Optothermal Technique for Measuring Thermal Conductivity
The optothermal technique, pioneered by Professor Alexander A. Balandin and his research group at the University of California, is a non-contact, steady-state method for measuring the thermal conductivity of graphene and other two-dimensional (2D) materials. The technique utilizes a conventional micro-Raman spectrometer, in which the excitation laser serves simultaneously as a localized heat source and a temperature probe. The atomic thickness of graphene and 2D materials, with correspondingly small heat flux through the cross-section, allows for substantial local heating of the suspended samples, detectable with Raman shifts, which is essential for the technique. The suspended portion of the sample is required for forming the in-plane heat wave front and for accurately determining the dissipated power. The method can be applied to the supported samples with more elaborate data extraction algorithms, which would account for the actual light–matter interaction volume and solve the heat diffusion equation numerically. The fact that the Balandin group’s optothermal technique utilizes conventional spectrometers and does not require sophisticated cleanroom fabrication of microheaters made it popular worldwide in a short period of time. The temperature resolution of the optothermal technique can be lower than that achievable with resistance-based temperature detectors in the thermal bridge or the “3-omega” techniques. At the same time, the optothermal technique is free from the damage or contamination to the sample, which is unavoidable in the thermal bridge or other techniques that require elaborate nanofabrication and test structure preparation. Thermal bridges and microheaters attached to the samples result in residual polymeric layers and other defects, which introduce ambiguity in the thermal measurements. In this sense, the Balandin group’s optothermal technique, which only requires the sample suspension and proper contact to heat sinks at the edges, proves itself a convenient and accurate approach for determining the thermal conductivity of 2D materials.
The Optothermal Technique Measurement Procedures
In Balandin group’s optothermal technique, a focused laser beam heats a suspended graphene layer, or other 2D material, while the temperature rise is determined from the Raman spectral shift of characteristic phonon peaks. In the first reports (A.A. Balandin et al., Nano Letters, 8, 902 (2008); S. Ghosh et al., Nature Mater., 9, 555 (2010)), the Balandin Group used the G peak of graphene, which reveals strong temperature sensitivity. The technique’s measurement procedure consists of the following main steps.
(1) Calibration: The sample temperature is varied externally using a controlled hot-cold cell while maintaining a low laser power to prevent local heating from the laser beam. The resulting temperature dependence of the frequency of the selected phonon peak in the Raman spectrum provides the calibration factor, i.e., the temperature coefficient. This relationship allows for the conversion of Raman shifts into local temperature changes. In the original work, the G peak frequency of graphene, ωG(T), was used, and the temperature coefficient of the Raman peak of graphene, ξG, was introduced. In the subsequent publications, the 2D band of graphene was also utilized, giving consistent results. One should keep in mind, however, that the 2D band of graphene is a resonant spectral feature, which depends not only on phonon characteristics but on electron band structure as well. It is generally recommended to use narrow peaks in the Raman spectrum, which correspond to phonons from the Brillouin zone center.
(2) Thermal Measurement: During the actual thermal measurement, the laser power, ΔP, is incrementally increased to induce heating of the suspended sample. The corresponding Raman shift, Δω, is converted to the temperature rise, ΔT, using the calibration relation ΔT = Δω/ξ. The absorbed power and temperature distribution are then related through the heat diffusion equation, which is solved, analytically or numerically, to determine the thermal conductivity, K. The sample shape and size can be selected to simplify the measurements and increase their accuracy. In the original report, ribbon-shaped graphene samples were utilized. They had a width of ~ 2 mm – 3 mm, which was comparable to the diameter of the laser spot and allowed for the use of a one-dimensional analytical expression for the approximate solution of the heat diffusion equation. The length of the ribbons on the order of ~ 10 mm ensured that the sample size is larger than the grey phonon mean free path, and the transport can be considered at least partially diffusive. The suspended geometry results in heat transport that occurs primarily in-plane direction, minimizing substrate heat losses.
