||CMES: Computer Modeling in Engineering & Sciences, Vol. 1, No. 1, pp. 121-126, 2000
||Full length paper in PDF format. Size = 495,969 bytes
||finite point methods, meshless methods, mesh generation, monte carlo methods
||This paper describes the application of the meshless
Finite Point (FP) method
to the solution of the nonlinear semiconductor Poisson equation.
The FP method is a
true meshless method which uses
least-squares fit and point collocation.
The nonlinearity of the semiconductor Poisson equation is treated by
Newton-Raphson iteration, and sparse matrices are employed to 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
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
capability of the method to treat arbitrary
boundary conditions is shown by comparison with finite difference