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Naoki Nakamura, [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), Masayuki Murata, Abdulkareem Alasli, Hosei Nagano

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Accurate and simple measurement of power generation efficiency and figure of merit of thermoelectricScience and Technology of Advanced MaterialsISSN: 1468-6996 (Print) 1878-5514 (Online) Journal homepage: www.tandfonline.com/journals/tsta20Accurate and simple measurement of powergeneration efficiency and figure of merit ofthermoelectric modules based on optical heatingand non-contact temperature detection methodsNaoki Nakamura, Fuyuki Ando, Ken-ichi Uchida, Masayuki Murata,Abdulkareem Alasli & Hosei NaganoTo cite this article: Naoki Nakamura, Fuyuki Ando, Ken-ichi Uchida, Masayuki Murata,Abdulkareem Alasli & Hosei Nagano (2025) Accurate and simple measurement of powergeneration efficiency and figure of merit of thermoelectric modules based on optical heatingand non-contact temperature detection methods, Science and Technology of AdvancedMaterials, 26:1, 2551485, DOI: 10.1080/14686996.2025.2551485To link to this article:  https://doi.org/10.1080/14686996.2025.2551485© 2025 The Author(s). Published by NationalInstitute for Materials Science in partnershipwith Taylor & Francis Group.Published online: 10 Sep 2025.Submit your article to this journal Article views: 467View related articles View Crossmark dataFull Terms & Conditions of access and use can be found athttps://www.tandfonline.com/action/journalInformation?journalCode=tsta20https://www.tandfonline.com/journals/tsta20?src=pdfhttps://www.tandfonline.com/action/showCitFormats?doi=10.1080/14686996.2025.2551485https://doi.org/10.1080/14686996.2025.2551485https://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructions&src=pdfhttps://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructions&src=pdfhttps://www.tandfonline.com/doi/mlt/10.1080/14686996.2025.2551485?src=pdfhttps://www.tandfonline.com/doi/mlt/10.1080/14686996.2025.2551485?src=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2025.2551485&domain=pdf&date_stamp=10%20Sep%202025http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2025.2551485&domain=pdf&date_stamp=10%20Sep%202025https://www.tandfonline.com/action/journalInformation?journalCode=tsta20FOCUS ISSUE ARTICLEAccurate and simple measurement of power generation efficiency and figure of merit of thermoelectric modules based on optical heating and non-contact temperature detection methodsNaoki Nakamuraa, Fuyuki Andob, Ken-ichi Uchidab,c, Masayuki Muratad, Abdulkareem Alaslia and Hosei NaganoaaDepartment of Mechanical Systems Engineering, Nagoya University, Nagoya, Japan;  bResearch Center for Magnetic and Spintronic Materials, National Institute for Materials Science (NIMS), Tsukuba, Japan;  cDepartment of Advanced Materials Science, The University of Tokyo, Kashiwa, Japan;  dResearch Institute for Energy Efficient Technologies, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, JapanABSTRACTIn this study, we propose an accurate, simple, and versatile measurement method for power generation efficiency and device figure of merit ZT of thermoelectric devices. Toward the energy harvesting applications of thermoelectric generators, the performance characterization under low heat inflow and temperature difference is crucial. However, when the conventional solid-state heat flow meter is used, the uncertainty of power generation performance increases as heat input decreases. We have solved these problems by using a laser for heat input, improving the simplicity and accuracy of power generation efficiency measurements, especially at low heat flow. The direct and non-contact measurement of the temperature difference by using a thermography allowed us to determine ZT as well as power generation efficiency. The obtained mean power generation efficiency and ZT values are consistent with the values obtained by the conventional method within the error range, thereby validating the reliability of the proposed method. The relative uncertainties of the efficiency and ZT were estimated to be less than 3% and 12% for our method, respectively, whereas those were 19% and 24% in situations where the temperature difference was less than 6 K for the conventional method.IMPACT STATEMENTA fully non-contact method was proposed to evaluate η and ZT of thermoelectric devices, achieving uncertainties of less than 3% and 12%, respectively, using laser heating and thermographic temperature measurement.ARTICLE HISTORY Received 31 March 2025  Accepted 19 August 2025  Revised 11 August 2025 KEYWORDS Thermoelectric figure of merit; thermoelectric generator; laser heating; thermographyCONTACT Hosei Nagano nagano@mech.nagoya-u.ac.jp Department of Mechanical Systems Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan; Fuyuki Ando ANDO.Fuyuki@nims.go.jp Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanSCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2025, VOL. 26, NO. 1, 2551485 https://doi.org/10.1080/14686996.2025.2551485© 2025 The Author(s). Published by National Institute for Materials Science in partnership with Taylor & Francis Group.  