Effect of Film Thickness on Energy Transport Characteristics in Aluminum Thin Film

Abstract

Energy transfer in an aluminum thin film is considered due to a temperature disturbance at the film edges. Temperature oscillation is introduced at the high-temperature edge of the film, and the thermal response of the film is assessed through use of an equivalent equilibrium temperature. Transient frequency-dependent and frequency-independent solutions of the Boltzmann equation are obtained for phonon intensity distributions in the lattice subsystem. An electron–phonon coupling parameter is incorporated in order to account for the thermal communication between electrons and lattice subsystems in the film. The dispersion relations are used in the solution of the frequency-dependent Boltzmann equation. The study is extended to include the effect of film thickness on energy transport characteristics. It is found that oscillation of the equivalent equilibrium temperature takes place within the film because of temperature oscillation at the high-temperature film edges and, as the film thickness increases, the amplitude of the temperature oscillation reduces considerably. The electron temperature closely follows the phonon temperature, provided that the characteristics of the electron temperature oscillation are different than the temperature oscillation in the lattice subsystem.