Thermal properties of thin films studied by ultrafast laser spectroscopy: Theory and experiment

The one-dimensional non-homogeneous hyperbolic energy equation within a semi-infinite domain, applied to pump–probe transient reflectance measurements for subpicosecond and picosecond laser pulses was studied. The result of this study is an analytical model in the form of a Volterra-type integral equation that describes the surface temperature response of the thin film induced by an ultra-short laser pulse and takes into account contributions of the transient heat flux and the volumetric heat source. The criterion based on dimensionless time ξp = t/2τ (where τ is the relaxation time of phonons due to collisions) is introduced, in order to predict the temperature response caused by the surface heat flux and/or volumetric source. This analytical solution is validated by using experimental pump–probe transient reflectance measurements of thin gold with a time resolution of 50 fs. A good agreement between the experimental results and the theoretical model is found.