(3) Dissipated Power Measurement: The laser power, PD, measured at the surface of the sample, by placing a detector at the location of the sample, has to be converted to the power actually absorbed by the sample, DP. In the original experiments, Balandin Group developed a clever technique, which allowed them to determine the power absorbed by a graphene sample by measuring the integrated Raman peak intensity of graphene and bulk graphite, and then calculating the amount of absorbed power. This approach avoids the ambiguity of measuring the absolute Raman scattering cross-section. It only needs the measurement of the ratio of integrated Raman intensities of graphene and graphite. The original graphite and graphene, exfoliated from this specific graphite sample, have the same absorption and scattering characteristics per atomic plane, which simplifies the data analysis (S. Ghosh et al., New J. Phys., 11, 95012 (2009)). Accurate accounting of light absorption is critical, as it depends on wavelength, strain, defects, and surface contamination. Assuming a constant absorption of 2.3% per graphene layer is not justified. The absorption has to be measured under the conditions of the experiment and for a specific excitation wavelength. In the subsequent measurements by other groups, the dissipated power was determined by placing a detector under the suspended graphene or other 2D material when the sample design allowed for it (S. Chen, et al., Nature Mater., 11, 203 (2012); H. Li, et al., Nanoscale, 6, 13402 (2014)).
(4) Heat Diffusion Modeling: The steady-state temperature distribution in the suspended layer can be modeled by solving the heat diffusion equation with boundary conditions fixing the temperature at the heat sinks, typically room temperature. A Gaussian heat source is assumed to model the absorbed laser power. Depending on the sample structure, one can use approximate 1D, 2D, or 3D solutions of the heat diffusion equation. Numerical simulations with tools like COMSOL Multiphysics are often employed for the precise extraction of the thermal conductivity, K. Determining the thermal conductivity typically requires an iterative procedure in which the K value is varied until the simulated temperature rise equals the experimental one for a given dissipated power and sample shape.
Optothermal Method Verification and Scaling Up for Macroscopic Samples
The Balandin’s group developed a scaled-up version of the optothermal technique for measuring thermal conductivity of thin films using the same Raman spectrometer. In this modification, one needs to fabricate a sample holder with mechanical clips, which ensure a proper thermal contact of the suspended film under study. Due to the film thickness, most of the light power will be absorbed or reflected, with no power penetrating through the film. One needs to measure the reflection coefficient to determine the amount of reflected power. The thermal conductivity has to be determined by solving the heat diffusion equation numerically. Various models can be used to define the light-matter interaction volume, which in turn determines the geometry of the heat. In some cases, analytical approximations can be used. For macroscopic samples such as suspended or supported thin films, several techniques can be used to verify the results. The Balandin’s group verified the optothermal technique data with the measurement results obtained from the “laser flash” (H. Malekpour and A. A. Balandin, J. Raman Spectroscopy, 49, 106 (2018)), “hot disk” (J. D. Renteria, et al., Adv. Funct. Mater., 25, 4664 (2015); B. Wang, et al., Adv. Mater., 1903039 (2019)), and the transient time-resolved magnetooptical techniques (F. Kargar, et al., ACS Nano, 14, 2424 (2020).
Figure 3: Experimental data showing the dependence of the G-peak position in graphene on the temperature. The laser power is kept at a minimum to avoid local heating. The temperature is controlled externally in the cold-hot cell. The curve serves as a calibration for the next step – thermal conductivity measurements. The position of the G-peak indicates the local temperature rise due to laser heating.
In conclusion, the Balandin group’s optothermal technique is a non-contact, steady-state method compatible with standard micro-Raman systems. It allows for (i) direct measurement of in-plane thermal conductivity in suspended or supported thin-film samples; (ii) simultaneous monitoring of structural quality, e.g., defects, strain, and doping via Raman spectra; (iii) adaptation to a broad range of van der Waals materials and composite thin films. This method has become a standard experimental tool in nanoscale thermal transport research, enabling numerous discoveries on phonon engineering and heat management in low-dimensional materials.
Key References for the Optothermal Measurement Technique
[1] A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett., 8, 902 (2008).
[2] S. Ghosh, D. L. Nika, E. P. Pokatilov, and A. A. Balandin, “Heat conduction in graphene: experimental study and theoretical interpretation,” New J. Phys., 11, 95012 (2009).
[3] S. Ghosh, W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, “Dimensional crossover of thermal transport in few-layer graphene,” Nature Mater., 9, 555 (2010).
[4] A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nature Mater., 10, 569 (2011).
[5] D. L. Nika and A. A. Balandin, “Phonons and thermal transport in graphene and graphene-based materials,” Reports Prog. Phys., 80, 36502 (2017).
[6] H. Malekpour and A. A. Balandin, “Raman-based technique for measuring thermal conductivity of graphene and related materials,” J. Raman Spectroscopy, 49, 106 (2018).
[7] A. A. Balandin, “Phononics of graphene and related materials,” ACS Nano, 14, 5170 (2020).