Analysis of the depletion layer of exponentially graded P-N junctions withnonuniformly doped substrates

A detailed analysis of the depletion layer of exponentially graded p-n junc tions is presented, which improves previous efforts in this field in differ ent aspects. 1) We obtain analytical expressions for the depletion layer wi dths which are nearly as simple as those given by the widely used step and linearly graded junction models, but by far more accurate. In addition, we derive simple closed-form expressions for the punch;through and reach-throu gh voltages. 2) The analysis is extended to the case of substrates with non uniform doping profile, a case rarely treated in the literature, but of gre at importance for the design of many devices.