001) GaAs
20-4-3
0
3
Voltage (V)
Cur
rent
den
sity
(kA/
cm2 )
NH4OH/wet
NH4OH/dry
-2
Bond temp.: 575°Cn-InP: 3.5×1018/cm3
(b) (001) InP/(001) GaAs
10.500
1
4
5
HF/dry
3
2
Voltage (V)
Cur
rent
den
sity
(kA/
cm2 )
NH4OH/wet
Bond temp.: 650°Cn-InP: 1×1018/cm3
155
voltage is applied), but not too large so that the term IR in Eq. 5-(2) stays negligible,
the equations reduce to
−= )exp()exp(2
nkTqV
kTqVbATI G 5-(3)
And Vb can be calculated as
)ln(0
2
IAT
qkTVb = 5-(4)
where I0 is the extrapolated value of the current density at V=0, found by plotting
ln(I) against V, as shown in Figure 5-11.
Figure 5-11 Method of obtaining the I0
Cur
rent
den
sity
(kA/
cm2 )
10-1
10-2
10-3
10-4
10-5
10-6
0.50.10 0.2 0.3 0.4
Voltage (V)
(a) Forward bias
-0.5-0.10
Voltage (V)
-0.2 -0.3 -0.4
-10-3
-10-4
-10-5
-10-6
-10-7
(b) Reverse bias
I0
I0
156
Table 5-3 Summary of Vb and resistance
The calculated values of Vb and resistance are summarized in Table 5-3. The
Vb values for (001)/(001) samples are comparable to the values reported in the past
under the similar bonding temperature [10-13]. Also, we can see that HF/dry
treatment gives smaller Vb than NH4OH/wet treatment if we compare 2 (001)/(001)
samples. This fact is consistent with a report in which an amorphous layer of native
oxide was observed on some samples prepared by NH4OH/wet, while such layer was
not observed on HF/dry samples [14]. It also agrees with the report that HF treatment
gives lower Vb than NH4OH treatment [13].
On the other hand, the Vb for (113)B/(001) sample is as small as that of
(001)/(001) samples when both were bonded at 650 ºC with HF/dry. In fact, the Vb is
a little lower for (113)B/(001) interface: Figure 5-12 is a log plot of the curves in Fig.
5-9 at low voltage, showing that near zero voltage, (113)B/(001) interface is
conducting more current than (001)/(001) interface. Hence, it seems the overall
inferior conductivity of (113)B/(001) sample is due to the higher resistance. A reason
Sample
Barrier height (eV)
NH4OH/wet NH4OH/dry HF/dry
(113)B (001)InP
0.3090.528 0.492
Resistance (10-4 Ω•cm2)
0.280
1.42.7
575 °C
3.0 1.0
NH4OH/wet
0.377
650 °C
1.0
Bond temperature
HF/dry
575 °C 650 °C650 °C
157
for lower Vb could be due to higher doping concentration on (113)B InP layer. On 2
other (113)B/(001) samples bonded at 575 ºC and treated by NH4OH, both Vb and
resistance are larger compared to those of the 650 ºC/HF/dry sample. It has been
shown that Vb increases as the bonding temperature is lowered [10]. Hence, it makes
sense that the 575 ºC/NH4OH samples have larger Vb. Also, if we compare these 2
NH4OH-treated samples, the dry-finishing improves the conductivity over wet-
finishing. We need further investigation such as SIMS measurement to draw a
definite conclusion, however, the results obtained here suggest that the Methanol may
not be able to be completely removed from the bonded interface even with the escape
channels, and the trapped residue of Methanol could have formed an amorphous
layer.
10 0
10-1
10-2
10-3
0.50.10 0.2 0.3 0.4
Voltage (V)
Cur
rent
den
sity
(kA
/cm
2 )
Figure 5-12
Log-plot of data in Figure 5-9
to show that (113)B/(001)
interface has lower Vb
(001) n-InP: 1×1018/cm3
(113)B n-InP: 3.5×1018/cm3
158
[4] Discussion
To summarize finding from the results, we can make following statements:
1) (113)B/(001) sample has higher resistance compared to (001)/(001) sample
2) Vb is higher for NH4OH treated interface, which could be due to amorphous
layer at the interface as observed by other researchers
3) Dry-bonding samples have lower Vb than wet-bonding samples, which
implies that there is residue of Methanol trapped on wet-bonding samples
4) Vb and resistance are improved by higher bonding temperature
It is easily expected that high temperature can improve the conductivity of the
interface by enhancing atomic bonding between 2 wafers, crystallizing amorphous
layer, and diffusing impurities out. We see significant differences on Vb and
resistance between the 650 ºC/HF/dry and 575 ºC/NH4OH/wet samples of
(113)B/(001) combination, while the differences are small between 650 ºC/HF/dry
and 650 ºC/NH4OH/wet samples of (001)/(001) combination, suggesting that higher
temperature reduced any amorphous layer or impurities at the interface associated
with NH4OH and Methanol. One interesting experiment would be to bond at 575 ºC
with HF/dry treatment and test I-V, however as stated in Chapter 3, I was not able to
obtain bonding by this method. Hence, we cannot make a clear statement here, but
based on a previous report [10], 575 ºC/HF/dry may have I-V performance slightly
worse than 650 ºC/HF/dry, but would be better than 575 ºC/NH4OH/dry.
159
It is difficult to give quantitative explanation for the increased resistance value
of (113)B/(001) interface without performing any further experiment. However, one
possible reason is the large mismatch of electrical charge at the interface. As shown
in Fig. 2-18, the (001) surface is covered by one type of atoms, either group-III or
group-V atoms. Hence, its surface is very polar. If we assume that the surface is
covered by group-V atoms, it has the highest excess electron density among the other
surface orientations [15]. Meanwhile, (113)B surface consists of both group-III and
V atoms. The density of dangling bonds is similar between (113)B and (001), but the
excess electron density is much lower for (113)B since some charges cancel out.
Hence, the high-polar/low-polar interface may have resulted to create resistivity.
Again, this is not a definite conclusion. In reality, the wafer surface may be different
from ideal structure shown in Fig. 2-18 due to surface reconstruction or passivation,
which will change the excess electron density [15].
5.04 Summary
In this chapter, I have summarized all the aspects regarding the wafer bonding
of (113)B InP and (001) GaAs for VCSEL fabrication. It was shown that InGaAsP-
barrier MQWs grown on (113)B InP was not tolerant against annealing. A few
designs were tested to find the most heat-resistive MQW design, which was the
constant-III design. On the other hand, the MQWs with InP barrier did not have a
problem of degradation by annealing. Although the InP-barrier MQW is not
appropriate for electrically-pumped VCSEL, it can be used for optically-pumped one.
160
Next, we have investigated current conductivity across orientation- and
lattice-mismatched interface of (113)B InP/(001) GaAs, and also the effect of surface
treatment method before the bonding. The barrier height Vb of this interface was
about 0.3 eV and as low as that of orientation-matched (001) InP/(001) GaAs
interface when bonded at high temperature of 650 ºC. The Vb and resistance were
higher when bonded at low temperature of 575 ºC and treated by NH4OH. Also, the
Vb was higher for the interface formed by Methanol-wet surfaces. To decide an
appropriate bonding condition, we have to compromise between obtaining good
conductivity and minimizing the annealing effect on the MQW. Since the current
conducts through large bonded area in the VCSEL structure of our plan, we can
compromise the conductivity and choose low-temperature bonding condition to
protect MQW quality. Hence, when fabricating an electrically-pumped VCSEL, our
conclusion here is to use 575 ºC/NH4OH/dry method.
161
References
[1] Y. Okuno, unpublished data, 1997.
[2] P. M. Petroff, R. C. Miller, A. C. Gossard, and W. Wiegmann, “Impurity trapping,
interface structure, and luminescence of GaAs quantum wells grown by molecular
beam epitaxy”, Appl. Phys. Lett. 44, pp.217-9, 1984.
[3] A. M. Karim, “Wafer bonded 1.55 µm vertical cavity laser arrays for wavelength
division multiplexing”, Ph.D. Dissertation in Electrical and Computer Engineering,
University of California, Santa Barbara, 2001.
[4] J. Geske, Y. L. Okuno, J. E. Bowers, V. Jayaraman, "Vertical and lateral
heterogeneous integration", Appl. Phys. Lett. 79, pp.1760-2, 2001.
[5] R. M. Cohen, “Interdiffusion in alloys of the GaInAsP systems”, J. Appl. Phys.
73, pp.4903-15, 1993.
[6] E. J. Skogen, J. S. Barton, S. P. Denbaars, and L. A. Coldren,”, IEEE J. Select.
Topics Quantum Electron. 8, pp.863-9, 2002.
162
[7] J. H. Teng, J. R. Dong, S. J. Chua, D. A. Thompson, B. J. Robinson, A. S. W. Lee,
J. Hazell, and I. Sproule, “Impurity-free intermixing in compressively strained
InGaAsP multiple quantum well structures”, Mat. Sci. Sem. Proc. 4, pp.621-4, 2001.
[8] J. Camassel, H. Peyre, and R. W. Glew, “Quantitative investigation of
interdiffusion effects in balanced-strain InGaAs(P)/InGaAsP heterostructures:
constant x vs. constant y”, Mat. Sci. Eng. B28, pp.353-6, 1994.
[9] V. Jayaraman, M. Mehta, A. W. Jackson, Y. Okuno, J. Piprek, J. E. Bowers,
"High-Power 1320-nm Wafer-Bonded VCSELs With Tunnel Junctions", IEEE
Photon. Tech. Lett., 15, pp.1495-7, 2003.
[10] H. Wada, Y. Ogawa, T. Kamijoh, “Electrical characteristics of directly-bonded
GaAs and InP”, Appl. Phys. Lett. 62, pp.738-40, 1993.
[11] Y. Okuno, K. Uomi, M. Aoki, T. Tsuchiya, "Direct wafer bonding of III-V
compound semiconductors for free-material and free-orientation integration", IEEE J.
Quantum. Electron. 33, pp.959-69, 1997.
[12] M. Hammar, F. Wennekes, F. Salomonsson, J. Bentell, K. Streubel, S. Rapp, D.
Keiper, and R. Westphalen, “Systematics of electrical conductivity across InP to
GaAs wafer-fused interfaces”, Jpn. J. Appl. Phys. 38, pp.1111-4, 1999.
163
[13] R. H. Horng, W. C. Peng, D. S. Wuu, W. J. Ho, and Y. S. Huang, “Surface
treatment and electrical properties of directly wafer-bonded InP epilayer on GaAs
substrate”, Solid-State Electron. 46, pp.1103-8, 2002.
[14] N. Y. Jin-Phillipp, W. Sigle, A. Black, D. Babic, J. E. Bowers, E. L. Hu, M.
Rühle, “Interface of directly bonded GaAs and InP”, J. Appl. Phys. 89, pp.1017-24,
2001.
[15] M. Wassermeier, J. Sudijono, M. D. Johnson, K. T. Leung, B. G. Orr, L.
Däweritz, and K. Ploog, “Scanning tunneling microscopy of the GaAs (311)A surface
reconstruction”, J. Crystal Growth 150, pp.425-30, 1995.
164
Chapter 6 Optically pumped VCSEL with no
guiding
6.01 Introduction
We have established conditions for MOCVD growth of VCSEL cavity on
(113)B InP substrate, and wafer bonding it to (001) GaAs substrate. We are ready to
fabricate and test VCSEL. As a very first VCSEL of this type, we fabricated
optically pumped device with no post-bonding processing for following reasons.
First, the fabrication is very simple so that we can test the concept quickly. Second,
there is no processing such as mesa-etching, so that there is least chance of having
unintentional asymmetry in device geometry. Related to this fact, thirdly, there is no
birefringence by electro-optic effect or asymmetric geometry, so that we can see the
effect of gain anisotropy only. Fourth, we can use the MQW with InP barriers, which
is more heat-resistive than the InGaAsP-barrier MQW, as shown in the last chapter.
