An Approximation of Three-Dimensional Semiconductor Devices by Mixed Finite Element Method and Characteristics-Mixed Finite Element Method. Issue 3 (5th August 2015)

• Record Type: Journal Article
• Authors: Yang, Qing; Yuan, Yirang
• Is Part Of: Numerical mathematics. Volume 8:Issue 3(2015)
• Page Start: 356
• Page End: 382
• Publication Date: 2015-08-05
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.my12031
• Languages: English
• ISSNs: 1004-8979

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>The mathematical model for semiconductor devices in three space dimensions are numerically discretized. The system consists of three quasi-linear partial differential equations about three physical variables: the electrostatic potential, the electron concentration and the hole concentration. We use standard mixed finite element method to approximate the elliptic electrostatic potential equation. For the two convection-dominated concentration equations, a characteristics-mixed finite element method is presented. The scheme is locally conservative. The optimal <italic>L</italic>²-norm error estimates are derived by the aid of a post-processing step. Finally, numerical experiments are presented to validate the theoretical analysis.</p> </abstract>