physics of semiconductor nanostructures
DESCRIPTION
Physics of Semiconductor Nanostructures. 鄭舜仁 ( http://www.cc.nctu.edu.tw/~sjcheng/Frameset05.htm ) Department of Electrophysics, National Chiao Tung University. 2006 Spring Semester. Reference Books & Articles: - PowerPoint PPT PresentationTRANSCRIPT
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Physics of Semiconductor Nanostructures
Reference Books & Articles:
[1] "The physics of low-dimensional semiconductors: an introduction", by John H. Davies, Cambridge university press (1998). URL: http://userweb.elec.gla.ac.uk/j/jdavies/ldsbook (Chapter 1,3,4,6,9,10)
[2] Thesis “Correlations in semiconductor quantum dots” , Marek Korkusinski, June 2004, University of Ottawa (Chapter1,2,3 )
[3] Thesis “Collective Excitations and Coulomb Drag in Two-Dimensional Semiconductor Systems” , Shun-Jen Cheng, September 2001, Universität Würzburg (Chapter2 )
[4] “ A Guide to Feyman Diagrams in the Many-Body Problem, R.F. Mattuck (Dover Books) (1992)[5] “Electronic structure of quantum dots”, S. M. Reimann and M. Manninen, Reviews of Modern Physics, 74, 1283 (2002)
[6] “Magnetism in condensed matter”, Stephen Blundell, Oxford University Press (2001) (Chapter 1 &2)
[7] “Quantum theory of the optical and electronic properties of semiconductors”, H. Haug and S. W. Koch, World Scientific (Chapter 1)
[8] “Excitonic artificial atoms: engineering optical properties of quantum dots”, Pawel Hawrylak, Phys. Rev. B 60, 5597 (1999).
鄭舜仁(http://www.cc.nctu.edu.tw/~sjcheng/Frameset05.htm)
Department of Electrophysics, National Chiao Tung University
Evaluation:1. Exercises: 50%2. Oral presentation: 50%
2006 Spring Semester
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Semiconductor nanostructures
Mesa-etched dot Self-Assembled Quantum Dots
Three-dimensional STM image of an uncovered InAs quantum dot grown on GaAs(001). J. Marquez, et al, Appl. Phys. Lett. 78 (2001) 2309.
- - - - -- - - - --+
1m~100nmGate-defined dot
Quantum ring
1µm~100nm
~20nm
~20nm
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Semiconductor nanostructures
Colloidal nanocrystals
~ few nm
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Carbon nanotubes: One dimensional system
(Courtesy Cees Dekker, Delft Institute of Technology, the Netherlands.) This research was reported in the 7 May 1998 issue of Nature.
Here are some real-world nanotube materials, produced by laser ablation of a graphite target containing metal catalyst additives. On top is an atomic force microscopy image of a chiral tube with a diameter of 1.3 nanometers (Technical University, Delft: www.pa.msu.edu/cmp/csc/nanotube.html).
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OutlineOutline:1. Introduction to semiconductor nanostructures [1,2](1w)2. Formation of semiconductor nanostructures [1,2](0.5w)
gate-defined quantum dots (QDs)self-assembled QDssynthesized nanocrystals (NCs)quantum wires, quantum rings…
3. Single-particle properties [1,2,3](2w)band theory in solidsk.p theory envelope function approximationquantum diskparabolic modelspherical quantum dots (QDs)quantum rings*strain effects *asymmetric nanostructures
4. Electric and magnetic fields [1] (1w)nanostructures in magnetic fieldsnanostructures in magnetic fields :Stark effectsFermi’s golden ruleThe Aharonov-Bohm effect*Quantum Hall effects in 2D and 0D systems*
5. Many-particle problems [1,4] (3w)Hartree & Hartree-Fock approximation(0.5w)Second quantization(2.5w)Configuration interaction methodTechnique of exact diagonalization*Many electrons in QDs
6. Transport properties[5,6] (2w)Coulomb Blockade spectroscopy(1w)Hund’s rule(1w)Quantum Hall droplets in QDs*
7. Optical properties[1,7,8](2w)Dipole approximation & Fermi’s golden rulesemission and absorption spectrumFine structure of the optical spectrum of QDs
