Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 1 / Section B / 12 / ii / Solution

The Shockley-Queisser limit is a radiative detailed-balance limit for a single-junction photovoltaic device under specified illumination and temperature. Its idealized absorber collects above-gap photons, thermalizes their excess energy and loses carriers only through the radiative processes required by absorptance and emission. Sub-gap photons are not harvested. A favorable gap balances current loss at large gap against voltage loss at small gap.^[ref]

For a step-like absorber,The dark radiative current decreases rapidly with gap, so the qualitative ordering for the supplied absorbers isThe curve rises beneath the diagonal $V=E_g/q$. The deficit $\Delta V=E_g/q-V_{\mathrm{OC}}^{\mathrm{rad}}$ reflects finite-temperature carrier statistics and the entropy associated with absorption and emission, including angular dilution of sunlight. Under ordinary unconcentrated illumination it is of order a few tenths of a volt, with a weaker gap dependence than $V_{\mathrm{OC}}$ itself. In a fixed blackbody-sun model its absolute value grows modestly with increasing gap, while its fraction of $E_g/q$ decreases. Above-gap thermalization is an efficiency loss but is not, by itself, the definition of this voltage deficit.

A measured perovskite device can have a larger deficit from nonradiative recombination and contact losses. The gaps alone do not determine those material-specific losses or a unique numerical voltage: solar spectrum, concentration, cell temperature and optical emission geometry must also be specified.