New analytical expressions for dark current calculations of highly doped regions in semiconductor devices

We studied highly doped quasi-neutral regions of semiconductor devices with position dependent doping concentration in the absence of illumination. An important parameter of a highly doped region is its dark current. To clarify how the doping profile influences the dark current, simple analytical expressions are useful. To this end, we first transformed the transport equations to a simple dimensionless form. This enables us to write already existing analytical expressions in an elegant way. It is demonstrated how, from any analytical dark current expression, a direct counterpart can be derived. Next, we derived a dimensionless form for a nonlinear first-order differential equation for the effective recombination velocity. Starting from the analytical solution of this differential equation for uniformly doped regions and using linearization techniques, we obtained two new simple and accurate expressions for the dark current. The expressions are valid for general doping profiles with different minority carrier transparencies. The exact solution is included between both new approximate solutions. The new expressions are compared with previous approximate solutions.