8. Magnetic properties[6](2w)Magnetism of QDsSemi-magnetic QDsSpintronics
總授課時間約 14週Oral presentation: 2週Home work: 4~6次
[#]: reference#; *: optional; (nw): n weeks
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OutlineOutline:1. Introduction to semiconductor nanostructures [1,2](1w)2. Formation of semiconductor nanostructures [1,2](0.5w)
gate-defined quantum dots (QDs)self-assembled QDssynthesized nanocrystals (NCs)quantum wires, quantum rings…
3. Single-particle properties [1,2,3](2w)band theory in solidsk.p theory envelope function approximationquantum diskparabolic modelspherical quantum dots (QDs)quantum rings*strain effects *asymmetric nanostructures
4. Electric and magnetic fields [1] (1w)Electrostatic potentialStark effectsFermi’s golden ruleThe Aharonov-Bohm effect*Quantum Hall effects in 2D and 0D systems*
5. Many-particle problems [1,4] (3w)Hartree & Hartree-Fock approximation(0.5w)Second quantization(2.5w)Configuration interaction methodTechnique of exact diagonalization*Many electrons in QDs
6. Transport properties[5,6] (2w)Coulomb Blockade spectroscopy(1w)Hund’s rule(1w)Quantum Hall droplets in QDs*
7. Optical properties[1,7,8](2w)Dipole approximation & Fermi’s golden rulesemission and absorption spectrumFine structure of the optical spectrum of QDs
8. Magnetic properties[6](2w)Magnetism of QDsSemi-magnetic QDsSpintronics
總授課時間約 14週Oral presentation: 2週Home work: 4~6次
[#]: reference#; *: optional; (nw): n weeks
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Introduction to semiconductor nanostructures
• Semiconductor (SC).
• Fabrication
• Scale of nanometer.
• Interesting Physics in SC nanostructures:
- transport measurement
- optical spectroscopy
- magnetic (& spin) properties
• Observations & Measurements
• Possible Applications
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Physics of Semiconductor Nanostructures
What’s SC?Why SC?
What’s “structure”?What’s “nano-scale”?Why nanostructures?
Why study the physics?What’s interesting physics?How to study the physics?Understand better the physics, then…
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insSCmetal
Conductor
(Cu, Ag..)
Semiconductor
(Si, GaAs..)
Insulator
(SiO2,..)
Resistivity
(Ohm.cm)26 10~10 92 10~10 2214 10~10
Metal, Insulator, and Semiconductor
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Band Diagram of Solids
1s
2s
2p
3s
2N
2N
6N
N
Single atom Solid
Valence band
conduction band
Energy
position
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Metal, Insulator, and Semiconductor
Valence Band (VB)
Conduction Band (CB)
metal insulator semiconductor
T>0 doping
+ + + + + +
Energy gap (Eg)
insSCmetal RRR
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Semiconductor Heterostructures*
A B
Confinementpotential
* 2000 Nobel prize in physics
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Is Nanometer small or large?A10101 9 mnm
Lattice constant: nm01 10~10
F of bulk: nm21 10~10
Effective Bohr Radius: nm110~
Length scales in semiconductors (SC’s)
Coherent length:
Mean free path:
0.1nm
1m
100nm
10nm
1nm
100m
10m
E
mes
osco
pic
a
22 1
FFF kE
(see “Electronic transport in mesoscopic systems”, S. Datta, Cambridge Univ. Press)
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Low-Dimensional Systems
Quantum Well (quasi-2D)
Quantum Wire (quasi-1D)
Quantum Dot (quasi-0D)
<<100nm, in usual.
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Formation of Quantum Dots
- - - - -- - - - -
-+
etching
~10nm
1m~100nm
Self-assembled dots
Gate-defined dot Pillar dot
1m~100nm
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Advanced ApplicationsFundamental InterestAtom physics,Many-body physics,Quantum opticsetc…..
Quantum-dot lasers,Photodetectors,Single electron devices,Single photon devices,Quantum computing,etc….
