Finite boxes—A generalization of the finite-difference method suitable for semiconductor device simulation

A two-dimensional numerical device-simulation system is presented. A novel discretization scheme, called "finite boxes," allows an optimal grid-point allocation and can be applied to nonrectangular devices. The grid is generated automatically according to the specified device geometry. It is adapted automatically during the solution process by equidistributing a weight function which describes the local discretization error. A modified Newton method is used for solving the discretized nonlinear system. To achieve high flexibility the physical parameters can be defined by user-supplied models. This approach requires numerical calculation of parts of the coefficients of the Jacobian. Supplementary algorithms speed up convergence and inhibit the commonly known Newton overshoot. The advantages and computer resource savings of the new method are described by the simulation of a 100-V diode. We also present results for thyristor and GaAs MESFET simulations.