Coupled finite element/boundary element method for semiconductor quantum devices with exposed surfaces

We present a study of the boundary conditions for the potential at exposed semiconductor surfaces in split-gate structures, which views the exposed surface as the interface between the semiconductor and air. A two-dimensional numerical algorithm is presented for the coupling between the nonlinear Poisson equation in the semiconductor (finite element method) and Laplace’s equation in the dielectric (boundary element method). The utility of the coupling method is demonstrated by simulating the potential distribution in an n-type AlGaAs/GaAs split-gate quantum wire structure within a semiclassical Thomas–Fermi charge model. We also present a comparison of our technique to more conventional Dirichlet and Neumann boundary conditions.