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 exp osed 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 betw een the nonlinear Poisson equation in the semiconductor (finite elemen t method) and Laplace's equation in the dielectric (boundary element m ethod). The utility of the coupling method is demonstrated by simulati ng the potential distribution in an n-type AlGaAs/GaAs split-gate quan tum wire structure within a semiclassical Thomas-Fermi charge model. W e also present a comparison of our technique to more conventional Diri chlet and Neumann boundary conditions.