A heavily doped p-type silicon layer

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Earth, Climate & Energy Physics · Semiconductor physics and devices

Energy from Physics, Ch The illuminated junction: generation, collection and the cell's characteristic

Problem

A heavily doped p-type silicon layer, of the kind placed under a metal contact, has NA=1×1018 cm−3N_A = 1\times10^{18}\,\mathrm{cm^{-3}}. Use B=4.7×10−15 cm3 s−1B = 4.7\times10^{-15}\,\mathrm{cm^3\,s^{-1}} and Cp=9.9×10−32 cm6 s−1C_p = 9.9\times10^{-32}\,\mathrm{cm^6\,s^{-1}} at low injection; a defect level limits the lifetime independently to τdefect=0.5 μs\tau_{\rm defect} = 0.5\,\mu\mathrm{s}. ((a)) Find the radiative, Auger and combined minority-carrier lifetimes and the share of the total recombination rate that goes by the Auger route, stating which intrinsic route makes the largest non-defect contribution. ((b)) Find the doping above which Auger recombination is faster than radiative recombination. ((c)) Find the doping at which the Auger route alone would be as fast as this defect route.

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