本研究主軸在於開發三維球體網格模型，以球座標為主架構，加入離子撞擊游離模型，建立一模擬器來模擬半導體元件在P-N接面時崩潰的物理現象。在理論架構上，我們運用波松方程式、電子流連續方程式與電洞流連續方程式，將三維的元件等效電路模型化，模擬半導體元件中載子的漂移擴散、產生與復合特性。在模型架構方面，則是研究在球體中立體網格的特性，以梯形立體來近似球面弧型的曲率，並建立模擬元件所需之各項參數。接著應用此模擬器，模擬分析在球接面下，不同的擴散半徑與相異參雜濃度下其崩潰電壓的改變，並與三維直角座標模型進行比較，證實本研究模型不僅具備精準度，更大幅縮短模擬時間為原先的十萬分之一，最後再針對本模型的應用與特性做探討。

The thesis develops a 3D spherical grid model, base on spherical coordinate and combined with impact-ionization model for the spherical P-N junction breakdown simulation. At theory aspect, we use poisson’s equation, electron and hole continuity equation to transfer the equivalent circuit into a model, and simulate the drift-diffusion current, generation and recombination current. At the structure, study the feature of spherical grid, and use trapezoid mesh to approximate the curvature, then build up the parameters. The breakdown voltage at spherical junction will be simulated with different radius and doping, and the result will be compared with Cartesian coordinate to verify this model. This model not only shows a good accuracy but also shows a less simulation time. Finally we investigate the application and feature of the 3D spherical grid model.

[1] Chia-Hung Pai, “Development of 3D impact-ionization model and its applications to breakdown simulation of spherical PN junction”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2011.
[2] Bo-Chi Chen, “Breakdown Simulation of a Spherical P-N Junction with a String of 3D Symmetrical Grids”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2012.
[3] Szu-Ju Li, “An Equivalent Circuit of Impact-Ionization and its Applications on Semiconductor Devices”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2002.
[4] Martin Wilke, Michael Töpper, Hue Quoc Huynh, Klaus Dieter Lang, Fraunhofer Institut für Zuverlässigkeit and Mikrointegration, “Process Modeling of Dry Etching for the 3D-Integration with Tapered TSVs”, IEEE 62nd Berlin, Germany, June, 2012.
[5] Simon M. Sze, Semiconductor Devices: Physics and Technology,2^ndEd., p. 564: Wiley, New York, 2002.
[6] Chih-Wei Tsai , “Surface Recombination Current and non-Bernoulli Equation for 2-D Semiconductor Device Simulation”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2002.
[7] Jing-Fu Dai, “Development of 2-D and 3-D numerical device simulator including an improved L-ILU solver and the circuit representation of PDM”, PH. D. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2004.
[8] Yu-sheng Tso, “Analysis and simulation cylindrical coordinates of curved PN junction properties”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2010.
[9] Meng-Syun Li, “Rectangular Transform of Trapezoidal Mesh and Its Application to Cylindrical MOSFETs”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2011.
[10] Ruei-Nan Chang “Parameter Extraction of Impact Ionization Rate in Two-Dimensional PIN Diode Simulation”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2011.
[11] Chia-Cherng Chang, “Improvement of 2-D and 3-D Semiconductor Device Simulation Using Equivalent-circuit Model”, PH. D. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2006.
[12] Wei-Lung Huang, “Integration of Band Solver and LILU Solver for 3-D Semiconductor Device Simulation”, M. S. Thesis, Institute of EE, National Central University,Taiwan, Republic of China, June. 2008.