摘要(英) |
This thesis is mainly about the electrical simulation of semiconductor components by using C language program of spherical mesh structure. The unit of the model is based on tetrahedron. First, we use tetrahedron to construct basic hexahedral components, and then the model of the spherical shell, since the tetrahedron is the smallest unit in the three-dimensional model, it has the highest flexibility when
composing other models. The theoretical part uses the finite element method and the center of gravity method to construct the tetrahedron. We use Poisson’s Equation, Electron
continuity equation, and Hole continuity equation to simulate the diffusion, drift, generation, recombination, and other characteristics of semiconductor components. In the computing architecture part, we use Newton-Raphson′s method to perform calculations, and developed a model architecture that can simulate the characteristics of semiconductor components. In the results part, we simulated the series resistance、diode、MOS capacitance composed of hexahedrons, spherical resistance and the spherical shell diode composed of tetrahedra. The results are also in line with our expectations, and we can confirm that our simulation is feasible. |
參考文獻 |
[1] Alexander, C.K. and Sadiku. Fundamentals of Electric Circuits 4/E. M.C.H.2009.
[2] P. Feldmann and R.A. Rohrer, “Proof of the Number of independent Kirchhoff
Equations in an Electrical Circuit”, IEEE Transactions on Circuits and Systems,
vol. 38, No. 7, pp.681 - 684, IEEE, Jul. 1991.
[3] Atkinson, Kendall E./ Han, Weimin. Elementary Numerical Analysis. Wiley.2003.
[4] R. A. Jabr, M. Hamad, Y. M. Mohanna, “Newton-Raphson Solution of Poisson’s
Equation in a PN Diode,” Int. J. Electrical Eng. Educ., Jan. 2007.
[5] M. Putti and C. Cordes, “Finite Element Approximation of the Diffusion Operator
on Tetrahedra”, SIAM J. SCI. COMPUT., Vol. 19, No. 4, pp. 1154– 1168, Society
for Industrial and Applied Mathematics, July 1998.
[6] Simon M. Sze and Ming-Kwei Lee. Semiconductor Devices: Physics and
Technology (3rd Edition). Wiley.2012.
[7] R.E. Bank, D.J.Rose, W.Fichtner, “Numerical methods for semiconductor
device,”IEEE Trans, Electron Devices, vol.30, on.9, Sep.1983.
[8] S. Micheletti, “Stabilized finite elements for semiconductor device simulation,”
Compute & Visual Sci., vol. 3, pp. 177-183, 2001.
43
[9] T. D. Pauw and W. F. Pfeffer, “The Divergence Theorem for Unbounded Vector
Fields”, Transactions of the American Mathematical Society, Vol. 359, No. 12, pp.
5915 - 5929, American Mathematical Society, Dec. 2007.
[10] M. Marrero-Martín and J. García, B. González and A. Hernández, "Circuit models
for PN integrated varactors," IEEE Trans, Palma de Mallorca, pp. 1-4, 2011.
[11] Xizhen Zhang, Chuanhui Cheng, Huichao Zhu, Tao Yu, Daming Zhang, and
Baojiu Chen, “A New MOS Capacitance Correction Method Based on FiveElement Model by Combining Double-Frequency C−V and I–V Measurements ”,
IEEE Electron Device Letters, vol. 37, no. 10, Oct. 2016.
[12] William H. Hayt and John A. Buck. Engineering Electromagnetics 9/e.新月. 2019.
[13] Y.P.Chen, “3D grounded Cube Element and Matrix Coefficient Verification and
its Applications to Semiconductor Device Simulation” National Central
University, M.S.Thesis, June.2021.
[14] Y.T.Liao, “3D Bridged Cube Element and Matrix Coefficient Verification and Its
Applications to Semiconductor Device Simulation” National Central University,
M.S.Thesis, June.2021.
[15] Y. C. Lai, “1D Matrix Coefficient Verification And Semiconductor Device
Simulation”, Nation Central University, M. S. Thesis, Jun. 2020. |