Log-scale method with equivalent circuit model in semiconductor device simulations

Semiconductor device simulations sometimes have to solve for large-scale and small-scale variables at the same time, especially with density-gradient models and hydrodynamic models. The usual way is to use the scaling factors, but scaled variables are still not of the same order of magnitude. We propose a log-scale method to make all variables of similar orders without scaling factors. All variables in similar orders of magnitude will help Newton-Raphson iterations to easily converge in device simulations. We use the divergence theorem of Gauss to discretize Poisson's and continuity equations, using the element-by-element method and develop an equivalent circuit model. The electron and hole concentrations are presented for a diode and an MOS capacitor by using the log-scale method and the equivalent circuit model. The numerical results show the great capability of the equivalent circuit model with log-scale method.