A modified finite difference model to the reverse recovery of silicon PIN diodes

Abstract

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.