Assessment and parameterisation of Coulomb-enhanced Auger recombination coefficients in lowly injected crystalline silicon

In traditional band-to-band Auger recombination theory, the low-injection carrier lifetime is an inverse quadratic function of the doping density. However, for doping densities below about $3×1018$ $cm−3$⁠, the low-injection Auger lifetimes measured in the past on silicon were significantly smaller than predicted by this theory. Recently, a new theory has been developed [A. Hangleiter and R. Häcker, Phys. Rev. Lett. 65, 215 (1990)] that attributes these deviations to Coulombic interactions between mobile charge carriers. This theory has been supported experimentally to a high degree of accuracy in n-type silicon; however, no satisfactory support for it has been found in p-type silicon for doping densities below $3×1017$ $cm−3$⁠. In this work, we investigate the most recent lifetime measurements of crystalline silicon and support experimentally the Coulomb-enhanced Auger theory in p-type silicon in the doping range down to $1×1016$ $cm−3$⁠. Based on the experimental data, we present an empirical parameterisation of the low-injection Auger lifetime. This parameterisation is valid in n- and p-type silicon with arbitrary doping concentrations and for temperatures between 70 and 400 K. We implement this parameterisation into a numerical device simulator to demonstrate how the new Auger limit influences the open-circuit voltage capability of silicon solar cells. Further, we briefly discuss why the Auger recombination rates are less enhanced under high-injection conditions than under low-injection conditions.