Fifth, there is no Joule heating by electrical current conduction, so we can expect
better performance than electrical pumping. Finally as sixth reason, the whole
structure can be undoped so that we don’t have to worry free-carrier absorption.
Since the fabrication and testing are quick, we fabricated VCSELs with small-
strained MQW and larger-strained MQW, in order to see if the orientation-
mismatched wafer bonding can result in polarization-affecting asymmetry.
165
6.02 Fabrication
The fabrication process consists material growth on substrates and 2 wafer
bonding procedures, hence, there is not much to mention. The active region design is
already mentioned in Chapter 5 and is shown on Fig. 5-1, but I repeat here for a
convenience. The cavity is set to have a total optical thickness of (5/2)λ where
λ=1300 nm, and has 3 sets of MQW placed at peaks of standing wave ((3/4)λ, (5/4)λ,
(7/4)λ). Figure 6-1 shows (a) PL spectra and (b) cavity reflectivity spectra from 2
cavities, one with unstrained (small-strained) MQWs and the other with (largely)
strained MQWs. One set of unstrained MQW had 5 50-Å +0.375% compressively-
strained 1.46Q wells and 6 100-Å InP barriers, whereas the strained MQW was the
(a) PL (b) cavity reflectivity
Figure 6-1 (a) PL spectra and (b) cavity reflectivity spectra cavities with unstrained MQWs
(thin solid line) and with strained MQWs (thick dotted line)
PL in
tens
ity (a
rb. u
nit)
Unstrained MQW Strained MQW
0
4000
1200 1300
Wavelength (nm)
3000
2000
1000
0
50
1100 1300 1500
Wavelength (nm)
Ref
lect
ivity
(%)
166
same except that it had +0.8% compressively-strained 1.46Q wells. Both MQWs had
PL peaks at 1292 nm. The cavity reflectivity was measured as described in Chapter
3, and the spectra minima correspond to the optical thickness. The cavity with
unstrained MQW had the thickness of 1290 nm, whereas the one with strained MQW
had 1320 nm thickness. The absorption of the pump light occurs only at the wells,
and that is why we have 3 sets of MQW to increase the amount of absorption. A
similar cavity design was preciously employed for optical amplifier [1].
Both cavities were first bonded to 24-pair DBR. After InP substrate and etch-
stop layer were selectively etched off, they were next bonded to 30-pair DBR. The
Figure 6-2 Cross-sectional view of completed VCSEL. On the left side is intensity profile of
electric field E2, on the right side is crystallographic orientation.
(001) GaAssubstrate
MQWs
InP 270.3 nm
InP 135 nm
InP 135 nm
InP 270.3 nm
DBR23.5 pair
DBR30 pair
E2
[001]
[113]
[001]
Bonded interface
Bonded interface
167
DBRs were grown by conventional solid-source MBE, and one pair of the DBRs
consisted of 110-nm Al0.9Ga0.1As and 95.2-nm GaAs, both in 0.25λ thickness. The
GaAs substrate and one AlGaAs layer of 24-pair side were selectively etched off,
resulting in 23.5-pair DBR, and all the cleanroom works are done. The bonding for
this VCSEL was done by “BHF/DI/dry” method shown on Table 3-1 at 650 ºC.
Figure 6-2 shows cross-sectional structure of completed device, together with electric
field intensity E2 simulated by software Vertical. The DBRs are calculated to have
reflectivity of 99.978% for 30 pair, and 99.85% for 23.5 pair. This design of DBRs is
similar to the predecessors’ design [2,3].
Figure 6-3 shows reflectivity of finished structure, together with a fitting by
Vertical. Its active region had unstrained MQW, and we see a small dip around 1290
nm corresponding to the cavity thickness. The Vertical fitting was done by setting
both cavity and DBRs having designed optical thickness but at λ=1290 nm. Hence, it
means that all the physical thickness was off from the design by 1.29/1.3. The figure
also shows a PL spectrum from a piece of the same cavity bonded onto a GaAs
substrate. The peak is at 1300 nm, so the PL didn’t blue-shift as seen in Fig. 5-3.
Indeed it is 8 nm red-shifted from the peak in Fig. 6-1, however, this can be due to
non-uniformity growth of the wafer. Also from the results of Fig. 6-1 (b), this active
region has cavity thickness and gain peak just 8 nm apart, which is good for room
temperature operation, but not for high-temperature operation. Another active region
with strained MQW, on the other hand, has cavity mode 28-nm longer than gain peak,
168
provided that the PL peak does not shift after the 2 bonding processes, and this mode
offset is ideal for wide temperature operation.
Figure 6-3 Reflectivity of finished VCSEL structure (solid), and its Vertical fitting (dotted),
together with a PL spectrum from the cavity bonded onto a GaAs substrate.
6.03 Polarization characteristics
[1] Measurement setup
The VCSELs were pumped by a 980-nm edge-emitting laser. Since there is
no guiding structure made on the VCSELs, a beam spot of the pump laser defines
gain-guided device. As a typical 980 nm laser which has highly compressively-
PL (Bonded to GaAs sub.)Measurement
PL intensity (arb. unit)
0
4000
2000
1100 1300 1500
Wavelength (nm)
0
50
Ref
lect
ivity
(%)
100
Vertical simulation
169
strained InGaAs MQW as a gain medium, the pump laser is linearly TE polarized. It
was reported that polarization of the optically-pumped VCSEL was influenced by the
polarization of pump laser, though the influence is small as 1-2 degree of polarization
angle [4]. The decay rate of spin relaxation process, γs (shown in Fig. 2-1 and Eq. 2-
(1) to (3)), has reported to range from 10-200 ps [5]. It is expected to be faster than
the decay rate of total carrier number, γ, which is said to be about 1 ns, but it is
supposed to be slower or comparable to photon lifetime in VCSEL cavity, κ-1, which
is reported to be on the order of ps [5,6]. Therefore, the carrier spin effect cannot be
totally disregarded in our experiment. Also as an edge-emitting laser, the beam shape
of pump laser is elliptic. This means that the shape of gain-guided VCSEL is elliptic,
and such asymmetry is likely to affect the polarization.
Figure 6-4 (a) shows schematics of measurement setup, and (b) shows cross-
sectional relation of pump laser and VCSEL positions. The light was coupled by
free-space optics, except that multi-mode fiber was used to couple into the optical
spectrum analyzer (OSA). As theoretically shown from stress and matrix element in
Chapter 2, it is expected that [33−2 ] axis of our VCSELs is the maximum gain axis,
and [−110] to be minimum. Therefore, the VCSELs were positioned in a way that
their [33−2 ] and [
−110] axes are both 45° off from the pump laser's TE and TM axes.
In this way, there was no pumping preference between 2 axes either by the effect
from pump laser polarization or by elliptic beam shape. As for a question whether the
2 axes of [33−2 ] and [
−110] are really the maximum and minimum gain axes, we tested
170
Figure 6-4 (a) measurement setup
Figure 6-4 (b) Cross-sectional relation of pump laser and VCSEL crystallographic axes
the VCSELs with different positioning, varying the angle between VCSEL and pump
beam, and confirmed that these 2 axes are indeed maximum/minimum gain axes.
Also, we had half-wave rotator and polarizer1 to switch polarization axis of pump
laser from TE to TM axis, and with 45° off configuration, we saw the same results
between TE-pump and TM-pump axes.
switch polarizationof pump laser
OSA
980 nmlaser Polarizer2VCSEL
Currentdriver
CL CL CL CL
Polarizer1
Half-waverotator
CL: collimating lens
optical spectrumanalyzer
Pump laserTE polarization axis
VCSEL [332]maximum gain axis
Pump laserbeam shape
VCSEL [110]minimum gain axis
45°
Pump laser - SwitchedTM polarization axis
171
[2] Results and analysis on unstrained MQW VCSEL
Figure 6-5 shows curves of polarization-resolved light output power plotted
versus pump power (L-P), from the VCSEL with unstrained MQWs. The output
power is that of the strongest mode measured by OSA at 0.1 nm resolution. On this
measurement, the polarization was stable at [33−2 ] axis over a wide operation range,
and maximum polarization suppression ratio to [−110] axis was 32 dB. I note that the
maximum extinction ratio specification for the polarizer2 was 30 dB, though it is
likely that the measurement was not limited by the polarizer. The linear plot of the
[33−2 ]-polarized power shows that threshold power to be about 105 mW. The power
is seen to saturate at about 220 mW, but this is because the power plotted is only for
one mode.
Figure 6-6 (a) and (b) shows polarization-resolved spectra obtained on Fig. 6-
5 measurement at 137 mW and 216 mW pump power. Thinner lines are for [33−2 ]
polarization and thicker ones are for [−110]. The peak wavelength for both
polarizations was the same, which is expected from the absence of birefringence.
However, at [−110] polarization, there was always another peak at about 0.4 nm longer
wavelength, which had almost the same intensity as that of the strongest peak. Due to
this peak, the maximum power suppression ratio between 2 polarization axes was
about 25 dB. Also from Fig. 6-6 (b), we can see that the VCSEL operated multi-
mode at high pump power. The size of pump beam spot was about 10 µm-diameter,
172
Figure 6-5 Polarization-resolved L-P curves from the VCSEL with unstrained MQW:
log plots of both polarization (left scale) and linear plot of [332] polarization (right scale).
Solid symbols are measurement points of spectra on Figure 6-6.
Figure 6-6 Polarization-resolved spectra at (a) 137 mW and (b) 216 mW
Pump laser power (mW)
OSA
sin
gle-
mod
e po
wer
(dBm
)
-90
-30
-40
-50
-60
-80
-70
200100 25050 150
Polarizer2 @[332]
Polarizer2 @[110]
Spot #10
0.0006
0.0005
0.0004
0.0003
0.0001
0.0002
Linear single-mode pow
er (arb. unit)O
SA
pow
er (d
Bm)
-30
-60
-9013001295 1305 13001295 1305
-30
-60
-90
(a) 137 mW (b) 216 mW
173
therefore, even though the gain-guiding is weak, higher mode can be excited.
It is not clear why this lower-frequency peak was present on [−110]-polarized
power, but one possible source is the photoelastic effect. That is, an external stress
applied to the crystal changes its refractive index such as [7]:
∆є1 = α • σ є1(ω) = n(ω)2 6-(1)
where є1(ω) is the real part of the dielectric constant which is related to the refractive
index n(ω), and ∆є1 is a change of є1(ω) by the stress σ, related by the photoelastic
constant α. There is not much information about the value of α on particular case of
our (113)-oriented crystal. But it was reported for cases that stress was added to
[001] or [111] direction on In1-xGaxAsyP1-y crystals lattice-matched to InP. For both
directions, the α was negative at 1300-nm wavelength for y ≥0.4 [7]. Since the value
of y of our VCSEL’s strained well is 0.6, we can assume that the α is negative for this
well. From Figure 2-8, we see that σxx > σyy on (113), therefore, we have
∆є1xx < ∆є1
yy < 0 6-(2)
This means that the index is larger on y-direction, which is [−110]. Therefore, this can
be the source of the lower-frequency peak present on [−110]-polarized power.
Figure 6-7 shows change of peak wavelength of the strongest mode for both
polarization with pump power. Again the peak wavelength was the same, except the
near-threshold region where the [−110] polarized power had longer peak wavelength.
174
Figure 6-7 Change of peak wavelength of the highest mode for 2 polarizations
This is unexpected since the longer wavelength implies higher effective refractive
index and better confinement, and there is supposed to be no birefringence to cause
such difference. The wavelength change rate is found as 0.015 nm/mW. This
wavelength shift is due to an increase of the cavity optical thickness, which is said to
be at about 0.1 nm/°C. Therefore, temperature-raising rate of this VCSEL by the
pump power is found as 0.15 °C/mW, and we can estimate the VCSEL temperature at
pump power of 250 mW to be about 60 °C. On the other hand, material gain is
expected to shift about 0.5 nm/°C. Then it means that at 250 mW, the material gain
peak is 19 nm red-shited from that at room temperature. The room-temperature PL
peak value in Fig. 6-3 is 1300 nm, then at 250 mW, this peak is supposed to be
Pump laser power (mW)
Wav
elen
gth
of h
ighe
st m
ode
(nm
)
1298
1302
1301
1300
1299
200100 25050 150
Polarizer2 @[332]
Polarizer2 @[110]
175
shifted to 1319 nm, which is about 17 nm longer than the lasing wavelength observed.
