陳宜良臺灣大學：數學研究所張濬朋Chang, Jui-PengJui-PengChang2007-11-282018-06-282007-11-282018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/59403我們是研究半導體數學中的量子擴散漂移模型（QDD Model） 又叫做密度梯度模型（DG Model），在這個巨關模型中包含了 電子密度的非線性拋物線方程和電子位能的波松方程。而我們是 利用有限差分方法來離散化這個模型方程，而且利用牛頓疊代法 來解這個離散系統，最後我利用了Ballistic二極體結構來展示 這個數值方法。We study the quantum drift diffusion model (QDD) which was known (Density Gradient Model DG model) of semiconductor. This macroscopic model consists of a nonlinear parabolic equation for electron density, which coupled with a Poisson equation for electrostatic potential. We solve this system numerically by finite difference method, which can maintain the positivity of density in whole space. Numerical results for a ballistic diode structure are presented.Content: 中文摘要 5 Abstract 6 1.Introduction 7 1-1 Quantum models of semiconductor 7 2.The Quantum Drift Diffusion model (QDD) 8 2-1 Derivation of the stationary Quantum Drift Diffusion model 8 2-2 Scaling analysis of Quantum Drift Diffusion model 11 2-3 The boundary condition 14 3.Numerical analysis 15 3-1 Discretization in Space 15 3-2 Iteration Method 17 3-3 Numerical results 19 Appendix (A) 22 Appendix (B) 26960289 bytesapplication/pdfen-US半導體數學擴散漂移模型量子模型SemiconductorQuantum drift diffusion modelthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59403/1/ntu-94-R89221017-1.pdf