Analytical solution for non-equilibrium energy transfer in gold: Influence of ballistic contribution of electrons on energy transfer

The analytical solution for non-equilibrium energy transfers in gold substrate and ballistic contribution of electrons to the energy transfer mechanism is examined. The non-equilibrium energy equation including the ballistic contribution of electrons is obtained using the electron kinetic theory approach. The analytical solution using the perturbation method is introduced to formulate lattice and electron temperature distributions in the film. A numerical method using the finite difference scheme is employed to predict and compare electron and lattice site temperatures to those obtained from the analytical solution. It is found that temperature remains high in the surface region of the gold film due to the cases: (i) accounting for the ballistic contribution of electrons to non-equilibrium energy transfer, and (ii) excluding the ballistic contribution to the non-equilibrium energy transfer. This is true for electron and lattice temperatures.