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

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).

24 pages, 6 figures, 1 table, submitted to Review of Scientific Instruments

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• Thermal expansion and transport in van der Waals solids from first-principles calculations
• Temperature dependence of anisotropic thermal conductivity tensor of bulk black phosphorus
• Crystal growth of hexagonal boron nitride (hBN) from Mg-B-N solvent system under high pressure

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• Temperature mapping of stacked silicon dies from x-ray diffraction intensities
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