Normalized photoacoustic techniques for thermal diffusivity measurements of buried layers in multilayered systems

The one-dimensional heat diffusion problem for a three-layer system is solved assuming the surface absorption model. The analytical solution is shown to be suitable for the implementation of normalized depth-profilometric photoacoustic methodologies involving the open photoacoustic-cell configuration for thermal diffusivity measurements in buried underlayers within a three-layer stack. Our normalization procedures eliminate the frequency-dependent instrumental electronic contribution (transfer function) and some thermophysically nonrelevant proportionality factors in the theoretical equations, thus making the depth-profilometric analysis feasible. The measurement methodology is achieved by normalizing the theoretical photoacoustic signal from the three layers with the corresponding signal from the uppermost two layers, involving linear fits to measure the thermal diffusivity of the third underlayer. Three different multilayered materials were examined using the proposed methodologies. High reproducibility of the thermal diffusivity measurements and good agreement with values reported in literature were found. Besides the foregoing procedures, a lumped photoacoustic model was developed, which yields the effective thermal-diffusivity value of the multilayer stack.