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A method is developed to calculate the length into a sample to which a Frequency Domain Thermoreflectance (FDTR) measurement is sensitive. Sensing depth and sensing radius are defined as limiting cases for the spherically spreading FDTR measurement. A finite element model for FDTR measurements is developed in COMSOL multiphysics and used to calculate sensing depth and sensing radius for silicon and silicon dioxide samples for a variety of frequencies and laser spot sizes. The model is compared to experimental FDTR measurements. Design recommendations for sample thickness are made for experiments where semi-infinite sample depth is desirable. For measurements using a metal transducer layer, the recommended sample thickness is three thermal penetration depths, as calculated from the lowest measurement frequency.

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Recent experimental studies have measured the infrared (IR) spectrum of tip-scattered near-field thermal radiation for a SiC substrate and observed up to a 50 cm −1 redshift of the surface phonon polariton (SPhP) resonance peak [1, 2]. However, the observed spectral redshift cannot be explained by the conventional near-field thermal radiation model based on the point dipole approximation. In the present work, a heated tip is modeled as randomly fluctuating point charges (or fluctuating finite dipoles) aligned along the primary axis of a prolate spheroid, and quasistatic tip-substrate charge interactions are considered to formulate the effective polarizability and self-interaction Green's function. The finite dipole model (FDM), combined with fluctuational electrodynamics, allows the computation of tip-plane thermal radiation in the extreme near-field (i.e., H/R 1, where H is the tip-substrate gap distance and R is the tip radius), which cannot be calculated with the point dipole approximation. The FDM provides the underlying physics on the spectral redshift of tip-scattered near-field thermal radiation as observed in experiments. In addition, the SPhP peak in the near-field thermal radiation spectrum may split into two peaks as the gap distance decreases into the extreme near-field regime. This observation suggests that scatteringtype spectroscopic measurements may not convey the full spectral features of tip-plane extreme near-field thermal radiation.