A fractional-diffusion theory for calculating thermal properties of thin films from surface transient thermoreflectance measurements

The transient thermo reflectance (TTR) method consists of measuring changes in the reflectivity of a material (thin film) tender pulsed laser heating, and relating these changes to the corresponding surface temperature variat ions. Analytical solutions of the diffusion problem are then used to determ ine the thermal conductivity of the material following an iterative matchin g process between the solutions and the experimental results. Analytical so lutions are attainable either when the material absorbs the laser energy vo lumetrically or when the material absorbs the laser energy at the surface. Either solution allows for the determination of only one thermal property, (thermal conductivity or diffusivity), with the other one assumed to be kno wn. A new, single, analytical solution to the transient diffusion equation with simultaneous surface and volumetric heating, found using fractional ca lculus, is presented in a semi-derivative form. This complete solution prov ides the means to determine the two thermal properties of the material (the rmal conductivity and diffusivity) concomitantly. In this preliminary study , the solution component for surface heating is validated by comparison wit h experimental data for a gold sample using the classical thermoreflectance method. Further results, for surface and volumetric heating, are obtained and analyzed considering a GaAs sample.