Evaluation of Uncertainties of One-Directional Analytical Model for Thermoreflectance Technique

One dimensional (1-D) analytical models are generally used for the evaluation of thermal effusivity of film or substrate in thermoreflectance measurement. However, the range of uncertainties associated with the 1-D assumptions needs to be quantified in order to determine the applicability of 1-D models. In the current study, a two-dimensional (2-D) numerical model was created in a commercial software package, COMSOL, to investigate the difference of results obtained by 1-D or 2-D models. The analysis used a frequency lock-in strategy and the result was verified by a comparison of 1-D numerical simulation to 1-D theoretical values. Parametric studies were performed by considering film thickness, heating laser radius, volumetric heating, thermal resistance between layers, and anisotropic thermal conductivities. The results and conclusions provide a general guidance and reference for the parametric design of thermoreflectance measurements.