基於波茲曼-帕松方程之半導體電子傳輸數值模擬

Abstract

本文利用直接數值方法求解半古典的Boltzmann-BGK(Bhatnagar-Gross-Krook)方程與Poisson方程組成的系統以模擬電子在半導體裝置中的傳輸行為。數值方法方面，使用離散座標法(Discrete Ordinate Method)以及高解析算則如全變量消逝法(Total Variation Diminishing, TVD)和加權型基本不振盪(Weighted Essentially Non-Oscillatory, WENO)算則。算則將電子當作遵守Maxwell-Boltzmann統計以及Fermi-Dirac統計的粒子來模擬一維電子流動行為。本文使用不同的電子移動率(Mobility)假設來得到不同的鬆弛時間近似。最後再比較施加不同偏壓下的電子流動行為。

The electron transport in semiconductor devices is simulated by using direct algorithm for solving the semiclassical Boltzmann-BGK equation coupled with Poisson equation. The numerical method is based on the discrete ordinate method and high-resolution methods such as TVD (Total Variation Diminishing) method and WENO (Weighted Essentially Non-Oscillatory) method. The algorithm is implemented for solving one-dimensional electron flow that treats electron as particles obey the Maxwell-Boltzmann and Fermi-Dirac statistics. In this paper, using different mobility model to obtain different relaxation time approximation. Finally, simulating the electron flow under different voltage bias for comparison.