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In this work, we develop a numerical fitting routine to extract multiplethermal parameters using frequency-domain thermoreflectance (FDTR) formaterials having non-standard, non-semi-infinite geometries. The numericalfitting routine is predicated on either a 2-D or 3-D finite element analysisthat permits the inclusion of non semi-infinite boundary conditions, which cannot be considered in the analytical solution to the heat diffusion equation inthe frequency domain. We validate the fitting routine by comparing it to theanalytical solution to the heat diffusion equation used within the widerliterature for FDTR and known values of thermal conductivity for semi-infinitesubstrates (SiO2, Al2O3 and Si). We then demonstrate its capacity to extractthe thermal properties of Si when etched into micropillars that have radii onthe order of the pump beam. Experimental measurements of Si micropillars withcircular cross-sections are provided and fit using the numerical fittingroutine established as part of this work. Likewise, we show that the analyticalsolution is unsuitable for the extraction of thermal properties when thegeometry deviates significantly from the standard semi-infinite case. This workis critical for measuring the thermal properties of materials having arbitrarygeometries, including ultra-drawn glass fibers and laser gain media.

A Numerical Fitting Routine for Frequency-domain Thermoreflectance Measurements of Nanoscale Material Systems having Arbitrary Geometries