The radiative recombination coefficient of silicon: reassesment of its charge carrier density dependence

It is well-known that the radiative recombination coefficient B
rad
of silicon decreases with increasing charge carrier densities, usually modelled via the scaling factor B
rel
parameterized by Altermatt et al. Additionally, photon recycling (PR) is effectively lowering the radiative recombination rate. This work aims to comprehensively reassess those influences on radiative recombination. Firstly, it is clarified that Altermatt’s parameterization of B
rel
is largely dominated by the effect of band-gap narrowing (BGN) on the intrinsic charge carrier density, and that a change of the band-to-band absorption coefficient is not observable. Next, a photon-reabsorption model is suggested, which accounts for free-carrier absorption (FCA) and can predict PR and luminescence intensity. The model is shown to be useful in improving the interpretation of very high lifetime measurements, in particular towards an improved quantification of Auger recombination. Furthermore, it is found that FCA may have a significant influence on photon reabsorption beyond charge carrier densities of 10
¹⁶
cm
^-3
for relatively thick samples, in particular affecting luminescence. This means that the assumption of direct proportionality between luminescence intensity and radiative recombination, which is fundamental to most luminescence-based measurement techniques, may fail for such conditions, but can be corrected using this work’s model.