目前功率元件大多透過平面化製程技術(Planar process)在的矽基板上形成大量的 P-N接面，其中擴散摻雜物會因阻擋遮罩層的形狀，導致P-N接面邊緣呈現圓弧形或球形的結構，而所形成的曲率接面會限制並影響功率元件的耐壓能力，所以在元件製造之前我們需要更嚴謹的半導體的數值模擬分析。因此，在我們的研究下發現圓柱與球座標下的梯形網格對於圓弧接面有較高的對稱性，並且所得到的數值解較為精準且快速，因此這些特性將對於需要切割更多網格子的三維元件模擬上，節省了更多的模擬時間與計憶體空間。有見於此，首先我們將進行三維的球座標之梯形網格子開發。接著，將運用所開發的圓柱與球座標之梯形網格子進行一連串的物理性質探討與分析包括: 1.圓弧形PN 二極體崩潰特性之理論分析並且作PN二極體在二維與三維梯形網格下的VB (崩潰電壓)、(E)電場、φ (電位)、( d n p r ,r ,r )空乏區寬度相關公式的推導並且驗證公式推導與數值模擬結果之正確性[16-19]，2.主要是設計一個模擬的參數萃取方法讓我们可以從元件的I-V量測,量出撞擊游離系數alpha對電場E的變化撞擊游離系數alpha可分為電子撞擊游離系數alpha_n,與電洞撞擊游離系數alpha_p，3.利用球形元件三維數值模擬之技術開發，進一步分析探討多閘極MOSFET之轉角與短通道效應[9-11]，4.利用更符合元件物理需求圓柱坐標與球形坐標的梯形網格子來分析GAA(gate-all-around) 或是 surrounding gate MOSFETs如何來壓制轉角效應與改善短通道效應[1-5]，5.熱傳導方程式轉換成圓柱座標與球形座標的梯形網格模型在半導體元件內之傳導狀況[20] The breakdown voltage in a PN junction will be changed by the curvature of a circular junction or a spherical PN junction. In order to understand the depletion-width dependence on curve curvature in 2D or 3D, we need to analyze the dependence by analytical equations or 3D numerical simulation. In our previous study, it is found that 2D trapezoid mesh is very suitable for the simulation of 2D circular PN junction due to the high accuracy and high speed.Based on this result, we will develop a 3D trapezoid mesh for 3D spherical simulation. It is easier to use a 3D trapezoid cell to fill a 3D spherical space than a 3D triangle cell. In this project, we will also study the following device physics: 1. Develop the analytical equations for VB (breakdown voltage), E (electric field), φ (electrostatic potential), depletion-width ( d n p r ,r ,r ), and verify these equations by 2D and 3D simulation with the trapezoid meshes [16-19]. 2. Develop an algorithm to extract the E-field dependence of the impact ionization factors ( , n p α α ). 3. Analyze the multigate MOSFET corner effect and short channel effect [9-11]. 4. Study GAA (gate-all-around) or surrounding gate MOSFETs to eliminate the corner effect and to improve the short channel effect [1-5]. 5. Apply the heat-conduction equation to 2D and 3D device simulation with our 2D and 3D trapezoid meshes. 研究期間：10008 ~ 10107
