In this paper, Silvaco Atlas TCAD device-circuit mixed simulation and MATLAB programming are used to compute the reverse recovery processes of silicon PIN diodes. The latter is based on solving the ambipolar diffusion equation (ADE) with the moving boundaries. The results of the ADE-based Fourier expansion (FE) and finite difference (FD) method are first compared with that from the Atlas simulation. It is found that the result from the FE method agrees very well with that from the Atlas simulation, while the result from the FD method is much worse. The reason is attributed to approximating the second-order partial space differentiation by a FD form with a time-dependent constant space step in the FD method. One clear phenomenon is that the voltage in a FD simulation shows a very steeper drop followed by a very steeper rise. To solve this problem, we propose a modified finite difference (MFD) method in which the space discretization step is fixed when solving the ADE by a single-step back-Euler method and the new coordinates of two moving boundaries of the un-depleted N⁻ region are iterated through the zero-value of the boundary carrier density, current and voltage requirement. Then a new grid is set up based on the new boundary coordinates and a cubic spline interpolation is used to transfer p(x, t) from the old grid to the new one. The result from our MFD method agrees very well with those from Atlas and FE simulation. In addition two sets (a slow set and a fast one) of carrier concentration dependent Shockley-Read-Hall recombination life time parameters are used to study the validity of the usual boundary conditions at two boundaries of the un-depleted N⁻ region in the ambipolar diffusion approximation. Our results in some cases the boundary conditions may fail.

本文采用Silvaco Atlas TCAD器件-电路混合仿真和MATLAB编程来计算硅PIN二极管的反向恢复过程。后者基于求解具有移动边界的双极扩散方程（ADE）。首先将基于ADE的傅立叶展开（FE）和有限差分（FD）方法的结果与来自Atlas仿真的结果进行比较。结果表明，有限元方法的结果与Atlas仿真的结果非常吻合，而FD方法的结果则差得多。原因归因于在FD方法中通过具有时间相关的恒定空间步长的FD形式来近似二阶局部空间微分。一个明显的现象是，FD仿真中的电压显示出非常陡峭的下降，接着是陡峭的上升。为了解决这个问题，⁻通过边界载流子密度，电流和电压要求的零值迭代区域。然后根据新的边界坐标建立新的网格，并使用三次样条插值将p（x，t）从旧网格转移到新网格。我们的MFD方法得到的结果与Atlas和FE模拟得到的结果非常吻合。另外两套载流子浓度依赖性肖克莱-读取-霍尔重组寿命时间参数（一组慢和快速一个）用于研究的通常的边界条件的有效性在未耗尽N中的两个边界^-区域在双极扩散近似。我们的结果在某些情况下边界条件可能会失败。