Finite mobility effects on the radiative efficiency limit ofpn-junction solar cells

Abstract

The maximum power conversion efficiency of a solar cell as defined by the Shockley-Queisser (SQ) radiative recombination limit relies on the assumption that the collection probability for all photogenerated electron/hole pairs is unity. This assumption implies a virtually infinite mobility ${\ensuremath{\mu}}_{\mathrm{n}}$ of the photogenerated charge carriers. In order to compute the radiative efficiency limit with finite mobilities, we solve the continuity equation for minority carrier transport including an additional photon recycling term that accounts for emission of photons by radiative recombination and their subsequent reabsorption. This approach quantitatively connects the SQ approach with the classical diode theory. Even when assuming radiative recombination as the only loss mechanism, the maximum efficiency achievable within our model is reduced drastically when ${\ensuremath{\mu}}_{\mathrm{n}}$ drops below a critical value. This critical value depends on the absorption coefficient, the doping density of the absorber material, as well as on the thickness and the light trapping scheme of the solar cell. Thus, these material and device parameters gain a fundamental importance as soon as finite carrier mobility is considered. Our theory yields a criterion that has to be fulfilled by any photovoltaic material in order to guarantee charge separation even in an otherwise most ideal case. Exemplary application of our model to three real photovoltaic materials, crystalline silicon $(c\text{\ensuremath{-}}\mathrm{Si})$, amorphous silicon $(a\text{\ensuremath{-}}\mathrm{Si}:\mathrm{H})$, as well as $\mathrm{Cu}(\mathrm{In},\mathrm{Ga}){\mathrm{Se}}_{2}$ (CIGS), shows that mobilities of $c\text{\ensuremath{-}}\mathrm{Si}$ and CIGS are three, respectively, 1 order of magnitude above this critical limit whereas the effective hole mobilities in $a\text{\ensuremath{-}}\mathrm{Si}:\mathrm{H}$ are scattered around the critical value. A comparison between solar cells and light-emitting diodes with finite mobility and finite nonradiative lifetime reveals that materials for these complementary devices have to fulfill different requirements.