6.973 Semiconductor OptoelectronicsLecture 16: Carrier Density Rate EquationRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyOutline:• Relating Emission Rates to Gain• Population Inversion Factor• Current InjectionNet Optical Gain in SemiconductorsNet Optical Gain in SemiconductorsDiode Lasers and Photonic Integrated CircuitsL. A. Coldren, S. W. CorzinePopulation Inversion in SemiconductorsPopulation Inversion in SemiconductorsPopulation inversion:Applied voltage is equal to Fermi level separation…Bands At Population InversionBands At Population Inversion0 1 2 3 4-2.2-2-1.8-1.6-1.4-1.2-1-0.8E (eV)Position (µm)pi nSingle Mode Rate EquationsSingle Mode Rate EquationsFor emission and absorption into one mode (one color, polarization, direction), all the rate constants are the same…Optical GainOptical GainUnderfilled: beam smaller than gain mcdium…gainSingle Mode Rate EquationsSingle Mode Rate EquationsgainPopulation Inversion FactorPopulation Inversion FactorConfinement FactorConfinement FactorgainCurrent InjectionCurrent InjectionJnJp11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5050100150200250300350400Position (um)Current (A/cm2)hole currentelectroncurrentCarrier Density Rate EquationCarrier Density Rate EquationSingle ModeSingle ModePhoton Density Rate EquationPhoton Density Rate EquationSingle Mode Rate EquationsSingle Mode Rate EquationsSemiconductor Optical AmplifiersSemiconductor Optical AmplifiersPhoton density & carrier density are not uniform along the length of the deviceRate Equations for AmplifiersRate Equations for AmplifiersWrite down carrier density and photon density rate equationat every point in space ( j )….Rate Equations for AmplifiersRate Equations for AmplifiersRate Equations for AmplifiersRate Equations for AmplifiersOO in-silicon, wg detect, electro-opticAM/AK ingaasn, soa, electro-opticKL/MM organic, si vs gaas, ingaasnSG/CD soa, in-si,
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