半導體元件物理中卜瓦松方程式的蒙地卡羅法解

Abstract

使用蒙地卡羅法解線性的卜瓦松方程式的正確性已由許多作者獲得驗證([3], [5], [6], [7], [8], [9])。然而對於一個二維度MOSFET的真實模型，是一個非線性卜瓦松方程式偕同 Dirichlet 和 Neumann 的邊界條件。在這篇論文裡，將介紹一個新的模擬演算法使用遞迴Fixed Random Walk Monte Carlo Method來解非線性的卜瓦松方程式。對於二維度的MOSFET半導體元件，一個典型的靜電學電位問題將被闡明。

The validity of solving linear Poisson's equation by Monte Carlo method has been justified by many authors ([3], [5], [6], [7], [8], [9]). However a realistic model for 2D MOSFET is a nonlinear Poisson's equation with both Dirichlet and Neumann boundary conditions. A new simulation algorithm is introduced in this thesis to solve nonlinear Poisson's equation adaptively by fixed random walk Monte Carlo method. A typical electrostatics potential problem for 2D MOSFET semiconductor device is illustrated.