Solar Cell: I-V, Fill Factor and the Shockley-Queisser Limit

An interactive single-diode solar cell with the Shockley-Queisser detailed-balance limit. The ideal model $I(V) = I_L - I_0[\exp(V/(n V_T)) - 1]$ gives $I_{sc} = I_L$ at $V = 0$ and $V_{oc} = n V_T \ln(I_L/I_0 + 1)$ at $I = 0$; the power $P = V I$ peaks at the maximum-power point, with fill factor $\mathrm{FF} = V_{mp} I_{mp}/(V_{oc} I_{sc})$ and efficiency $\eta = P_{mpp}/P_{in}$. Panel A draws the $I$-$V$ and $P$-$V$ curves with $I_{sc}$, $V_{oc}$, the maximum-power point and the fill-factor rectangle for a realistic cell (a typical sub-gap voltage deficit from non-radiative recombination, so the knee is visible); a load point sweeps from short circuit to open circuit. Panel B rains photons above the gap onto the cell, generating electron-hole pairs and the photocurrent. Panel C is the radiative detailed-balance Shockley-Queisser efficiency versus bandgap (a blackbody sun diluted to the chosen incident power, recombination from the cell 300 K blackbody), peaking near 30% at about 1.3 eV, with the realistic cell efficiency shown below the limit. The short-circuit current, the open-circuit voltage capped below the bandgap, the maximum-power point, and the Shockley-Queisser efficiency peak near 1.3 eV are the physical content.