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## Creator

[Abdulkareem Alasli](https://orcid.org/0000-0002-1681-0492), [Ryo Iguchi](https://orcid.org/0000-0002-8112-4608), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Hosei Nagano](https://orcid.org/0000-0003-4926-2768)

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Abdulkareem Alasli, Ryo Iguchi, Ken-ichi Uchida, Hosei Nagano; Measurements of in-plane thermophysical properties on nanoscale-thick films by lock-in thermography. Appl. Phys. Lett. 27 January 2025; 126 (4): 044102 and may be found at https://doi.org/10.1063/5.0245566.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Measurements of in-plane thermophysical properties on nanoscale-thick films by lock-in thermography](https://mdr.nims.go.jp/datasets/1a004645-5280-46a8-8ba1-fe97e5e43476)

## Fulltext

1  Measurements of in-plane thermophysical properties on nanoscale-thick films 1 by lock-in thermography 2  3 Abdulkareem Alasli,1,* Ryo Iguchi,2 Ken-ichi Uchida2,3, and Hosei Nagano1 4  5 1 Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8601, Japan 6 2 National Institute for Materials Science, Tsukuba 305-0047, Japan 7 3 Department of Advanced Materials Science, Graduate School of Frontier Sciences, The 8 University of Tokyo, Kashiwa 277-8561, Japan 9 * Authors to whom correspondence should be addressed: al.asli.abdulkareem.m6@f.mail.nagoya-10 u.ac.jp 11  12 Abstract 13 We demonstrate a versatile technique for measuring the in-plane thermal conductivity, in-plane 14 thermal diffusivity, and volumetric heat capacity of nanoscale-thick films by means of lock-in 15 thermography. The technique relies on the thermal analyses of the imaged lock-in temperature 16 distribution over the surface of the films generated by an on-chip line heater. This enables 17 simultaneous estimation of the properties for a free-standing membrane or multilayered thin films 18 deposited on the membrane. We validate the usability of the technique by determining the 19 thermophysical properties of Ni films with different nanoscale thicknesses. This technique also 20 enables the measurements under an external magnetic field, facilitating investigating magneto-21 thermal transport properties. Thus, the proposed approach will be useful for exploring nanoscale 22 thermal transport properties in thin films and thermal management systems. 23 2  Thin films refer to a class of materials of small thicknesses ranging from sub-nanometers 24 to a few micrometers. Due to their unique properties, thin films are widely implemented in various 25 applications including electronics,1 microelectromechanical systems,2,3 thermal barrier coatings,4 26 optoelectronics,5 spintronics,6 magnetics,7 and thermoelectrics.8 Characterizing thermophysical 27 properties and understanding thermal behaviors of thin films are crucial for optimizing the 28 performance and stability of these applications. They also play a key-role in elucidating the 29 physical phenomena behind the store, conversion, and transport of thermal energy in such thin 30 structures, thereby pushing the limits for developing more advanced materials and systems with 31 enhanced heat transfer and energy efficiency. 