Multi-scale Methods for Inverse Modeling in 1-D MOS Capacitor
Pingwen Zhang 1, Yi Sun 1, Haiyan Jiang 1, Wei Yao 21 School of Mathematical Sciences, Peking University, Beijing, 100871, People's Republic of China
2 China Predictive Technology Laboratory, DigitalDNA Lab.-China, Motorola (China) Electronics Ltd., Beijing,100022, China
In this paper, we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon (MOS) capacitor. First, the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problem is presented. Some matrix analysis tools are applied to explore the parameters' sensitivities. And third, the parameters are extracted using Levenberg-Marquardt optimization method. The essential difficulty arises from the effect of multi-scale physical difference of the parameters. We explore the relationship between the parameters' sensitivities and the sequence for optimization, which can seriously affect the final inverse modeling results. An optimal sequence can effivciently overcome the multi-scale problem of these parameters.Numerical experiments show the efficiency of the proposed methods.
Key words: Inverse problem; MOS capacitor model; Finite element method; Adaptive moving mesh; Levenberg-Marquardt method.