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 only sensitive to 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 guidelines 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 conductivity 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.

Anisotropic thermal conductivity of 4H and 6H silicon carbide measured using time-domain thermoreflectance

“…We measure the anisotropic thermal conductivity and using TDTR by varying the laser spot size and the modulation frequency, 23 as shown in Figure 1b where the subscript (= , ) denotes the direction in cylindrical coordinates, is the thermal conductivity, and is the volumetric heat capacity. Since TDTR measures the surface temperature rise within the RMS radius of the laser spot, whether the TDTR signal is sensitive to depends on how large the laser spot radius w is compared to the in-plane thermal diffusion length , .…”

“…The uncertainties (2 ) of the control parameters are estimated as follows: 10% for the thermal conductivity of Al, 5% for the heat capacity of Al and the substrate, 5% for the Al thickness, and 4% for the laser spot size. 23,31 We summarize the calculated 4 ⋅ [ ] for the SI 4H-SiC, n-type 4H-SiC and SI 6H-SiC in Table 1, so that the uncertainties 2 can be directly calculated as square root of the diagonal elements. The SI and n-type 4H-SiC have higher and than those of SI 6H-SiC sample, which agree well with the first principles predictions that the thermal conductivity of H-SiC ( = 2, 4, 6)…”

Picosecond transient thermoreflectance for thermal conductivity characterization

“…Both systems can be modified to measure in-plane thermal conductivity as well. For TDTR, techniques such as offset laser beams [44] and varying pump or probe laser spot size [11] have been implemented. For ps-TDTR, our recently developed grating imaging technique [9], [45] can be integrated with ease.…”

“…However, it also means that it is challenging to investigate low-k materials using FDTR. Both TDTR and FDTR can also measure in-plane thermal conductivity by carefully varying spot sizes and modulation frequencies [3], [11].…”

Transient and local two-phase heat transport at macro-scales to nano-scales

“…6 and 7a. Although lateral conduction of heat in the Hf80 metal, fluid, and substrate are seemingly neglected, the TDTR hot-spot (2w) is much larger than the thermal penetration depth (' th ) so the temperature gradient is mainly one-dimensional (1D) in the through-plane directions 49 . This also allows the natural and forced convection above the hot-spot (at a depth greater than ' th ) to conceptualized experimentally as a spatiotemporal boundary condition-i.e., all the 3D heat and mass transfer outside the (2)) and hot-spot wall temperature (equation (5)).…”