A two-dimensional, steady state Monte Carlo (MC) device simulator which is especially suited for the simulation of submicron MOSFETs has been developed and implemented in the MINIMOS program. The semiconductor model takes into account a nonparabolic, anisotropic bandstructure, three dimensional optic and acoustic phonon scattering, ionized impurity and surface roughness scattering.
A new self-scattering algorithm has been developed to perform the free-flight time calculation. The use of a piecewise linear total scattering rate allows for an efficient reduction of self-scattering events. Charge assignment to nonuniform grids is accomplished by a convolution method using non-trivial weighting functions. A trajectory multiplication algorithm is required to deal with widely varying carrier concentration magnitudes occurring in a real device. A unique MC-Poisson coupling scheme has been adopted, which exhibits a significantly better convergence rate than conventional schemes do. This technique is based on the so called MC-Drift-Diffusion (DD) coupling, a method which proves to be correct within the semiclassical Boltzmann transport theory.
The coupling coefficients between the MC- and the DD-model are the carrier energy tensor and the mobility, which depend on the first three moments of the distribution function. An extended DD-like current relation, which is motivated by the first momentum equation, along with these nonlocal coefficients exactly reproduces the MC-transport behaviour. Approaching thermal equilibrium the extended current relation simplifies to the conventional DD-relation.
The MC-Poisson coupling is done by including the continuity equation and the
extended current relation in the iteration loop. Each MC-step performs
an update of the coupling coefficients.
Simulation of MOSFETs with gate lengths lower than 
clearly shows
velocity overshoot phenomena.
Self-consistency is mandatory for such small devices, otherwise the overshoot
phenomena will be overestimated. The self-consistent
potential is smoother than that of a DD-simulation, thus reducing the maximum
field in the device.