32  The thermophysical properties of thin films often exhibit distinct values and behaviors from 33 their bulk counterparts.9–11 This fact and the small physical dimension of the material made the 34 accurate assessing of the properties quite challenging with conventional measurement techniques.10 35 For instance, the thermal conductivity κ of thin films is often anisotropic, i.e., in-plane κ and out-36 of-plane κ conduct heat differently even for materials whose bulk form is isotropic. In-plane κ and 37 out-of-plane κ may depend on the nanoscale thickness of the thin films and usually demonstrate 38 lower values than of the bulk materials.10,12 To accurately determine κ under these constraints, 39 various methods, such as laser- and electrothermal-based techniques, have been intensively 40 developed.13 Among them, the 3ω method14 and transient thermoreflectance technique in both 41 time15 and frequency16 domains took the lead. Despite the outstanding performance of these 42 methods for out-of-plane κ measurements, achieving the similar sensitivity and accuracy for in-43 plane κ measurements remains a challenge.17,18 Determining additional thermophysical properties, 44 such as in-plane thermal diffusivity D and volumetric heat capacity 𝜌𝑐p, also entails analogous 45 difficulties, where a wide range of complex and time-consuming experiments19 with larger 46 3  uncertainties are involved. This motivates the development of different approaches for measuring 47 in-plane thermophysical properties of thin films. 48  A versatile approach for measuring multiple in-plane thermophysical properties of thin 49 films can be achieved by means of lock-in thermography (LIT). LIT is an active thermal imaging 50 technique that enables noncontact detection of the thermal response in a material to a periodic 51 heating with high temperature resolution.20 LIT has distinguished itself in measuring various 52 properties including D,21 interfacial thermal resistance,22 mapping thermophysical properties of 53 composites,23 thermoelectric figure of merit,24,25 magneto-thermoelectric effects,26–28 thermo-spin 54 effects,29,30 as well as magnetocaloric,31 elastocaloric,32 and electrocaloric effects.33 Reference 34 55 has offered a LIT-based method for analyzing the in-plane thermophysical properties of a single 56 free-standing thin film at micrometer-scale thickness with a line-shaped laser light as a heating 57 source. Nevertheless, the measurements are impeded by the need to ascertain the optical properties 58 of the film to quantify the coupled power from the laser, which is essential to determine in-plane κ 59 and 𝜌𝑐p.34 The measurement accuracy is also noticeably affected by the width and uniformity of 60 the laser line, and the need for double-side black paint coating (~15 μm on each side) to enhance 61 the absorptivity and emissivity of thin films.34 In this paper, we facilitate the LIT-based method to 62 enable the determination of the in-plane D, in-plane 𝜅 , and 𝜌𝑐p  for nanoscale-thick single or 63 multilayered films with high sensitivity and reliability. With the versatility of this technique, we 64 extend the measurements under magnetic fields, enabling systematic investigations on magneto-65 thermal transport/resistance properties of thin films. 66  Figure 1 illustrates the main principle of the LIT-based measurement method. This method 67 enables the determination of thermophysical properties in single-layer or multilayer thin film 68 structures. The setup consists of an infrared camera connected to an LIT processing system and a 69 4  current source. The sample can take the form of a single-layer or multilayer thin film structure, 70 either free-standing or deposited on a suspended membrane. The heating source is a thin metallic 71 line heater deposited on the other side of the structure with the configuration shown in Fig. 1. The 72 line heater is excited by the current source with a half square-wave-modulated charge current with 73 the frequency f, amplitude 𝐽c, and DC offset 𝐽c/2. Subsequently, an oscillating heat release due to 74 the Joule heating 𝑄 = 𝑅𝐽c2 is induced in the line heater with the same f, where R is the resistance 75 of the line heater. 