1. Quantum Dots

2. Outline Introduction Some basic physics Fabrication methods
Applications
Lasers
Optical nonlinearity
Quantum optics
Future outlook

3. 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

4. Some Basic Physics Density of states (DoS) Structure
e.g. in 3D:
Structure
Degree of Confinement
Bulk Material 0D
Quantum Well 1D 1
Quantum Wire 2D
Quantum Dot 3D
d(E)

5. 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
x=0
x=L V

6. 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?)

7. 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  d function-like peaks in absorption

8. 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 ~
Small L  larger energy level separation
Properties determined by size of QD
Energy levels must be sufficiently separated to remain distinguishable under broadening (e.g. thermal)

9. Fabrication Methods
Goal: to engineer potential energy barriers to confine electrons in 3 dimensions
3 primary methods
Lithography
Colloidal chemistry
Epitaxy

10. 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.

11. 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:
Sample papers: Steigerwald et al. Surface derivation and isolation of semiconductor cluster molecules. J. Am. Chem. Soc., 1988.

12. 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

13. 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.
InAs islands randomly nucleate.
Random distribution of InxGa1­xAs ring-shaped islands.
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.

14. QD Lasers Advantages Material gain
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.

15. 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 mm) 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

16. 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:

17. 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

18. 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

19. 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

20. 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

21. 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!

22. 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!

23. 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 , 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 , 1991.
Steigerwald et al. Surface derivation and isolation of semiconductor cluster molecules. J. Am. Chem. Soc., 110(10), p , 1988.
A. Scherer and H.G. Craighead. Fabrication of small laterally patterned multiple quantum wells. Appl. Phys. Lett., 49 (19), p , 1986.

24. References (2)
Lasers
Y. Arakawa. Progress in GaN-based quantum dots for optoelectronics applications. JSTQE, 8(4), p , 2002.
N. Ledenstov et al. Quantum-dot heterostructure lasers. JSTQE, 6(3), p , 2000.
V. Klimov. Optical gain and stimulated emission in nanocrystal quantum dots. Science, 290, p
L. Parvesl et al. Optical gain in silicon nanocrystals. Nature, 408, p , 2000.
Optical nonlinearity
Du et al. Synthesis, characterization, and nonlinear optical properties of hybridized CdS-Polysterene nanocomposites. Chem. Mater., 14, p , 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 , 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, , 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), , 2002.
Yuan et al. Electrically driven single-photon source. Science, 295, p , 2002.
Solomon et al. Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity, Phys Rev Lett, 86(17), p , 2001.
Michler et al. A quantum dot single-photon turnstile device. Science, 290, p , Dec. 2000
A. Imamoglu et al. Quantum information processing using quantum dot spins and cavity QED. Phys Rev Lett., 83(20), p , 1999.