A meshless method for the numerical solution of the 2- and 3-D semiconductor Poisson equation

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 a weighted 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 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 capability of the method to treat arbitrary boundary conditions is shown by comparison with finite difference results.