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:
[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).
Evaluation:
1. Exercises: 50%
2. Oral presentation: 50%
Semiconductor nanostructures
Gate-defined dot
Mesa-etched dot
1m~100nm
- - - -- - - - -
1µm~100nm
Self-Assembled
Quantum Dots
+~20nm
~20nm
Quantum ring
Three-dimensional STM image of an uncovered
InAs quantum dot grown on GaAs(001).
J. Marquez, et al,
Appl. Phys. Lett. 78 (2001) 2309.
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).
Outline
Outline:
6. Transport properties[5,6] (2w)
1. Introduction to semiconductor nanostructures [1,2](1w)
Coulomb Blockade spectroscopy(1w)
2. Formation of semiconductor nanostructures [1,2](0.5w)
Hund’s rule(1w)
gate-defined quantum dots (QDs)
Quantum Hall droplets in QDs*
self-assembled QDs
7. Optical properties[1,7,8](2w)
synthesized nanocrystals (NCs)
Dipole approximation & Fermi’s golden rules
quantum wires, quantum rings…
emission and absorption spectrum
3. Single-particle properties [1,2,3](2w)
Fine structure of the optical spectrum of QDs
band theory in solids
8. Magnetic properties[6](2w)
k.p theory
Magnetism of QDs
envelope function approximation
Semi-magnetic QDs
quantum disk
Spintronics
parabolic model
spherical quantum dots (QDs)
quantum rings*
strain effects *
asymmetric nanostructures
4. Electric and magnetic fields [1] (1w)
nanostructures in magnetic fields
nanostructures in magnetic fields :Stark effects
Fermi’s golden rule
The 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)
[#]: reference#; *: optional; (nw): n weeks
Configuration interaction method
Technique of exact diagonalization*
Many electrons in QDs
總授課時間約14週
Oral presentation: 2週
Home work: 4~6次
Outline
Outline:
6. Transport properties[5,6] (2w)
1. Introduction to semiconductor nanostructures [1,2](1w)
Coulomb Blockade spectroscopy(1w)
2. Formation of semiconductor nanostructures [1,2](0.5w)
Hund’s rule(1w)
gate-defined quantum dots (QDs)
Quantum Hall droplets in QDs*
self-assembled QDs
7. Optical properties[1,7,8](2w)
synthesized nanocrystals (NCs)
Dipole approximation & Fermi’s golden rules
quantum wires, quantum rings…
emission and absorption spectrum
3. Single-particle properties [1,2,3](2w)
Fine structure of the optical spectrum of QDs
band theory in solids
8. Magnetic properties[6](2w)
k.p theory
Magnetism of QDs
envelope function approximation
Semi-magnetic QDs
quantum disk
Spintronics
parabolic model
spherical quantum dots (QDs)
quantum rings*
strain effects *
asymmetric nanostructures
4. Electric and magnetic fields [1] (1w)
Electrostatic potential
Stark effects
Fermi’s golden rule
The 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)
[#]: reference#; *: optional; (nw): n weeks
Configuration interaction method
Technique of exact diagonalization*
Many electrons in QDs
總授課時間約14週
Oral presentation: 2週
Home work: 4~6次
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
Why study the physics?
What’s interesting physics?
How to study the physics?
Understand better the
physics, then…
What’s SC?
Why SC?
What’s “structure”?
What’s “nano-scale”?
Why nanostructures?
Metal, Insulator, and Semiconductor
Conductor
(Cu, Ag..)
Resistivity
(Ohm.cm)
10 6 ~ 102
Semiconductor Insulator
(Si, GaAs..)
(SiO2,..)
10 2 ~ 109
 metal   SC  ins
1014 ~ 10 22
Band Diagram of Solids
Single atom
Solid
3s
conduction band
2p
Valence band
2s
N
6N
Energy
2N
2N
1s
position
Metal, Insulator, and Semiconductor
Rmetal  RSC  Rins
metal
insulator
semiconductor
Conduction Band (CB)
Energy gap (Eg)
Valence Band (VB)
T>0
doping
++++++
Semiconductor Heterostructures*
* 2000 Nobel prize in physics
A
B
Confinement
potential
Is Nanometer small or large?

