2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 1EE 235/NSE 203Lec. 11-12• Recap: Density of states for bulk, QW, QWires and QD• Bulk – 3D• Quantum Well – 2D • Quantum Wires – 1D• Quantum Dot – 0D – Quantum Dots• Stranski-Krastanow Self-Assembled QDs• Colloidal QDs2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 2Density of States1975 : R.Dingle and C.HenryUSA Patent Application1982 : Y.Arakawa and H.Sakaki, Appl. Phys. Lett.,2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 3Fermi-Dirac DistributionElectrons in thermal equilibrium distribute themselves according to the Fermi-Dirac distribution, i.e., the probability fe(E,T) of finding an electron in a state of energy E at a temperature T is given bykBT ~ 26.5 meVµ is Fermi energykBis Boltzmann’s constant.Fermi-Dirac distribution for holes2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 4Electron Energy Distributionn(E) is the product of • the number of electron states per volume per unit energy, g(E), also know as the Density of States• and the probability of the states being filled, f(E,T), also know as the Fermi-Dirac distributionHence, the total number of electrons per volume in the system, N, isThe electron density, n(E), defined as number of electronisper unit volume per unit energy interval is,For bulk material (or lack of quantum confinement), the density of states2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 5Electron Energy Distribution- 2The number of electrons, n(E), per unit energy interval is,X =2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 63-, 2-, 1-, and 0- dimensional SystemsImpact of Inhomog. broadeningThermal populationDimensionalitydensity of statesEnergy2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 7Classification of Band AlignmentsTYPE ITYPE II ATYPE II BBAAB(Staggered)(Misaligned)AgAE∆E >0∆E >0∆E >0gAEEgA∆E >0∆E <0∆E <0v gA∆E >Ev∆Ec>0∆Ev>0∆Ev<02007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 8Absorption in SemiconductorAssuming is indepent of k; Fv=1 and fc=0 Æ Efc=Efv=Efmris effective reduced mass2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 9Loss in Semiconductor2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 10Gain in Semicond.2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 11Gain in QWsThe density of states as a function of energy E for electron (or heavy hole or light hole) in a quantum well can be described as the sum of a series of step functions, each having equal quantity and representing the onset of each subband.Given the conduction band (or valence band) Fermi level, the total number of carriers can be found. Typically, however, we are given the reverse. We try to find the Fermi level for a given carrier concentration. For most situations, we can assume the number of electrons and holes (both heavy and light) are equal. Also, we assume there is ONE valence band Fermi level.2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 12QW Gain spectra2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 13Threshold Current Densitiesof Semiconductor Lasersafter Ledentsov et al., IEEE J. Sel. Top. Quantum El. 6, 439 (2000)Threshold Current Density (A/cm²)2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 14Some facts of QD laser technology development• 1985 Observation of InGaAs clusters in GaAsL. Goldstein, et al, Appl. Phys. Lett. 47(10), 1985 “Growth by molecular beam epitaxy and characterization of InAs/GaAs strained-layer superlattices”,.• 1993 Bright PL intensity from such clustersD. Leonard et al Appl. Phys. Lett. 63(23), 1993• 1994 First lasing with QD active mediumA.Yu.Egorov et al, Semiconductor 28, 1994N.Kirstaedter et al, Electron. Lett. 30, 1994• 1998 1.3 µm QD laser (Atomic Layer Epitaxy)D.L.Huffaker et al, Appl. Phys. Lett. 73(18), 1998• 1999 1.3 µm QD laser (Quantum dots in Quantum Well or DWELLTM)L.F.Lester et al Photon. Technol. Lett. 11(8), 1999A.R.Kovsh et al, Semiconductor, 1999 / Zhukov et al, Appl.Phys.Lett. 75, 1999Quantum Dot start-ups• 2001 ZIA Lasers Ltd, Albuquerque, New Mexico, USA (22 mln USD pumped in) – team from University of New Mexico (Profs.Lester and Malloy)• 2003 NL Nanosemiconductot GmbH (5 mln Euro pumped in) – team from Ioffe Inst. (Prof.Ledentsov)Most cited paper in EL !!!1.3 µm as a driving force for GaAs OE R&D2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 15MBE technology Pump(ion-, cryo-, turbo-, sublimate-, diffuse-)e-gunHEED screenSubstrateholderShuttersEffusion cellsIon gauge Cryo-shirtsVacuum (1e-10 Tr) is better than in between Earth and MarsD= 1``3``3x2`` or 4``4x8`` or 7x6`` or 15x4``1984198019912000Capacity of a reactor2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 162007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 172007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 18Reflection High Energy Electron DiffractionA high energy beam (5-100keV) is directed at the sample surface at a grazing angle. The electrons are diffracted by the crystal structure of the sample and then impinge on a phosphor screen mounted opposite to the electron gun. The resulting pattern is aseries of streaks. The distance between the streaks being an indication of the surface lattice unit cell size.2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 192007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 202007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 21In-situ control by high energy electron diffraction during MBE process2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 22Energy minimization as a driving force2007/3/7 EE 235/NSE203 Nanoscale Fabrication; Lec. 11; Prof. Chang-Hasnain 23Growth, lithography, etching (and regrowth)Growth on high index surfacesGrowth on prepatternedsubstratesStranski-KrastanovgrowthStrain induced lateral confinementFabrication of Nanostructures: Change of Technology ParadigmComplex serial e-beam patterning => massively parallel self-organizationImperial Academy of Sciences, Vienna 19382007/3/7 EE
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