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

An interface formulation for the Poisson equation in the presence of a semiconducting single-layer material