university of california santa barbara polarization control … · 2005-06-22 · [8] y. okuno,...

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



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



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


5.02 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


6.02 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


7.02 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

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[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.


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,


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


0 45 90

(001) (111) (110)(112)(113)

Figure 2-7


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).


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


0 45 90

(001) (111) (110)(112)(113)

Figure 2-11


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


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


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


[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.


[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-


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

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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





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.




[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.


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.




[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


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


OS

A si

ngle

-mod

e po

wer

(dB

m)

-90

-30

-40

-50

-60

-80

-70

Polarizer2 @[332] Polarizer2 @[110]

200100 200100


Spot #2 Spot #3


OS

A si

ngle

-mod

e po

wer

(dB

m)

-90

-30

-40

-50

-60

-80

-70


300100 200 200100


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.




[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.


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.


Tota

l mod

e po

wer

(dBm

)

-10

-20

-30

-40

-60

-50


200100 200100



Tota

l mod

e po

wer

(dBm

)

100 200 200100


-10

-20

-30

-40

-60

-50

best

SR

wor

st S

R

best

SR

wor

st S

R

[110]-ellipsed =12 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(Fig. 8-7)



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




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



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


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


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-


Electron. 5, pp.530-6, 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


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)


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

232

Figure AE-2 Morphology of InP layer on various (111) substrates

A0 B0

A1 B1

A2 B2

233

Figure AE-3 Morphology of 1.1Q InGaAsP layer on various (111) substrates

A0 B0

A1 B1

A2 B2

234

Figure AE-4 Morphology of 1.3Q InGaAsP layer on various (111) substrates

A0 B0

A1 B1

A2 B2

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


Diff

ract

ion

inte

nsity

(arb

. uni

t)


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


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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

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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”,

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Santa Barbara, 2003.

university of california santa barbara polarization control … · 2005-06-22 · [8] y. okuno,...

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