Analysis of the depletion layer of exponentially graded p-n junctions with nonuniformly doped substrates

A detailed analysis of the depletion layer of exponentially graded p-n junctions is presented, which improves previous efforts in this field in different aspects. (1) We obtain analytical expressions for the depletion layer widths 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-through voltages. (2) The analysis is extended to the ease of substrates with nonuniform doping profiles, a case rarely treated in the literature, but of great importance for the design of many devices.