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Conditioning of the Quantum-Corrected Energy Transport Model Part I: Theorey

By 蔡宗穎


[[abstract]]這量子校正能量運輸模型是由波松、密度梯度、電子電洞連續方程和能量傳遞等方程式所構成的,並且使用Gummel方法來個別討論這七條偏微分方程系統。我們透過線性化後的Jacobian矩陣去進一步分析這七條方程式個別的條件作用。而在本論文當中,我們也證明出漂流擴散和能量傳遞方程式在透過等比例的行或列縮放會出現好的條件作用,而密度梯度方程則會在等比例縮放前就已經是擁有好條件作用的方程組。 The quantum-corrected energy transport (QCET) model consists of Poisson, density gradient (DG), electron-hole current continuity and energy transport (ET) equations. The Gummel method leads to a decoupled system of seven nonlinear PDEs. We study the Jacobian matrices of the linearlized equations. We then give a thorough conditioning analysis for each one of these seven PDEs. We proved the drift-diffusion (DD) and ET equations are well-conditioned by proper row and column scalings, and DG equations are well-conditioned without scaling

Topics: 條件作用, 量子校正能量運輸模型, [[classification]]14
Year: 2012
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