Semiconductor nano-technology,Material engineering,etc…
E
dN/dE (density of states)
bulk
~100meV(for GaAs)
10nmNano-scale
Room temp.kT~25meV
Aspects of Nanostructures
Nano-Technology
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I
V
I
V+_
w
Current transport through a classical resistance
Conductance (G)
WL
WG
GVI
law sOhm'
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Quantum Point Contact
(see also J.H. Davies Fig.5.22/p186)
B.J. van Wees, PRL 60, 848(1988).
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Quantum Point Contact
Vg
1
2
3
4
5
)/2( 2 heG_
: metal (gate): two-dimensional electron gas
h: Planck’s constantI
VgVg
~250nm
+V
W
807.25812
resistance sKlitzing' von
2e
hRK
*see also quantum Hall effect (Nobel prizes in ’85,’98) p228 in textbook.
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Quantum Point Contact (metal)
Quantized conductance through individual rows of suspended gold atoms H. OHNISHI, et al., Nature 395, p780 (‘98)
F of metal: nm10 10~10
~0.9nm
)( ,, SCFMF
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Coulomb Blockade in Quantum Dot (Q.D.)
J. Weis, et al. Phys. Rev. Lett. 71, 4019-4022 (1993)
IG
Vg
Vg Vg
Quantum dot
“single” electron transister (SET)
G
S D G
S D
(a review article about Q.D.: S.M. Reimann and M. Manninen, Review of Modern Physics, 74,1283 (2000))
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Quantum Hall Droplet
Vg
dotSource
Drain
N-1
B
B
B
E
2 2
Spin polarization
T.H.Oosterkamp, PRL, 82, 2931 (1999)
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Photoluminescence (PL) from Quantum Wells
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Photoluminescence (PL) from (parabolic) Quantum Well
R.C. Miller, et al. Phys. Rev. B 29, 3740 (’84)Also see sec. 4.3 in textbook
40meV
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PL from Ensemble of Quantum Dots
Sylvain Raymond and cowokers, NRC, Canada
~20nm
Artificial atoms!!!
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Magneto-PL from Ensemble of Quantum Dots
B
s
p+
p-
d+ d
d-
Sylvain Raymond et al. PRL(2004)
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- Fermi’s golden rule- intitial state: ground state.- final state: GS & “all” excited states
ffi EENGSiPNfNA )(|,)1(,|),( 2
i
ii chP ,,
The interband polarization operator
Hawrylak, ChengM.Bayer et al, Nature 405, 923 (2000)
B=0 experiment theoryX6
Gs-to-GS
Single-Dot PL Spectrum
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PL from Single Quantum Dot
Robin Williams and cowokers, at NRC, Canada
20meV
~20nm
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U. Banin, Y. Cao,D. Katz, and O. Millo, Nature vol.400, 542 (1999)
InAs NC
Coulomb Blockade spectrum of a Single Nanocrystal
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Experiment Calculation
Chemical potential
( ) ( 1)N GS GSE N E N
µ4
N=1 2 3 4 5 6 7 8
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Semiconductor Nanocrystals
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B0
M
B
Paramagnetism
B0
M
B
Diamagnetism
M
SQUID
B
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Paramagnetism of QDs: experimental results
0 10000 20000 30000 40000 50000-0.0006
-0.0003
0.0000
0.0003
0.0006
0.0009
(em
u m
ol-1
Oe-1
)
Magnetic Field (Oe)
PbSe QD0 50 100 150 200
0
2000
4000
6000
8000
10000
100 Gauss 1000 Gauss 10000 Gauss
1/ (
mol
Gau
ss /
emu)
Temperature (K)
0 40 80 120 160 200-0.0002
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
(em
u / m
ol G
auss
)
Temperature (K)
100 Gauss 1000 Gauss 10000 Gauss
Cd0.996Mn0.004Se
1
M
SQUID
B
T
CdMnSe QD
B
Wen-Bing Jian et al, to be published Wen-Bing Jian et al
Low-field paramagnetism
0
0
magnetic susceptibility
: paramagnetism
: damagnetism
M
B
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Observation of Nanostructures
• Scanning Electron Microscope (SEM)
Electron beam10-40kV
Resolution>10nm *
* See, for instance, “University Physics”, by Harrison Benson, John Wiley & Sons, Inc.
