Thermal Conductivity Of Thin Films Research Articles

On optimizing the experimental setup for estimation of the thermal conductivity of thin films

AbstractThe aim of this study is to show the optimal arrangement of a measurement system for estimating the thermal conductivity of thin films from temperature profiles. For this purpose, two different experimental setup systems, with square and circular cross sections, were designed to estimate the thermal conductivity of thin films and, in particular, of two ion exchange membranes. Both systems were placed horizontally and vertically in order to evaluate the best orientation to more accurately determine thermal conductivity. A three-dimensional numerical simulation was performed using Comsol Multiphysics to predict the heat flow and temperature gradient and to evaluate the effect of the geometry and the orientation on the contact resistances. Each system was first calibrated without the membrane inside in order to estimate all the necessary thermal properties of the different materials of the model. Next, the membrane was placed inside the model, so that the model now includes the thermal conductivity of the membrane as the only unknown parameter. The numerical results were compared with the various measured temperature profiles to estimate the thermal conductivity. The thermal conductivity values of the well-known Nafion 117 membrane and other thicker membrane were determined. A very good agreement with reliable literature values was obtained. The approach presented here, combining experimental and simulated temperature profiles, may provide the basis for a practical alternative to better estimate the thermal conductivity of thin films.

Measuring Thermal Conductivity of Single Thickness Fibrous Gas Diffusion Layers Using Transient Plane Source Method

In a proton exchange membrane fuel cell (PEMFC), the gas diffusion layer (GDL) is a porous material placed between the flow field plates and the catalyst layer. Its primary responsibility is to distribute reactants evenly across the surface of the catalyst layer while allowing for the removal of excess water and heat produced during operation. The GDL is typically made of a carbon-based material, such as carbon paper or carbon cloth, which is treated with polytetrafluoroethylene (PTFE) to become hydrophobic. This treatment allows it to repel water and facilitate the transport of gases such as hydrogen and oxygen during operation. The thermal conductivity of the GDL plays a crucial role in managing the heat and water of PEMFCs.The Guarded Heat Flow (GHF) technique is a well-established steady-state method for measuring the thermal conductivity of carbon fiber papers. This is achieved by testing two different thicknesses of a material that have an identical structure [1-3]. Using this two-thickness method, as per ASTM standard C177-19e1 [4], enables the bulk thermal conductivity to be deconvoluted from the thermal contact resistance at the interface between the sample and the measurement device's surface (an interfacial phenomenon). However, materials with identical structures for two-thickness measurements are not always available for commercial GDLs. In this study, we compare the transient plane source (TPS) thin film method, which measures the thermal conductivity of single thickness GDL samples, with the two-thickness GHF method for measuring thermal conductivity.In this study, GDL samples with the same bulk structure and manufactured in two thicknesses were used: Sigracet series 24BA and 34BA with original thicknesses of 190 µm and 280 µm, respectively. A custom-built Thickness Under Compression and Resistance Under Compression machine (TUC-RUC) was utilized to measure the thickness of the samples under loads ranging from 0.35 MPa to 2 MPa. The thickness under compression was measured for five samples (25.4 mm diameter) of each type of GDL. The standard deviation for each sample thickness was below 4%. As shown in Fig. 1, the stress-strain response of the GDL samples was measured and analyzed to assess the similarity in their mechanical structures. Consistent with the assumptions that both samples have the same structure, the GDL samples with two different thicknesses displayed identical stress-strain behavior under compression, as shown by the curve-fit for stress-strain behavior in proposed Fig. 1.The thermal conductivity of the samples was measured using both the TPS thin films method, as per ISO 2207-2:2022 [5], and the GHFM. On the TPS, three samples of each type of GDL were measured three times. The measured thermal conductivities increased with compression, ranging from 0.15 to 0.47 W/mK, with a standard deviation of less than 5% for each measurement. The results from the TPS technique for a single thickness of GDL were compared with the two-thickness measurements conducted using the GHFM, as shown in Figure 2. The GHFM tests were conducted on three samples of each type of GDL at five compressive loads, and the standard deviation on the deconvoluted thermal conductivity was less than 7% for each measurement. The values measured by the two techniques were found to be in good agreement, with a relative difference of within 6%. This study demonstrates that the transient plane source (TPS) method, when combined with an accurate thickness measurement technique, is a precise technique for determining the bulk thermal conductivity of commercial GDLs produced in a single thickness.[1] H. Sadeghifar, N. Djilali, and M. Bahrami, “Effect of Polytetrafluoroethylene (PTFE) and micro porous layer (MPL) on thermal conductivity of fuel cell gas diffusion layers: Modeling and experiments,” Journal of Power Sources, vol. 248, pp. 632–641, Feb. 2014, doi: 10.1016/j.jpowsour.2013.09.136.[2] M. Ahadi, M. Andisheh-Tadbir, M. Tam, and M. Bahrami, “An improved transient plane source method for measuring thermal conductivity of thin films: Deconvoluting thermal contact resistance,” International Journal of Heat and Mass Transfer, vol. 96, pp. 371–380, May 2016, doi: 10.1016/j.ijheatmasstransfer.2016.01.037.[3] E. Sadeghi, N. Djilali, and M. Bahrami, “Effective thermal conductivity and thermal contact resistance of gas diffusion layers in proton exchange membrane fuel cells. Part 1: Effect of compressive load,” Journal of Power Sources, vol. 196, no. 1, pp. 246–254, Jan. 2011, doi: 10.1016/j.jpowsour.2010.06.039.[4] “Test Method for Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus.” ASTM International. Doi: 10.1520/c0177-19e01.[5] “ISO22007-2, Plastics-determination of thermal conductivity and thermal diffusivity-part 2: transient plane heat source (hot disc) method”, 2022. Figure 1

