On the temperature dependence of the electronic thermal conductivity in metals when the electron and phonon subsystems are not in local equilibrium

Abstract

The knowledge of the temperature dependence of the thermal conductivity is necessary in many aspects. It is required, for example, as an important input parameter for the calculation of temperature distributions in metals after interaction with laser pulses. Although extensive compilations exist on this subject they may be of limited value because the data were obtained under steady state conditions where the electrons and phonons are described by a single common temperature. At short laser pulses, however, the electron and phonon subsystems are not in local thermal equilibrium and have to be characterized by different temperatures. It is shown that the validity of the often used linear dependence of the thermal conductivity on the electron temperature is limited to some few thousand kelvin and becomes definitely wrong at higher temperatures. A formula including the thermoelectric effects is derived that is valid throughout the whole temperature range as well as for the case of local thermal equilibrium and nonequilibrium.