6.973 Semiconductor OptoelectronicsLecture 5: p-N HeterojunctionsRajeev J. RamElectrical EngineeringMassachusetts Institute of TechnologyReading:• Chuang, Chapter 2, Heterojunction DiodesOutline:• Minority Carrier Densities• Minority Carrier TransportHeterojunctionHeterojunctionDiodeDiodekinkVo= built-in potentialBand Diagram for DiodeBand Diagram for DiodeCalculation of depletion width:two equations and two unknownsMajority and Minority CarriersMajority and Minority CarriersEquilibrium VA=0Majority carriers:Minority carriers:Band Diagram for DiodeBand Diagram for DiodeNon-equilibrium VA=0No recombination in depletion regionMajority and Minority CarriersMajority and Minority CarriersNon-equilibrium VA=0Electrons injected from n-side into p-side:On p-side hole Fermi level (EFp) is approximately equal to EFo:Excess Carrier PopulationsExcess Carrier PopulationsForward Bias J=564 A/cmForward Bias J=564 A/cm2210010410610810101012101410161018-0.5 0 0.5 1 1.5 2 2.5Carrier Density (cm-3)Position (microns)-2 101602 10164 10166 10168 10161 10171.2 1017-0.5 0 0.5 1 1.5 22.5Carrier Density (cm-3)Positions (microns)log scalelinear scaleQuasiQuasi--equilibrium Transportequilibrium TransportContinuity Equation:Electrostatics with slowly varying potential:For small deviations from equilibrium, current will flow if the chemical potential is not constant:For now, µnis just some constant of proportionalityQuasiQuasi--equilibrium Transportequilibrium TransportRecombination in SemiconductorsRecombination in SemiconductorsContinuity Equation:• Since recombination requires both electrons and holes,…where B is the bimolecular recombination coefficientIn equilibrium:• Thermal generation of carriers is independent of electron and hole concentration for small N and PContinuity Equation:Recombination in SemiconductorsRecombination in SemiconductorsUnder bias (w/o illumination):Minority carrier continuity:Minority Carrier RecombinationMinority Carrier Recombinationsince minority carrier population is typically smallDrift-diffusion:Continuity equation:Minority Carrier RecombinationMinority Carrier RecombinationApproximations:• Effective mass approximationslowly varying potentials• Parabolic bandscarriers are near bandedges• 3-D density of statesthermal energy is larger than energy level spacing•Electrostatic potential can be incorporated within Ec(r)slowly varying potential• Drift-diffusion approximationBoltzmann statisticssmall perturbation from equilibrium• Weak excitationonly thermal generationgeneration rate is independent of carrier densityminority carrier drift is negligibleDiode LawDiode Law-2 101602 10164 10166 10168 10161 10171.2 1017-0.5 0 0.5 1 1.5 22.5Carrier Density (cm-3)Positions (microns)Minority Carrier Transport:P-side Boundary Condition:N-side Boundary Condition:Diode LawDiode Law-2 101602 10164 10166 10168 10161 10171.2 1017-0.5 0 0.5 1 1.5 22.5Carrier Density (cm-3)Positions (microns)P-side:N-side:Diode LawDiode LawNeglecting recombination in the active region…diffusionDiode Under IlluminationDiode Under Illuminationpp--typetypeGaAsGaAsNN--typetypeAlGaAsAlGaAslightDiode Under IlluminationDiode Under IlluminationContinuity Equation:Under bias (w/o illumination):Under bias (w/ illumination):P-side:N-side:Diode Under IlluminationDiode Under IlluminationDiode Under IlluminationDiode Under IlluminationdiffusionSimWindowsSimWindowsSoftwareSoftwareSelf-consistent solution of modifieddrift-diffusion & Poisson’s
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