Ultrathin Transparent Nickel Electrodes for Thermoelectric Applications

AbstractIn this work, ultrathin nickel films are developed for application as transparent electrodes in thermoelectric devices. The quality of the films is determined systematically by electrical, optical, and morphological characterization in a series of samples with different thickness. The thermal properties of the films show a dramatic dependence of the Seebeck coefficient on the film thickness. This dependence, with values ranging from −16 to +5 𝜇V K−1 for thicknesses from 10 to 2 nm, includes a change in the behavior of the thermoelectric response from n‐ to p‐type. It has also been demonstrated that the accurate estimation of the thermal conductivity in thin films is challenging due to substrate effects. In this situation, a differential measurement method based on scanning thermal microscopy is proposed, as in these conditions the measurements are less sensitive to the substrate effects. In further works, the dependence of the thermal properties of ultrathin nickel films can be exploited as a tuning parameter for the design of thermoelectric devices.

Structure and Thermal Conductivity of Thin Films of the Si$${}_{{1-x}}$$Ge$${}_{{x}}$$ Alloy Formed by Electrochemical Deposition of Germanium into Porous Silicon

Structure and Thermal Conductivity of Thin Films of the Si$${}_{{1-x}}$$Ge$${}_{{x}}$$ Alloy Formed by Electrochemical Deposition of Germanium into Porous Silicon

Estimating the Thermal Conductivity of Thin Films: A Novel Approach Using the Transient Plane Source Method

Abstract The conventional transient plane source (TPS) method for thin films is used for films and adhesives with thicknesses between 50 and 200 μm. Measurements with the conventional TPS method are usually inaccurate due to thermal contact resistance between the insulating sensor layers, the film and the sensor, and the film and the background material. A new approach to measuring thin films with the TPS is introduced, where the heat flow is constrained to one dimension, and a slab layer made from the same background material is introduced between the thin film and the TPS sensor. This decouples the effects of the thermal contact resistance (TCR) of the sensor to the thermal resistance of the film. The new approach is tested on four different thin films with stainless steel as the background material. The results are compared to guarded heat flowmeter measurements. Excellent agreement (< 12% error) between the two methods is achieved, showing that the new method proposed is fast, accurate, and convenient alternative for determining the thermal conductivity of thin films.

