Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film

The analytical solution for non-equilibrium temperature field in solid substrate is presented. Closed form solutions for electron and lattice site temperature rise are obtained for a solid layer heated at the surface with a time-decaying intensity pulse. In the analytical solutions, a perturbation method of strained parameters is introduced. Temperature simulations are carried out for a gold layer with different thicknesses. It is found that increasing layer thickness lowers electron and lattice site temperatures at the surface. Electron temperature at the surface decays sharply with progressing heating period, which is more pronounced for thin layer. Moreover, lattice site temperature continues to rise despite reducing electron temperature in the surface region. The results obtained from the analytical solution for the lattice site temperature agrees well with the numerical predictions.