Szu-Ju Li

Computer‐aided evolution for solving the analytic Kronig‐Penny model

Abstract The Kronig‐Penney model consists of a periodic potential function, which is used to derive the concepts of allowed and forbidden energy bands. Here, to circumvent the tedious evolution, it is helpful to use computer methods to derive the textbook equation of the analytic Kronig‐Penney model. The hierarchical methodology with the shorter symbols can effectively reduce the complication in the expression of the 4 × 4 matrix. By defining the symbol sequence, we can easily reduce terms by cancellation. With these methods and computer‐aided evolution, we can derive the Kronig‐Penney model from the matrix expression to the textbook form without the extremely laborious evolution.

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

Abstract 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 Poissons 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.