Generalized expression for the self-normalized signal in photothermal experiments for multilayered materials in the frequency domain

The analytical solution for diffusion of heat for a four-layered material, in a surface absorption model, is used to describe a simple diagram-based construction methodology for obtaining the analytical solution for a general photothermal signal in the transmission and front photothermal configurations. The general expressions derived can be used for analysis during the application of self-normalized photothermal experimental techniques to thermal diffusivity measurements in the frequency domain. The thermally thick limit of these equations can be used to obtain an effective thermal diffusivity expression for multilayered systems that can be used to retrieve the thermal diffusivities of buried layers. If such a system consists of alternating layers of two different materials, as is the case for some heterostructures and superlattices, it is possible to obtain the thermal impedances at the interfaces of the consecutive layers. Although the resulting self-normalized expressions are complex, their thermally thick limit reduces them to linear equations for the photothermal phase and amplitude (amplitude in semi-log scale). This simplifies the analysis required to obtain quantitative results.