  In this paper, we consider a semiconducting device with an active zone made
of a single-layer material. The associated Poisson equation for the
electrostatic potential (to be solved in order to perform self-consistent
computations) is characterized by a surface particle density and an
out-of-plane dielectric permittivity in the region surrounding the
single-layer. To avoid mesh refinements in such a region, we propose an
interface problem based on the natural domain decomposition suggested by the
physical device. Two different interface continuity conditions are discussed.
Then, we write the corresponding variational formulations adapting the so
called three-fields formulation for domain decomposition and we approximate
them using a proper finite element method. Finally, numerical experiments are
performed to illustrate some specific features of this interface approach.