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Observation of Nanostructures
• Transmission Electron Microscope (TEM)
Electron beam50-100kV
Resolution>0.5nm
Observation of Nanostructures
diffraction
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Scannning Tunneling Microscope (STM)* * Nobel prize in 1986
Three-dimensional STM image of an uncovered InAs quantum dot grown on GaAs (001). J. Marquez, et al, Appl. Phys. Lett. 78 (2001) 2309.
I=const
Resolution:0.001nm (vertical)0.1nm (horizontal)
Observation of Nanostructures
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Possible Applications
。 Quantum dot infrared photodetectors, QDIPs
。 Optical memories
。 Single-Photon sources
-- Aslan, B.,Liu, H.C., Korkusinski, M., Cheng, S.-J., and Hawrylak, P., Appl. Phys. Lett. 82, 630 (2003)
--Petroff, P.M., in:Single Quantum Dots: Fundamentals, Application, and New Concepts, Peter Michler (Ed.) (Spring,Berlin,2003);-- Lundstrom, T., Schoenfeld, W. Lee, H., and Petroff, P.M., Science 286,2312(1999)
--Michler, P., Kiraz, A., Becher, C., Schoenfeld, W.V., Petroff, P.M., Zhang, L., Hu, E, and Imamoglu, A., Science 290, 2282 (2000)
--Moreau, E., Robert, I., Manin, L., Thierry-Mieg, V., Gerard, J.M., and Abram, I., Phys. Rev Lett. 87,183601 (2001)
--Santori, C., Pelton, M., Solomon, G., Dale, Y., and Yamamoto, Y., Phys. Rev. Lett. 86, 1502 (2001)--M.Pelton et al, Phys. Rev. Lett.89, 233602 (2002)
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0.0
0.2
0.4
0.6
0.8
1.0
100 150 200 250 300 3500.0
0.2
0.4
0.6
0.8
1.0
Nor
mile
zed
phot
ores
pons
e
P-polarizationT=6 K
sample A sample B sample C
P
S
IR
45o
z
Figure 2
(b)
(a)
Sca
led
phot
ores
pons
e
Photon energy (meV)
S-polarizationT=6 K
sample A sample B sample C
0.0
0.2
0.4
0.6
0.8
1.0
30 40 50 60 70 800.0
0.2
0.4
0.6
0.8
1.0
Nor
mili
zed
phot
ores
pons
e
P-polarizationT=6 K
sample A sample B sample C
Figure 3
(b)
(a)
Nor
mili
zed
phot
ores
pons
e
Photon energy (meV)
S-polarizationT=6 K
sample A sample B sample C
I
•Intra-band photocurrent spectrum
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Possible Applications
。 QD lasers
。 Terahertz radiation
--Arakawa, Y., and Sasaki, H., Apl. Phys. Lett. 40, 939 (1982); Fafard, S., Hinzer, K., Raymond, S., Dion, M.,McCAffrey, J., Feng, Y., and Vharbonneau, S., Science 22, 1350 (1996); Maximov, M.V., Shernyakov, Yu.M., Tsatsul'nikov, A.F., Lunev, A.V., Sakharov, A.V., Ustinov, V.M., Egorov, A.Yu., Zhukov, A.E., Kovsh, A.R., Kop'ev, P.S.,Asryan, L.V., Alferov, Zh.I., Ledentsov, N.N., Bimberg, D., Kosogov, A.O., and Werner, P., J. Appl. Phys. 83, 5561 (1998); Ledentsov, N.N., Ustinov, V.M., Shchukin, V.A., Kop'ev, P.S., Alferov, ZH.I., and Bimberg, D., Semiconductors 32, 343 (1998); Fafard, S., Wasilewski, Z.R., Allen, C. Ni., Hinzer, K., McCaffrey, J.P., and Feng, Y., Appl. Phys. Lett.75, 986 (1999)
--Anders, S., Rebohle, L., Schrey, F.F., Schrenk, W., Unterrainer, K., and Strasser, G., Appl. Phys. Lett. 82, 3862 (2003)
--Apalkov, V.M. and Chakraborty, T., Appl. Phys. Lett. 78, 1820 (2001)
--Wingreen, N.S. and Stafford C.A., IEEE J. Quant. Electron. 33, 1170 (1997)
。 Single electron transistor, quantum computation,…
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NCs for Biosensing