A p-type silicon base has

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

Problem

A p-type silicon base has NA=1×1016 cm−3N_A = 1\times10^{16}\,\mathrm{cm^{-3}}, electron mobility μn=1350 cm2 V−1 s−1\mu_n = 1350\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and recombination lifetime τ=2 μs\tau = 2\,\mu\mathrm{s} at 300 K300\,\mathrm{K}. The wafer is 500 μm500\,\mu\mathrm{m} thick; treat the junction as lying at the front surface. Monochromatic 1000 nm1000\,\mathrm{nm} light, with absorption length 1/α=156 μm1/\alpha = 156\,\mu\mathrm{m} in silicon, enters with photon flux Φ0=1×1017 cm−2 s−1\Phi_0 = 1\times10^{17}\,\mathrm{cm^{-2}\,s^{-1}} just inside the front surface (reflection already excluded). ((a)) Find the electron diffusion coefficient DnD_n and diffusion length LnL_n, and check that the thick-base collection estimate fc(x)≈e−x/Lnf_c(x)\approx e^{-x/L_n} applies to this wafer. ((b)) Find the collection probability of a pair generated 20 μm20\,\mu\mathrm{m} from the junction and of one generated at one absorption length, 156 μm156\,\mu\mathrm{m}. ((c)) Treating the base as semi-infinite, show that the fraction of entering photons whose pairs are collected is αLn/(1+αLn)\alpha L_n/(1+\alpha L_n), and find this fraction and the collected current density.

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