The ultimate efficiency of a threshold absorber,

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion

Energy from Physics, Ch How efficient a solar cell can be: detailed balance, tandems and the field

Problem

The ultimate efficiency of a threshold absorber, ηu(Eg)=EgΦ(Eg)/(f⊙σT4)\eta_{\rm u}(E_g) = E_g\Phi(E_g)/(f_\odot\sigma T^4), depends on the gap only through the reduced variable xg=Eg/kBTx_g = E_g/k_BT, and its maximum over xgx_g is ηu=0.44\eta_{\rm u} = 0.44 at xg=2.17x_g = 2.17, whatever the source temperature TT. ((a)) A red dwarf star radiates as a blackbody at T⋆=4000 KT_\star = 4000\,\mathrm{K}. Find the band gap EgE_g, in eV\mathrm{eV}, of the threshold absorber that maximises the ultimate efficiency of a single-threshold converter illuminated by this star. ((b)) State the value of the maximum ultimate efficiency itself, and explain in one sentence why it does not depend on T⋆T_\star.

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