Effects of thermal annealing on thermal conductivity of LPCVD silicon carbide thin films

The thermal conductivity (k) of polycrystalline SiC thin films is relevant for thermal management in emerging SiC applications like microelectromechanical and optoelectronic devices. In such films, k can be substantially reduced by microstructure features including grain boundaries, thin film surfaces, and porosity, although these microstructural effects can also be manipulated through thermal annealing. Here, we investigate these effects by using microfabricated suspended devices to measure the thermal conductivities of nine low-pressure chemical vapor deposition SiC films of varying thicknesses (from 120 to 300 nm) and annealing conditions (as-grown and annealed at 950 and 1100 °C for 2 h, and in one case 17 h). Fourier-transform infrared spectroscopy, x-ray diffraction spectra, and density measurements are also used to characterize the effects of annealing on the microstructure of selected samples. Compared to as-deposited films, annealing at 1100 °C typically increases the estimated grain size from 5.5 to 6.6 nm while decreasing the porosity from around 6.5% to practically fully dense. This corresponds to a 34% increase in the measured thin film thermal conductivity near room temperature from 5.8 to 7.8 W/m K. These thermal conductivity measurements show good agreement of better than 3% with fits using a simple theoretical model based on the kinetic theory combined with a Maxwell–Garnett porosity correction. Grain boundary scattering plays the dominant role in reducing the thermal conductivity of these films compared to bulk single-crystal values, while both grain size increase and porosity decrease play important roles in the partial k recovery of the films upon annealing. This work demonstrates the effects of modifying the microstructure and, thus, the thermal conductivity of SiC thin films by thermal annealing.

Simultaneous Determination of Thermal Conductivity and Heat Capacity in Thin Films with Picosecond Transient Thermoreflectance and Picosecond Laser Flash

ABSTRACT Combining the picosecond transient thermoreflectance (ps-TTR) and picosecond laser flash (ps-LF) techniques, we have developed a novel method to simultaneously measure the thermal effusivity and the thermal diffusivity of metal thin films and determine the thermal conductivity () and the heat capacity () altogether. In order to validate our approach and evaluate the uncertainties, we analyzed five different metal films (Al, Cr, Ni, Pt, and Ti) with thicknesses ranging from 297 nm to 1.2 µm. Our results on thermal transport properties and heat capacity are consistent with reference values, with the uncertainties for the thermal conductivity and the heat capacity measurements below 25% and 15%, respectively. Compared with the ps-TTR technique alone, the combined approach substantially lowers the uncertainty of the thermal conductivity measurement. Uncertainty analyses on various materials show that this combined approach is capable of measuring most of the materials with a wide range of thicknesses, including those with low thermal conductivity (e.g., mica) down to thicknesses as small as 60 nm and ultrahigh thermal conductivity materials (such as cubic BAs) down to 1400 nm. Simultaneous measurement of thermal conductivity and heat capacity enables exploration of the thermal physical behavior of materials under various thermodynamic and mechanical perturbations, with potential applications in thermal management materials, solid-state phase transitions, and beyond.

Effect of nanostructuring on thermoelectric performance of SiGe thin films

We experimentally investigated the effect of nanostructuring on the thermoelectric performance of SiGe thin films. Nanoscale porous structures were fabricated using lithography in a top-down approach to reduce the thermal conductivity of the thin films and the thermoelectric figure of merit (ZT) was evaluated. The thermal conductivity of nanostructured SiGe thin films is up to 24% lower than that of thin film without nanostructure while the electrical conductivity is up to about 19% lower, resulting in a 4% increase in ZT value to 0.041 at RT. Since the mean free path (MFP) of phonons in SiGe is short compared to the characteristic length of the nanostructures, the effect of nanostructuring on thermoelectric performance is limited. Nanostructuring is known as a promising method to increase ZT values. However, it is only effective when the thermal phonon MFPs are comparable to the characteristic length of the nanostructure.

A dual-domain 3 ω method for measuring the in-plane thermal conductivity of high-conductive thin films

The thermal conductivity measurement of films with submicrometer thicknesses is difficult due to their exceptionally low thermal resistance, which makes it challenging to accurately measure the temperature changes that occur as heat flows through the film. Thus, specialized and sensitive measurement techniques are required. 3ω method is a widely used and reliable tool for measuring the thermal conductivity of films. However, the high in-plane thermal conductivity in thin films results in rapid heat dissipation across the thin film, resulting in poor measurement sensitivity and making it difficult to accurately measure the temperature gradient with the traditional 3ω method. Also, the traditional 3ω method requires cross-plane thermal conductivity to derive the in-plane counterpart. Here, we introduce a dual-domain 3ω method that adopts AC-modulated heating and electrode arrays facilitating surface temperature profiling: (1) the sensitivity was significantly improved due to the employment of low-thermal-conductivity-substrate, and (2) cross-plane thermal conductivity is not required for the analysis of in-plane counterpart. This measurement platform allows us to control heat penetration in depth via varied heating frequencies as well as spatial temperature detection through laterally distributed electrodes on the thin film surface. By utilizing the described method, we have determined the in-plane thermal conductivity of a copper film, having a thickness of 300 nm, which was found to be 346 Wm−1K−1 and validated by the Wiedemann–Franz law.

