Transcript Semiconductor Nanospheres and Quantum Dots

Quantum Dots
Outline
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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)
DoS 
dN dN dk

dE dk dE
– e.g. in 3D:
k space vol
N (k ) 
vol per state
4 3k 3

(2 )3 V
Structure
Degree of
Confinement
Bulk Material
0D
dN
dE
E
Quantum Well
1D
1
Quantum Wire
2D
1/ E
Quantum Dot
3D
d(E)
Discrete States
• Quantum confinement  discrete states
• Energy levels from solutions to Schrodinger Equation
• Schrodinger equation:
V

2

 2   V (r )  E
2m
• For 1D infinite potential well
( x) ~ sin( nLx ), n  integer
x=0
• If confinement in only 1D (x), in the other 2 directions  energy
continuum
T otalEnergy 
n2h2
8 mL2

p 2y
2m

p z2
2m
x=L
In 3D…
• For 3D infinite potential boxes
 ( x, y, z ) ~ sin( nLxx ) sin( mLyy ) sin( qLzz ), n, m, q  integer
Energylevels 
n2h2
8 mL x 2

m2h2
8 mL y 2
q 2h2
 8mL 2
z
• 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?)
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
e2
h 2
En  
; a0  2 2 ;   reduced mass
2
2a0 n
4 e
• In QDs, excitons generated inside the dot
• The excitons confined to the dot
– Degree of confinement determined by dot size
– Discrete energies
• Exciton absorption  d function-like peaks in absorption
Size Matters
• Small enough to see quantum effect
• A free electron:
– 3/2kBT = 2k2/2m
 l ~ 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
Energy levels must be sufficiently
• Properties determined by size of QD 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”)
CdSe core with ZnS shell QDs
Red: bigger dots!
Blue: smaller dots!
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.
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
InxGa1xAs 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 describes the
• Oscillator Strength depends on
– Relative motion of the electron and hole
– Number of electron and hole pairs
relative strength of a transition:
|  | P | 0 |2
fx 
me h x
• Larger dot
– Weak confinement, electron-hole more correlated, more
nonlinearity
– Higher states have smaller fx, the oscillator strength eventually
saturates
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
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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.
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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
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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)
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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
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Du et al. Synthesis, characterization, and nonlinear optical properties of hybridized CdS-Polysterene
nanocomposites. Chem. Mater., 14, p. 4473-4479, 2002.
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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.
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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.
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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.