6.973 Semiconductor OptoelectronicsLecture 32: Optimizing Quantum WellsRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyOutline:• Mathews-Blakeslee Critical Thickness• Quantum Well Thickness• Quantum Well DepthHeterostructureHeterostructureMaterialsMaterialsundoped8x1017P- dopedn-doped8x1017InP substrateInP ridgeelectronsholesMinimum of 3 materials for good optical and electrical confinementMinimum:Quantum wellQW barrierWaveguide claddingTypical:Quantum wellQW barrierWaveguide core (SCH)Waveguide claddingElectrical contact layeroptical modeHeteroepitaxyHeteroepitaxyEnergy of a Strained LayerEnergy of a Strained LayerEnergy of a Strained Layer with DislocationsEnergy of a Strained Layer with DislocationsAdding dislocations helps relieve the strain in the layer…higher density of dislocations smaller d more strain reliefEnergy of a Strained Layer with DislocationsEnergy of a Strained Layer with DislocationsBut the dislocations have local strain as well…dislocationslayertotaldislocationslayertotalNo dislocationsDislocationsCritical ThicknessCritical Thicknesshttp://www.ioffe.rssi.ru/SVA/NSM/Semicond/The necessary material parameters can be found at…Solve for h wherehc vs. |ε//|solid lines: ε<0: a*=0.15ε>0: a*=0.05ε//=- 4 % -sudden appearance of dislocations at a film thickness hcexperimental results (semiconductors): misfit-dependencehc = a*|ε//|-3/2Critical ThicknessCritical Thicknesshttp://theorie.physik.uni-wuerzburg.de/~much/dislocations.htmlThreading dislocation turns into a strain relieving misfit dislocationUsually Dislocations are not SpontaneousUsually Dislocations are not SpontaneousMultilayer Strained LayersMultilayer Strained Layersundoped8x1017P- dopedn-doped8x1017InP substrateInP ridgeelectronsholesoptical modeFor a single layer…For a multilayer structure…InP850 nm980 nm1300 nm1550 nm655 nmMaterials SelectionMaterials SelectionStrain CompensationStrain CompensationG. Zhang, et al. Applied Physics Letters (1993) electronsholesActive: InGaAs (compressive)Substrate: GaAsBarrier: GaAs (unstrained)vsGaAsP (tensile strained)5 QWOptimal Quantum WellsOptimal Quantum WellsEcEfcEvEc∆Ev∆EfvE21EcEfcEvEc∆Ev∆EfvE21Reduce thickness of quantum well to • decrease number of subbands• increase subband spacingOptimal Quantum WellsOptimal Quantum WellsEcEfcEvEc∆Ev∆EfvE21However, thin quantum wells to • reduced confinement and larger carrier population in barrier• reduced overlap between electron and hole envelope wavefunctionsEcEfcEvEc∆Ev∆EfvE21Silver & O’Reilly, IEEE JQE, July 1995InGaAsPInGaAsPMaterialsMaterials• This diagram is different from before since it accounts for the distortion on the bands introduced by strainEcIn0.53Ga0.47AsEfcEvEc∆Ev∆EfvEg= 750 meVE21• When Lqw= 9.6 nm, then E21= 800 meV• Thinner wells require compressively strained quantum wellsInGaAsInGaAsQuantum Well at 1550 nmQuantum Well at 1550 nmLin & Lo, IEEE PTL, March 1993Strained Strained InGaAsInGaAsQuantum Wells at 1550 nmQuantum Wells at 1550 nm• Thin wells have larger quantum confined blue shift so ‘bulk’ bandgap needs to be reducedHH1HH2HH1HH2HH3LH1Lattice Matched (9 nm)1.5% Compressive (2.8 nm)Lattice Matched (9 nm)1.5% Compressive (2.8 nm)Strained Strained InGaAsInGaAsQuantum Wells at 1550 nmQuantum Wells at 1550 nmDensity of StatesEnergy• Thin wells have fewer subbands, lighter effective masses and lower DOSJth per well [mA/cm2]Strain0% 1%Lattice Matched (9 nm)1.5% Compressive (2.8 nm)Yokoyama & Seki, IEEE, 1996Strained Strained InGaAsInGaAsQuantum Wells at 1550 nmQuantum Wells at 1550 nmExperimentsExperiments101010111012100500Quantum Well OptimizationQuantum Well OptimizationInGaAsInGaAson on GaAsGaAs• Optimal quantum well has near E21~ 980 nmOptimal Quantum Well DepthOptimal Quantum Well DepthEcEfcEvEc∆Ev∆EfvE21EcEfcEvEfvE21Deep well Shallow wellDeeper wells have • better wavefunction confinement• smaller carrier density in barriers• higher leakage currents• slow transport between wellsEcEfcEvEc∆Ev∆EfvE21•For E21= 800 meV, largest confinement is InP at 1350 meV(InGaAsP)Quantum Wells at 1550 nmQuantum Wells at 1550 nm• Most designs ‘split the difference’ with 1100 meV