𝑄 diffuses symmetrically within the membrane/thin film structure depending on 76 their effective in-plane thermal diffusivity 𝐷eff, effective in-plane thermal conductivity 𝜅eff, and 77 effective volumetric heat capacity (𝜌𝑐p)eff defined as follows:35  78 𝐷eff =∑ 𝜅𝑛𝑡𝑛∑𝜅𝑛𝐷𝑛𝑡𝑛, (1) 79 𝜅eff =∑ 𝜅𝑛𝑡𝑛∑ 𝑡𝑛, (2) 80 (𝜌𝑐p)eff =∑(𝜌𝑐p)𝑛𝑡𝑛∑ 𝑡𝑛, (3) 81 where 𝑡𝑛  is the thickness of the layer n. The infrared camera images the transient temperature 82 modulation 𝑇̃ response on the thin film side by taking the directional spectral emissivity of the thin 83 film and detectable wavelength range of the camera sensor into consideration. The LIT system 84 accordingly extracts the amplitude 𝐴  and phase lag 𝜙  of 𝑇̃  at the first harmonic by the Fourier 85 analysis at each pixel. The 𝐴 and 𝜙 images show the spatial distribution of the magnitude and time 86 delay of 𝑇̃ due to the heat diffusion, respectively. By performing the thermal analyses on the LIT 87 images, we can obtain the in-plane 𝐷eff, in-plane 𝜅eff, and (𝜌𝑐p)eff [Fig. 1 (b)], as detailed below. 88  To perform the thermal analyses, we solve the one-dimensional heat equation along the 89 transverse axis 𝑥 for an infinitely large thermally thin n-layer structure with the line heater located 90 at x = 0 (Fig. 1).34,36 By accounting for the heat loss effects of thermal radiation and convection 91 5  through the combined heat transfer coefficient h,12,34 𝐴 and 𝜙 of the steady periodic solution of 𝑇̃ 92 at in relation to the first harmonic of Joule heating are respectively 93 𝐴(𝑥) = |𝑇̃(𝑥)| =𝑅𝐽c2𝜋𝜅eff𝑙𝑡tot(√(𝜔𝐷eff )2+ (2ℎ𝑡tot𝜅eff)2)−1/2𝑒− |𝑥|/ΛA, (4) 94 𝜙 (𝑥) = − arg[𝑇̃(𝑥)] = +|𝑥|Λ𝜙+ tan−1 Λ𝐴Λ𝜙−𝜋4, (5) 95 where 𝜅eff is the effective thermal conductivity of the structure, l the heater length, 𝑡tot = ∑ 𝑡𝑛 the 96 sum of the layer thicknesses, and 𝜔 = 2𝜋𝑓 the angular frequency. Λ𝐴 and Λ𝜙 are respectively the 97 thermal diffusion lengths of A and , which are expressed as 98 Λ𝐴 = (√(𝜔2𝐷eff )2+ (ℎ𝑡tot𝜅eff)2+ℎ𝑡tot𝜅eff)−1/2, (6) 99 Λ𝜙 = (√(𝜔2𝐷eff )2+ (ℎ𝑡tot𝜅eff)2−ℎ𝑡tot𝜅eff)−1/2. (7) 100 By utilizing Eqs. (4)-(7), in-plane 𝐷eff, in-plane 𝜅eff, and (𝜌𝑐p)eff are obtained as follow, as also 101 summarized in Fig. 1(b). In-plane 𝐷eff can be first obtained from the geometric mean 102 √Λ𝐴Λ𝜙 = √2𝐷eff𝜔, (8) 103 by measuring Λ𝐴 and Λ𝜙 at a specific 𝜔.37 On the other hand, in-plane 𝜅eff and h can be determined 104 from the difference  105 1Λ𝐴2 −1Λ𝜙2 =2ℎ𝑡tot𝜅eff, (9) 106 and A [Eq. (4)] at the line heater position with the knowledge of 𝑡tot, l, 𝐽c, and R. It is important to 107 6  emphasize here that a temperature calibration of the LIT system is required for this step to 108 determine A quantitatively (Sec. S1 in the supplementary material). Finally, (𝜌𝑐p)eff can be 109 extracted from  110 (𝜌𝑐p)eff=𝜅eff𝐷eff. (10) 111 Equations (4)-(10) can be used to directly determine the effective properties of multilayered or the 112 properties of single thin film structures from a single LIT measurement. However, to obtain the 113 individual properties of each layer n in the multilayered thin film structure, a sequence of LIT 114 measurements and analyses must be performed on sequenced deposited layers with taking into 115 account Eqs. (1)-(3). It is critical to point out that this solution is valid under the following 116 conditions. First, the suspended multilayered film/membrane structures should be thermally thin, 117 meaning that the temperature gradient in the out-of-plane direction is negligibly small. This can be 118 satisfied when the total thickness of the multilayer is much smaller than Λ. 119 To demonstrate the proposed LIT-based method, we measured and analyzed the thermal 120 response from Ni thin films at different thicknesses. The 50-, 100-, and 150-nm-thick Ni thin films 121 were deposited on a commercially available 200-nm-thick SiN membrane from NTT-AT 122 Corporation, Japan, by the magnetron