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 $S_{\mathrm{po}}$ 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, $S_{\mathrm{po}}$ generally increases for all of them in a very similar manner at high surface doping densities $N_{\mathrm{surf}}.$ Pyramidal texturing generally increases $S_{\mathrm{po}}$ by a factor of five. The frequently used forming gas anneal lowers $S_{\mathrm{po}}$ mainly in low-doped emitters, while an aluminum anneal (Al deposit followed by a heat cycle) lowers $S_{\mathrm{po}}$ at all $N_{\mathrm{surf}}.$

A mathematical model is developed that is based on a coupled system of partial differential equations. The model contains a dynamic and two-phase description of the proton exchange membrane fuel cell (PEMFC) and a membrane model that accounts for Schroeder's paradox. The mass transport in the gas phase and in the liquid phase is considered as well as the phase transition between liquid water and water vapor. The transport of charges and the electrochemical reactions are part of the model. A potential sweep experiment is simulated using the mathematical model and measured using a test cell with an active area of 1 cm(2). In this way, the dynamic effect of liquid water formation and transport on the current-voltage characteristic of the fuel cell is investigated. A hysteresis effect is found in the measured time-dependent current-voltage relation. The limiting current density is time-dependent. Qualitative agreement of simulated and measured results is achieved. An analysis of the observed hysteresis of the current-voltage characteristics, based on the modeling results, is given. (c) 2005 The Electrochemical Society