A silicon cell has and at

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 silicon cell has Jsc=35 mA cm−2J_{sc}=35\,\mathrm{mA\,cm^{-2}} and J0=2×10−13 A cm−2J_0 = 2\times10^{-13}\,\mathrm{A\,cm^{-2}} at 300 K300\,\mathrm{K}, and carries a series resistance Rs=0.8 Ω cm2R_s = 0.8\,\Omega\,\mathrm{cm^2}. Its JscJ_{sc} does not change with temperature and its open-circuit voltage falls at dVoc/dT=−1.7 mV K−1\mathrm{d}V_{oc}/\mathrm{d}T = -1.7\,\mathrm{mV\,K^{-1}}, the silicon value. ((a)) Using Green's fit FF0≈[voc−ln⁡(voc+0.72)]/(voc+1)\mathrm{FF}_0 \approx [v_{oc}-\ln(v_{oc}+0.72)]/(v_{oc}+1) (with voc=eVoc/kBTv_{oc}=eV_{oc}/k_BT) and the series-resistance correction FF≈FF0(1−1.1rs)+rs2/5.4\mathrm{FF}\approx \mathrm{FF}_0(1-1.1r_s)+r_s^2/5.4, with rs=Rs/Rchr_s = R_s/R_{\rm ch} and Rch=Voc/JscR_{\rm ch}=V_{oc}/J_{sc}, predict the fill factor of this cell at 300 K300\,\mathrm{K}. ((b)) Predict whether the fractional fill-factor loss caused by the same fixed RsR_s becomes larger or smaller once the cell heats to 340 K340\,\mathrm{K}, and support your answer with a repeat of the calculation at 340 K340\,\mathrm{K}.

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