9.1 The Mesoscopic Regime

Classical physics describes the everyday, macroscopic, world, but quantum mechanics describes the microscopic world of atoms and molecules. Traditionally, semiconductor devices could be thought of as macroscopic objects describable by semiclasical concepts (i.e. we describe particle dynamics by equations like Newton s law of motion generalized to include the concept of bandstructure). It is now possible, however, to produce devices and structures for which these semiclassical concepts break down. Such devices are still larger than the atomic or molecular scale, but they are smaller than some critical length scales above which traditional transport theories apply. The size scale between the microscopic and macroscopic regimes is known as the mesoscopic regime. Our objectives in this chapter are to describe some key approaches and important results concerning transport at the mesoscopic scale.

The mean-free-path for scattering is an important length scale for carrier transport. One can show (see homework problem 9.1) that the mean-free-path, ?, is related to the diffusion coefficient, D, by D ? ? ? _R, where is the so-called Richardson velocity. For room-temperature electrons in pure silicon, ? ?700 , while for GaAs, ? ?200 . (At T=77K, the mean-free-path for electrons in pure GaAs increases to ?1 m.) Another characteristic length associated with scattering is the energy relaxation length for hot electrons, which is on the order of a few hundred Angstroms for Si and a few thousand Angstroms for GaAs. Semiconductor devices with critical regions of...