基于梯度法的PN结数值计算

Numerical Simulation of PN Junction Based on Gradient Method

描述半导体PN结特性的方程为一组非线性方程,又称为泊松方程。梯度法是一种有效求解非线性方程的数值方法,将其应用于求解实际的物理问题,如PN结特性方程,有助于加深对物理概念的理解。推导了梯度法的一般原理,并通过将泊松方程线性化,成功应用梯度法求解了PN结的内建电场,电位,平衡载流子浓度等参数沿结方向的分布。进一步研究了外加偏压和掺杂浓度等参数对PN结特性的影响。数值结果表明,采用梯度法求解玻尔兹曼方程比牛顿迭代法精度更高。梯度法在求解非线性方程组所描述的半导体PN结问题上是可行的。

The equations describing the characteristics of semiconductor PN junction is a group of nonlinear equations,called Poisson equation.Gradient method is an effective numerical method for solving the nonlinear equations.Applying it to solving practical physical problems,such as the characteristic equation of PN junction,is conducive to deeply understanding the concept of physics.Firstly,the general principle of gradient method is deduced.By linearizing the Poisson equation,the gradient method is applied successfully to solving the distribution of the built-in electric field,potential,equilibrium carrier concentration and other parameters.The effects of external bias voltage and doping concentration on PN junction were also investigated.The numerical results show that the gradient method is feasible in solving the problems of PN junction.