A modified finite difference model to the reverse recovery of silicon PIN diodes. (September 2020)

• Record Type: Journal Article
• Authors: Zhang, Manhong
• Is Part Of: Solid-state electronics. Volume 171(2020)
• Publication Date: 2020-09
• Subjects: PIN diode -- Reverse recovery -- Ambipolar diffusion equation -- Fourier expansion -- Finite difference; Semiconductors -- Periodicals; Semiconducteurs -- Périodiques; 621.38152
• DOI: 10.1016/j.sse.2020.107839
• Languages: English
• ISSNs: 0038-1101

Abstract

Highlights: It is found that due to approximating the second-order partial space differentiation by a finite difference (FD) form with a time-dependent constant space step, the FD method has a large error in describing the current-voltage (IV) reverse recovery of a silicon PIN diode. In the un-depleted N − region in a silicon PIN diode, the total carrier number can be obtained either by directly integrating the carrier density from the ambipolar diffusion equation (ADE) or by integrating the continuity equation when simulating the reverse recovery of a PIN diode. Their difference points out the accuracy of a numerical algorithm. A modified FD (MFD) method is proposed to use a time-independent constant space discretization step to approximate the second-order partial space differentiation by a FD form. The ADE is solved by using a single-step back-Euler method. Then a new grid is set up based on new boundary coordinates and a cubic spline interpolation is used to transfer the carrier density distribution from the old grid to the new one. Through the comparison of the data with two sets of SRH life time parameters (slow-set and fast-set), it is found that in some cases the current boundary condition at the boundary of P + N − or N − N + junction may fail in the usual ADE-based computation. 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.