liitroductionThe extensive use of thin filnis in modern techniques as well as the observation of new physical phenomena due to the finite size of the specimens have led to their active investigation in recent years [1 to 101. These new phenomena may be used as a source of additional inforination on the basic physical properties of crystals: structures of energy bands, mechanisms of bulk and surface scattering of charge carriers, etc. The concept of a "thin film" means that the thickness of the fihn is comparable with a length characteristic of some phenomenon. The efiects met with in films may be divided into two groups -the quantum and classical size effects. Quantum size effects take place when the sample dimensions become of the order of the de Uroglie wavelength of a typical charge carrier [9, 101. Classical size-dependent effects occur in a sample when a t least one of the lengths characterizing the motion of charge carriers becomes of the order of the film thickness or of the characteristic length of the potential variation near the surface (the Debye length). Examples of such lengths are the mean free path, the cooling length, bipolar diffusion length, intcrvalleyscattering length, etc. Which particular size effect is to be observed depends upon which of these parameters becomcs comparable with the specimen thickness.The present review deals with a theoretical study of the influence of size cffects upon the charge carrier mean frcc path. I n othcr words, we are intcrestcd in the influence of surface scattering upon the transport phenomena in semiconductive filnis.Size-dependent effects associated with the mean free path have been studied for many years. The first consistent theory of the conductivity in filnis was suggestctl by Fuchs [ l l ] on the basis of a frce electron gas niodel under the assumption of a spherical Fcrmi surface. The surface scattering was takeii into account by using the due boundary conditions for the distribution function. The boundary conditions to be attachecl to the noltzmann equation constitute the central point in the study of the mean free path size cffects; they contain all the information concerning the surface and are in a scnse similar to the collision integral of the bulk scattering problem. The Fuchs boundary conditions are phenomenological and disregard the details of the surface structure. A rigorous formulation of the boundary conditions based upon thc general concepts of the theory of electron surface scattering as well as their application to specific situations and energy band structures were discussed comprehensively in other reviews L12, 131.Sondheimer [14] extended the Fuchs theory to the galvanomagnetic effects in a transverse magnetic field; he was the first to predict the resistance oscillations in a magnetic field. The studies carried out by Fuchs and Sondheimer wcre generalized to the case of scattering by two film surfaccs with different spccularities in [15, 161.The E'uchs theory was generalized as well to take account of the spccific structure of energy ...