Physics of Semiconductor Nanostructures
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Transcript of Physics of Semiconductor Nanostructures
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
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
Semiconductor nanostructures
Colloidal nanocrystals
~ few nm
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).
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
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
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
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…
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
Band Diagram of Solids
1s
2s
2p
3s
2N
2N
6N
N
Single atom Solid
Valence band
conduction band
Energy
position
Metal, Insulator, and Semiconductor
Valence Band (VB)
Conduction Band (CB)
metal insulator semiconductor
T>0 doping
+ + + + + +
Energy gap (Eg)
insSCmetal RRR
Semiconductor Heterostructures*
A B
Confinementpotential
* 2000 Nobel prize in physics
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)
Low-Dimensional Systems
Quantum Well (quasi-2D)
Quantum Wire (quasi-1D)
Quantum Dot (quasi-0D)
<<100nm, in usual.
Formation of Quantum Dots
- - - - -- - - - -
-+
etching
~10nm
1m~100nm
Self-assembled dots
Gate-defined dot Pillar dot
1m~100nm
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
I
V
I
V+_
w
Current transport through a classical resistance
Conductance (G)
WL
WG
GVI
law sOhm'
Quantum Point Contact
(see also J.H. Davies Fig.5.22/p186)
B.J. van Wees, PRL 60, 848(1988).
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.
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
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))
Quantum Hall Droplet
Vg
dotSource
Drain
N-1
B
B
B
E
2 2
Spin polarization
T.H.Oosterkamp, PRL, 82, 2931 (1999)
Photoluminescence (PL) from Quantum Wells
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
PL from Ensemble of Quantum Dots
Sylvain Raymond and cowokers, NRC, Canada
~20nm
Artificial atoms!!!
Magneto-PL from Ensemble of Quantum Dots
B
s
p+
p-
d+ d
d-
Sylvain Raymond et al. PRL(2004)
- 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
PL from Single Quantum Dot
Robin Williams and cowokers, at NRC, Canada
20meV
~20nm
U. Banin, Y. Cao,D. Katz, and O. Millo, Nature vol.400, 542 (1999)
InAs NC
Coulomb Blockade spectrum of a Single Nanocrystal
Experiment Calculation
Chemical potential
( ) ( 1)N GS GSE N E N
µ4
N=1 2 3 4 5 6 7 8
Semiconductor Nanocrystals
B0
M
B
Paramagnetism
B0
M
B
Diamagnetism
M
SQUID
B
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
Observation of Nanostructures
• Scanning Electron Microscope (SEM)
Electron beam10-40kV
Resolution>10nm *
* See, for instance, “University Physics”, by Harrison Benson, John Wiley & Sons, Inc.
Observation of Nanostructures
• Transmission Electron Microscope (TEM)
Electron beam50-100kV
Resolution>0.5nm
Observation of Nanostructures
diffraction
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
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)
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
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,…
NCs for Biosensing