Such a cavity mode-gain offset is likely to lead to output power saturation, i.e.,
rollover. It is not known if the thermal impedance is different on (113)B from (001)
plane, but even if it is different, it will not affect heat transfer in bulk layers.
On the other had, since the barrier material of the MQWs is InP, the carrier
over-flow at high temperature is supposed to be small. The bandgap difference ∆Eg
between well and InP barrier is:
∆Eg = 1.351 (Eg of InP) - 3.1
24.1 (1st transition in well) = 0.397 (eV)
6-(3)
If we assume that 2/3 of ∆Eg is the conduction band discontinuity ∆EC [8], it is equal
to 0.265 eV. This value is much larger than kT even with T = 100 °C = 373 K, that is
calculated to be 0.032 eV (∆Eg changes as temperature, but the change is small).
Therefore, We can expect that the carrier confinement is good over a wide
temperature range.
[3] Results of unstable polarization
The L-P result shown on Fig. 6-5, labeled as spot #1, is very good. However,
this was not the case when we changed the pumping spot on the VCSEL wafer. 2
graphs of Figure 6-8 show L-P results measured on other spots labeled as #2 and #3.
The result of spot #2 shows that the [−110] polarized power is unstable and increase at
high pump power. The spot #3 shows very unstable polarization behavior, frequently
176
Figure 6-8 L-P results measured on spots #2 and #3 of the VCSEL of Fig. 6-5
Figure 6-9 L-P results measured on 2 spots of the VCSEL with strained MQW
Pump laser power (mW)
OS
A si
ngle
-mod
e po
wer
(dB
m)
-90
-30
-40
-50
-60
-80
-70
Polarizer2 @[332] Polarizer2 @[110]
200100 200100
Pump laser power (mW)
Spot #2 Spot #3
Pump laser power (mW)
OS
A si
ngle
-mod
e po
wer
(dB
m)
-90
-30
-40
-50
-60
-80
-70
Polarizer2 @[332] Polarizer2 @[110]
300100 200 200100
Pump laser power (mW)
Spot #a Spot #b
177
switching between [33−2 ] and [
−110] axes. In this way, the complete polarization
control was not achieved on the VCSEL with unstrained MQW, or small-strained
MQW to be exact. This fact means that the anisotropy in this MQW is not strong
enough, and contribution from bonded interface is negligible as predicted in Chapter
2. As for lasing wavelength, the results for #2 and #3 were similar to Fig. 6-7, that is,
the peak wavelength was the same between 2 polarization for the most operation
range.
The reason why we obtained various results on spot #1-3 is possibly because
of unintentional asymmetry on the VCSEL wafer. Such asymmetry, for example, can
be due to imperfect bonding with air or particle trapped at bonded interface in
asymmetric shape. Also, it can be due to the presence of plain defects. On Fig. 2-19,
we can see that the defects were not formed in symmetric way in microscopic scale.
The asymmetry may enhance [33−2 ] polarization resulting in good results, or enhance
[−110] polarization and result in unstable polarization.
[4] Results on strained MQW VCSEL
In order to verify whether a large strain in MQW is effective for better
polarization performance, we next tested the VCSEL with strained MQW. Figure 6-9
shows L-P measurement results from 2 spots, labeled #a and #b. I mostly saw these
stable polarization results, although unstable results similar to Fig. 6-8 were still
observed. Overall, polarization was more stable than the other VCSEL with
178
unstrained MQW. Therefore, we conclude that increasing strain in MQW increased
the gain anisotropy, which was strong enough over other asymmetry factor. The
lasing wavelength on #a and #b showed the exact same trend as mentioned earlier,
i.e., it was the same on 2 polarizations.
A problem on these measurements was that since there is no structure on
VCSEL wafer and the “device” is defined by where we collimate the pump beam, it is
difficult to obtain statistical data of polarization. We obtained good results such as
Fig. 6-5 and Fig. 6-9, however, showing just a few measurement results are not
enough to claim that we have accomplished polarization control. We need to make
some structure on VCSEL wafer to define device so that we can take statistics.
6.04 Summary
I have summarized the first results of optically-pumped operation of VCSELs
with no guiding structure, but with gain guiding by pump laser beam. 2 types of
active regions were tested, one having unstrained (small-strained) MQW and the
other with (largely) strained MQW. With the unstrained MQW, we obtained varying
results on the VCSEL. We observed a stable polarization operation with [33−2 ]-
polarized power dominant over [−110]-polarized power. The maximum suppression
ratio between these axes was 32 dB by single mode. We also observed an unstable
operation such that the dominant polarization switched between [33−2 ] and [
−110], or
[−110]-polarized power increased as pump laser power increased. These results are
179
attributed to the fact that the gain anisotropy in MQW is small, and polarization is
influenced by other unintentional asymmetries. On the other hand, a VCSEL with
strained MQW showed results with more stable polarization.
In Chapter 2.03, I showed that matrix element asymmetry is large even
without strain, as shown in Fig. 2-13. However, this asymmetry discussed was only
for heavy-hole states, and we completely neglected contributions from light-hole
states. Even though the transition to heavy-hole is dominant in compressively-
strained gain media, light-hole state is close to the heavy-hole state when the strain is
small. The energy difference between 2 states is expressed as [9]:
)2()( zzzzyyxxLHHH bbEES εδεεε −−=−+−=−=∆ 6-(4)
where b is a deformation potential which has a negative value as listed in Appendix
A, εzz is a linear function of lattice-mismatch δ as explicitly shown by Eq. 2-(34).
Hence, the energy difference of Eq. 6-(4) is also a linear function of δ. On our
“unstrained” MQW with δ = 0.375% on (113)B plane, by using b value of InP, we get
∆S of 0.022 eV, which is small compared to conduction to heavy-hole transition
energy, 1.24/1.3 = 0.954 eV. On strained MQW with δ = 0.8% we get ∆S =0.046 eV.
We recall from Eq. 2-(75) that the light-hole state has opposite polarization character
from that of the heavy-hole. Therefore, if the light-hole is not far enough from the
heavy-hole state, we don’t get as much gain asymmetry as we expect from Eq. 2-(76).
So it is effective to add large strain enough to eliminate light-hole mixing.
180
As mentioned earlier, with no structure made on VCSEL wafer, it is difficult
to obtain statistical data of polarization. In order to achieve the goal of this thesis, we
need to prove the polarization stability from various aspects, which not only include
large suppression ratio over a wide range of operation, but also high yield of
polarization-stable devices, and stability over high-speed modulation. These aspects
will be discussed in the next chapter.
181
References
[1] E. S. Björlin, “Long-wavelength vertical cavity semiconductor ptical amplifiers”,
Ph.D. Dissertation in Electrical and Computer Engineering, University of California,
Santa Barbara, 2002.
[2] K. A. Black, “Fused long-wavelength vertical cavity lasers”, Ph.D. Dissertation in
Materials, University of California, Santa Barbara, 2000.
[3] A. M. Karim, “Wafer bonded 1.55 µm vertical cavity laser arrays for wavelength
division multiplexing”, Ph.D. Dissertation in Electrical and Computer Engineering,
University of California, Santa Barbara, 2001.
[4] R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, K. H. Gulden, and M.
Moser, “Memory effect for polarization of pump light in optically pumped vertical-
cavity semiconductor lasers”, IEEE J. Quantum Electron. 34, pp.1455-1460, 1998.
[5] A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically
pumped VCSEL’s”, IEEE J. Quantum Electron. 35, pp.342-51, 1999.
182
[6] J. Mulet and S. Balle, “Spatio-temporal modeling of the optical properties of
VCSELs in the presence of polarization effect”, IEEE J. Quantum Electron. 38,
pp.291-305, 2002.
[7] S. Adachi and K. Oe, “Internal strain and photoelastic effects in Ga1-xAlxAs/GaAs
and In1-xGaxAsyP1-y/InP crystals”, J. Appl. Phys. 54, pp.6620-7, 1983.
[8] L. A. Coldren and S. W. Corzine, “Diode lasers and photonic integral circuits”,
Wiley, New York, 1995.
[9] S. L. Chuang, “Efficient band-structure calculations of strained quantum wells”,
Phys. Rev. B 43, pp.9649-61, 1991.
183
Chapter 7 Optically pumped VCSEL with index
guiding
7.01 Introduction
In this chapter, we are to finish the VCSEL investigation which was undone in
the last chapter. For this purpose, the VCSEL of second generation had index-
guiding structure in order to identify device. The VCSEL was again optically
pumped, so that most of the advantages I listed in the last chapter apply here. The
only difference is that the shape of index guiding structure is likely to affect the
polarization characteristics. That is, as mentioned in Chapter 1, even if we design
perfectly symmetric device geometry, the actual device usually end up to have small
asymmetry due to reasons such as processing error. In order to eliminate such
uncertainty, we intentionally made the device geometry in asymmetric shape in
various directions. Based on results of the last chapter, we only fabricated VCSELs
with largely-strained MQW active region.
7.02 Structure design and fabrication
The structure and fabrication process was almost the same as that for the 1st
generation VCSEL, except that an etching was performed for index-guiding mesa
structure. The active region was with strained MQW, and it was the same wafer as
that used in Chapter 6. The DBRs were also the same as those in the last chapter,
184
except that the number of the pairs was 31 for the bottom and 25.5 for the top DBR.
The mesa etching was done on the first GaAs layer of 31-pair DBR, which was
bonded to the active region first. The thickness of a GaAs layer was 95 nm, and it
was wet-etched by 50-nm depth, so that AlGaAs layer beneath was not exposed.
Figure 7-1 shows cross-sectional structure of the device, and dimensions of
the index guiding mesa. It was made in circular and elliptic shapes, and each in 3
different sizes. The ellipse was also made in 4 different orientations, hence, there are
15 kinds of mesa altogether. Figure 7-2 shows the orientations of the 4 ellipses
relative to (113)B active region. The VCSEL was again pumped in a way that its
Figure 7-1 Cross-sectional structure of the VCSEL (left), and dimensions of the index guiding
aperture (right). λλλλ0 λλλλx are for Eq. 7-(1) and Fig. 7-5.
50 nm
λ0λx λx
d
d = 9, 12, 15 umd’= (4/3)d
dd’
Aperture shape
* Elliptic* Circle
⇒
2nd bonded interface
1st bonded interface
185
Figure 7-2 Axial relation between the 4 index-guiding ellipses, (113)B active region of
VCSEL, and pump laser polarization
Figure 7-3 Mask pattern used for the VCSEL fabrication
GaAs etched area
ID metal patternon finished surface
Pump laserTE polarization axis
VCSEL [332]maximum gain axis
[110]
[332]
90deg
0deg
45°
186
[33−2 ] and [
−110] axes are both 45° off from the pump laser's TE polarization axis.
The ellipse labeled “[332]” is expected to increase scattering loss for [−110]-polarized
light since the size of index guiding is smaller in [−110] direction, hence, the [33
−2 ]
polarization originating from the gain anisotropy is expected to be enhanced. While
the ellipse “[110]” is expected to increase loss for [33−2 ]-polarized light, so that it
will distract the gain polarization. The other ellipses and circle devices are expected
not to disturb the gain anisotropy.
Figure 7-3 illustrates mask pattern used for the fabrication. The black area
was etched on the GaAs layer. The black lines are all connected to the circle in the
middle, so that they work as escape channels also. The gray area was formed on the
finished VCSEL surface by depositing Gold, in order to identify each device. The
letter “12” means that the device has index-guiding mesa with d = 12 µm, and
direction of the letters placed indicates that the mesa is in ellipse elongating toward
the letters.
