在本篇論文中，我們將推導三維圓球pn接面的電位、電場、空乏區寬度等的公式，比起一維的公式，三維圓球的公式變得很複雜，然而，經過簡單的計算，仍可得到球接面的空乏區寬度，我們也比較公式的結果與三維的數值模擬的結果。利用這些球接面的公式，我們可以更快速地觀察到空乏區寬度、最大電場、崩潰電壓等對球接面半徑的變化。同理，空乏區寬度、最大電場、崩潰電壓等對球接面參雜濃度的變化也可快速得到。

In this thesis, we try to derive the analytical equations of the potential, the electric field, and the depletion width in a three-dimensional spherical pn junction. The analytical equations for spherical pn junction is more complex than that for 1D pn junction. However, the depletion width can be obtained by a simple calculation. We compare the analytical results with the results from 3D numerical simulation. With these analytical equations, we can quickly investigate the dependence of the depletion width, the maximum electric field, and the breakdown voltage on the radius of a spherical pn junction. Similarly, the dependence of the depletion width, the maximum electric field, and the breakdown voltage on the doping of a spherical pn junction can be obtained quickly.

[1] J.Y. Peng, “Current Characteristic and Electric-field Analysis in 2-D SOI Semi-conductor Devise Simulation,” Natl. Central Univ., Chung-Li city, Taiwan,R.O.C.,2008.
[2] D. K. Cheng, “Field and Wave Electromagnetics,” Addison-Wesley PublishingCompany, Inc., 1989.
[3] M. Shur, “Introduction to Electronic Devices,” Chapter 3, John Wiley & SonsInc.,1996.
[4] E. S. Yang, “Microelectronic Devices,” Chapter 5, McGraw-Hill, 1988.
[5] S. Selberherr, “Analysis and Simulation of Semiconductor Devices,”Springer-Verlag, New York, pp. 111-112, 1984.
[6] V. I. Smirnov, “A Course of Higher Mathematics,” Chapter 5, Oxford New York,
　 1964.
[7] B. J. Baliga, “Power Semiconductor Devices,” PWS publishing Company,Boston, 1996.
[8] J. He, et al., "Equivalent function transformation: a semi-empirical analytical Method for predicting the breakdown characteristics of cylindrical- and spherical-abrupt PN junctions," Solid-State Electronics, vol. 44, pp. 2171-2176, Dec 2000.