Kinetics of Bounded Systems

Abstract

To derive the general kinetic equations in the previous chapters, we did not employ the condition of homogeneity, except for Chapter 5, where the basis of phonon wave vectors was used in the initial equations. Nevertheless, in each concrete case, a detailed analysis has been carried out either for homogeneous systems, when the momentum (or quasimomentum) conservation rule is valid, or for the systems with slowly varying macroscopic parameters, when one can effectively employ the Wigner representation of the density matrix. On the other hand, if a system has the abrupt inhomogeneities which can be defined in a regular way, for example, the interfaces between different materials, or just the surfaces, the quasi-classical kinetic equations should be considered together with the boundary conditions at such interfaces. In this chapter we derive the boundary conditions for the Wigner distribution functions of electrons and phonons in the presence of non-ideal (rough) surfaces and interfaces and study the influence of the surfaces and interfaces on transport phenomena.