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

Abstract

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 surfacedoping 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 aluminumanneal(Al deposit followed by a heat cycle) lowers Spo at all Nsurf.