Picosecond magneto-optic thermometry measurements of nanoscale thermal transport in AlN thin films

The thermal conductivity Λ of wide bandgap semiconductor thin films, such as AlN, affects the performance of high-frequency devices, power devices, and optoelectronics. However, accurate measurements of Λ in thin films with sub-micrometer thicknesses and Λ > 100 W m−1 K−1 is challenging. Widely used pump/probe metrologies, such as time–domain thermoreflectance (TDTR) and frequency–domain thermoreflectance, lack the spatiotemporal resolution necessary to accurately quantify thermal properties of sub-micrometer thin films with high Λ. In this work, we use a combination of magneto-optic thermometry and TiN interfacial layers to significantly enhance the spatiotemporal resolution of pump/probe thermal transport measurements. We use our approach to measure Λ of 100, 400, and 1000 nm AlN thin films. We coat AlN thin films with a ferromagnetic thin-film transducer with the geometry of (1 nm-Pt/0.4 nm-Co)x3/(2 nm-TiN). This PtCo/TiN transducer has a fast thermal response time of <50 ps, which allows us to differentiate between the thermal response of the transducer, AlN thin film, and substrate. For the 100, 400, and 1000 nm thick AlN films, we determine Λ to be 200 ± 80, 165 ± 35, and 300 ± 70 W m−1 K−1, respectively. We conclude with an uncertainty analysis that quantifies the errors associated with pump/probe measurements of thermal conductivity, as a function of transducer type, thin-film thermal conductivity, and thin-film thickness. Time resolved magneto-optic Kerr effect experiments can measure films that are three to five times thinner than is possible with standard pump/probe metrologies, such as TDTR. This advance in metrology will enable better characterization of nanoscale heat transfer in high thermal conductivity material systems like wide bandgap semiconductor heterostructures and devices.

Thermal conductivity measurement of thermoelectric films using transient Photo-Electro-Thermal technique

Accurate and rapid measurement of thermal conductivity of thin films has been a challenge so far in the field of thermoelectric (TE) materials and devices. Herein, we proposed to use a transient photo-electro-thermal (TPET) technique to measure the thermal conductivity of TE thin-films with convenience. Combining theoretical and experimental methods, we found that the TPET technique using laser beam heating can significantly reduce the influence of Peltier effect and thus achieve high test accuracy. The measurement uncertainty of TPET technique for TE films can be depressed below 10%. Furthermore, this method is not only applicable for free-standing thin film, but also for thin film deposited on as-known substrates. Finally, thermal conductivity of several films including p-type Bi0.5Sb1.5Te3, n-type Ag2Se, and n-type Bi2Te3 deposited on PI film at different temperature are accurately measured, which demonstrates the wide applicability of TPET technique on semiconductor films.

Analytical Determination of the Effective Thermal Conductivity of Heterophase Surface Layers, Coatings, and Thin Films in Heavy-Loaded Tribosystems

Analytical Determination of the Effective Thermal Conductivity of Heterophase Surface Layers, Coatings, and Thin Films in Heavy-Loaded Tribosystems

Estimating thin-film thermal conductivity by optical pump thermoreflectance imaging and finite element analysis

We introduce a noncontact experiment method to estimate thermal conductivity of nanoscale thin films by fitting high spatial resolution thermoreflectance images of surface spot heating to a finite element simulated temperature distribution. The thin-film top surface is heated by a 1μm diameter focused, 825 nm wavelength laser spot. The surface temperature distribution in the excited sample is imaged by thermoreflectance microscopy with submicrometer spatial resolution and up to 10 mK temperature resolution. Thin-film thermal conductivity is extracted by fitting a measured surface temperature distribution to a 3D finite element temperature model. The method is demonstrated by estimating thermal conductivity for an isotropic thin-film metal (nickel, 60–260 nm) on a glass substrate. The fitted Ni thermal conductivity was 50 ± 5 W/m K, which is in good agreement with the literature. Also, we present a detailed finite element analysis for an anisotropic thin-film semiconductor sample to show how the method could be extended to estimate thermal conductivity of anisotropic thin films. Advantages of the new method are easy sample preparation (no top surface transducer film or integrated heater required), rapid in situ measurement, and application to a broad range of thin-film materials.