Figure 7-4 shows surface morphology of the sample after (a) 1st bonding of
patterned 31-pair DBR and active region, and (b) 2nd bonding. Even though these
pictures were taken with phase polarizer so that surface roughness is enhanced, the
picture (a) suggests that the InP layer had sagging because of the pattern beneath, so
that the interface of 2nd bonding might not be flat as shown in Fig. 7-1. The bonding
procedure was different from the last chapter as the 1st bonding was done by
“NH4OH/wet” method shown on Table 3-1, and 2nd bonding was by “NH4OH/dry”,
187
and both was bonded at 575 °C. Since the bonding temperature was low, there are
very little cross-hatch defects observed on surface after bonding.
Figure 7-4 Pictures of surface morphology of the VCSEL after bonding
Figure 7-5 Resonant wavelength with and without the air-gap, λλλλ0 and λλλλx, by Vertical
(a) after 1st bond (a) after 2nd bond
200 µm
0
100
1290 1300 1320
Wavelength (nm)
Ref
lect
ivity
(%)
80
60
40
20
λ0λx
1310
188
The air-gap formed at the interface of bottom DBR and active region provides
index guiding. For such a thin gap, the amount of index perturbation can be
estimated by a simple effective index model:
0
0
λλλ x
nn −
=∆ 7-(1)
where λ0 and λx are, as shown in Fig. 7-1, resonant wavelength with and without the
air-gap, calculated by Vertical. Figure 7-5 shows the results of calculation. The
reflection dips show the resonant wavelengths, and they are λ0 = 1308.90 nm and λx =
1299.55 nm. Therefore, (∆n/n) = 0.714%, which is enough to provide index-guiding.
8.03 Polarization performance
[1] CW measurement
First I would like to show L-P results of CW operation measurement of the
VCSEL. Figure 7-6 is a bird-view picture of the measurement setup. It was modified
from the setup described by Fig. 6-4 (a): the half-wave rotator and polarizer1 were
taken off, and a circularizer was put instead, which circularizes the beam shape of
pump laser. Also the polarizer used in this setup had maximum extinction ratio
specification of 50 dB. The white dashed line indicates free-space light path. In
order to choose a particular device for measurement, we implemented an IR camera,
to which the light can be coupled through a mirror. The mirror can be moved in and
out of the light path just by flipping it up and down. Because of the IR camera, we
were able to see through the index-guiding mesa, so that we could make sure that the
189
Pump laser
Circularizer
VCSEL
movable
mirror
polarizer
IR cam
era
coupling lens tom
ulti-mode fiber
Figure 7-6Bird-view picture of the m
easurement setup
190
devices actually had the mesa shape as designated, and we didn’t have to rely on the
ID metal pattern. The output light was coupled to the OSA by multi-mode fiber, and
its spectrum was measured with 0.1 nm resolution. To obtain the total output power,
the spectrum was integrated over 10-nm range.
Figure 7-7 shows examples of L-P curves taken on [332]- and [110]-ellipses
with d = 9 and 12 µm. For both sizes, we see that the [332]-ellipses have stable
polarization at [33−2 ]-axis for entire range of measurement, whereas the [110]-
ellipses are seen to show that the polarization became unstable at high pumping
power. Also, it seems that the suppression ratio between [33−2 ]- and [
−110]-polarized
power is smaller for the [110]-ellipses than the [332]-ellipses. This is as expected
since the elliptic shape should generate birefringence and dichroism in favor of
[33−2 ]-axis on [332]-ellipse and opposite on [110]-ellipse. The axes of VCSEL and
the polarizer were aligned by eye, so that there might be an error in ±5°, but at least,
the direction of maximum/minimum polarization axes were the same for all devices.
Although their polarization performances were different, almost all devices
had [33−2 ]-axis as dominant polarization axis. A 360-degree polarization
measurement was performed on some of 0deg- and 90deg-ellipses and circle devices,
to confirm this fact. This may mean that the dichroism by the gain anisotropy of
MQWs is much more influential than the birefringence and dichroism by the shape
asymmetry. But it can also mean that the VCSELs are rather gain-guided than index-
guided. The beam size of the pump laser at the VCSEL was about 10 µm-diameter.
191
Figure 7-7 L-P curves taken on [332]- (top) and [110]-ellipses (bottom) with d = 9 (left) and
12 µµµµm (right)
Therefore, for all sizes and shapes, the fundamental mode of the VCSELs may not see
the index-guiding, while higher modes are likely to be index-guided. This can be a
reason why the polarization of the [110]-ellipses becomes unstable at high power.
Pump laser power (mW)
Tota
l mod
e po
wer
(dBm
)
-10
-20
-30
-40
-60
-50
Polarizer2 @[332] Polarizer2 @[110]
200100 200100
Pump laser power (mW)
Pump laser power (mW)
Tota
l mod
e po
wer
(dBm
)
100 200 200100
Pump laser power (mW)
-10
-20
-30
-40
-60
-50
best
SR
wor
st S
R
best
SR
wor
st S
R
[110]-ellipsed =12 µm
[332]-ellipsed =12 µm
[110]-ellipsed =9 µm
[332]-ellipsed =9 µm
(b)
(d)(c)
(a)
192
We didn’t see clear correlation between the device size and device
performance, such as threshold pump power and output power. This may be because
the device is gain-guided and mesa size doesn’t matter. But also, I like to note that
the measurement condition depends on the critical alignment of components, even
though I did best to optimize the condition. Hence, such device performance cannot
be rigidly compared with each other. The only device property we discuss here is
polarization.
One problem on our results is that we were not able to measure up to higher
power. The VCSELs had high threshold pump power Pth of about 100 mW. In order
to protect the pump laser from catastrophic failure, the measurement was limited up
to 250 mW. Therefore, we measured the laser performance only up to 2.5×Pth. To
claim complete polarization control, it is desirable to measure up to higher power.
Nonetheless, I believe that the statistical results and modulation results are enough to
show the effectiveness of our polarization control scheme.
[2] Statistical data
As seen in the last chapter, VCSELs on the same wafer can have good
polarization and bad polarization properties. Hence, it is more effective to show
statistically that the one type of VCSEL is better than the other type or not. From the
L-P curves of each devices, the best and worst values of suppression ratio (SR)
between [33−2 ]- and [
−110]-polarized power were taken as shown on Fig. 7-7 (b) and
193
(d). The worst value was taken at the pump power higher than 1.5×Pth. Their
statistics were summarized in 2 ways.
First, Figure 7-8 shows the distribution of best and worst SR for each index
guiding shape. On [332]-ellipses on top, we can see that almost all of their best SRs
are larger than 20 dB, more than half of them being larger than 25 dB. Also, most of
their worst SRs are larger than 20 dB, and the worst of the worst SR was 7 dB. On
the other hand on [110]-ellipses, we see that their best SRs are more scattered to
lower range, and most prominently, more than half of the devices had their worst SRs
of 5 dB or less. These results show that the most of the on [110]-ellipse devices had
SR deterioration, while [332]-ellipses did not. The 0deg- and 90deg-ellipses show a
mixed result of the [110] and [332]-ellipses. The result of circle devices is somewhat
similar to [110]-ellipse, which is unexpected since the circle shape is not to give any
birefringence or dichroism. However, I like to note that the number of measurement
is small for circle, and it may not be enough to draw a conclusion statistically.
On Figure 7-9, I show the distribution of a difference of (best SR)-(worst SR).
That is, this figure shows how much the SR deteriorated in the measured operation
range. For [332]-ellipses, most devices had SR deterioration of 5 dB or less, and just
2 devices had over 10 dB deterioration. For [110]-ellipses, it seems the deterioration
amount varies. Half of their devices have SR deterioration of 10 dB or less, but this
is not necessary because those devices had stable polarization, but also because their
best SRs were not good. The 0deg- and 90deg-ellipses show, again, a mixed result of
the [110] and [332]-ellipses, and the circles are as bad as the [110]-ellipses. On this
194
Figure 7-8 Distribution of best and worst SR for each index guiding shape
15
10
5
0
<0 0-5 6-10 11-15 16-20 21-25 25<
Range of SR (dB)
[110]-ellipticall sizes
best SR
worst SRabove 1.5×Pth
[332]-ellipticall sizes
Num
ber o
f VC
SELs
15
10
5
0
Num
ber o
f VC
SELs
15
10
5
015
10
5
0
Num
ber o
f VC
SELs
Num
ber o
f VC
SELs circle
all sizes
0&90deg-ellipticall sizes
195
Figure 7-9 Distribution of a difference (best SR)-(worst SR) for each index guiding shape
15
10
5
0
0-5 6-10 11-15 16-20 21-30
Range of SR change (dB)
Num
ber o
f VC
SELs
15
10
5
0
Num
ber o
f VC
SELs
15
10
5
015
10
5
0
Num
ber o
f VC
SELs
Num
ber o
f VC
SELs
[110]-elliptic
[332]-elliptic
circle
0&90deg-elliptic
15 µm
12 µm
9 µm
d
196
Figure 7-10 Possible examples of misalignment between the VCSEL and pump laser beam.
figure, device sizes are also indicated by the color, but it seems there is no clear
correlation between the size and polarization performance.
In this way, the statistic shows that the [332]-ellipse devices had superior
polarization performance with high and stable SR. The results also show that the
devices in shapes other than [332]-ellipse do not have statistically stable polarization,
even with the shapes which do not have preference between with [33−2 ]- and [
−110]-
axes. This may mean that the gain anisotropy of strained MQW is not high enough,
however, there is a possibility that unintentional asymmetry disturbed polarization.
Such asymmetry could be, as stated in the last chapter, imperfect bonding with
asymmetric trap at bonded interface or presence of plain defects. Another possibility
is that the pump laser may not be always at the center of each device. Figure 7-10
shows possible examples of misalignment between the device and pump laser beam.
As shown, such misalignment can result in anisotropy and polarization deterioration.
The conclusion I like to draw is that if one makes a VCSEL on (113)B with any mesa
Shape of index guiding
Shape of pump laser beam
197
structure, the mesa shape should be asymmetric such as [332]-ellipse, rather than
symmetric one, in order to obtain the best polarization performance.
[3] Spectra observation
On Fig. 6-6, the polarization-resolved spectra of gain-guided VCSEL showed
that the peak wavelength for both polarizations was the same, but that the [−110]
polarization had another peak at about 0.4 nm longer wavelength. The VCSELs in
this chapter have index-guiding mesa, which is expected to affect lasing frequency. I
like to show some examples to see whether that is really the case.
Figures 7-11~14 show spectra from each device at each pumping power.
Thinner lines are for [33−2 ]-polarized power and thicker dotted lines are for [
−110]-
polarization. Figure 7-11 shows results from 2 [332]-ellipses, both with d=12 µm.
The spectra on the left are from the device of Fig. 7-7 (b). Figure 7-12 is the results
from 2 12-µm [110]-ellipses which had unstable polarization, the left side being from
the same device as that on Fig. 7-7 (d). On Figure 7-13, the left side is a [110]-ellipse
and right side is a circle, both had stable polarization. Figure 7-14 includes the
spectra of stable polarization of 15-µm 0deg-ellipse and unstable polarization of 15-
µm 90deg-ellipse. Overall, it seems there is no clear correlation between the
frequency splitting ∆ω between peaks of 2 polarized power and the device shape. On
most of devices, around threshold, the [−110]-polarized power has a peak longer than
that of [33−2 ]-polarized power. The amount of splitting is about 0.2~0.3 nm.
