A new elliptical-beam method based on time-domain thermoreflectance (TDTR) to measure the in-plane anisotropic thermal conductivity and its comparison with the beam-offset method

Abstract

Materials lacking in-plane symmetry are ubiquitous in a wide range of applications such as electronics, thermoelectrics, and high-temperature superconductors, in all of which the thermal properties of the materials play a critical part. However, very few experimental techniques can be used to measure in-plane anisotropic thermal conductivity. A beam-offset method based on timedomain thermoreflectance (TDTR) was previously proposed to measure in-plane anisotropic thermal conductivity. However, a detailed analysis of the beam-offset method is still lacking. Our analysis shows that uncertainties can be large if the laser spot size or the modulation frequency is not properly chosen. Here we propose an alternative approach based on TDTR to measure in-plane anisotropic thermal conductivity using a highly elliptical pump (heating) beam. The highly elliptical pump beam induces a quasi-one-dimensional temperature profile on the sample surface that has a fast decay along the short axis of the pump beam. The detected TDTR signal is exclusively sensitive to the in-plane thermal conductivity along the short axis of the elliptical beam.By conducting TDTR measurements as a function of delay time with the rotation of the elliptical pump beam to different orientations, the in-plane thermal conductivity tensor of the sample can be determined. In this work, we first conduct detailed signal sensitivity analyses for both techniques and provide guidelines in determining the optimal experimental conditions. We then compare the two techniques under their optimal experimental conditions by measuring the in-plane thermal a) Electronic mail: Ronggui.Yang@Colorado.Edu of both methods in measuring the in-plane anisotropic thermal conductivity. In the end, the two methods are compared by measuring the in-plane thermal conductivity tensor of a ZnO [11][12][13][14][15][16][17][18][19][20] sample. II. METHODOLOGIESBoth the elliptical-beam method and the beam-offset method are based on TDTR, which is a powerful and versatile technique that has been applied to measure thermal properties of a wide range of thin films, 14-16 multilayers, 17,18 nanostructured and bulk materials, 19,20 and their interfaces. 21-23 TDTR uses two synchronized light sources, referred to as the pump (heating) and the probe (sensing) beams. The pump beam deposits a periodic heat flux on the sample surface and induces a temperature change in the sample, which is then monitored by measuring the change in the intensity of the reflected probe beam. A schematic diagram of a typical TDTR system is shown in Figure 1(a). More details of the system implementation have been described elsewhere. [24][25][26][27][28][29] Particularly, there are two features of the system relevant to this work that are worth mentioning here: (1) The polarizing beam splitter (PBS) in front of the objective lens is gimbal-mounted so that the pump beam can be steered to enable the operation of the beam-offset method while the position of the probe beam is unaffected. (2) A pair of cylindrical lenses can b...

Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments

“…This allowed the solution to be written in terms of Hankel transforms. However, by using two-dimensional Fourier transforms, the solutions presented here could easily be adapted to handle a range of non-symmetric situations, such as those involving elliptical beams [26] or pump and probe beams with an offset [27]. These can provide deeper insights into the heat conduction mechanisms that occur at the nanoscale and further means of validating the GK equation or other non-Fourier conduction laws.…”

Thermoelectric effect and devices on IVA and VA Xenes

“…251 Advanced approaches include configurations with a variable spot size, 264 a beam-offset 265 and an ellipticalbeam. 266 Measurement of cross-plane thermal conductivity of 2D materials such as BP 267 and WSe 2 250 have also been reported. Among the above three commonly used methods, optothermal Raman method has the advantages in easy sample preparation, accessible equipment and convenient operation, whereas MFSD and TDTR are more accuracy-and cost-effective, respectively.…”

“…The complexity of the thermal model potentially also enables TDTR to determine the in‐plane thermal conductivity or thermal transport orientation 251 . Advanced approaches include configurations with a variable spot size, 264 a beam‐offset 265 and an elliptical‐beam 266 . Measurement of cross‐plane thermal conductivity of 2D materials such as BP 267 and WSe 2 250 have also been reported.…”

Accurate measurement of in-plane thermal conductivity of layered materials without metal film transducer using frequency domain thermoreflectance

“…For example, the in-plane thermal conductivity and the cross-plane thermal conductivity of transversely isotropic materials can be separately measured by tuning the laser spot size and/or the modulation frequency of the lasers. 5,[17][18][19] Further, the beam-offset approach developed by Feser et al 20 and the elliptical beam approach by Jiang et al 21 and Li et.…”

“…The existence of metal films, however, would cause in-plane heat spreading that suppresses the sensitivity to the in-plane thermal conductivity, especially for transducers with high thermal conductivity such as aluminum and gold. 21,23 Although using thinner transducers with low thermal conductivity such as NbV helps to increase the measurement sensitivity, 24 accurate measurement of remains challenging for materials with low in-plane thermal conductivity < 5 W/mK. 23 This is the author's peer reviewed, accepted manuscript.…”