Steady-state currents in p-n junction filaments or grains in case of large surface recombination velocities at lateral surfaces

Recently it has been pointed out that the saturation current of a semiconductor filament which constitutes part of a p-n junction diverges when the surface recombination velocity at the faces become infinitely large. Here it is pointed out that this is to be expected on physical grounds since, whenever the carrier concentration is kept off equilibrium by an outside agent, and at the same time recombination lifetimes in the bulk or in surface layers tend to zero, concentration gradients tend to infinity. As also previously noted, the situation can be remedied by using realistic (finite) surface recombination velocities in model calculations. However, this procedure leads to mathematical complexities which have been circumvented recently by the introduction of a heuristic approach. It is the aim of this paper to assess the validity of the heuristic approach by means of detailed and exact calculations.