一种描述硅PIN二极管反向恢复过程的二阶有限元方法  

A Second Order Finite Element Method for the Reverse Recovery of Silicon PIN Diodes

作　　者：翟弋 张满红 宫婷婷 ZHAI Yi;ZHANG Manhong;GONG Tingting(College of Electrical and Electronic Engineering,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学电气与电子工程学院,北京102206

出　　处：《河北师范大学学报（自然科学版）》2022年第6期564-574,共11页Journal of Hebei Normal University：Natural Science

基　　金：江苏省自然科学基金(BK20191296);中央高校基本科研业务费专项资金资助课题(2019B19114)。

摘　　要：在现有文献中,为计算硅PIN二极管反向恢复过程,应用线性有限元(LFEM)方法将双极性扩散方程(ADE)写成变分形式.研究表明,为从变分函数中推导出ADE,p■(δp)/■t相关项必须被忽略.通过结合傅里叶展开(FE)和LFEM方法形成一个新的有限元法,发现所忽略p■(δp)/■t相关项对应于在傅里叶展开中删除p=p(x,t)方程中的一项,其中p=p(x,t)是未耗尽N^(-)区中随空间和时间变化的载流子浓度.另外,对于多个有限元的实现,提出了二阶有限元法(SFEM),并在描述硅PIN二极管反向恢复过程时将其性能与线性有限元法(LFEM)进行了比较.结果表明,在算法引起的其他误差和空间离散化点的数量减少时,二阶有限元法(SFEM)比线性有限元法(LFEM)精度更好,且与p■(δp)/■t项相关的误差也减少.In many references,the application of the linear finite element(LFEM)method to compute the reverse recovery processes of silicon PIN diodes depends on writing the ambipolar diffusion equation(ADE)in a variational formulation.A careful examination shows that,in order to derive the ADE from the variational function,a term related to p■(δp)/■t must be ignored.By combining Fourier expansion(FE)and LFEM method to form a new FEM method with a single finite element,we find dropping the p■(δp)/■t related term corresponds to removing a term in the equations of p(x,t)in the FE method,here p=p(x,t)is the space and time dependent carrier density in the undepletcd N^(-)region.For the multiple-finitc-element implementations,we propose a second order FEM(SFEM)and compare its performance with LFEM.Our results show that the SFEM has a better accuracy than the LFEM.The p■(δp)/■t term related error in the FEM methods is reduced,when other errors induced by the algorithm and the number of space discretization points are reduced.

关 键 词：PIN二极管 反向恢复 双极扩散方程 傅里叶展开 有限元法 

分 类 号：O472.4[理学—半导体物理]