Quantum Dots

Outline

• Introduction • Some basic physics• Fabrication methods• Applications

– Lasers– Optical nonlinearity– Quantum optics

• Future outlook

Introduction

• Quantum dots (QD) a.k.a. “quantum boxes” and “artificial atoms” – Discrete energy levels

• Focus on optical properties of quantum dots– But interesting electronic transport properties also!

• Technological impact • Interesting science

Some Basic Physics

• Density of states (DoS)

– e.g. in 3D:

Structure Degree of Confinement

Bulk Material 0D

Quantum Well 1D 1

Quantum Wire 2D

Quantum Dot 3D (E)

dE

dN

E

E1/

dE

dk

dk

dN

dE

dNDoS

V

k

kN

3

3

)2(

34

stateper vol

volspacek )(

Discrete States

• Quantum confinement discrete states• Energy levels from solutions to Schrodinger Equation• Schrodinger equation:

• For 1D infinite potential well

• If confinement in only 1D (x), in the other 2 directions energy continuum

ErVm

)(2

22

integer n ,)sin(~)( Lxnx

mp

m

p

mLhn zy

228

22

2

22

Energy Total

x=0 x=L

V

In 3D…

• For 3D infinite potential boxes

• Simple treatment considered here– Potential barrier is not an infinite box

• Spherical confinement, harmonic oscillator (quadratic) potential

– Only a single electron• Multi-particle treatment• Electrons and holes

– Effective mass mismatch at boundary (boundary conditions?)

integer qm,n, ,)sin()sin()sin(~),,( zyx Lzq

Lym

Lxnzyx

2

22

2

22

2

22

888levelsEnergy

zyx mL

hq

mLhm

mLhn

Optical Excitation

• Exciton: bound electron-hole pair (EHP)• Excite semiconductor creation of EHP

– There is an attractive potential between electron and hole

– mh* > me

* hydrogenic syetem

– Binding energy determined from Bohr Theory

• In QDs, excitons generated inside the dot• The excitons confined to the dot

– Degree of confinement determined by dot size– Discrete energies

• Exciton absorption function-like peaks in absorption

mass reduced ;4

;2 22

2

020

2

e

ha

na

eEn

Size Matters

• Small enough to see quantum effect• A free electron:

– 3/2kBT = 2k2/2m ~ 60 at 300K For quantum effects: ~10s

• In semiconductors, use me* (effective mass) instead:

− me */me ~ 1/10

For quantum effects: 100s (10s nm) Number of atoms ~ 103 - 106

• Small L larger energy level separation• Properties determined by size of QDEnergy levels must be

sufficiently separated to remain distinguishable under broadening (e.g. thermal)

Fabrication Methods

• Goal: to engineer potential energy barriers to confine electrons in 3 dimensions

• 3 primary methods– Lithography– Colloidal chemistry– Epitaxy

Lithography

• Etch pillars in quantum well heterostructures – Quantum well heterostructures give 1D confinement

• Mismatch of bandgaps potential energy well

– Pillars provide confinement in the other 2 dimensions

• Electron beam lithography• Disadvantages: Slow, contamination, low density, defect

formation

A. Scherer and H.G. Craighead. Fabrication of small laterally patterned multiple quantum wells. Appl. Phys. Lett., Nov 1986.

Colloidal Particles

• Engineer reactions to precipitate quantum dots from solutions or a host material (e.g. polymer)

• In some cases, need to “cap” the surface so the dot remains chemically stable (i.e. bond other molecules on the surface)

• Can form “core-shell” structures• Typically group II-VI materials (e.g. CdS, CdSe)• Size variations ( “size dispersion”)

Evident Technologies: http://www.evidenttech.com/products/core_shell_evidots/overview.php

Sample papers: Steigerwald et al. Surface derivation and isolation of semiconductor cluster molecules. J. Am. Chem. Soc., 1988.

CdSe core with ZnS shell QDsRed: bigger dots!

Blue: smaller dots!