sputtering method. Further details on the structural 123 characterization of the thin films are provided in Sec. S2 of the supplementary materials. The Au 124 line heater with four-pads configuration was fabricated on the other side of the membrane by the 125 lift-off process at a width of 15 μm and a thickness of 50 nm. For the LIT measurements, the thin 126 film/membrane structure is positioned in the focal plane of a science grade infrared camera 127 (SC5600, FLIR Systems, USA) with 5× lens and spectral response range of 2.5-5.1 μm with the 128 thin film side facing the lens. For measuring the thermophysical properties of only the SiN 129 membrane, the imaged side was coated with ~80 nm ultrapure (99.9%) high emissivity graphite by 130 7  vapor-deposition based carbon coater (CADE-4TE, Meiwafosis CO., Japan) since the SiN 131 membrane is highly transparent in the wavelength range of the camera.38 This was not needed for 132 the other Ni/SiN samples owing to the finite emissivity of the Ni films. The measurements of all 133 samples were performed while applying 𝐽c with a half-square wave form at f = 20 Hz to the line 134 heater at room temperature to minimize the effect of heat losses.25 R was measured by the four-135 probe method and the amplitude of 𝐽c  was adjusted to sustain a relatively equivalent 𝑄  for all 136 measured samples. The thermal analyses were performed on LIT images obtained from >2000 137 periods at the maximum camera frame rate (100 Hz) at the full frame size after recaching the 138 thermal equilibration.  139 Figure 2(a) shows the calibrated 𝐴/𝑄 and  images at f = 20.0 Hz for the samples with 140 different Ni thicknesses. Figure 2(b) shows the corresponding line profiles along the x direction. 𝐴 141 is divided by 𝑄 to eliminate the electrical properties of the line heater effect on the thermal response. 142 A clear temperature modulation signal induced by 𝑄 from the line heater can be observed with the 143 thermal diffusion pattern over the surface of the membrane and thin film structures. The magnitude 144 of 𝐴/𝑄  is maximized at the position of the line heater (x = 0 mm). The 𝐴/𝑄  ( ) values then 145 exponentially decay (linearly change) with the distance from the heater with symmetrical 146 distribution [Fig. 2(b)]. Furthermore, the magnitude of 𝐴/𝑄 notably decreases with the increment 147 of the Ni thickness. The exponential decay rate of 𝐴/𝑄 and the slope of  also decrease with the 148 Ni thickness increment, indicating a higher in-plane 𝐷eff for the thicker Ni films on the membrane. 149 These behaviors are consistent with Eqs. (4)-(7) as also emphasized by the fitting lines in Fig. 2(b), 150 highlighting the ability of the LIT method in detecting the variations in thermal response in thin 151 films due to the nanoscale thickness change. 152 Consequently, the thermophysical properties of the SiN membrane were directly obtained 153 8  by analyzing the corresponding LIT images in Fig. 2 at T = 298 K. The in-plane D of SiN was 154 determined to be 1.43 mm2·s−1 from √Λ𝐴Λ𝜙 [Eq. (8)] by fitting the averaged 𝐴 and 𝜙 data [Fig. 2 155 (b)] using Eqs. (3) and (4), respectively. Λ𝐴 was extracted from the exponential decay rate of A, 156 while Λ𝜙 is extracted from the slope of 𝜙. Here, there is no direct effect from the 𝐴 calibration or 157 heat losses since √Λ𝐴Λ𝜙 depends only on in-plane 𝐷 and 𝜔 [Eq. (8)]. Subsequently, the in-plane 158 𝜅 and h were obtained as 2.78 W·m−1·K−1 and 4.74 W·m−2·K−1, respectively, from 1Λ𝐴2⁄ − 1Λ𝜙2⁄  159 and 𝐴  at the line heater (x = 0) [see Eq. (3)], involving two unknowns with two equations. 