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

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.