The balance-equation approach to nonlinear hot-carrier transport theory, formulated by Lei and Ting (1984), is addressed in this comprehensive review. A central feature is the role of strong electron-electron interactions in promoting rapid thermalization about the drifted transport state and the concomitant substantial simplification of the transport theory. This physical feature is embodied in the initial density matrix chosen to represent the unperturbed carrier system. Force and energy balance equations are formulated for the dc steady state, ac dynamic and transient cases of charge conduction, including memory effects. The scattering mechanisms include impurity and phonon interactions along with dynamic nonlocal screening effects due to carrier-carrier interactions. Both linear and nonlinear resistivities are discussed in the degenerate and nondegenerate statistical regimes. Interesting phenomena such as electron cooling and thermal noise and diffusion are discussed as well. Semiconductor microstructure transport is described for both linear and nonlinear hot carrier conduction. In this connection, quasi-2D-systems, heterojunctions, and quantum well superlattices are treated with attention to steady state, transient and high frequency transport, including, for example, superlattice plasmon resonance structure. Type-II superlattice transport is reviewed as well as type-I, and electron-hole drag is treated in conjunction with negative minority electron mobility in a quantum well. Multivalley semiconductors are discussed in some detail. Furthermore, attention is also focused on the center-of-mass velocity fluctuation, Langevin-type equation and thermal noise and diffusion for microstructures and multivalley systems. A number of particularly important phenomena are examined from the balance-equation point of view, such as nonequilibrium phonons, higher order scattering effects and weak localization, hydrodynamic equations for weakly nonuniform systems, and the intracollisional field effect. Alternative formulations and interpretations of the balance-equation approach are reviewed. The distinction between this many-particle, isothermal, balance-equation theory and the noninteracting (single-particle) adiabatic transport theory is discussed to clarify issues subject to controversy in the literature. Finally, we give a brief review of recent developments in the balance-equation approach: investigation of the distribution function in balance-equation theory, improved calculations for GaAs/AlGaAs heterojunctions, extension of the balance equations to an abitrary energy band and recent work on superlattice miniband transport.
