Semi-classical study of the limitations of the "mean-field" approximation for the accurate simulation of nanometric devices

For nanoscale electron devices, the role of a single-electron (or a single-impurity) can have a large impact on their electrical characteristics. A new method for introducing the long-range and short-range Coulomb interaction in Monte Carlo particle based simulations is presented. The method is based on directly dealing with a many-particle system by solving a different Poisson equation for each electron. The present work shows the numerical viability of this approach for the accurate simulation of nanoscale devices. The method is compared with the traditional "mean-field" approximation used in Monte Carlo simulators. The incapability of the "mean field" approximation to deal with the short-range Coulomb interaction is manifested. It is shown, numerically, that the "mean-field" approximation produces dramatic errors when small spatial steps are used.