Non-equilibrium phonon gas in a chalcogenide semiconductor with exponential temperature dependence of conductivity

The distribution function for a phonon gas in the non-equilibrium case of current crowding in a chalcogenide glassy semiconductor is considered. The approximate internal energy of the gas and its heat capacity is calculated. The change in the heat capacity caused by phase changes, which according to the results of the numerical calculations, are similar to the second-order phase transition, is analyzed. The law of temperature variation with time is calculated for a homogeneous current crowding without a heat sink, taking into account the exponential dependence of the conductivity on the temperature. It is shown that the temperature dependences of the concentration and energy of phonons do not undergo significant changes and are linear. The results of this work should be useful in developing chalcogenide glass-based phase-change memory devices, where strong heating by an electric current is possible and, as a consequence, a significant effect of phonons on the current flow should occur.