准连续式电势函数分布的全搜索求解方法

Analytical Approach to Quasi-Continuous Potential and Field Profile by Full-Searching Least Squares

本文给出一种准连续式电势函数分布的超定方程组在椭圆圆柱坐标系下的全搜索求解方法。为了提高计算精度，引入矩阵的尺度变换；为了减少对称正半定矩阵的病态与奇异性，引入二次插值搜索；为了防止驻点的存在，引入鞍点搜索，从而能够精确地获得电势与电场的准连续式分布函数。

A new analytical approach for solution to the overdetermined equations of the quasi-continuous potential and field profiles of the reverse-biased p-n junctions with the elliptical cylindric coordinates is proposed in the paper.The dimensional transformation and the searching algorithm for two-interpolation and standing point are used in least-squares for increasing in calculation precision and ameliorating nonsingularity and ill-condition of the symmetric positively semidefinite matrix caused by nonlinearity of the potential and electrical field.