Time-domain thermoreflectance (TDTR) measurements of anisotropic thermal conductivity using a variable spot size approach

TL;DR

This paper introduces a variable spot size TDTR method to accurately measure both in-plane and through-plane thermal conductivities of anisotropic materials, addressing challenges in characterizing layered and 2D materials.

Contribution

The work extends TDTR with a variable spot size approach to simultaneously measure anisotropic thermal conductivities, providing guidelines for optimal measurement conditions and reliability.

Findings

Successfully measured thermal conductivities of diverse anisotropic materials.

Identified the importance of matching modulation frequency to measurement conditions.

Provided a practical guideline for selecting laser spot size and frequency for accurate measurements.

Abstract

It is challenging to characterize thermal conductivity of materials with strong anisotropy. In this work, we extend the time-domain thermoreflectance (TDTR) method with a variable spot size approach to simultaneously measure the in-plane (Kr) and the through-plane (Kz) thermal conductivity of materials with strong anisotropy. We first determine Kz from the measurement using a larger spot size, when the heat flow is mainly one-dimensional along the through-plane direction, and the measured signals are sensitive to only Kz. We then extract the in-plane thermal conductivity Kr from a second measurement using the same modulation frequency but with a smaller spot size, when the heat flow becomes three-dimensional, and the signal is sensitive to both Kr and Kz. By choosing the same modulation frequency for the two sets of measurements, we can avoid potential artifacts introduced by the frequency-dependent Kz, which we have found to be non-negligible, especially for some two-dimensional layered materials like MoS2. After careful evaluation of the sensitivity of a series of hypothetical samples, we provided a guideline on choosing the most appropriate laser spot size and modulation frequency that yield the smallest uncertainty, and established a criterion for the range of thermal conductivities that can be measured reliably using our proposed variable spot size TDTR approach. We have demonstrated this variable spot size TDTR approach on samples with a wide range of in-plane thermal conductivity, including fused silica, rutile titania (TiO2 [001]), zinc oxide (ZnO [0001]), molybdenum disulfide (MoS2), hexagonal boron nitride (h-BN), and highly ordered pyrolytic graphite (HOPG).