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Transcript of Quantum Dots
OutlineIntroduction Some basic physicsFabrication methodsApplicationsLasersOptical nonlinearityQuantum opticsFuture outlook
IntroductionQuantum dots (QD) a.k.a. quantum boxes and artificial atoms Discrete energy levelsFocus on optical properties of quantum dotsBut interesting electronic transport properties also!Technological impact Interesting science
Some Basic PhysicsDensity of states (DoS)
e.g. in 3D:
Discrete StatesQuantum confinement discrete statesEnergy levels from solutions to Schrodinger EquationSchrodinger equation:
For 1D infinite potential well
If confinement in only 1D (x), in the other 2 directions energy continuum
In 3DFor 3D infinite potential boxes
Simple treatment considered herePotential barrier is not an infinite boxSpherical confinement, harmonic oscillator (quadratic) potentialOnly a single electronMulti-particle treatmentElectrons and holes Effective mass mismatch at boundary (boundary conditions?)
Optical ExcitationExciton: bound electron-hole pair (EHP)Excite semiconductor creation of EHPThere is an attractive potential between electron and holemh* > me * hydrogenic syetemBinding energy determined from Bohr Theory
In QDs, excitons generated inside the dotThe excitons confined to the dotDegree of confinement determined by dot sizeDiscrete energiesExciton absorption d function-like peaks in absorption
Size MattersSmall enough to see quantum effectA free electron:3/2kBT = 2k2/2ml ~ 60 at 300KFor quantum effects: ~10s In semiconductors, use me* (effective mass) instead:me */me ~ 1/10For quantum effects: 100s (10s nm)Number of atoms ~ 103 - 106Small L larger energy level separationProperties determined by size of QDEnergy levels must be sufficiently separated to remain distinguishable under broadening (e.g. thermal)
Fabrication MethodsGoal: to engineer potential energy barriers to confine electrons in 3 dimensions
3 primary methodsLithographyColloidal chemistryEpitaxy
LithographyEtch pillars in quantum well heterostructures Quantum well heterostructures give 1D confinementMismatch of bandgaps potential energy wellPillars provide confinement in the other 2 dimensionsElectron beam lithographyDisadvantages: Slow, contamination, low density, defect formationA. Scherer and H.G. Craighead. Fabrication of small laterally patterned multiple quantum wells. Appl. Phys. Lett., Nov 1986.
Colloidal ParticlesEngineer 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 structuresTypically group II-VI materials (e.g. CdS, CdSe)Size variations ( size dispersion)Evident Technologies: http://www.evidenttech.com/products/core_shell_evidots/overview.phpSample 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 GrowthGrowth on patterned substrates Grow QDs in pyramid-shaped recessesRecesses formed by selective ion etchingDisadvantage: density of QDs limited by mask patternT. 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 GrowthSelf-organized QDs through epitaxial growth strainsStranski-Krastanov growth mode (use MBE, MOCVD)Islands formed on wetting layer due to lattice mismatch (size ~10s nm)Disadvantage: size and shape fluctuations, orderingControl island initiation Induce local strain, grow on dislocation, vary growth conditions, combine with patterningAFM 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.
QD LasersAdvantagesMore efficient, higher material gain, lower thresholdConcentration of carriers near band edge Less thermal dependence, spectral broadeningMaterial gain Theoretical prediction:G=104 cm-1, Jth=5A/cm2 at RTCompared to bulk InGaAsP:N~1018, G~102 cm-1Ledenstov et al. Quantum-dot heterostructure lasers. JSTQE, May 2000.
QD Heterostructure LasersStack QD vertically to increase density of QD (~10 layers)Carrier escape at high THigher modal gain (shape of mode x bulk gain)III-V based structuresInAs-(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 CWInGaN QDs in GaN (RT): Jth ~ 1 kA/cm2
Excitons and Nonlinear OpticsExcitons enhance nonlinearity of materials at resonancesQuantum confinementDiscrete energy levels concentrate oscillator strength to lowest level transitionsOscillator Strength depends onRelative motion of the electron and holeNumber of electron and hole pairsLarger dotWeak confinement, electron-hole more correlated, more nonlinearityHigher states have smaller fx, the oscillator strength eventually saturates
Nonlinear OpticsEmbed QDs (e.g. CdS, CdSe) in polymer (typically) host material to increase (3)
Device applications: optical switches, wavelength conversion
Bulk PS: linearHigher orders of nonlinearity present
n = n0 + (n2+n4I)I
Quantum OpticsQuantum mechanical system in solid-state!Cavity QED: Modified spontaneous emission Spontaneous emission lifetime not intrinsic to atom but to coupling of atom & vacuumCavity modifies DoS of vacuumCouple QD to cavityChange in lifetime of spontaneous emission From 1.3 ns (no cavity) to 280 ps
Solid line = PL spectrumDashed line = SE lifetime
Single Photon SourcesSingle photon emission through recombination of a single excitonVerified by studying g(2)(), the 2nd order coherence functionObserved photon-anti-bunching (quantum state of light)Optically pumped single photon sourceQDs in high Q microcavity at low T (~5K)Lifetime of single exciton state shorter than lifetimes of the other statesPotential 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 640nm) 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 (370nm) 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 oscillationsPhoton statisticsCollapse and revivals of population inversion in exiton and biexiton states
Future OutlookDevelopment of QD lasers at communication wavelengthsGain and stimulated emission from QDs in polymersPolymeric optoelectronic devices?Probe fundamental physicsQuantum computing schemes (exciton states as qubits)Basis for solid-state quantum computing?Biological applicationsMaterial engineeringHow to make QDs cheaply and easily with good control?Lots to do!
SummaryDiscrete energy levels, artificial atomFabrication: top-down, bottom-up approachesLithography, colloidal chemistry, epitaxyMaking better lasersEnhancing optical nonlinear effectsQuantum optics
Lots of room for further research!
ReferencesBooksY. 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.GeneralP. 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. FabricationT. 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)LasersY. Arakawa. Progress in GaN-based quantum dots for optoelectronics applications. JSTQE, 8(4), p. 823-832, 2002.N. Ledens