HEXAHEDRAL FINITE-ELEMENTS FOR THE STATIONARY SEMICONDUCTOR-DEVICE EQUATIONS

In this paper we discuss some discretization methods for the semiconductor device equations based on hexahedral partitions of the domain. These include a finite difference box integration method and a mixed finite element method for the continuity equations. From the latter an algebraic system is derived which can be interpreted as an extension to three dimensions of the well-known one-dimensional Scharfetter-Gummel scheme. We prove that if the hexahedral partition is almost regular, in the sense that all the elements are almost regular hexahedra, and we neglect small terms, then the method is asymptotically convergent to first order. We also discuss the evaluations of the approximate terminal currents which we prove to be convergent and conservative. The conventional box integration finite element method is obtained as a special case on the almost regular hexahedral mesh. Furthermore, we show that the finite difference method may be interpreted as a lumped finite element method. © 1990.