在此篇論文中，為了減少製程上資源的浪費，我們主要使用C語言軟體模擬半導體元件特性，開發出三維重心版模組，以四面體網格當基本元素，模擬三維半導體元件，相較於以往二維重心版模組，三維模組更能應用於不規則接面處，增加網格模組的彈性空間；首先模擬簡單的四面體電阻與PN-Junction的特性曲線來驗證其程式架構，接著把四面體網格模組轉換至梯形網格模組，並將梯形元件延伸至圓柱體元件，分析圓弧面相較於直角網格的差異性，使網格系統能更精確的模擬半導體元件。

In this thesis, in order to reduce the process cost, we use C language software to simulate characteristics of semiconductor device. We developed 3D barycenter module which is composed of tetrahedral mesh elements to simulate 3D semiconductor device. The 3D module is better than 2D module and it increases the flexibility to fit the environment. First of all, a simple tetrahedral resistor and PN junction will be simulated and compare to the theoretical for verification. Next, the tetrahedral module will be applied to trapezoidal module, and extended to cylindrical semiconductor device. The 3D module can help us improve the accuracy of semiconductor device.

[1] P. Causin, M. Restelli, and R. Sacco, “A simulation system based on mixed-hybrid finite elements for thermal oxidation in semiconductor technology,” Computer Methods in Applied Mechanics and Engineering., vol. 193, no. 33, pp. 3687-3710, Aug. 2004.
[2] M. B. Patil, “New discretization scheme for two-dimensional semiconductor device simulation on triangular grid,” IEEE Trans, Computer-Aided Design of Integrated Circuits and Systems, vol. 17, no. 11, pp. 1160-1165, Nov. 1998.
[3] D. J. Riley and C. D. Turner , “Interfacing unstructured tetrahedron grids to structured-grid FDTD,” IEEE Trans, Microwave and Guided Wave Letters, vol. 5, no. 9, pp. 284 - 286, Sep 1995.
[4] G. W. Tang, “Generation of Tetrahedral/Prismatic Meshes and Its Applications in Microchannel Flows,” D. S. Thesis, Institute of AA, National Cheng Kung University, Taiwan, Republic of China, 2006.
[5] H. J. Jhih, “Simulation and Analysis in Three-Dimension Cylindrical MOSFETs,”M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2015.
[6] D. A. Neamen, Semiconductor physics and devices, 3rd ed. McGraw-Hill Companies Inc., New York, 2003.
[7] R. E. Bank, D. J. Rose, and W. Fichtner, “Numerical methods for semiconductor device,” IEEE Trans, Electron Devices, vol. 30, no. 9, Sep. 1983.
[8] S. B. Park, C. S. Kim and S. U. Lee, “Error Resilient 3-D Mesh Compression,” IEEE Trans, Multimedia, vol. 8, no. 5, pp. 885 - 895, Oct. 2006.
[9] H. J. Kai, “Finding the internal vector from the plane equation in obtuse triangle element for 2D Semiconductor device simulation,”M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2016.
[10] M. J. Zeng, “Development of Triangular element and its applications to arbitrary 2D Semiconductor device,” M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2014.
[11] W. T. Shen, “Finding internal vector from the edge vector in obtuse triangle element for 2D Semiconductor Device Simulation,”M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2016.
[12] J. S. Zhao, F. L. Chu and Z. J. Feng, “Kinematics of Spatial Parallel Manipulators With Tetrahedron Coordinates,” IEEE Trans, Robotics, vol. 30, no. 1, pp. 233-243, Feb. 2014.
[13] A. Yoshii, H. Kitazawa, M. Tomizawa and S. Horiguchi and T. Sudo, “A three-dimensional analysis of semiconductor devices,” IEEE Trans, Electron Devices, vol. 29, no. 2, pp. 184 189, Feb 1982.
[14] J. Burgler , P. Conti , G. Heiser , S. Paschedag , W. Fichtner ,“Three-dimensional simulation of complex semiconductor device structures,” IEEE Trans, International Symposium on VLSI Technology, Systems and Applications, pp. 106 - 110, May 1989.
[15] C. C. Chang, C. H. Huang, J. F. Dai, S. J. Li, and Y. T. Tsai, “3-D Numerical Device Simulation Including Equivalent-Circuit Model”, IEDMS, 2002.
[16] C. C. Chang, “Improvement of 2-D and 3-D Semiconductor Device Simulation Using Equivalent-circuit Model”, Ph.D. Dissertation, Institute of EE, National Central University, Taiwan, Republic of China, Jun. 2006.
[17] K. Tanaka, A. Notsu, and H. Matsumoto, “A new approach to mesh generation for complex 3D semiconductor devices structures,” IEEE Trans, Simulation of Semiconductor Process and Devices, Sep. 1996.
[18] Y. C. Lin, “Breakdown simulation of a spherical PN junction in cylindrical coordinates”, M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2012.
[19] M. S. Li, “Rectangular Transform of Trapezoidal Mesh and Its Application to Cylindrical MOSFETs”, M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2011.
[20] L. C. Han, “Development of 3D Trapezoidal Model and its Application to Semiconductor Device Simulation,”M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic of China, 2015.