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研究生:蔡炘澤
研究生(外文):Hsin-Tse Tsai
論文名稱:QCET 模型的最大長度之期後誤差估計 第三部份:1D 與2D 模擬
論文名稱(外文):Maximum Norm A Posteriori Error Estimate for the Quantum-Corrected Energy Transport Model Part III: 1D and 2D Simulations
指導教授:劉晉良劉晉良引用關係
指導教授(外文):Jinn-Liang Liu
學位類別:碩士
校院名稱:國立新竹教育大學
系所名稱:應用數學系碩士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:58
中文關鍵詞:量子校正的能量運輸模型半導體期後誤差估計誤差指標適應性加切
外文關鍵詞:quantum-corrected energy transport modelQCETsemiconductorposteriori error estimateerror indicatorthe final adaptive mesh
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  • 下載下載:22
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此量子校正的能量運輸模型是由七條自身伴隨的非線性的偏微分方
程式所組成,它所探討的是奈米導體裝置中,電子流和電洞流的穩定性,能量轉換的穩定性,再加上古典電位能和量子電位能的穩定性。我們引用Kopteva [14] 二維空間期後誤差估計的方法在無因次的量子校正的能量運輸模型上,這個誤差估計的方法能幫助我們在網格點適應性加切時,能當作為誤差指標。對於QCET偏微分方程模型,我們在一維二極管模型問題的期後誤差估計數值試驗,已經取得七個很好的誤差指標。根據一維模型數據經驗,在二維模型中加入七個條方程式做為網格點適應性加切的誤差指標。在二維量子校正的能量運輸模型問題中,在相同收斂條件下做網格點適應性加切,數值呈現,新的誤差估計方法比舊的誤差估計方法,總網格數減少了11%。

The quantum-corrected energy transport (QCET) model consisting of seven self-adjoint nonlinear PDEs describes the steady state of electron and hole flows, their energy transport, and classical and quantum potentials within a nano-scale semiconductor device. We develop a second-order maximum norm a posteriori error estimate proposed by Kopteva [14] for the QCET which after scaling involves the scaled Debye length, intrinsic carrier density, Planck constant, and thermal conductivity as the singular perturbation parameters. This estimate can be used as an error indicator for the refinement process in an adaptive algorithm. We present explicit formulas for computing the error indicators which are indispensable for the adaptive computations of the semiconductor device simulation for advanced nano-devices. Our numerical experiments on the a posteriori error estimation for the 1D QCET model problem have shown good results of the proposed error indicators for all seven PDEs of the QCET model. With the 1D QCET Model's numerical results, we take the seven PDEs to make adaptive finite element mesh in the 2D QCET model. For the 2D QCET problem, it is shown that the total number of nodes of the final adaptive mesh using the new estimation method has been decreased to 11% from that of the old method under the same stopping criteria of the adptive algorithm.

1 Introduction 1

2 The QCET Model 3

3 A Dimensionless QCET Model 9

4 A Posteriori Error Estimation for General Semilinear PDE12

5 Numerical Results 23

6 Conclusion 50

7 References 51
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