Radiative recombination in silicon photovoltaics: Modeling the influence of charge carrier densities and photon recycling

In order to push silicon solar cell efficiencies further towards their limit, as well as to ensure accuracy of luminescence based characterization techniques, an accurate modeling of radiative recombination is important. It is well-known that the radiative recombination coefficient Brad of silicon shows a substantial charge carrier density dependence (c-dependence), often modelled via the scaling factor Brel quantified by Altermatt et al. Another effect lowering the total radiative recombination is photon recycling (PR), which depends mainly on the width and optical properties of the sample. PR also depends on free-carrier absorption (FCA), which introduces a further c-dependence. This work comprehensively reassesses and quantifies those influences on radiative recombination in silicon for photovoltaic (PV) applications. Firstly, it is evidenced that Altermatt's Brel model is dominated by the effect of band-gap narrowing (BGN). This clarifies that it should not be combined with a different BGN model to avoid modeling inconsistencies. It is thereby further confirmed that the band-to-band absorption coefficient of silicon does not show a relevant c-dependence for PV conditions. Next, a PR model is suggested which calculates a scaling factor Brel,PR. The model is proven useful in improving the interpretation of very high lifetime measurements. Finally, it is found that the c-dependence introduced by FCA affects the direct proportionality between luminescence signal and radiative recombination beyond charge carrier densities of 1016 cm−3 for samples thicker than typical wafer widths, and should then be considered in characterization techniques like e.g. calibrated lifetime measurements via photoluminescence.