Reflecting boundary conditions for graded p-n junctions

In a graded junction, the formalism for handling reflecting boundary conditions must be modified. Since a significant drift term is present, zero recombination velocity at the surface does not imply a zero excess carrier gradient but rather zero overall flux. A model for analyzing p-n junctions fabricated by implantation or diffusion is presented, assuming the dominant recombination mechanism in the graded region is Auger. The model enables optimization of diode design. By proper selection of parameters, mainly by reducing surface concentration or by increasing the steepness of the dopant profile, it is possible to drastically reduce the saturation current generated by the graded region.