6.973 Semiconductor OptoelectronicsLecture 17: Recombination Processes in SemiconductorsRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyOutline:•Analytic Gain Model• Bimolecular Recombination• Auger RecombinationConfinement FactorConfinement FactorSingle Mode Rate EquationsSingle Mode Rate EquationsOptical Gain in SemiconductorsOptical Gain in SemiconductorsDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineOptical Gain in SemiconductorsOptical Gain in SemiconductorsPeak gainDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineRecombination in SemiconductorsRecombination in SemiconductorsContinuity Equation:• Since recombination requires both electrons and holes,…where B is the bimolecular recombination coefficient• Thermal generation of carriers is independent of electron and hole concentration for small N and PApproximate Occupancy FunctionApproximate Occupancy FunctionBoltzmann Approximation (not valid when g(N) >0)…Bimolecular RecombinationBimolecular RecombinationSpontaneous EmissionSpontaneous EmissionSince the active region is charge neutral (intrinsic region of pin diode)…Optical Gain with Injection CurrentOptical Gain with Injection Current• steady-state• no optical input• neglecting amplified spontaneous emissionOptical Gain with Injection CurrentOptical Gain with Injection CurrentDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineRecombination in SemiconductorsRecombination in SemiconductorsIn fact, there are important processes that are not bimolecular…Recombination at defect sites:Auger recombination:Auger RecombinationAuger Recombination• Coulomb scattering resulting in an interband transition• Scattering potential for Fermi’s Golden RuleDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineCCCH Auger RecombinationCCCH Auger RecombinationDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineAuger RecombinationAuger RecombinationStates that satisfy energy & momentum conservation are deep within valence band for wide bandgap semiconductors…GaAs Eg=1.42 eVInGaAsP Eg=0.8 eVDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzineRecombination in SemiconductorsRecombination in SemiconductorsRecombination in SemiconductorsRecombination in Semiconductors•Radiative recombination efficiency decreases at high carrier densities (high currents)Single Mode Rate EquationsSingle Mode Rate EquationsOptical Gain with Injection CurrentOptical Gain with Injection CurrentDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W.
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