Cj. Wordelman et al., A meshless method for the numerical solution of the 2-and 3-D semiconductor Poisson equation, CMES-COMP M, 1(1), 2000, pp. 121-126
This paper describes the application of the meshless Finite Point (FP) meth
od to the solution of the nonlinear semiconductor Poisson equation. The FP
method is a true meshless method which uses a weighted least-squares fit an
d point collocation. The nonlinearity of the semiconductor Poisson equation
is treated by Newton-Raphson iteration, and sparse matrices are employed t
o store the shape function and coefficient matrices. Using examples in two-
and three-dimensions (2- and 3-D) for a prototypical n-channel MOSFET, the
FP method demonstrates promise both as a means of mesh enhancement and for
treating problems where arbitrary point placement is advantageous, such as
for the simulation of carrier wave packet and dopant cloud effects in the
ensemble Monte Carlo method. The validity of the solutions and the capabili
ty of the method to treat arbitrary boundary conditions is shown by compari
son with finite difference results.