A colleague argues that a single-junction cell of gap

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

A colleague argues that a single-junction cell of gap Eg=1.10 eVE_g = 1.10\,\mathrm{eV}, illuminated by the blackbody Sun (T⊙=5772 KT_\odot = 5772\,\mathrm K, 1361 W m−21361\,\mathrm{W\,m^{-2}}) at cell temperature 300 K300\,\mathrm K, can reach η=40%\eta = 40\%: "The photon flux above 1.10 eV1.10\,\mathrm{eV} gives Jsc=52 mA cm−2J_{sc} = 52\,\mathrm{mA\,cm^{-2}}. Since no voltage above the gap is ever available, the most optimistic open-circuit voltage is the gap voltage itself, Voc=Eg/e=1.10 VV_{oc} = E_g/e = 1.10\,\mathrm V. Taking a fill factor of FF=0.95\mathrm{FF} = 0.95, typical of an ideal diode characteristic, the maximum power density is P=JscVoc FF=(0.052 A cm−2)(1.10 V)(0.95)=0.0544 W cm−2=544 W m−2,\begin{aligned} P &= J_{sc}V_{oc}\,\mathrm{FF} = (0.052\,\mathrm{A\,cm^{-2}})(1.10\,\mathrm V)(0.95) \\ &= 0.0544\,\mathrm{W\,cm^{-2}} = 544\,\mathrm{W\,m^{-2}}, \end{aligned} so η=544/1361=0.40\eta = 544/1361 = 0.40." ((a)) Identify every step above that is inconsistent with detailed balance, and say why. ((b)) Give a corrected estimate of the efficiency for this gap, and check it against the published maximum for the blackbody Sun.

Browse the problem library