Model-Based Estimation of the Anisotropic Thermal Properties of Materials from Photothermal Deflection Spectroscopy Data Using Bayesian Inference

Abstract

Estimating the thermal properties of thin film on substrate material systems is important in many thermal engineering applications. The photothermal deflection spectroscopy technique is extended for the in situ characterization of anisotropic thin films on substrates. A comprehensive thermal model is developed for systems with an arbitrary number of films on a substrate that includes the effects of anisotropic thermal conductivity and thermal boundary resistance.

Using the thermal model, the beam deflections in a photothermal deflection spectroscopy experiment are found for a system with finite probe beams. The theoretical beam deflection model is used to infer material properties within a Bayesian statistical framework. A maximum a posteriori estimator based on the Levenberg-Marquardt algorithm is used to solve the resulting ill-posed inverse problem. Synthetic data from bulk, thin film on substrate, and multilayered film samples is analyzed to demonstrate the ability and limitations of the estimator to infer the true thermal properties. The estimation of effective thermal properties for multilayer material systems is also discussed and demonstrated. Methods for evaluating the validity of estimates and subsequently improving these estimates using design of experiments are given.