198
Figure 7-11 Polarization-resolved spectra from 2 [332]-ellipses
143 mW
249 mW236 mW
197 mW
103 mW
143 mW
197 mW
89 mWO
SA
pow
er (d
Bm)
-10
-70
-40
OSA
pow
er (d
Bm)
-60
-8013081304 1312
-20
-40
13121308 1316
[332]-ellipsed =12 µm
[332]-ellipsed =12 µm(Fig. 8-7)
[332]-ellipsed =12 µm(Fig. 8-7)
Polarizer2 @[332] Polarizer2 @[110]
199
Figure 7-12 Polarization-resolved spectra from 2 [110]-ellipses
OSA
pow
er (d
Bm)
-10
-70
103 mW
-40
OSA
pow
er (d
Bm)
-60
-8013121308 1316
223 mW-20
-40
183 mW
143 mW
157 mW
197 mW
13121308 1316
223 mW
210 mW
[110]-ellipsed =12 µm
[110]-ellipsed =12 µm(Fig. 8-7)
Polarizer2 @[332] Polarizer2 @[110]
200
Figure 7-13 Polarization-resolved spectra from [110]-ellipse (left) and circle (right)
116 mW
249 mW
210 mW
157 mW
89 mW
130 mW
223 mW
183 mW
OSA
pow
er (d
Bm)
-10
-70
-40
OSA
pow
er (d
Bm)
-60
-8013141310 1318
-20
-40
13101306 1314
circled =9 µm
[110]-ellipsed =15 µm
Polarizer2 @[332] Polarizer2 @[110]
201
Figure 7-14 Polarization-resolved spectra from 0deg- and 90deg-ellipses
61 mW
143 mW
-60
-80
197 mW-20
-40
103 mW
103 mW
236 mW
183 mW
143 mW
OSA
pow
er (d
Bm)
-10
-70
-40
OSA
pow
er (d
Bm)
-60
-8013061302 1310
-20
-40
13101306 1314
90deg-ellipsed =15 µm
0deg-ellipsed =15 µm
-60
-80
-20
-40
Polarizer2 @[332] Polarizer2 @[110]
202
The evolution of the frequency splitting ∆ω, one the other hand, seems to be
related to polarization stability. On [332]-ellipses of Fig. 7-11, ∆ω becomes small as
pump power increases, and polarization stays stable. The device on the right side,
compared to the left one, has smaller ∆ω near threshold, and ∆ω is 0 at 143 mW and
higher pump power. On the other hand on Fig. 7-12, ∆ω of the [110]-ellipse on the
left does not change, and [−110]-polarized power becomes equivalent with [33
−2 ]-
polarized power at 223 mW. The ∆ω of the right side device evolves in a strange
way. It is about 0.3 nm most of the time, while at 210 mW, it suddenly enlarges to
0.8 nm and 2 polarized powers become equivalent. Another [110]-ellipse shown on
the left on Fig. 7-13, as well as a circle on the right side, show similar behavior as that
of [332]-ellipses of Fig. 7-11, that is, the ∆ω becomes smaller as pump power
increases, and polarization stays stable.
The 2 devices of Fig. 7-14 show different behavior than the other. On the 15-
µm 0deg-ellipse of the left, the ∆ω is 0 above threshold (≥ 143 mW), but [−110]-
polarized power always has another peak at about 0.4 nm longer wavelength. Hence,
this device operated in a very similar way to the gain-guided VCSEL in Chapter 6. It
seems that the [−110]-polarized power grew high at 236 mW, but the [33
−2 ]-polarized
power also grew high so that the SR did not deteriorate. The 15-µm 90deg-ellipse of
the right side of Fig. 7-14 shows very unstable polarization behavior and yet has very
small ∆ω. Note that the spectra of 2 polarized power are almost completely
overlapped at 61 mW and 143 mW. A major difference of this device from the others
203
is that the ∆ω is 0 below threshold at 61 mW, while all the other devices had [−110]-
polarized power at longer wavelength. This may be because the device had
unexpected strong anisotropy such as defects.
These observations suggest that near threshold, the devices mostly operated
gain-guided and had ∆ω in a way that [−110]-polarized power has longer wavelength.
As pump power increases, higher modes become dominant and the devices see the
effect of index guiding. This makes ∆ω either small or remaining the same,
depending on the shape of index guiding. However, correlation between ∆ω and the
device shape is not clear. This may be again because of unintentional asymmetry
such as pump laser/VCSEL misalignment. Anisotropy from such misalignment can
result in deteriorated polarization or unexpectedly-good polarization behavior.
[4] Stability over transmission
Lastly, a result of high-speed modulation of our VCSEL is presented. It is an
effective way to show the stability of polarization. A group of Dr. Kuksenkov and
Dr. Temkin performed series of modulation experiments on VCSELs. They
compared VCSEL with unstable polarization and with stable polarization, and clearly
showed that a VCSEL with unstable polarization had higher BER, originating from
higher polarization-switching noise [1].
Another character of polarization-unstable VCSEL is that the BER becomes
different between with and without a polarizer in the measurement link [2-4]. This
204
can be explained by looking at Fig. 1-2 and considering modulation between below
and above Isw. When there is no polarization-sensitive part in the link, the total output
power is proportional to the driving current although the dominant polarization axis
changes, so that BER is low as long as the modulation speed is lower than
polarization-switching speed. If there is a polarizer in the link and only the power at
axis #1 is modulated, we can easily expect that the BER will be high since the power
at axis #1 diminishes above Isw. If a polarization-stable VCSEL is modulated, there is
no difference on BER with and without a polarizer [5]. In a practical case, the
transmission may have to go through polarization-sensitive parts. For such concern,
it is important for the transmitter to have stable polarization.
Figure 7-15 BER measurement link
980 nmlaser
(Polarizer)VCSEL
Circularizer
Attenuator(power monitor)
Terminated
Circulator
Bias Tee
DC currentsource
BERT
Electricalamplifier
18dB
PIN receiver
36dB
patterngenerator
1G
205
In this thesis, we performed a BER measurement with and without the
polarizer to demonstrate stable polarization. The device used is a 9-µm [332]-ellipse
and is the same as that of Fig. 7-7 (a). Figure 7-15 illustrates the measurement link.
The polarizer was aligned to the [33−2 ]-axis for “with” measurement, or it was taken
out from the link for “without”. Measurement was done by modulating the 980-nm
pump laser, hence, the modulation speed was limited by the speed of pump laser and
was set at 1 Gb/s. The circulator was put to cut the power at 980-nm range down by
40 dB. The circulator and optical fiber used to couple light into the PIN receiver
were all single mode. Total fiber length was about 2 m. The signal was 27-1 pseudo-
random bit sequence in the non-return to zero format.
Due to the configuration, modulation depth was not known precisely. The
modulation condition was 6 V peak-to-peak with 50-Ω termination. The bias current
of the pump laser was 350 mA which corresponds to 210-mW pump power. The
laser had series resistance of 1.5 Ω. If the modulation width was ±0.1 V, it would
correspond to driving current of about ±70 mA, which corresponds to the pump
power modulation of about ±30 mW, as a rough estimation. The output power of the
VCSEL at the attenuator was set as –16 dB at 210-mW pump power.
Figure 7-16 shows (a) eye diagram taken on the pump laser (without
circulator), and the diagrams taken on VCSEL (b) with the polarizer aligned to the
[33−2 ]-axis and (c) without the polarizer. Modulation condition is as mentioned
above, except (a) which was taken at 200-mA bias current. There is no deterioration
206
on VCSEL: the diagrams from VCSEL seem to have more noise, but this is because
of low receiving power of -16 dB. More importantly, they look the same for with and
without the polarizer. These diagrams are noisy because of poor electrical matching.
Figure 7-17 shows BER plots with and without the polarizer. The 2 results
are on the same line, which means that the polarization was stable under the
modulation. Also, we don’t see a noise floor, which also means stable polarization of
this device.
Figure 7-16 Eye diagram of (a) pump laser, (b) VCSEL with polarizer,
and (c) VCSEL without polarizer
(a) pump laser
(b) VCSEL
w/polarizer
(c) VCSEL
w/o polarizer
207
Figure 7-17 BER plots of the VCSEL with and without the polarizer
It would be desirable to perform this measurement on more than 1 device,
however due to our time limitation, we were not able to do so. Also, the modulation
speed of 1 Gb/s is slower than the decay rate of spin relaxation process γs, which is, as
mentioned before, supposed to be in a range of 10-200 ps. Hence, it may be
interesting to modulate the VCSEL at 5 Gb/s or faster, although the speed may get
limited by the decay rate of total carrier number γ which is supposed to be about 1 ns.
Nevertheless, the result we got here is a solid confirmation of stable polarization
under fast-speed operation of practical range.
-19 -18.5 -18 -17.5 -17
[332]-ellipsed =9 µm
10-5
10-6
10-7
10-8
10-9
10-10
Average received power (dB)
Bit E
rror
Rat
e
w/o polarizerw/ polarizer
208
7.04 Summary
I have shown by statistics and fast modulation experiment that we were able
to fabricate polarization-stable VCSEL. The second generation VCSEL of this
chapter had the strained MQW active region, and also had the index-guiding structure
which either enhanced or distracted the polarization stability, depending on its shape.
Such effect of index guiding shape was statistically shown. With the index guiding of
[332]-ellipse, the VCSELs had stable and large suppression ratio between [33−2 ]- and
[−110]-polarization, which were maximum and minimum power axes. With [110]-
ellipse index guiding, the suppression ratio was less and unstable over the
measurement range. We performed high-speed modulation of 1 Gb/s on a [332]-
ellipse VCSEL. The BER was the same between the measurements with and without
the polarizer, which confirms that the VCSEL had stable polarization under the
modulation, and qualifies the VCSEL as applicable transmitter for optical
communication system.
209
References
[1] D. V. Kuksenkov and H. Temkin, “Polarization related properties of vertical-
cavity surface-emitting lasers”, IEEE J. Select. Topics Quantum Electron. 3, pp.390-
5, 1997.
[2] D. V. Kuksenkov, H. Temkin, and S. Swirhun, “"Polarization instability and
performance of free-space optical links based on vertical-cavity surface-emitting
lasers”, IEEE Photon. Tech. Lett. 8, pp.703-5, 1996.
[3] N. Nishiyama, A. Mizutani, N. Hatori, M. Arai, F. Koyama, and K. Iga, "Lasing
characteristics of InGaAs-GaAs polarization-controlled vertical-cavity surface-
emitting laser grown on GaAs (311)B substrate”, IEEE J. Select. Topics Quantum
Electron. 5, pp.530-6, 1999.
[4] H. Uenohara, K. Tateno, T. Kagawa, Y. Ohiso, H. Tsuda, T. Kurokawa, and C.
Amano, “Polarization-controlled 850-nm-wavelength vertical-cavity surface-emitting
lasers grown on GaAs (311)B substrates by metal-organic chemical vapor
deposition”, IEEE J. Select. Topics Quantum Electron. 5, pp.537-45, 1999.
210
[5] T. Kagawa, O. Tadanaga, H. Uenohara, K. Tateno, and C. Amano, “Polarization
control of VCSEL on (311)B substrate and its effects on transmission characteristics”,
IEICE Trans. Electron. E84-C, pp.351-7, 2001.
211
Chapter 8 Conclusion and future work
8.01 Summary of this work
In this thesis, we have proposed and investigated polarization control on the
long-wavelength VCSEL. The polarization control was achieved through growing
the active region on a (113)B InP substrate, which was integrated to (001) GaAs-
based DBRs by wafer bonding technique.
I began with examining the current status of VCSEL polarization. I showed
schematically and theoretically that the conventional VCSEL on (001) plane has low
polarization stability. More theoretical analysis was performed on variety of physical
aspects of our VCSEL. We saw that in order to achieve high stability, a large
dichroism such as anisotropic gain is needed. I showed that (113) and other planes of
(11n) family have asymmetry which results in asymmetric stress and optical gain in
strained MQW. The stress and gain properties were investigated separately, and yet
reached to the same conclusion. I gave a summary of defects, and I also examined
stress from defects and material mismatch on wafer-bonded structure. Such stress
was expected to be small, but could be a source of polarization.
After summarizing experimental procedures such as MOCVD and wafer
bonding, we moved onto the MOCVD growth of active region on (113)B InP
substrate. From theoretical work, (113)B was expected to produce a large anisotropy
of optical gain when it was strained. A work of MOCVD growth produced various
results. We saw how the growth condition affected quality of grown materials. With
212
optimized growth condition, we were able to grow a strained MQW with good
quality. Doping efficiency on (113)B surface was found to be better than that on
(001) surface for both n-type and p-type doping. This result was unique, and
provided us an opportunity to fabricate and examine a tunnel junction.
