Non-equilibrium energy transport in a thin metallic film: Analytical solution for radiative transport equation

Non-equilibrium energy transfer in thin aluminum film is examined and analytical solution for the radiative transport equation is presented for the electron and lattice subsystems. Electron-phonon coupling is incorporated in the radiative transport equation to account for the energy exchange between the electron and the lattice sub-systems during their thermal communications. The radiative transport equations are reduced to a system of integral equations in the form of Fredholm integral equation of the second kind and they are solved analytically through the integral transformations technique. The analytical solution for temperature distribution in lattice and electron sub-systems is simulated for various film thicknesses. The analytical solution of two-equation model is also presented to compare the findings of the radiative transport in the film. The analytical solution of the radiative transport equation is validated through the numerical predictions. It is found that numerical predictions agree well with the findings of the analytical solution. Lattice site and electron temperatures obtained from the analytical solution differ from those resulted from the two-equation model for the aluminum film thickness of 0.1 µm because of the ballistic behavior of the phonons emitted at high temperature edge of the film.