Time-resolved vibrational-pump visible-probe spectroscopy for thermal conductivity measurement of metal-halide perovskites.

Understanding thermal transport at the microscale to the nanoscale is crucially important for a wide range of technologies ranging from device thermal management and protection systems to thermal-energy regulation and harvesting. In the past decades, non-contact optical methods, such as time-domain and frequency-domain thermoreflectance, have emerged as extremely powerful and versatile thermal metrological techniques for the measurement of material thermal conductivities. Here, we report the measurement of thermal conductivity of thin films of CH3NH3PbI3 (MAPbI3), a prototypical metal-halide perovskite, by developing a time-resolved optical technique called vibrational-pump visible-probe (VPVP) spectroscopy. The VPVP technique relies on the direct thermal excitation of MAPbI3 by femtosecond mid-infrared optical pump pulses that are wavelength-tuned to a vibrational mode of the material, after which the time dependent optical transmittance across the visible range is probed in the ns to the μs time window using a broadband pulsed laser. Using the VPVP method, we determine the thermal conductivities of MAPbI3 thin films deposited on different substrates. The transducer-free VPVP method reported here is expected to permit spectrally resolving and spatiotemporally imaging of the dynamic lattice temperature variations in organic, polymeric, and hybrid organic-inorganic semiconductors.

Structural optimization of silicon thin film for thermoelectric materials

The method to optimize nanostructures of silicon thin films as thermoelectric materials is developed. The simulated annealing method is utilized for predicting the optimized structure. The mean free path and thermal conductivity of thin films, which are the objective function of optimization, is evaluated by using phonon transport simulations and lattice dynamics calculations. In small systems composed of square lattices, the simulated annealing method successfully predicts optimized structure corroborated by an exhaustive search. This fact indicates that the simulated annealing method is an effective tool for optimizing nanostructured thin films as thermoelectric materials.

A simple numerical method for evaluating heat dissipation from curved wires with periodic applied heating

In many situations, the dual-purpose heater/thermometer wires used in the three-omega method—one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces—must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that, in some cases, curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calculate the temperature of three-omega heating wires with arbitrary wire geometries. This method provides experimentalists with a simple quantitative procedure for calculating how large the systematic error caused by a particular wire asymmetry will be. We show calculations of two useful cases: a straight wire with a single bend of arbitrary angle and a wire that forms a circle. We find that the amplitude of the in-phase temperature oscillations near a wire that forms a circle differs from the prediction using the analytic straight-line source solution by <12%, provided that the thermal penetration depth is less than ten times the radius of curvature of the wire path. The in-phase temperature amplitude 1.5 wire widths away from a 90° bend in a wire is within 11% of the straight-line source prediction for all penetration depths greater than the wire width. Our calculations indicate that the straight-line source solution breaks down significantly when the wire bend angle is less than 45°.

Estimating the uncertainty of measurements of thermal conductivity of thin films of thermoelectrics with the 3-omega method

Using the method of computer simulation, the uncertainty of measurements of the thermal conductivity of silicon, which is often used as substrates, and also thin films based on bismuth, is estimated. The influence of the application of an additional dielectric layer between the thermoelectric film and the resistive heater on the measurement results is shown.

Controlled Lattice Thermal Conductivity of Transparent Conductive Oxide Thin Film via Localized Vibration of Doping Atoms.