Epitaxy: Patterned Growth

• Growth on patterned substrates – Grow QDs in pyramid-

shaped recesses– Recesses formed by

selective ion etching– Disadvantage: density of

QDs limited by mask pattern

T. Fukui et al. GaAs tetrahedral quantum dot structures fabricated using selective area metal organic chemical vapor deposition. Appl. Phys. Lett. May, 1991

Epitaxy: Self-Organized Growth

• Self-organized QDs through epitaxial growth strains– Stranski-Krastanov growth mode (use MBE, MOCVD)

• Islands formed on wetting layer due to lattice mismatch (size ~10s nm)

– Disadvantage: size and shape fluctuations, ordering– Control island initiation

• Induce local strain, grow on dislocation, vary growth conditions, combine with patterning

AFM images of islands epitaxiall grown on GaAs substrate.

(a) InAs islands randomly nucleate.

(b) Random distribution of InxGa1 xAs ring-shaped islands.

(c) A 2D lattice of InAs islands on a GaAs substrate.

P. Petroff, A. Lorke, and A. Imamoglu. Epitaxially self-assembled quantum dots. Physics Today, May 2001.

QD Lasers

• Advantages– More efficient, higher

material gain, lower threshold

• Concentration of carriers near band edge

– Less thermal dependence, spectral broadening

• Material gain – Theoretical prediction:

• G=104 cm-1, Jth=5A/cm2 at RT

– Compared to bulk InGaAsP:

• N~1018, G~102 cm-1

Ledenstov et al. Quantum-dot heterostructure lasers. JSTQE, May 2000.

QD Heterostructure Lasers

• Stack QD vertically to increase density of QD (~10 layers)– Carrier escape at high T– Higher modal gain (shape of

mode x bulk gain)

• III-V based structures• InAs-(In,Ga,Al)As near IR

(1.83 m) to red• (In,Al)GaN-GaN wide

bandgap, can emit in the blue end of spectrum, even UV (with Al)

InGaAs QDs in AlGaAs (RT):

Jth ~ 60 A/cm2, Pout ~ 3W CW

InGaN QDs in GaN (RT):

Jth ~ 1 kA/cm2

Excitons and Nonlinear Optics

• Excitons enhance nonlinearity of materials at resonances

• Quantum confinement– Discrete energy levels concentrate oscillator strength to

lowest level transitions

• Oscillator Strength depends on– Relative motion of the electron and hole– Number of electron and hole pairs

• Larger dot– Weak confinement, electron-hole more correlated, more

nonlinearity

– Higher states have smaller fx, the oscillator strength eventually saturates

Oscillator Strength describes the relative strength of a transition:

xex hm

Pf

2|0|||

Nonlinear Optics

• Embed QDs (e.g. CdS, CdSe) in polymer (typically) host material to increase (3)

• Device applications: optical switches, wavelength conversion

•Bulk PS: linear

•Higher orders of nonlinearity present

n = n0 + (n2+n4I)I

Quantum Optics

• Quantum mechanical system in solid-state!

• Cavity QED: Modified spontaneous emission – Spontaneous emission

lifetime not intrinsic to atom but to coupling of atom & vacuum

• Cavity modifies DoS of vacuum

• Couple QD to cavity• Change in lifetime of

spontaneous emission – From 1.3 ns (no cavity) to 280

ps

Solid line = PL spectrum

Dashed line = SE lifetime

Single Photon Sources

• Single photon emission through recombination of a single exciton– Verified by studying g(2)(), the 2nd

order coherence function– Observed photon-anti-bunching

(quantum state of light)• Optically pumped single photon

source– QDs in high Q microcavity at low

T (~5K)– Lifetime of single exciton state

shorter than lifetimes of the other states

• Potential for quantum information processing, quantum computing

• Fluorescent inks containing quantum dots could be the key to creating identification codes that are invisible to the naked eye and very hard to counterfeit. The “Info-ink” codes developed could be ideal for use on passports or ID cards.

• info-inks, composed of a polymer, a solvent and a mixture of quantum-dots, can be painted or printed onto the surface of a document or object. By adjusting the number and emission wavelength of the quantum dots in the ink it is possible to create a digital fluorescence code that is unique to that object. Calculations suggest that the use of six different wavelengths and ten intensity values could create one million distinct codes.

•  •  •  • To date, Chang and colleagues have made Info-inks containing CdSe nanocrystals

(quantum dots), polystyrene and toluene. Experiments with five different emission wavelengths (535, 560, 585, 610 and 640 nm) have allowed the creation of inks containing a 3-digit code.