160 Accordingly, 𝜌𝑐p is 1.95 MJ·m−3·K−1. The obtained values here are consistent with the literature 161 results for SiN membranes of similar thickness39,40 However, it is important to emphasize that the 162 accuracy of the 𝐴 calibration (Secs. S1 and S3) play a key role in the accurate assessment of the 163 in-plane 𝜅  and 𝜌𝑐p . Moreover, the unavoidable usage of the black coating layer for the SiN 164 membrane also affects the accuracy of the measurements. However, this effect can be compensated 165 with the knowledge of the thickness and the thermophysical properties of the coating layer.12,37 166 With considering the thermophysical properties of SiN, the thickness dependence of the in-167 plane 𝐷, in-plane 𝜅, and 𝜌𝑐p at T = 298 K was obtained for the deposited Ni thin films, as plotted 168 in Figs. 3(a)-3(c), respectively. The in-plane 𝐷, in-plane κ, and 𝜌𝑐p for the Ni thin films exhibit 169 obvious thickness dependence. The values of the in-plane 𝐷 and in-plane κ (𝜌𝑐p) for the Ni films 170 increase (decrease) with the thickness and approach the value of bulk Ni at a thickness of 150 nm. 171 These behaviors are consistent with the previous observation on metal nanocrystalline materials.41–172 45 The main reasons behind these behaviors can be attributed to the notable sputtered grain-173 boundary,46 impurities, softening of surface phonons,43 and defects in the nanocrystalline structure. 174 The surface scattering of electrons also contributes to the reduction of the in-plane 𝜅  (and 175 9  consequently the in-plane 𝐷) with decreasing thickness, given the considerable role of electronic 176 part of 𝜅 in thin metallic films.47–49 This also coincides with the observations that the electrical 177 conductivity diminishes as the thickness of thin films decreases.50,51 These effects decrease with 178 the thickness increment and thus the properties approach the values of the bulk materials. The 179 reported in-plane κ values of 83-nm-thick50 and ~400-nm-thick46 Ni thin films are respectively ~25 180 and ~65 W·m−1·K−1, which are consistent with our measurements. These results show the 181 capability of the LIT-based method in measuring the nanoscale thickness dependency of the in-182 plane thermophysical properties for thin films. It is important to emphasize here that achieving 183 accurate and reliable measurements necessitates addressing potential sources of systematic error, 184 implementing strategies to minimize them, and accounting for the sensitivity limitations inherent 185 to the method, as detailed in Sec. S3 of the supplementary material. 186 To showcase the versatility of the method, we conducted the same LIT measurements and 187 thermal analyses on the samples while applying a magnetic field H. A uniform H with the 188 magnitude 𝜇0𝐻  = 150 mT, with 𝜇0  being the vacuum permeability, was applied using an 189 electromagnet. The potential sources of systematic errors (Sec. S3 in the supplementary material) 190 were carefully considered in both parallel 𝐇∥ and perpendicular 𝐇⊥ orientations to the axis of the 191 in-plane thermal gradient ∇𝑇  induced by the line heater (Fig. 1). We focused here on the field 192 orientation dependence of the in-plane κ for the Ni film as a direct indicator of the magneto-thermal 193 resistance effect since 𝜌𝑐p  is typically field independent.24 Figure 4 shows the 194 thickness dependence of in-plane 𝜅 for various magnetic field configurations (see also Sec. S4 in 195 the supplementary material showing the corresponding LIT images). The results show good 196 consistency with the values estimated from the LIT measurements performed with the absence of 197 H. A small but finite decay in the in-plane 𝜅 was observed in the 100- and 150-nm-thick Ni films 198 10  at the 𝐇∥ and 𝐇⊥ measurements, while no clear H dependence was observed for the 50-nm-thick 199 film. Moreover, no obvious anisotropic magneto-thermal resistance behavior can be claimed for all 200 the films. This result can be attributed to the low magneto-thermal resistance of Ni at room 201 temperature,52,53 which falls below the sensitivity of the used LIT system with respect to the low 202 directional spectral emissivity of the metal thin films. Here we emphasize that all measurement and 203 analysis procedures can be performed without any restrictions in the presence of magnetic fields. 