Amorphization using impurity doping is a promising approach to improve the thermoelectric properties of tin-doped indium oxide (ITO) thin films. However, an abnormal phenomenon has been observed where an excessive concentration of doped atoms increases the lattice thermal conductivity (κl). To elucidate this paradox, we propose two hypotheses: (1) metal hydroxide formation due to the low bond enthalpy energy of O and metal atoms and (2) localized vibration due to excessive impurity doping. To verify these hypotheses, we doped ZnO and CeO2, which have low and high bond enthalpies with oxygen, respectively, into the ITO thin film. Regardless of the bond enthalpy energy, the κl values of the two thin films increased due to excessive doping. Fourier transform infrared spectroscopy was conducted to determine the metal hydroxide formation. There was no significant difference in wave absorbance originating from the OH stretching vibration. Therefore, the increase in κl due to the excessive doping was due to the formation of localized regions in the thin film. These results could be valuable for various applications using other transparent conductive oxides and guide the control of the properties of thin films.

Thermal Conductivity of β-Phase Ga2O3 and (AlxGa1-x)2O3 Heteroepitaxial Thin Films.

Heteroepitaxy of β-phase gallium oxide (β-Ga2O3) thin films on foreign substrates shows promise for the development of next-generation deep ultraviolet solar blind photodetectors and power electronic devices. In this work, the influences of the film thickness and crystallinity on the thermal conductivity of (2̅01)-oriented β-Ga2O3 heteroepitaxial thin films were investigated. Unintentionally doped β-Ga2O3 thin films were grown on c-plane sapphire substrates with off-axis angles of 0° and 6° toward ⟨112̅0⟩ via metal-organic vapor phase epitaxy (MOVPE) and low-pressure chemical vapor deposition. The surface morphology and crystal quality of the β-Ga2O3 thin films were characterized using scanning electron microscopy, X-ray diffraction, and Raman spectroscopy. The thermal conductivities of the β-Ga2O3 films were measured via time-domain thermoreflectance. The interface quality was studied using scanning transmission electron microscopy. The measured thermal conductivities of the submicron-thick β-Ga2O3 thin films were relatively low as compared to the intrinsic bulk value. The measured thin film thermal conductivities were compared with the Debye-Callaway model incorporating phononic parameters derived from first-principles calculations. The comparison suggests that the reduction in the thin film thermal conductivity can be partially attributed to the enhanced phonon-boundary scattering when the film thickness decreases. They were found to be a strong function of not only the layer thickness but also the film quality, resulting from growth on substrates with different offcut angles. Growth of β-Ga2O3 films on 6° offcut sapphire substrates was found to result in higher crystallinity and thermal conductivity than films grown on on-axis c-plane sapphire. However, the β-Ga2O3 films grown on 6° offcut sapphire exhibit a lower thermal boundary conductance at the β-Ga2O3/sapphire heterointerface. In addition, the thermal conductivity of MOVPE-grown (2̅01)-oriented β-(AlxGa1-x)2O3 thin films with Al compositions ranging from 2% to 43% was characterized. Because of phonon-alloy disorder scattering, the β-(AlxGa1-x)2O3 films exhibit lower thermal conductivities (2.8-4.7 W/m·K) than the β-Ga2O3 thin films. The dominance of the alloy disorder scattering in β-(AlxGa1-x)2O3 is further evidenced by the weak temperature dependence of the thermal conductivity. This work provides fundamental insight into the physical interactions that govern phonon transport within heteroepitaxially grown β-phase Ga2O3 and (AlxGa1-x)2O3 thin films and lays the groundwork for the thermal modeling and design of β-Ga2O3 electronic and optoelectronic devices.

Phonon and Thermal Properties of Thin Films Made from WS2 Mono- and Few-Layer Flakes

We first report the temperature phonon properties of a large-area thin film (lateral size: ∼mm, thickness ∼50 nm) made from WS2 mono and few layers deposited on the SiO2/Si substrate. We show that temperature phonon properties probed by Raman spectroscopy significantly differ for bulk and thin-film systems in a temperature range of 90–450 K; however, both exhibit strong temperature-dependent phonon energy nonlinear behavior. Employing the optothermal Raman method, we also estimate thin-film thermal conductivity (κ = 4.3 W/(m K)) and thermal interface conductance (g = 5.5 MW/(m2 K)) at room temperature. We find that the thermal properties of thin films (κ and g) are 1 order of magnitude lower than that for bulk or monolayer WS2, which is caused by a reduction in flake size and an increase in boundary scattering. This finding is important for heat management in future applications of thin films made from two-dimensional (2D) nanoflakes.