A generalized heat conduction solution for ultrafast laser heating in metallic films

A generalized analytical solution for the electron and lattice temperature profiles in a metallic film exposed to an ultrafast laser source is obtained using the superposition and Fourier methods in conjunction with solution structure theorems. The generalized temperature profile in algebraic form is applicable for the solution of three thermal models, namely, phonon-electron two-temperature interaction model, electron kinetic theory model, and the improved electron kinetic theory model. By selecting the appropriate coefficients as appear in the original governing partial differential equation of a particular model, temperature profiles for both the electron and lattice can readily be obtained. A comparison of the aforementioned models in graphical form is made. Results from the phonon-electron two-temperature interaction model agree well with the improved electron kinetic theory model for electron and lattice temperatures. However, due to the omission of the time rate change of heat diffusion and laser source, temperature predictions from the electron kinetic theory model are slightly higher than temperatures from the other two models; particularly, the effect is more profound at the location of the energy incident surface. Otherwise all three models compare extremely well for the lattice site temperatures.