However, an obstacle on this work originated from wafer bonding procedure
which included high-temperature annealing process. The annealing and bonding
experiments revealed problems on materials grown on (113)B substrates. We saw
that the quality of MQWs deteriorated by annealing. An MQW with InP barriers was
found to be heat-resistive. For electrically-pumped VCSEL, an MQW with constant-
III design was found to be the most heat-resistive among the other MQWs with
InGaAsP barriers. The annealing also resulted in deterioration of tunnel junction due
to Zn diffusion. Also, an electrical conductivity was investigated on the bonded
interface of (113)B n-InP and (001) n-GaAs. The orientation-mismatch resulted in
higher resistivity. We also found that the conductivity depended on surface chemical
treatment before the bonding.
Finally we fabricated 1.3-µm wavelength VCSELs and tested their
polarization behavior. The VCSELs were operated by optical pumping. First
generation VCSELs were gain-guided, and we fabricated 2 types of VCSELs having
different active regions, one with unstrained (small-strained) MQW and the other
with (largely-) strained MQW. The VCSEL with unstrained MQW showed mixed
result of stable and unstable polarization, while the other VCSEL with strained MQW
seemed to have mostly stable polarization. The results suggested that the anisotropic
213
gain in strained MQW was effective source of polarization control, and effect of other
source such as defect stress was minor, agreeing with our theoretical speculation.
In order to show polarization stability in more regiment way, the second
generation VCSEL was fabricated with index-guiding mesa structure in various
shape. Depending on the orientation of asymmetry of the shape, the index-guiding
either enhanced or distracted the polarization originating from gain anisotropy,
confirmed by statistical summary. Hence, with an appropriate index-guiding
structure, we can achieve a polarization-stable VCSEL. Using one of such VCSEL,
we performed high-speed modulation of 1 Gb/s. We obtained the same BER on the
measurements with and without the polarizer in the measurement link. This fact
means that the VCSEL had stable polarization which remained unchanged under the
fast modulation. The results lead us to the conclusion that we achieved the
fabrication of long-wavelength VCSEL with practical polarization stability, which
was proven by statistical data and high-speed modulation.
214
8.02 Electrically pumped VCSEL
Even though we have obtained good results with optical-pumping scheme,
there are some problems associated with the scheme. First, we were not able to
obtain data which correlates device size and device performance. Second, it seemed
that the devices worked gain-guided at low power so that the effect of index guiding
shape was smaller than expected. And thirdly and most importantly, a misalignment
of pump beam and VCSEL may cause unintentional asymmetry. Also, we cannot
modulate the VCSEL directly.
To eliminate such problems, fabrication of electrically-pumped VCSEL is
inevitable. In fact, a lot of this thesis work was done in an aim to fabricate an
electrically-pumped VCSEL, and a VCSEL was fabricated. However, it didn’t work.
The structure of fabricated VCSEL can be seen on the left side of Fig. 5-7. Its
fabrication process was optimized as explained in the thesis. The reason of failure is
possibly a very simple mistake. On Fig. 5-7, we see that the tunnel junction is
sandwiched by n-InP and p-InP cladding layers. On the area with no tunnel junction,
these layers are to form an abrupt n/p interface. If the layers are moderately doped
but not too high to cause tunneling, such a t n/p interface should result in high
resistivity. On the other hand, p-InP is doped with Zn, and as seen on Fig. 4-14, it
can degrade quality of the MQW. Therefore, it is important to not to dope this layer
too high, so that Zn will not migrate into the MQW.
A mistake on our VCSEL is that this p-InP cladding layer was designed too
thin and low-doped for a fear of Zn migration. As a result, the layer was possibly
215
depleted and did not form n/p interface, but formed n-i-n structure and became
conductive. I-V testing showed that the fabricated VCSEL had too-high conductivity.
Unfortunately, we did not have time and funding to correct the mistake and re-
fabricate the device.
8.03 Future work and conclusion
As discussed above, the future work needed is to fabricate a working
electrically-pumped VCSEL, and perform experiments similar to those in Chapter 7.
We already optimized fabrication condition, and we know the reason of failure of 1st
try. Hence, it will not be a difficult task. However, there is a room for improvement
on MQW design and growth, since it is not completely heat resistive. As suggested
in Chapter 5, we should investigate the MQW growth at higher V/III ratio to see
whether point defects can be eliminated from the epitaxial layers. Also, InGaAlAs
MQW may be more heat-resistive, although it is not possible to grow such MQW by
the MOCVD machine at UCSB.
With this thesis, we were able to achieve fabrication and demonstration of
polarization-controlled long-wavelength VCSEL. We have proved the polarization
stability in terms of various aspects such as CW operation, yield, and high-speed
operation. Even though there are rooms for improvements and further investigations,
I believe this thesis is possibly the most complete investigation on polarization-stable
VCSELs, and also the earliest work of polarization control on long-wavelength
VCSEL.
216
Appendix A Material parameters InP
In0.53 G
a0.53 A
s G
aAs A
lAs
InAs G
aP
Lattice constant (A)5.8688
5.86885.6533
5.66116.0584
5.4512 room
temp. Band G
ap (eV)1.351
0.7491.424
2.153*0.359
2.272*deform
ation potential a (eV)
-6.16-8.68
-7.96-5.79
-9.76b (eV
)-2.0
-1.70-1.5
-1.8-1.5
d (eV)
-5.0-4.55
-3.4-3.6
-4.6 Luttinger param
eter γ16.28
6.8519.67
4.2γ2
2.082.1
8.370.98
γ32.76
2.99.29
1.66Therm
al expansion constant (x10-6/K
)4.56
6.45.2
5.165.91
elastic constant (x1010 N
/m2)
C11
10.2211.88
12.028.329
14.12C
125.76
5.385.70
4.5266.253
C44
4.605.94
5.893.959
7.047 effective m
ass me
0.0770.043
0.0670.19
0.0270.254
mhh
0.610.3774
0.380.48
0.340.67
mlh
0.120.0516
0.090.2
0.0270.17
mso
0.200.15
0.290.05
0.46low
-frequency dielectric constant12.4
13.1810.06
14.611.1
piezoelectric constant e14 (C
/m2)
-0.035-0.16
-0.225-0.045
-0.10reflactive index (at band gap)
3.413.62
3.23.52
3.5
* Indirect band gapY
oung’s modulus:
Y =(C
11 - C12 )(C
11 + 2C12 )
(C11 + C
12 )
Shear modulus on (001): G
=(C
11 - C12 )
2P
oisson ratio on (001): ν =C
12
(C11 + C
12 )
217
Appendix B Rotation matrix operation
[1] Strain and stress
As shown in Chapter 2, parameters of different coordinate system are related
by a rotation matrix as
RRT
zzzyzx
yzyyyx
xzxyxx
••= ||||
333231
232221
131211
ααααααααα
ααααααααα
AB-(1)
where |
cos0sin
sin2
12
1cos2
1
sin2
12
1cos2
1
|||
333231
232221
131211
θθ
θθ
θθ
−
−
==RRRRRRRRR
R
|2022)2(2)2(
|)2(2
1 2
2
2n
nnnn
n −++−
+= AB-(2)
By organizing this we find that
ijjlikkl RR αα = where (k,l)=(x,y,z) and (i,j)=(1,2,3) AB-(3)
but note that we need to put R1y as R12, Rx3 as R13, so on. Also, for symmetry reason,
klkl αα = jiij αα = AB-(4)
Results of forward rotation transformation are summarized as follows.
218
332231322212112
2
22)(
22)2(
)2(2ααααααα
nnn
nn
xx +++
+−++
+=
)(2
1)(22
2313222112ααααα −
+++−
+=
nnn
xy
)()2(2
2)22()2(2 23132
2
332212112ααααααα +
+−+−++
+=
nn
nn
xz
221211 21
21 αααα +−=yy
)()2(2
)()2(2
12313222112
ααααα +−+
++−+
=n
nn
yz
332
2
231322212112 2)(
22)2(
21 ααααααα
nn
nn
nzz +++
++++
+=
AB-(5)
As for reverse transformation, following relation holds:
kljlikij RR αα = AB-(6)
And in the same manner, each component is calculated as follows:
xzyyxyxx nnnnnA ααααα 22)2(22 22211 ++++−=
zzyzn αα 2)2(22 2 ++−
zzxzyyxx nnnA ααααα 222)2( 2212 +++−=
zzyzxzxyxx nnnnnnA αααααα 2)2(2)2(2222 22213 ++−−+++−=
219
xzyyxyxx nnnnnA ααααα 22)2(22 22222 +++++=
zzyzn αα 2)2(22 2 +++
zzyzxzxyxx nnnnnnA αααααα 2)2(2)2(2222 22223 +++−++−−=
zzxzxx nnA αααα 233 2244 +−=
AB-(7)
where )2(2 2nA += .
Now let us work on strain energy density U mathematically. We put matrixes as
Σ=||
333231
232221
131211
εεεεεεεεε
TT
zzzyzx
yzyyyx
xzxyxx
RR Σ=•Σ•=||εεεεεεεεε
AB-(8)
Ω=||
333231
232221
131211
σσσσσσσσσ
TT
zzzyzx
yzyyyx
xzxyxx
RR Ω=•Ω•=||σσσσσσσσσ
AB-(9)
The U, shown by vectors on Eq. 2-(27), also can be expressed by matrixes as
][21|
222
|][21
31
23
12
33
22
11
312312332211 Σ•Ω=••= traceU
εεε
εεε
σσσσσσ
AB-(10)
On the other hand, a simple matrix manipulation finds
220
RRRRRR TTTTT •Σ•Ω•=•Σ•••Ω•=Σ•Ω )()()( AB-(11)
since IRR T =• then IT RR = . This leads to a relation:
][][ Σ•Ω=Σ•Ω tracetrace TT AB-(12)
|
222
|][21][
21
zx
yz
xy
zz
yy
xx
zxyzxyzzyyxxTTtraceU
εεεεεε
σσσσσσ ••=Σ•Ω=∴
AB-(13)
This result is evident since the energy should be the same no matter what coordinate
system we use. Also this agrees with a result by a brute-forth method, Eq. 2-(41).
[2] Luttinger-Kohn 4×4 Hamiltonian
Continuing from Eq. 2-(60)
)()()()( ** ϕθϕθ RRHRRH iti = 2-(60)
−−−+−−
−
=
3223
223322
232232
3223
333223
322333
)(
αβααβββααβαββααβ
αβββααβαβαβαββαα
θR
AB-(14)
ϕ =45°2
cosθα =2
sin θβ −= AB-(15)
221
−
−+
=
=
−
−
2cos000
02
sin00
002
sin0
0002
cos
2sin000
02
cos00
002
cos0
0002
sin
000000000000
)(
)2/3(
)2/1(
)2/1(
)2/3(
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
i
ee
ee
R
i
i
i
i
AB-(16)
The resulting hamiltonians are:
4222
10
2
**
*
*
0
2
0 )(2
00
00
2Ikkk
mPSRSPRRPS
RSP
mH zyx
ttt
ttt
ttt
ttt
t +++
−−−−
= γ
AB-(17)
)]43(
)1(22)(2[)2(
3]26
)2(224[)2(
1
2222
222223
222222222
2
2
zyx
zxzyzx
zyxzyxt
kkkn
kknnkkn
knk
kkknkkkn
nP
−++
−−−+
++
−++++−+
−=
γ
γ
AB-(18)
]8)3()5([
]2)4[()2()(2
])2(2226)1(2[)()2(
3
2222223
422222
232
223222
yxyx
yxyxyxy
yxzzt
kikknnknn
kiknknknkiknk
iknnnkknkn
R
++++−+
++−++++
+++−−−+
=
γ
γγγ
γγ
AB-(19)
222
])2(2)1(2)2(
)4)[((2)])2(26[2
])2()42[(2)2(
3
22222
2232
222
2224322
yxzy
xyxz
yxzt
kiknknkn
knniknknk
iknnknnkn
S
+−−−++
−−++−+
+−+−+
=
γγγ
γ
AB-(20)
4
**
*
*
)(
00
00
Ia
ASRSARRAS
RSA
H zzyyxxv
ttt
ttt
ttt
ttt
t εεε
εε
εε
εε
εε
ε +++
−−−−
= AB-(21)
])1(2))(12[(3
]23))(1)[(1()2(
1
2//
2
//22
22
xzzz
xzzzt
nnnd
nnnbn
A
εεε
εεε
−−−+
+−−−+
=AB-(22)
]23))(1)[(3()2(
1//
222 xzzz
t nndbn
R εεεε +−−−+
= AB-(23)
]23))(1)[(3(2)2(
1//
222 xzzz
t nndbnn
S εεεε +−−+−+
= AB-(24)
with ε// = εxx = εyy = δ and εxy = εyz = εxz = 0 from Eq. 2-(33).
