A Three-Phonon Process in the Electron-Phonon System

A three-phonon process via a nonlinear interaction of acoustic waves with conduction electrons is studied based on the semiclassical Boltzmann equation treatment. The Hamiltonian for this process is given in the form which is easily applied to the discussion of non-Ohmic behaviors observed in CdS and Bi. The order of magnitude of the new process is examined in terms of the effective third-order elastic constant, which depends strongly on the carrier concentration, the wave number and the temperature. In a restricted range of wave number, the new process predominates over the usual three-phonon process due to the anharmonic interaction in lattice vibrations in the following cases: (1) CdS with carrier concentrations 10 12 –10 15 cm -3 , (2) n -Ge with carrier concentration 10 16 cm -3 at low temperatures, (3) Bi in the absence of a magnetic field. In Bi in a strong magnetic field, the magnitude of the new process becomes much smaller than the usual one.