# Perturbation theories behind thermal mode spectroscopy for high-accuracy measurement of thermal diffusivity of solids

## TL;DR

Thermal mode spectroscopy (TMS) offers a high-precision, non-invasive method for measuring the thermal diffusivity of solids, especially effective for small samples and resistant to interface resistances, with accurate results even when diffusivity varies with temperature.

## Contribution

This paper applies perturbation analysis to demonstrate the advantages of TMS, including its applicability to high diffusivity, insensitivity to interface resistance, and accuracy with temperature-dependent diffusivity.

## Key findings

- TMS is effective for small specimens with high thermal diffusivity.
- Interface resistance does not significantly affect first-order diffusivity correction.
- TMS provides accurate diffusivity measurements even with temperature dependence.

## Abstract

Thermal mode spectroscopy (TMS) has been recently proposed for accurately measuring thermal diffusivity of solids from a temperature decay rate of a specific thermal mode selected by three- dimensional (anti)nodal information [Phys. Rev. Lett., 117, 195901 (2016)]. In this paper, we find out the following advantages of TMS by use of perturbation analyses. First, TMS is applicable to the measurement of high thermal diffusivity with a small size specimen. Second, it is less affected by thermally resistive films on a specimen in the sense that the resistance at the interface does not affect the first-order correction of thermal diffusivity. Third, it can perform doubly accurate measurement of the thermal diffusivity specified at a thermal equilibrium state even if the diffusivity depends on temperature in the sense that the measurement can be performed within tiny temperature difference from the given state and that the decay rate of the slowest decaying mode is not affected by the dependence.