The values for the Hamiltonian tH 0 for special cases are listed on Table AB-1.
223
Table AB-1 Components for rotated hamiltonian Ht0 for special cases [1]
)(2
3)2(2
23
22
32222 kkkkkP zyxt −+−−= γγ
)]4()2([23 22
3222
2 yxzyzyxt kikkkkkkR +−+++−= γγ
zyxt kkikS )(32 23 γγ −=
)2( 2223 zyx
t kkkP −+= γ
zyxyxt kikkikkR ))((
322))(2(
31
322
32 +−+−+−= γγγγ
zyxyxt kikkikkS ))(2(
32))((
32
322
32 −+++−−= γγγγ
)248381127(121
3
)21816115(121
8
2223
2222
zxzyx
zxzyxt
kkkkk
kkkkkP
−−++
+−+=
γ
γ
)]225563(2)198115(
)16266218)([(121
3
223
222
32
yxyxyxyx
zzyxt
kikkkkikkk
kkikkR
−−−+++
−+−=
γγ
γγ
zyxyx
yxzyxt
kikkikk
kikkkkS
)]9967()2254([2
]2216115)[(23121
3
32
22232
−+−+
−−+−=
γγ
γγ
]2( 2222 zyx
t kkkP −+= γ
]2)([3 222
3 yxyxt kkikkR γγ +−−=
zyx kikkS )(32 3 −= γ
n =0(110)
n =1(111)
n =3(113)
n =∞(001)
224
Appendix C Calculation of Strain and polarization by
various methods
a) R. H. Henderson and E. Towe
A group of Prof. Towe at University of Virginia did an extensive work on
properties of non-(100)-oriented semiconductors. Their strain calculation is,
however, a bit complicated and not consistent. Their formulas of off-diagonal strain
are taken from Ref. 2, and organized here for (11n) case:
21211
2121112 )()[2(2 CCnCC
F−+−= δε
])2()()2( 244
42121144
24 CnnCCCnn −+−+−+
)](2))(1)[(2( 442
12114412112
12113123 CnCCCCCnCCnF
+−+−++−== δεε
)2()[(2)2)((4 12112
12112
441211121144 CCCCnCCCCCCF +−+++−=
]4)(2)2)((2 3441211
2441211121144 CCCCCCCCC +++−−+
24411
644124411
212
21144
4 2)2(4 CCnCCCCCCCn +−+−+
AC-(1)
Note that in their case, ε23 ≠ nε12.
225
b) D.L. Smith and C. Mailhoit
They are probably the first people to formulate piezoelectric field on arbitrary-
oriented semiconductors. Their formula is summarized here for a case of a single
epilayer on a thick (11n) substrate, the same as we considered in Chapter 2 [3].
P= |1
|2 4414
mf
BACe
))(2( 1211 zyx gggCCA +++=δ
)1(431))(2( 22
442
1211 mfCgggCCB zyx ++++++=
))((2 2221211 xzzyyxzyx gggggggggCC −−−++−+
1=fn
m 1=n
g x1=
ng y
1= ng z =
∴ P= |1
|)21(4)()1(2)2()2(31
)2)(2(2
442
121122
121122
12112
14 nn
CnCCnCCnCCne
++−−+++++•δ
AC-(2)
By comparing this with the Eq. 2-(43) and 2-(25), we see that the strain part of this
equation looks fairly similar to ε12, but the denominator is different from D.
Transverse and longitudinal components of polarization field calculated by
these different methods are plotted in Figure AC-1, along with the results shown on
Fig. 2-11 by E. A. Caridi and J. B. Stark [4].
226
Figure AC-1 In-plane (top) and longitudinal (bottom) components of polarization field after
different authors’ methods
Pol
ariz
atio
n fie
ld P
/2e 1
4δ
Angle from (001) θ (degree)
0 45 90
1
0
-1
Pola
rizat
ion
field
P/2
e 14δ
(001) (111) (110)(112)(113)
1
0
-1
Caridi & Stazrk
(Fig. 2-11 Px)
Caridi & Stark
(Fig. 2-11 Pz)
Smith & Mailhiot
Henderson & Towe
227
Appendix D Poisson ratio on (11n) plane
When there is an uniaxial stress σxx applied (Fig. 2-3, left), an isotropic
material will deform in a way that
Yxx
xxσε =
Yxx
yxyyσνε −=
Yxx
zxzzσνε −= AD-(1)
where νi is Poisson ratio, Y is Young’s modulus of the material which can be
expressed as
)()2)((
1211
12111211
CCCCCCY
++−
= AD-(2)
The same relation applies to the case of uniaxial stress σyy. Therefore, by adding
contributions from σxx and σxx, we get following equations for biaxial stress case:
)(1yyxyxxxx Y
σνσδε −== )(1xxyxyyyy Y
σνσδε −== AD-(3)
By using Eq. 2-(37), we can obtain νxy and νyx as plotted for InP in Figure AD-2.
Their values on (001) plane come down to a value by a known expression:
ν = C12/(C11+C12) AD-(4)
However, on other planes such as (110), their values go up as high as 0.8.
228
Figure AD-1 Orientation dependence of Poisson ratio ννννxy, ννννyx for InP
by Eq. AD-(3) ad Eq. 2-(37)
Angle from (001) θ (degree)
0 45 90
(001) (111) (110)(112)(113)
0.90
0
Pois
son
ratio
0.72
0.54
0.36
0.18
νyx
νxy
229
Appendix E MOCVD growth on (111) InP
Among (11n) orientations, (111) plane has been extensively studied together
with (110) plane: they are both “low-index” orientations with simple surface atomic
structure but with distinctive properties. As shown in Chapter 2, the (111) has the
highest strain energy U, the minimum z-axis strain εzz, symmetric in-plane stress
leading to the absence of in-plane polarization, and the maximum longitudinal
polarization which leads to the highest piezoelectric effect. Many reports have been
made on growth on (111) plane, including a fabrication of AlGaAs/GaAs laser which
had lower threshold current than that of the same laser fabricated on (001) plane [5].
We first chose to grow the VCSEL active region on (111) substrate for
following reasons. As just mentioned, it is well explored and known to be easy to
grow on. Also, wafer bonding of (111) and (001) substrates was performed and good
current conduction across their bonded interface was shown [6]. The fact that there is
no in-plane polarization may sound a disadvantage, however, this fact will let us see
the effect of asymmetric stress from thermal expansion mismatch, which should be a
distinctive feature of the VCSEL by orientation-mismatched wafer bonding. We
were not able to fabricate VCSEL with the (111)-InP based active region by the
reason which will be explained.
This chapter summarizes the work done on (111) InP wafers. The first thing
to do is to find an appropriate surface orientation and MOCVD growth condition. It
is not easy to grow on exact-oriented (111) plane, so we need to grow on a slightly
230
misoriented (111) plane. Also a difference of (111)A and (111)B faces plays a big
part on growth mechanism. With the appropriate growth condition and substrate
orientation, we investigate quality of MQWs by the PL. Then we explain a problem
that hindered us from the VCSEL fabrication with the (111)-InP based material.
[1] Effect of substrate misorientation
Figure AE-1 illustrates side view of atomic structure of (111) plane. The top
surface is (111)A and covered by group-III atoms, while the back surface corresponds
to (111)B which is covered by group-V atoms. Each surface atom is binded by 3
dangling bonds and very stable. There is just one free dangling bond per one surface
atom, and as a result, (111) surface has lowest density of free dangling bonds. Lateral
and vertical lattice spacings are also shown where a is a lattice constant.
As previously mentioned, it is difficult to grow on the exact (111)A and
(111)B surfaces since they are very stable. It is effective to have slight misorientation
on the surface to make growth easier. It is because the misoriented surface has more
free dangling bonds and also surface steps will enable step-flow growth on MOCVD.
We prepared 6 types of substrates as shown in Fig. AE-1. “A0” is (111)A exact,
“A1” is (111)A misoriented to [11−2 ], “A2” is (111)A misoriented to [
−1
−12]. The
misorientation is at 2 degrees for all cases. “B0”, “B1”, “B2”, are equivalent
substrates but of (111)B. It is also possible to have misorientation to [−110], which is
231
Figure AE-1 Atomic structure of (111)-oriented material, direction of misorientation
for each substrate, where αααα is lattice constant
the direction coming out of the paper, but it is previously reported that it is less
effective than ±[11−2 ] misorientation [7].
First, some bulk materials were grown under the standard condition for (001)
substrates, Tg = 615 ºC and V/III = 50 for InP from Chapter 3. Figure AE-2~4 show
surface morphologies of epitaxial layers, InP on Fig. AE-2, 1.1Q-InGaAsP on Fig.
AE-3, and 1.3Q-InGaAsP on Fig. AE-4, all in a 0.2-µm thickness. On Fig. AE-2, we
can see that both InP layers on exact substrates, A0 and B0, have rough surface while
other layers on misoriented substrates have smooth surface, except that the A2 has a
slight rough morphology. On Fig. AE-3 and Fig. AE-4, InGaAsP layers on A1 and
A2 show roughened morphology, while those on B1 and B2 still have smooth
morphology. Not to mention, all layers on A0 and B0 have bad morphology. The
(3/8)α
(1/√3)α[112]
[111]
[111]
[112]
A2A1
A0
B2B1
B0
In P
235
results tell that a slight misorientation on (111) substrate is effective in obtaining
better morphology, and that (111)B is easier to grow on than (111)A.
The reason for difficulty in the crystal growth on (111)A is that its surface is
covered by Group-III atoms. In order for growth to happen, its surface needs supply
of group-V atoms. And since they have to stick by just one dangling bond, we need a
large over-supply of group-V sources. After group-V atoms cover the surface, group-
III atoms stick on top and since there are 3 free dangling bonds/atom, they stick easily
onto group-V atoms. This fact, in turn, means the group-III atoms have short
migration length, which is a defective condition in obtaining a smooth surface.
Therefore, there are 2 conflicting issues on MOCVD on (111)A surface. We need
over-supply of group-V sources but high V/III ratio will reduce group-III migration.
A compromised growth condition could be such as high Tg to enhance migration and
very high V/III ratio. The misorientation on substrate helps enhancing group-III
migration, resulting in better surface morphology as seen in figures. Also, we see in
figures that the morphology on A1 and A2 becomes worse as Ga content of growth
layer increases. That is, group-III composition of unstrained 1.1Q is In0.854Ga0.146AsP
and that of 1.3Q is In0.72Ga0.28AsP, hence, 1.3Q has Ga/In ratio roughly twice as high
as that of 1.1Q. It is widely known that Ga has much shorter migration length than In
in general, so our surface observation makes sense. We didn’t observe any PL from
InGaAsP layers on all (111)A substrates and on B0. A few growths at higher V/III
ratios were performed in an attempt to grow decent material on A1 or A2, but no PL
was obtained and surface morphology was not improved much. It could be possible
236
to grow better at an extreme growth condition such as that mentioned earlier, but the
high V/III ratio means high consumption of expensive TBP and TBAs and it’s not
favorable financially.
