Saturation current and excess carrier distribution in exponentially graded p-n junctions

Excess carrier distribution and saturation current generated by a graded p-n junction are investigated, approximating the dopant profile by an exponential function. Analytical solutions of the steady-state continuity equation are presented for lifetime dominated by Auger, radiative, or Shockley-Read recombination mechanisms, for both ohmic and electrically reflecting boundary conditions. The saturation current generated by the graded region is derived for each of the dominant mechanisms and boundary conditions. Unlike previous published works the result of this analysis is a set of concise analytical expressions that make them a useful tool for simulation and investigation of graded structures such as silicon solar cells. The results are calculated for HgCdTe diodes, demonstrating the effect of the profile slope as determined by surface and bulk concentrations and junction depth. It is shown that the contribution of the graded region to the saturation current, as compared to that of the substrate, is significant, and that by proper selection of the diode parameters it is possible to substantially reduce this contribution.