6.973 Semiconductor OptoelectronicsLecture 10: Absorption in SemiconductorsRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyReading: Chapter 9, ChuangChapter 4, C&COutline:• Review of Density of States• Reduced Density of States• Absorption Coefficient• Quick Look at Indirect Bandgap AbsorbersDensityDensity--ofof--StatesStatesis the volume of k-space that satisfiesDensityDensity--ofof--StatesStatesProofProofEngineering Material AbsorptionEngineering Material AbsorptionOverview of Absorption CalculationOverview of Absorption CalculationScattering rate from kto k ’photonStep 1: Determine Scattering PotentialStep 2: Calculate Matrix ElementsStep 3: Calculate State-State Transition RatesStep 4: Calculate State LifetimeEnergy and Crystal Momentum ConservationEnergy and Crystal Momentum ConservationScattering rate from kto k ’Momentum (crystal momentum) is conserved…Energy is conserved…Momentum ConservationMomentum ConservationMomentum of (thermalized) electron:Momentum of photon:Electron momentum is relatively unchanged…Momentum and Energy ConservationMomentum and Energy ConservationCombining the conditions for energy and momentum conservation…is called the reduced massMomentum and Energy ConservationMomentum and Energy ConservationFor a given photon energy, only narrow band of states contribute to absorption.ElectronElectron--Photon Scattering TimePhoton Scattering TimePhotons only interact with a small set of k states…ElectronElectron--Photon Scattering TimePhoton Scattering TimeNote: the reduced density of states differs from our ususal density of states by a factor of 2 since the electron doesn’t scatter into both spin states necessarilyAbsorption CoefficientAbsorption Coefficient# of photons absorbed per unit time per unit volume# of photons incident per unit time per unit areaWhere the intensity is the magnitude of the Poynting vector…Light Intensity and Vector PotentialLight Intensity and Vector PotentialAbsorption CoefficientAbsorption CoefficientIndependent of light intensity…think of it as a property of the solid.Engineering Material AbsorptionEngineering Material AbsorptionAbsorption CoefficientAbsorption CoefficienttheoryexperimentWhat About Silicon ?What About Silicon ?In indirect bandgap semiconductors, we can’t conserve momentum and energy simultaneously…So, …first-order perturbation theory fails ! Need to look at higher order terms…Silicon and Germanium AbsorptionSilicon and Germanium Absorptionlog αWavelength [µm]0.81.01.21.4SiGe1.61.80.6Absorption for Indirect SemiconductorsAbsorption for Indirect Semiconductorslog α0.81.01.21.4SiGe1.61.80.6Wavelength
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