Prof. Weiying Zheng, (ICMSEC, AMSS)

A positivity-preserving stabilized finite element method for quantum drift-diffusion model

2021 年 11 月 25 日（周四） 下午 16:00-17:00 腾讯会议（ID：605 4978 9293） 会议链接： https://meeting.tencent.com/dm/qw8QMyFVg88p

As the size of modern semiconductor devices goes to sub-nanometers, quantum mechanical phenomena become prominent and must be considered in numerical simulations. In 1989, Ancona and Iafrate derived a macroscopic model, called quantum drift-diffusion (QDD) model, which generalizes the classical DD model by incorporating a quantum correction to the electric potential. We derive an equivalent QDD model by expressing carrier densities with potential functions. The finite element method for the new model is positivity-preserving in the sense that discrete carrier densities are always positive. We propose a modified Newton iterative method to solve the nonlinear discrete problem. Numerical experiments for a FinFet device show that the iterative method is convergent for the source-drain bias voltage up to 15V and the source-gate bias voltage up to 5V. 

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