Parametric study of the frequency-domain thermoreflectance technique

Without requiring regression for parameter determination, one-dimensional (1D) analytical models are used by many research groups to extract the thermal properties in frequency-domain thermoreflectance measurements. Experimentally, this approach involves heating the sample with a pump laser and probing the temperature response with spatially coincident probe laser. Micron order lateral resolution can be obtained by tightly focusing the pump and probe lasers. However, small laser beam spot sizes necessarily bring into question the assumptions associated with 1D analytical models. In this study, we analyzed the applicability of 1D analytical models by comparing to 2D analytical and fully numerical models. Specifically, we considered a generic n-layer two-dimensional (2D), axisymmetric analytical model including effects of volumetric heat absorption, contact resistance, and anisotropic properties. In addition, a finite element numerical model was employed to consider nonlinear effects caused by temperature dependent thermal conductivity. Nonlinearity is of germane importance to frequency domain approaches because the experimental geometry is such that the probe is always sensing the maximum temperature fluctuation. To quantify the applicability of the 1D model, parametric studies were performed considering the effects of: film thickness, heating laser size, probe laser size, substrate-to-film effusivity ratio, interfacial thermal resistance between layers, volumetric heating, substrate thermal conductivity, nonlinear boundary conditions, and anisotropic and temperature dependent thermal conductivity.