Numerical modeling of highly doped Si:P emitters based on Fermi–Dirac statistics and self-consistent material parameters

We have established a simulation model for phosphorus-doped silicon emitters using Fermi–Dirac statistics. Our model is based on a set of independently measured material parameters and on quantum mechanical calculations. In contrast to commonly applied models, which use Boltzmann statistics and apparent band-gap narrowing data, we use Fermi–Dirac statistics and theoretically derived band shifts, and therefore we account for the degeneracy effects on a physically sounder basis. This leads to unprecedented consistency and precision even at very high dopant densities. We also derive the hole surface recombination velocity parameter $Spo$ by applying our model to a broad range of measurements of the emitter saturation current density. Despite small differences in oxide quality among various laboratories, $Spo$ generally increases for all of them in a very similar manner at high surface doping densities $Nsurf.$ Pyramidal texturing generally increases $Spo$ by a factor of five. The frequently used forming gas anneal lowers $Spo$ mainly in low-doped emitters, while an aluminum anneal (Al deposit followed by a heat cycle) lowers $Spo$ at all $Nsurf.$