204 Thus, despite the absence of clear directional magnetic-field- or magnetization-dependent effects 205 in the studied Ni thin films, the LIT-based method remains valuable as it allows for versatile 206 measurements of the giant magneto-thermal resistance and H dependence of the thermophysical 207 properties in spintronic multilayers. Importantly, although the current-perpendicular-to-plane giant 208 magneto-thermal resistance in spintronic multilayers has been observed using the time-domain 209 thermoreflectance method,54,55 our LIT-based method enables the investigation of the current-in-210 plane giant magneto-thermal resistance, accelerating studies on spintronic thermal management.56  211  In conclusion, we presented a method for determining the in-plane thermophysical 212 properties of nanoscale-thick films by means of the LIT technique. The in-plane 𝐷, in-plane κ, and 213 cp of a single or multilayered free-standing structure can be extracted from the thermal analyses 214 of the transient temperature distribution induced by Joule heating from a deposited metallic line 215 heater. This enables systematic and versatile investigations of thermophysical properties with high 216 sensitivity and reliability. The validity and sensitivity of the method were demonstrated by 217 measuring the thermal properties of the Ni thin films deposited on the suspended SiN membranes 218 at different Ni thicknesses. The method also facilitates performing measurements under magnetic 219 fields enabling the study of thermal magneto-resistance effects. Thus, the proposed LIT-based 220 approach will be useful for the investigation of magneto-thermal transport/resistance, and 221 11  thermoelectric properties, as well as thermal rectification effects in thin films.57 To expand the 222 scope of the method, future studies should incorporate direct electrical resistivity measurements of 223 thin films, which requires redesigning the thin film structure to integrate a four-probe configuration. 224 This enables more rigorous analysis of thermal and electrical transport properties.50 225  226 Supplementary material 227 See the supplementary material for details on the calibration of LIT detected temperature, structural 228 characterization of the thin films, systematic sources of errors, and magnetic field dependence of 229 temperature modulation signals. 230  231 Acknowledgments 232 This work was supported by CREST “Creation of Innovative Core Technologies for Nano-enabled 233 Thermal Management” (Grant No. JPMJCR17I1) and ERATO "Magnetic Thermal Management 234 Materials" (Grant No. JPMJER2201) from JST, Japan. 235  236 Disclosure statement 237 No conflict of interest was reported by the authors. 238  239 Data availability statement 240 The data that support the findings of this study are available from the corresponding author upon 241 reasonable request. 242  243 12  References 244 1 S. Gupta, W. Navaraj, L. Lorenzelli, and R. Dahiya, Npj Flex. Electron. 2, 8 (2018). 245 2 G. Sim, J. Krogstad, K. Reddy, K. Xie, G. Valentino, T. Weihs, and K. Hemker, Sci. Adv. 3, 246 e1700685 (2017). 247 3 S. Takamatsu, S. Goto, M. Yamamoto, T. Yamashita, T. Kobayashi, and T. Itoh, Sci. Rep. 9, 248 1893 (2019). 249 4 N. Padture, M. Gell, and E. Jordan, Science 296, 280 (2002). 