The main reason why charge transport in these small devices must be treated with "additional" physics in mind can be understood as follows. As the charge carriers (electrons and/or holes) move in the crystal under the action of the external force (namely, the electric field caused by the voltage applied to the transistor contacts), they suffer collisions of various types: with the thermal vibrations of the ions of the crystal (Si, Ge, ...), with the dopants (positively charged P or As donors, or negatively charged B acceptors in Si, for example), with other electrons or holes, etc. If the mean distance between two successive collisions (typically, a few nanometers) is much smaller than the dimensions of the transistor, carriers collide many times while transiting the device. On the one hand, this prevents the carriers from gaining kinetic energy much in excess of the thermal energy they would have even in the absence of a driving force. On the other hand, the many collisions can be treated statistically, by "lumping" their effect as a kind of average "friction" on the current, without worrying too much about the details of what happens to electrons or holes in a single collision. As a nice by-product of these simplifications, one has to worry only about what happens in a very small neighborhood of each carrier: electrons and holes have "lost memory" of what happened elsewhere, because of the many randomizing collisions they have suffered along the way. The problem now becomes "local": only the driving force (the electric field) at a given position in the device is needed to describe charge transport at that particular position. Older device simulation programs (mainly belonging to the class of "drift-diffusion" models) relied heavily on these simplifying considerations. They used the fact that carriers do not acquire too much kinetic energy to simplify the band structure of the crystal, and use simply an "effective mass" to handle the motion of the carriers. They also used "lumped" concepts, such as "mobility" and "diffusion constant", to account for carrier collisions in a grand-averaged and "local" way.

Now that transistors have reached dimensions approaching the mean distance between collisions, these simplifying approximations fail: carriers gain significant kinetic energy, in excess of 50 to 100 times larger than their thermal energy. Therefore, the details of the band-structure of the crystal become important. At the same time, only a few collisions occur as carriers move across the device. Thus, it becomes important to look at single collisions with more attention and to account for the driving force everywhere in the device when studying charge transport at a given position in the transistor ("nonlocal effects").

As devices shrink even more, their dimensions begin to approach the wavelength of the electron. Electrons must then be fully treated as full-fledged quantum mechanical particles. Rather than picturing them as tiny billiard balls, they must be regarded as waves traveling across the device, reflecting off boundaries and contacts, interfering with other waves. The reduced size of these "nanostructures" also causes standard statistical methods to fail, opening the field of "mesoscopic" physics. This realm is outside the scope of our pages, although Monte Carlo techniques are used also in the study of single-electron devices, and we refer to various Web-lists of hyperlinks to sites dealing with nanoelectronics. See also the pages by W. R. Frensley, University of Texas, Dallas, describing quantum transport, the physics of heterostructures, and the use of Wigner functions in the simulation of quantum devices, the pages describing the quantum device simulator NEMO, those dealing with quantum transport at the Delft Institute for MicroElectronics and Sub-micron technology (DIMES), our own preliminary attempt to use the Pauli Master Equation to simulate electron transport in very small devices, and the many links provided by S. Cannon at the University of Texas, Austin.