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