250 5 J. An, X. Zhao, Y. Zhang, M. Liu, J. Yuan, X. Sun, Z. Zhang, B. Wang, S. Li, and D. Li, Adv. 251 Funct. Mater. 32, 1 (2022). 252 6 A. Hirohata, K. Yamada, Y. Nakatani, I. Prejbeanu, B. Diény, P. Pirro, and B. Hillebrands, J. 253 Magn. Magn. Mater. 509, 166711 (2020). 254 7 X. Jiang, Q. Liu, J. Xing, N. Liu, Y. Guo, Z. Liu, and J. Zhao, Appl. Phys. Rev. 8, 031305 (2021). 255 8 I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, D. Koester, R. 256 Alley, and R. Venkatasubramanian, Nat. Nanotechnol. 4, 235 (2009). 257 9 A. Majumdar, J. Heat Transfer 115, 7 (1993). 258 10 D. Cahill, W. Ford, K. Goodson, G. Mahan, A. Majumdar, H. Maris, R. Merlin, and S. Phillpot, 259 J. Appl. Phys. 93, 793 (2003). 260 11 J. Rupp and R. Birringer, Phys. Rev. B 36, 7888 (1987). 261 12 C. Dames, Annu. Rev. Heat Transf. 16, 7 (2013). 262 13 D. Zhao, X. Qian, X. Gu, S. Jajja, and R. Yang, J. Electron. Packag. 138, (2016). 263 14 D. Cahill, Rev. Sci. Instrum. 61, 802 (1990). 264 15 D. Cahill, Rev. Sci. Instrum. 75, 5119 (2004). 265 16 A. Jacquot, G. Chen, H. Scherrer, A. Dauscher, and B. Lenoir, Sensors Actuators A Phys. 117, 266 203 (2005). 267 17 A. Schmidt, R. Cheaito, and M. Chiesa, J. Appl. Phys. 107, 024908 (2010). 268 18 D. Zhao, X. Qian, X. Gu, S. Jajja, and R. Yang, J Electron Packag 138, 040802 (2016). 269 19 L. Qiu, N. Zhu, Y. Feng, E. Michaelides, G. Żyła, D. Jing, X. Zhang, P. Norris, C. Markides, 270 and O. Mahian, Phys. Rep. 843, 1 (2020). 271 20 O. Breitenstein, W. Warta, and M. Langenkamp, Lock-in Thermography: Basics and Use for 272 Evaluating Electronic Devices and Materials (Springer, Berlin/Heidelberg, Germany, 2010). 273 21 T. Ishizaki, H. Nagano, S. Tanaka, N. Sakatani, T. Nakamura, T. Okada, R. Fujita, A. Alasli, T. 274 Morita, M. Kikuiri, K. Amano, E. Kagawa, H. Yurimoto, T. Noguchi, R. Okazaki, H. Yabuta, H. 275 Naraoka, K. Sakamoto, S. Tachibana, S. ichiro Watanabe, and Y. Tsuda, Int. J. Thermophys. 44, 276 13  51 (2023). 277 22 P. Liu, A. Alasli, L. Wang, and H. Nagano, Appl Therm Eng 255, 123929 (2024). 278 23 A. Alasli, R. Fujita, and H. Nagano, Int. J. Thermophys. 43, 176 (2022). 279 24 A. Alasli, A. Miura, R. Iguchi, H. Nagano, and K. Uchida, Sci. Technol. Adv. Mater. Methods 280 1, 162 (2021). 281 25 A. Alasli, T. Hirai, H. Nagano, and K. Uchida, Appl. Phys. Lett. 121, 154104 (2022). 282 26 A. Miura, H. Sepehri-Amin, K. Masuda, H. Tsuchiura, Y. Miura, R. Iguchi, Y. Sakuraba, J. 283 Shiomi, K. Hono, and K. Uchida, Appl. Phys. Lett. 115, 222403 (2019). 284 27 K. Uchida, S. Daimon, R. Iguchi, and E. Saitoh, Nature 558, 95 (2018). 285 28 T. Seki, R. Iguchi, K. Takanashi, and K. Uchida, Appl. Phys. Lett. 112, 152403 (2018). 286 29 S. Daimon, R. Iguchi, T. Hioki, E. Saitoh, and K. Uchida, Nat. Commun. 7, 13754 (2016). 287 30 K. Uchida, Proc. Jpn Acad. Ser. B 97, 69 (2021). 288 31 Y. Hirayama, R. Iguchi, X. Miao, K. Hono, and K. Uchida, Appl. Phys. Lett. 111, 163901 (2017). 289 32 T. Hirai, R. Iguchi, A. Miura, and K. Uchida, Adv. Funct. Mater. 32, 2201116 (2022). 290 33 R. Iguchi, D. Fukuda, J. Kano, T. Teranishi, and K. Uchida, Appl. Phys. Lett. 122, 082903 (2023). 291 34 A. Wolf, P. Pohl, and R. Brendel, J. Appl. Phys. 96, 6306 (2004). 292 35 A. Salazar, A. Sánchez-Lavega, and J. Terrón, J. Appl. Phys. 84, 3031 (1998).  293 36 H. Carslaw and J. Jaeger, Conduction of Heat in Solids, Second eition (Clarendon press, Oxford, 294 1992). 295 37 Y. Gu, X. Tang, Y. Xu, and I. Hatta, Jpn. J. Appl. Phys. 32, L1365 (1993). 296 38 C. Zhang, M. Giroux, T. Nour, and R. St-Gelais, Phys. Rev. Appl. 14, 024072 (2020). 297 39 M. Alam, M. Manoharan, M. Haque, C. Muratore, and A. Voevodin, J. Micromechanics 298 Microengineering 22, 045001 (2012). 299 40 X. Zhang and C. Grigoropoulos, Rev. Sci. Instrum. 66, 1115 (1995). 300 41 J. Thornton, J. Vac. Sci. Technol. 