NNSE 618 Lecture #20 2 First we will use Shockley approximation: •Drift-diffusion current •Abrupt depletion layer approximation •Non-degenerate = Boltzman statistics •Low injection = Fermi level do not change in the depletion layer = minority carrier densities << majority carrier densities = majority carrier density equals to doping concentration •No generation/recombination in the depletion layer Let’ apply bias and calculate current through the p-n junction Currents in p-n junction From Sze, 1981
NNSE 618 Lecture #20 3 Currents through p-n junction: Shockley model Minority carrier current Majority carrier current Total current is constant throughout the device Recombination region Recombination region
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NNSE 618 Lecture #20 4 Definitions of quasi-Fermi levels: Potential across the junction: Currents in p-n junction: Shockley theory Minority carrier concentrations at the edges of the depletion region (will serve as boundary conditions): From Sze, 1981 taVVaippeNnxn2)(aiVqtaVVdinneNnxp2)(kTEENkTEEnncFnciFniexpexpkTEENkTEEnpFpvvFpiiexpexpFnFpaEEqV