Numerical challenges in particle-based approaches for the simulation of semiconductor devices

The aim of this paper is to review and discuss the most challenging aspects of the particle-based methods for simulation of charge transport in semiconductor devices. Since the early theoretical works on the Ensemble Monte Carlo (EMC) method applied to device simulation, and several successive works addressing both the physics and the numerical aspects of the EMC method, the basic algorithmic approaches have been modified to exploit the continuous improvements of both hardware and software tools. Typical examples of the algorithmic evolution are the adoption of the full band representation of the electronic structure, the so-called cellular automaton (CA), and the simulation of increasingly complex three-dimensional (3D) structures. This paper will address some of the most significant problems which are still considered open in spite of the recent technological and scientific progresses.