[2] Optimizing growth condition and MQW growth
Our next mission is to find optimum growth condition on B1 and B2, and to
find which substrate is better to use. More InGaAsP materials were grown under
higher and lower V/III ratio, and PL emissions were compared. Figure AE-5 shows
PL from (a) 1.1Q layer and (b) 1.3Q layer on B1 and B2 substrates. For all cases, PL
wavelength tends to be longer on B1 substrate than B2, which suggests that B1
surface has higher As incorporation than B2. For 1.1Q on (a), we see results from
those grown at standard V/III of 45, which corresponds to the samples shown in Fig.
AE-3, and those at V/III of 90. At standard V/III, PL intensity from B1 sample is
about twice of that from B2, whereas their intensities were equivalent if grown at
higher V/III of 90. For 1.3Q on (b), PLs from samples grown at standard V/III of 41
and those at V/III of 20.5 are shown. There were also 1.3Q samples grown at higher
V/III, but no PL was observed and it was because the layer compositions went too far
off from lattice-matching condition. But since we didn’t have X-ray measurement
equipment working at the time of these growths, and since very good PL was
observed from low-V/III sample on B1, we didn’t pursue high-V/III option. The
standard V/III samples show the same result as 1.1Q samples, i.e., B1 having PL
intensity twice as much as that of B2. Lowering V/III yielded the intensity even
237
Figure AE-5 PL spectra from (a) 1.1Q and (b) 1.3Q InGaAsP grown on B1 and B2
with different V/III ratio
1000 1100 1200
0.0002
0.0001
0
V/III=45, B2 V/III=90, B2
PL in
tens
ity (a
rb. u
nit)
Wavelength (nm)
(a) 1.1Q InGaAsP
1200 1300 1400
0.0005
0.0004
0.0003
0.0002
0.0001
0
V/III=20.5, B1
V/III=20.5, B2
V/III=41, B1
V/III=41, B2
Wavelength (nm)
PL in
tens
ity (a
rb. u
nit)
(b) 1.3Q InGaAsP
V/III=45, B1 V/III=90, B1
238
higher on B1, twice of standard V/III sample. This intensity is indeed very high even
if compared to that from a good MQW on (001) substrate. The reason for strong PL
may not be just because of good crystalline quality, but could be due to other reasons
such as impurity incorporation (which was not investigated). Nonetheless, it is good
to have a strong PL from the material, and it is even better that we can grow such
material with low V/III ratio since it conserves group-V sources.
While low V/III was optimum to grow on B1, it seems high V/III ratio was
preferred to grow on B2. To understand the difference of B1 and B2, Figure AE-6
shows structure of both surfaces with steps created by misorientations. We can see
that the step on B1 surface creates additional group-V dangling bond and hence, its
surface is still covered by group-V only. On the other hand, the step on B2 surface
exposes a group-III atom which has similar property as the surface atom of (111)A.
Therefore, it makes sense that B2 requires higher V/III due to the presence of (111)A-
Figure AE-6 Structure of surface steps on B1 (left) and B2 (right)
B2B1
(001) (111)B(110)
(111)B (111)B
239
like atom. We can also view the surfaces as follows. As shown in Fig. AE-6, B1
surface consists of (111)B plane and (001) plane at the step, whereas the B2 consists
of (111)B and (110) plane at the step. The (110) is known to be very difficult plane
to grow on. From these observations, it makes sense to pursue further research on B1
substrate.
Next, an MQW was grown on B1 substrate with the optimum condition found
above, Tg = 615 ºC and V/III = 25 for InP (half of the standard). The MQW had 5
50-Å 1.4Q wells sandwiched by 6 100-Å 1.1Q barriers, and both materials had small
lattice-mismatches to InP, as they were calibrated on (001) substrate. Figure AE-7
(a) on B1 (b) on (001)
Figure AE-7 X-ray scan spectra of the MQW grown on (a) B1 by (333) diffraction
and on (b) (001) substrate by (004) diffraction
105
104
103
102
100
101
0-1000 10000-2000 1000-1000
satellite+1satellite
-1
substrate
MQW net strain
satellite+1
satellite-1
MQW net strain
substrate
Diffraction angle (arcsec)
Diff
ract
ion
inte
nsity
(arb
. uni
t)
Diffraction angle (arcsec)
240
shows X-ray scan from the MQW on (a) B1 and on (b) (001) substrate grown at the
same time. As indicated by the arrows, there are 2 sharp B1 substrate diffraction
peaks which were observed from all (111) samples at the exact same separation
between them. The scanning angle ωθ was normalized such that ωθ = 0 at stronger
peak of substrate. We need values of dS to calculate θS which corresponds to ωθ = 0.
For B1, the scan was measured by (333) diffraction, so that dS is equal to 1/3 of
vertical lattice spacing, which is (1/√3)α from Fig. AE-1 where lattice constant
α=5.8688Å from Appendix A. The (001) sample measures (004) diffraction and dS =
(1/4)α. Using Eq. 3-(2), we get θS = 43.0º for B1 and θS = 31.668º for (001)
substrates. On B1, there is a peak which corresponds to a net strain in the MQW, at
around –500 arcsec which is calculated to correspond to 0.2% compressive strain
using Eq. 3-(5) and Eq. 2-(34). On the other hand, the net strain in MQW on (001)
was very small so that we see the corresponding peak as a shoulder of the substrate
peak at around +100 arcsec, which means the net strain is slightly tensile. This
difference of net strain is because the incorporation ratio of As/P and Ga/In on (001)
is not the same as those on B1. We also see small satellite peaks associated with
MQW periodicity. The peaks are small because strain contrast between well and
barrier is small. From the separation of satellite peaks, we can calculate thickness of
1 pair of well/barrier, Λ, using Eq. 3-(7). It was calculated to be 157 Å from the scan
on B1 sample and 181 Å from the scan on (001) sample. The difference of these
results can be attributed to difference of growth rate on 2 substrates. However, the
measurement error is not negligible since the satellite peaks are weak.
241
Figure AE-8 shows PL peaks from the MQWs on B1 and (001). The peak is
much stronger on B1 than on (001), which is partly because the low V/III ratio is not
an optimum growth condition on (001). Nonetheless, the peak intensity from B1
sample is comparable to that of the best MQW on (001). The peak wavelength is
longer for B1 by about 70 nm, which again tells that the incorporation ratios are
different, especially As/P ratio, on these 2 substrates.
[3] Problem of using (111) substrate
The MOCVD growth on (111)B InP substrate was very successful, as we
were able to grow an MQW with very good optical property on B1. However, we
encountered to a problem in using (111) material for our final goal, fabricating
VCSEL by wafer bonding to GaAs-based DBRs. To do this, we grow the active
region on (111) InP substrate, and wafer-bond it to the GaAs DBR, then we need to
1200 1300 1400
0.0006
0.0004
0.0002
0
on B1on (001)
PL
inte
nsity
(arb
. uni
t)
Wavelength (nm)
Figure AE-8
PL peaks from MQW grown
on B1 and (001) substrates
at the same time
242
etch off the (111) InP substrate from its back side. If we grow active region on B1,
we need to etch off the B1 substrate from its backside, which has (111)A surface.
Now the problem is that it is hard to etch InP from (111)A plane. The etching of InP
generally occurs by attacking In atoms. In case of etching by HCl solution, etching
proceeds as In is dissolved by formation of In-Cl compound, and toxic PH3 gas is
generated. However on (111)A, the surface is consisted by In atoms tightly binded to
P atoms by 3 dangling bonds, and it is very difficult to break such In-P bonds. Hence,
the etching hardly proceeds even with concentrated HCl solution.
Table AE-1 summarizes possible solution tried and their results. There was a
report that hot HCl etched the (111)A plane at decent speed [8], however, that was
not the case on our etching experiment by HCl heated to 70 ºC. We covered surface
and sidewalls of the substrate piece and exposed only (111)A side, and there was no
etching going. The experiment of the above report is likely not taking care of
substrate sidewalls, and it possibly counted amount etched from sidewalls as etched
from (111)A. Br-based chemicals work similar way as HCl, and a mixture of 2 Br-
solutions etched (111)A plane, but etching was non-selective and hence, it is not
usable for the purpose of removing only the substrate. The experiment of side-
etching thick InGaAs layer didn’t go using ordinary InGaAs-etching solutions such as
H2SO4+H2O2 and H3PO4+H2O2 mixtures, as the etching was too slow to observe.
There is a reported technology of photo-chemical etching, used to selectively etch
InGaN on GaN [9], and similar technology may work on our case but we did not
tried. Since removing the substrate was not possible, options other than double-
243
Table AE-1 Possible methods to fabricate wafer-bonded VCSEL
with (111)B-based InP active regionEtch substrate by hot H
Cl
does not etch, etches InGaA
s
by HB
rdoes not etch
by Br2 +m
ethanoldoes not etch
by HB
r+Br2 m
ixtureetches (111)A
, but not selective with InG
aAs
Grow
thick InGaA
s layer (~1 µm)
beneath active region, releasedoes not w
ork (photo-chemical etching?)
substrate by side-etching the InGaA
s
Bond just one D
BR
and get another mirror by other m
eans
• Grow
InP/AlInG
aAs D
BR
TB
P-TMA
l adduct problem on M
OC
VD
• Use external m
irror B
ack-side has to be mirror-polished
• Double-side polished (111) w
afer not available
• In-house polishing doesn’t work on (111)A
Grow
active region on (111)AH
igh V/III anticipated by M
OC
VD
Method
Problem
244
bonding the DBR were investigated. It is possible to bond one DBR on (111)B
surface, then we need another mirror on the other side. Growing an InP/AlInGaAs
DBR could be an option, but with our MOCVD machine that was not the option.
Using an external mechanical mirror was not possible since we could not have the
backside (111)A surface mirror-polished. It might be possible to go back and try
growing on (111)A surface again, since there is no problem on etching from (111)B
surface. However, we would likely have to consume a lot of expensive group-V
sources to grow on (111)A, and it seemed not to worth trying.
[4] Summary
I was able to grow materials with good quality on (111)B substrate with 2º
mismorientation to [11−2 ], B1. The process of growth optimization was shown.
However, the materials were not usable for our final goal, active region of wafer-
bonded VCSEL, due to a fundamental problem of etching of the (111)B substrate.
The whole experiment in this chapter may have turned to be a waste, however,
the finding of superior optical quality on B1 can be beneficial for any other optical
devices. Also, strained materials on (111) possess piezoelectric effect which can be
used for unique devices such as modulator.
245
References
[1] S. L. Chuang, “Efficient band-structure calculations of strained quantum wells”,
Phys. Rev. B 43, pp.9649-61, 1991.
[2] R. H. Henderson and E. Towe, “Effective mass theory for III-V semiconductors
on arbitrary (hkl) surfaces”, J. Appl. Phys. 79, pp.2029-37, 1996.
[3] D. L. Smith and C. Mailhiot, “Piezoelectric effects in strained-layer superlattice”,
J. Appl. Phys. 63, pp.2717-9, 1988.
[4] E. A. Caridi and J. B. Stark, “Strain tensor elements for misfit-strained [hhk]-
oriented cubic crystals”, Appl. Phys. Lett. 60, pp.1441-3, 1992.
[5] T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto, and T.
Hijikawa, “Reduction of threshold current density of quantum lasers grown by
molecular beam epitaxy on 0.5° misoriented (111)B substrate”, Jpn. J. Appl. Phys.
26, pp.L302-5, 1987.
[6] Y. Okuno, K. Uomi, M. Aoki, and T. Tsuchiya, “Direct wafer bonding of III-V
compound semiconductors for free-material and free-orientation integration”, IEEE J.
Quantum Electron. 33, pp.959-69, 1997.
246
[7] Y. Ababou, R. A. Masut, and A. Yelon, “Low-pressure metalorganic vapor phase
epitaxy of InP on (111) substrates”, J. Vac. Sci. Technol. A16, pp.790-3, 1998.
[8] S. B. Phatak and G. Kelner, “Material-selective chemical etching in the system
InGaAsP/InP”, J. Electrochem. Soc. 126, pp.287-92, 1979.
[9] A. R. Stonas, “Gallium Nitride-based micro-opto-electro-mechanical systems”,
Ph.D. Dissertation in Electrical and Computer Engineering, University of California,
Santa Barbara, 2003.
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