Nonequilibrium Phonon Processes

Abstract

The coupled systems of electrons (“e”) and phonons (“ph”) in a conducting solid will be shifted from their equilibrium distribution under the influence of an external electric field F. Obviously, the momentum and energy imparted to the carriers by the field cannot be dissipated through “normal” e-e, e-ph and ph-ph-collisions, which conserve the total momentum and energy of the e-ph-system. A steady state can only be established by momentum-and energy-loss mechanisms such as “Umklapp”-processes, in which momentum is transferred to the crystal as a whole, or by scattering at the crystal-boundaries, where momentum and energy, predominantly of the phonons, are dissipated into a surrounding “heat bath”. Consequently, the nonelectronic dissipation mechanisms for nonequilibrium phonons determine the possibility of time dependent, nonstationary phenomena and can also influence the details of the usually realized steady-state transport (Klemens, 1951; Kaveh and Wiser, 1972). Quite generally one has to expect effects of nonequilibrium of both the e-and ph-subsystem due to the mutual “dragging along” through collisions in any conventional transport experiment at sufficiently low temperatures in sufficiently pure and perfect materials: “phonon drag” by electrons in the lattice thermal conductivity, “phonon drag” of electrons in the electrical conductivity (Sommerfeld and Bethe, 1933; Ziman, 1960; Bailen, 1958; Kaveh and Wiser, 1974; Parrott, 1957) and both drag effects in the thermopower (Ziman, 1960; Geballe and Hull, 1954; Herring, 1958).