基於波茲曼-帕松方程之半導體電子傳輸數值模擬

Direct Simulation of Electron Transport in Semiconductors Based on Boltzmann-Poisson Equation

勞冠豪(Kuan-Ho Lao)

指導教授 ： 楊照彥

國立臺灣大學/工學院/應用力學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.10929

摘要

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。

關鍵字

電子傳輸 ； 半古典Boltzmann-BGK方程 ； 離散座標法 ； 全變量消逝法 ； 加權型基本不振盪算則

並列摘要

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.

並列關鍵字

electron transport ； semiclassical Boltzmann-BGK equation ； discrete ordinate method ； TVD method ； WENO method

參考文獻

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