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