• The codes are read out by illuminating the ink with light from an ultraviolet (370 nm) LED to excite fluorescence from the dots. This fluorescence is captured by an optical fibre bundle and fed to a spectrometer connected to a PC. Analysis of the fluorescence spectrum reveals the code and thus the authenticity or identity of the item.

• Cds quantum dots in a high Q-cavity gives:• Rabi oscillations• Photon statistics• Collapse and revivals of population inversion in exiton and biexiton states•  •  

Future Outlook

• Development of QD lasers at communication wavelengths• Gain and stimulated emission from QDs in polymers

– Polymeric optoelectronic devices?

• Probe fundamental physics• Quantum computing schemes (exciton states as qubits)

– Basis for solid-state quantum computing?

• Biological applications• Material engineering

– How to make QDs cheaply and easily with good control?

• Lots to do!

Summary

• Discrete energy levels, artificial atom• Fabrication: top-down, bottom-up approaches

– Lithography, colloidal chemistry, epitaxy

• Making better lasers• Enhancing optical nonlinear effects• Quantum optics

• Lots of room for further research!

References

• Books– Y. Masumoto and T. Takagahara. Semiconductor Quantum Dots: Physics, Spectroscopy, and

Applications. New York: Springer-Verlag, 2002.– P. Harrison. Quantum Wells, Wires, and Dots: Theoretical and Computational Physics. New

York: Wiley, 2000.– D. Dieter et al. Quantum Dot Heterostructures. New York: Wiley, 1999.– R.E. Hummel and P. Wibmann. Handbook of Optical Properties vol 2: Optics of Small Particles,

Interfaces, and Surfaces. New York: CRC Press, 1995.• General

– P. Petroff, A. Lorke, and A. Imamoglu. Epitaxially Self-Assembled Quantum Dots. Physics Today, May 2001.

– F. Julien and A. Alexandrou. Quantum Dots: Controlling Artificial Atoms. Science 282:5393.– M. Reed. Quantum Dots. Scientific American, p 118-123, Jan 1993.

• Fabrication– T. Fukui et al. GaAs tetrahedral quantum dot structures fabricated using selective area metal

organic chemical vapor deposition. Appl. Phys. Lett., 58(18), p. 2018-2020, 1991.– Steigerwald et al. Surface derivation and isolation of semiconductor cluster molecules. J. Am.

Chem. Soc., 110(10), p. 3046-3050, 1988. – A. Scherer and H.G. Craighead. Fabrication of small laterally patterned multiple quantum

wells. Appl. Phys. Lett., 49 (19), p. 1284-1286, 1986.

References (2)

• Lasers– Y. Arakawa. Progress in GaN-based quantum dots for optoelectronics applications. JSTQE, 8(4),

p. 823-832, 2002.– N. Ledenstov et al. Quantum-dot heterostructure lasers. JSTQE, 6(3), p.439-451, 2000.– V. Klimov. Optical gain and stimulated emission in nanocrystal quantum dots. Science, 290,

p.314-317.– L. Parvesl et al. Optical gain in silicon nanocrystals. Nature, 408, p.440-444, 2000.

• Optical nonlinearity

– Du et al. Synthesis, characterization, and nonlinear optical properties of hybridized CdS-Polysterene nanocomposites. Chem. Mater., 14, p. 4473-4479, 2002.

– Ghosh et al. Nonlinear optical and electro-optic properties of InAs/GaAs self-organized quantum dots. J. Vac. Sci. Tech. B, 19(4), p. 1071-1023, 2001.

– R. E. Schwerzel et al. Nanocomposite photonic polymers. 1. Third-order nonlinear optical properties of capped cadmium sulfide nanocrystals in an ordered polydiacetylene host, J. Phys. Chem. A, 102, 5622-5626, 1998.

• Cavity QED and Single photon sources– Pelton et al. Efficient source of single photons: a single quantum dot in a micropost microcavity.

Phys Rev Lett.,89(23), 233602, 2002.– Yuan et al. Electrically driven single-photon source. Science, 295, p. 102-105, 2002.

– Solomon et al. Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity, Phys Rev Lett, 86(17), p. 3903-3906, 2001.

– Michler et al. A quantum dot single-photon turnstile device. Science, 290, p.2282-2285, Dec. 2000

– A. Imamoglu et al. Quantum information processing using quantum dot spins and cavity QED. Phys Rev Lett., 83(20), p. 4204-4207, 1999.