An efficient technique for solving the arbitrarily multilayered electrostatic problems with singularity arising from a degenerate boundary

Abstract

Engineers usually adopt multilayered design for semiconductor and electron devices, and an accurate electrostatic analysis is indispensable in the design stage. For variable design of electron devices, the BEM has become a better method than the domain-type FEM because BEM can provide a complete solution in terms of boundary values only, with substantial saving in modelling effort. Since dual BEM still has some advantages over conventional BEM for singularity arising from a degenerate boundary, the dual BEM accompanied by subregion technology, instead of tedious calculation of Fourier–Bessel transforms for the spatial Green's functions, was used to efficiently simulate the electric effect of diverse ratios of permittivity between arbitrarily multilayered domain and the fringing field around the edge of conductors. Results show that different ratios of permittivity will affect the electric field seriously, and the values of surface charge density on the edge of conductors are much higher than those on the middle part because of fringing effect. In addition, if using the DBEM to model the fringing field around the edge of conductors, the minimum allowable data of dielectric strength for keeping off dielectric breakdown can be obtained very efficiently.