1nm  10 9 m  10 A
Length scales in semiconductors (SC’s)
(see “Electronic transport in mesoscopic systems”, S. Datta,
Cambridge Univ. Press)
100m
mesoscopic
10m
1m
Mean free path:
Coherent length:
E
100nm
lF of bulk: 101 ~ 10 2 nm
10nm
Effective Bohr Radius:
~ 101 nm
a
1nm
0.1nm
E F  k F2 
Lattice constant: 10 1 ~ 100 nm
1
l2F
Low-Dimensional Systems
Quantum Well (quasi-2D)
Quantum Wire (quasi-1D)
Quantum Dot (quasi-0D)
<<100nm, in usual.
Formation of Quantum Dots
Gate-defined dot
Pillar dot
1m~100nm
1m~100nm
+
-----
-----
Self-assembled dots
~10nm
etching
Aspects of Nanostructures
bulk
Room temp.
kT~25meV
Nano-Technology
dN/dE (density of states)
~100meV
(for GaAs)
10nm
Nano-scale
Semiconductor nano-technology,
Material engineering,
etc…
E
Fundamental Interest
Atom physics,
Many-body physics,
Quantum optics
etc…..
Advanced Applications
Quantum-dot lasers,
Photodetectors,
Single electron devices,
Single photon devices,
Quantum computing,
etc….
Current transport through a classical resistance
I
I
w
+
V
_
V
Conductance (G)
Ohm' s law
I  GV
G
W
L
W
Quantum Point Contact
B.J. van Wees, PRL 60, 848(1988).
(see also J.H. Davies Fig.5.22/p186)
Quantum Point Contact
_
~250nm
Vg
Vg
G ( 2e 2 / h )
5
4
3
I
V
+
2
1
: metal (gate)
: two-dimensional electron gas
h: Planck’s constant
von Klitzing' s resistance 
h
RK  2  25812.807
e
W
Vg
*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)
lF of metal:100 ~ 101 nm
(lF , M  lF ,SC )
~0.9nm
Coulomb Blockade in Quantum Dot (Q.D.)
Quantum dot
J. Weis, et al.
Phys. Rev. Lett. 71, 4019-4022 (1993)
Vg
Vg
G
I
“single” electron transister
(SET)
S
D
S
D
G
G
(a review article about Q.D.:
S.M. Reimann and M. Manninen, Review of Modern Physics, 74,1283 (2000))
Vg
Quantum Hall Droplet
Spin polarization
 2
 2
E
B
B
dot
Source
Drain
N-1
T.H.Oosterkamp, PRL, 82, 2931 (1999)
Vg
B
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
Artificial atoms!!!
~20nm
Sylvain Raymond and cowokers, NRC, Canada
Magneto-PL from Ensemble of Quantum Dots
B
d+
d
dp+
p-
s
Sylvain Raymond et al. PRL(2004)
Single-Dot PL Spectrum
- Fermi’s golden rule
- intitial state: ground state.
- final state: GS & “all” excited states
The interband polarization operator
A( , N )   | f , ( N  1) P i  GS , N |  ( Ei  E f   )

2
P    hi ,  ci ,
i
f
experiment
M.Bayer et al, Nature 405, 923 (2000)
B=0
X6
theory
Gs-to-GS
Hawrylak, Cheng
PL from Single Quantum Dot
20meV
~20nm
Robin Williams and cowokers, at NRC, Canada
Coulomb Blockade spectrum of a Single Nanocrystal
U. Banin, Y. Cao,D. Katz, and O. Millo, Nature vol.400, 542 (1999)
InAs NC
Calculation
Experiment
N=1 2
Chemical potential
 N  EGS ( N )  EGS ( N  1)
µ4
3 4 5 6 78
Semiconductor Nanocrystals
B
M
SQUID
B
M
 
0
B
Paramagnetism
M
 
0
B
Diamagnetism
Paramagnetism of QDs: experimental results
M
magnetic susceptibility  
B
  0: paramagnetism
CdMnSe QD
Cd0.996Mn0.004Se
10000
  0: damagnetism
1


M
1/ (mol Gauss / emu)
B
100 Gauss
1000 Gauss
10000 Gauss
8000
PbSe QD
0.0009
6000
4000
2000
0
0
50
100
150
200
0.0006
SQUID
0.0003
0.0010
0.0000

-0.0003
-0.0006
100 Gauss
1000 Gauss
10000 Gauss
0.0008
 (emu / mol Gauss)
-1
-1
 (emu mol Oe )
Temperature (K)
0
10000
20000
30000
40000
50000
Magnetic Field (Oe)
Low-field paramagnetism
B
Wen-Bing Jian et al, to be published
0.0006
0.0004
0.0002
0.0000
-0.0002
0
40
80
120
160
200
Temperature (K)
T
Wen-Bing Jian et al
Observation of Nanostructures
• Scanning Electron Microscope (SEM)
Resolution>10nm *
10-40kV
Electron beam
* See, for instance, “University Physics”,
by Harrison Benson, John Wiley & Sons, Inc.
Observation of Nanostructures
• Transmission Electron Microscope (TEM)
Electron beam
50-100kV
diffraction
Resolution>0.5nm
Observation of Nanostructures
Scannning Tunneling Microscope (STM)*
* Nobel prize in 1986
I=const
Resolution:
0.001nm (vertical)
0.1nm (horizontal)
Three-dimensional STM image of an uncovered
InAs quantum dot grown on GaAs (001).
J. Marquez, et al, Appl. Phys. Lett. 78 (2001) 2309.
Possible Applications
。Quantum dot infrared photodetectors, QDIPs
-- Aslan, B.,Liu, H.C., Korkusinski, M., Cheng, S.-J., and Hawrylak, P., Appl. Phys. Lett. 82, 630 (2003)
。Optical memories
--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)
。Single-Photon sources
--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)
•Intra-band photocurrent spectrum
I

P-polarization
T=6 K
sample A
sample B
sample C
(a)
0.8
0.6
0.4
0.2
0.0
(a)
0.8
0.6
0.4
0.2
0.0
1.0
S-polarization
T=6 K
sample A
sample B
sample C
(b)
0.8
0.6
0.4
0.2
0.0
30
40
50
60
Photon energy (meV)
70
80
z
Scaled photoresponse
1.0
Normilized photoresponse
P-polarization
T=6 K
sample A
sample B
sample C
1.0
Normilezed photoresponse
Normilized photoresponse
1.0
0.8
S-polarization
T=6 K
sample A
sample B
sample C
(b)
45o
P
0.6
IR
S
0.4
0.2
0.0
100
150
200
250
Photon energy (meV)
300
350
Possible Applications
。QD lasers
--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)
。Terahertz radiation
--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