Aw. Smith et al., A SMOOTHED BOUNDARY-CONDITION FOR REDUCING NONPHYSICAL FIELD EFFECTS, IEEE transactions on computer-aided design of integrated circuits and systems, 16(4), 1997, pp. 420-423
In this paper, we examine the problem associated with abruptly mixing
boundary conditions in the contest of a two-dimensional semiconductor
device simulator, Explicitly, this paper addresses the transition betw
een an ohmic-type Dirichlet condition and a passivated Neumann boundar
y. In the traditional setting, the details of the transition between t
he two boundary types are not addressed and an abrupt transition is as
sumed, Subsequently, the calculated observables (most notably the pote
ntial) 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 nume
rical discontinuities are eliminated, The physical and mathematical ba
sis for this smoothed boundary condition is discussed and examples of
the technique's implementation given. It is round that the proposed bo
undary condition is numerically efficient and can be implemented in pr
e-existing device simulators with relative ease.