In this paper, we examine the problem associated with abruptly mixing boundary conditions in the context of a two dimensional semiconductor device simulator. Explicitly, this paper addresses the transition between an ohmic-type Dirichlet condition and a passivated Neumann boundary. In the traditional setting, the details of the transition between the two boundary types are not addressed and an abrupt transition is assumed. Subsequently, the calculated observables (most notably the potential) exhibit discontinuous derivatives near the surface at the point where the boundary type switches. This paper proposes an alternative condition which models the progression between the two boundary types through the use of a finite length, smoothed boundary whereby the numerical discontinuities are eliminated. The physical and mathematical basis for this smoothed boundary condition is discussed and examples of the technique's implementation given. It is found that the proposed boundary condition is numerically efficient and can be implemented in pre-existing device simulators with relative ease.

Points out that the Scharfetter-Gummel technique is widely used in algorithms for the simulation of isothermal semiconductor devices. Recent interest in the modeling of ultrasmall devices requires a nonisothermal analysis, i.e., a hydrodynamic model. Several nonisothermal extensions to the Scharfetter-Gummel technique for carrier flux have been proposed for homostructure devices. An extension is presented which is suitable for the simulation of both the carrier flux and carrier energy flux equations in heterostructure devices, with the capability of using Fermi-Dirac statistics. Comparison with the extensions of other authors provides verification of the discretization formulation developed here. Limiting cases are discussed with suitable approximations. Calculated values of fluxes are presented for selected nonisothermal and degenerate cases to highlight the need for inclusion of the Fermi-Dirac statistics in the flux formulations.>