11, 666 (1974). 301 42 G. Langer, J. Hartmann, and M. Reichling, Rev. Sci. Instrum. 68, 1510 (1997). 302 43 A. Lopeandía, F. Pi, and J. Rodríguez-Viejo, Appl. Phys. Lett. 92, 122503 (2008). 303 44 J. Yu, Z. Tang, F. Zhang, H. Ding, and Z. Huang, J. Heat Transfer 132, 012403 (2010). 304 45 J. Bourgoin, G. Allogho, and A. Haché, J. Appl. Phys. 108, 073520 (2010). 305 46 G. Langer, J. Hartmann, and M. Reichling, Rev. Sci. Instrum. 68, 1510 (1997). 306 47 P. Nath and K. Chopra, Thin Solid Films 20, 53 (1974). 307 14  48 L. Ouarbya, A. Tosser, and C. Tellier, J. Mater. Sci. 16, 2287 (1981). 308 49 J. Jin, J. Lee, and O. Kwon, Appl. Phys. Lett. 92, 171910 (2008). 309 50 A. Avery, S. Mason, D. Bassett, D. Wesenberg, and B. Zink, Phys. Rev. B 92, 214410 (2015). 310 51 Y. Zhu, X. Lang, W. Zheng, and Q. Jiang, ACS Nano 4, 3781 (2010). 311 52 G. White and S. Woods, Philos. Trans. R. Soc. London. Ser. A, Math. Phys. Sci. 251, 273 (1959). 312 53 J. Kimling, J. Gooth, and K. Nielsch, Phys. Rev. B 87, 094409 (2013). 313 54 J. Kimling, R. Wilson, K. Rott, J. Kimling, G. Reiss, and D. Cahill, Phys. Rev. B 91, 144405 314 (2015). 315 55 H. Nakayama, B. Xu, S. Iwamoto, K. Yamamoto, R. Iguchi, A. Miura, T. Hirai, Y. Miura, Y. 316 Sakuraba, J. Shiomi, and K. Uchida, Appl. Phys. Lett. 118, 042409 (2021). 317 56 K. Uchida and R. Iguchi, J. Phys. Soc. Japan 90, 122001 (2021). 318 57 G. Wehmeyer, T. Yabuki, C. Monachon, J. Wu, and C. Dames, Appl. Phys. Rev. 4, 041304 319 (2017). 320  321   322 15  Figures 323  324 Fig. 1. (a) Schematic of the in-plane thermophysical properties measurement method based on the 325 LIT technique. The sample can be a free-standing membrane or multilayered thin film deposited 326 on the membrane. A thin metallic line heater is deposited on the other side of the membrane as a 327 heating source. During measurements, the thin film is located to face the camera while the heater 328 is excited by a square-wave charge current with the frequency f and amplitude 𝐽c with DC offset 329 𝐽c/2. 𝐴 and 𝜙 denote the lock-in amplitude and phase of the temperature modulation induced by 330 the line heater, respectively. 𝐇∥ and 𝐇⊥ denote the in-plane external magnetic field applied along 331 the parallel (x) and perpendicular (y) directions to the in-plane thermal gradient ∇𝑇 induced by the 332 line heater, respectively. (b) Thermal analyses sequence of LIT images for obtaining the in-plane 333 thermal diffusivity 𝐷, in-plane thermal conductivity 𝜅, and volumetric heat capacity 𝜌𝑐p. 334 16   335 Fig. 2. (a) 𝐴/𝑄 and 𝜙 images and (b) corresponding line profiles for the SiN membrane and Ni/SiN 336 samples with different Ni thicknesses at f = 20 Hz. The line profiles were obtained by taking the 337 average of the raw profiles over the center areas (dashed rectangles) of the samples. x  =  0 in the 338 line profiles was determined by the position of the line heater. The solid red lines in (b) represent 339 the fitting results using Eqs. (4) and (5). The shown data in this figure were measured without 340 applying an external magnetic field. 341 17   342 Fig. 3. Ni thickness dependence of (a) in-plane 𝐷, (b) in-plane 𝜅, and (c) 𝜌𝑐p at T  =  298 K for the 343 Ni thin films. 𝐷  was obtained from the geometric mean √Λ𝐴Λ𝜙  with the thermal diffusion 344 length  Λ𝐴  obtained from the 𝐴  image and Λ𝜙  estimated from the 𝜙  image by fitting. 𝜅  was 345 obtained with the combined heat transfer coefficient h from the difference 1Λ𝐴2 −1Λ𝜙2  and 𝐴 at the line 346 heater (x = 0) by fitting with the knowledge of 𝐷. 𝜌𝑐p was then derived from 𝐷/𝜅. The dashed 347 lines represent the values for bulk Ni.24  348  349  350  351 18   352 Fig. 4. Ni thickness dependence of in-plane 𝜅  at T = 298 K for different magnetic field 353 configurations. 354