Since Stratton published his famous paper four decades ago, various transport models have been proposed which account for the average carrier energy or temperature in one way or another. The need for such transport models arose because the traditionally used drift-diffusion model cannot capture nonlocal effects which gained increasing importance in modern miniaturized semiconductor devices. In the derivation of these models from Boltzmann's transport equation, several assumptions have to be made in order to obtain a tractable equation set. Although these assumptions may differ significantly, the resulting final models show various similarities, which has frequently led to confusion. We give a detailed review on this subject, highlighting the differences and similarities between the models, and we shed some light on the critical issues associated with higher order transport models.

SIMON is a single electron tunnel device and circuit simulator that is based on a Monte Carlo method. It allows transient and stationary simulation of arbitrary circuits consisting of tunnel junctions, capacitors, and voltage sources of three kinds: constant, piecewise linearly time dependent, and voltage controlled. Cotunneling can be simulated either with a plain Monte Carlo method or with a combination of the Monte Carlo and master equation approach. A graphic user interface allows the quick and easy design of circuits with single-electron tunnel devices. Furthermore, as an example of the usage of SIMON, we discuss the essential problem of random background charge and present possible solutions.

A hybrid simulator suitable for modeling small semiconductor devices has been developed in which Monte Carlo and drift-diffusion models are combined. In critical device regions, the position-dependent coefficients of an extended drift-diffusion equation are extracted from a Monte Carlo simulation. Criteria for identifying these regions are described. Additional features which make the code more efficient are presented. First, a free-flight time calculation method using a new self-scattering algorithm is described. It allows for an efficient reduction of self-scattering events. Second, a unique Monte Carlo-Poisson coupling scheme has been developed which converges faster than all presently known schemes. It exploits the so-called Monte Carlo-drift diffusion coupling technique, which also forms the basis of the hybrid method. The simulator has been used to model submicron MOSFET's with gate lengths down to 0.15 /spl mu/m. In addition to the non-local effects occurring in these devices, the performance of the hybrid simulation method is analyzed.>