  A comprehensive survey is given of the thermoballistic approach to charge
carrier transport in semiconductors. This semiclassical approach bridges the
gap between the drift-diffusion and ballistic ("thermionic") models of carrier
transport, whose validity is limited to the range of very small and very large
values, respectively, of the carrier mean free path. The physical concept
underlying the thermoballistic approach, while incorporating basic features of
the drift-diffusion and ballistic descriptions, constitutes a novel, unifying
scheme. It is based on the introduction of "ballistic configurations" defined
by a random partitioning of the length of a semiconducting sample into
ballistic transport intervals, which are linked by points of local
thermodynamic equilibrium at which carriers are emitted or absorbed. By
averaging the carrier currents in the ballistic intervals over all ballistic
configurations, a position-dependent thermoballistic current is derived for
arbitrary magnitude of the carrier mean free path. This current is the key
element of the thermoballistic concept and forms the point of departure of the
calculation of various transport quantities. The present article starts out
with an account of the standard drift-diffusion and ballistic transport models,
and of a prototype model which paves the way for the fully developed form of
that concept. In the main body of the article, a coherent exposition of the
thermoballistic approach is given within a general formulation that takes into
account arbitrarily shaped, spin-split potential energy profiles and spin
relaxation during the carrier motion across ballistic intervals. The
calculational procedures devised for implementing the thermoballistic concept
are described. Specific examples relevant to present-day semiconductor and
spintronics research are considered.