This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.http://www.tandfonline.comhttps://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2025.2551485&domain=pdf&date_stamp=2025-09-091. IntroductionDue to rising energy costs, the depletion of fossil fuel resources and the increasing severity of environmental issues, energy systems are undergoing a significant transition [1]. Thermoelectric generator (TEG) can directly convert heat into electricity and has long been attracting attention as an environmentally friendly energy conversion method [2–5]. TEGs have been widely developed for application in automobiles [6,7], wearable devices [8,9], photovoltaic systems [10–12], and industrial waste heat power generation [13,14] due to their advantages of frictionless operation, high reliability and stability, and low installation and maintenance costs [15– 18]. In recent years, a combined Internet of Things (IoT)-thermoelectric system has also been considered, in which thermoelectric devices are used to generate electricity from factory waste heat to provide an independent power source for IoT devices. As TEGs are operated and systematized in these various fields, it is becoming more and more important to ensure stable power output. In particular, accurate performance evaluation at low heat input is increasingly required in the field of energy harvesting [19,20].The performance of thermoelectric devices is typically characterized in terms of the following two important parameters. One is the power generation efficiency η, which indicates how much output power is obtained from the input heat flow. The other is the device thermoelectric figure of merit ZT, which determines the thermoelectric performance of the device itself [21,22]. Proper evaluation of η requires simultaneous measurement of input heat flow Qin and output power Pout according to the following equation: The conventional method to determine Qin is a steady- state heat flow method using a solid-state heat flow meter (HFM) [23–26]. In this method, Qin can be calculated using the 1D Fourier’s law from the temperature difference ΔTM within HFM. Pout is simultaneously measured by a four terminal method, followed by the calculation of η. However, this method has several limitations. Firstly, we need to arrange the area of HFM with that of the thermoelectric device to realize the one-dimensional heat transport. Secondly, as ΔTM within HFM becomes smaller, the uncertainty of the absolute temperature causes a larger error in the estimated Qin. Meanwhile, ZT is mainly used to compare the thermoelectric performance of various devices without the effect of Carnot efficiency as follows: Although ZT is the common indicator in the field of thermoelectrics, the accurate measurement especially at low Qin has been difficult mainly due to the uncertainty of ΔTM within HFM and hence Qin.This study presents a new method to characterize thermoelectric performance using a laser and a thermography. Because we directly estimate Qin from an injected laser power [27–32] instead of a solid- state heat flow sensor, the measurement error is significantly reduced even in the low Qin condition. This enables an accurate measurement of η over a wide range of Qin, which has been difficult for the conventional method. In addition, the area of the laser injection can be flexibly changed according to the thermoelectric modules with various sizes and shapes. Furthermore, the proposed method can simultaneously and precisely measure ZT in low heat input by directly measuring the temperature distribution in the module. We applied this method to a commercially available thermoelectric device with the known η and ZT and compared the results with those obtained by the conventional method using HFM. As a result, our data shows a quantitative agreement with a specification of the device [33] and much lower error in low heat input than that by the conventional method. The proposed method will contribute to the acceleration of energy harvesting applications of thermoelectric devices.2. Measurement principles and setup2.1. Measurement principlesFigure 1 shows the schematic of our measurement principle. Qin is estimated by measuring the heat absorbed from the laser on the heating surface and subtracting the heat loss from the surface. The relationship between Qin and the laser output Qlaser can be described by Equation (3), which incorporates the absorptance α (using black coating) of the device surface and the convective heat loss Qcon and radiative heat loss Qrad to the surroundings:Qcon and Qrad are given by respectively, where Tamb is the ambient temperature, h ¼ 10 the heat transfer coefficient between the device surface and air, A the area of the device surface, and ε the emissivity of the surface. Pout is measured from Equation (6) by attaching a variable load resistance Rout: Sci. Technol. Adv. Mater. 26 (2025) 2                                                                                                                                              N. NAKAMURA et al.where I, V, and Rin are the current, voltage, and internal resistance of the thermoelectric device, respectively. The value of Rout is varied, and the maximum output power Pmax is calculated from the load resistance dependence. Then, since the value of Qin is a constant value, we can calculate the maximum efficiency from Qin and Pmax. ZT can be derived from the one-dimensional heat conduction equation and the electric circuit theory, and the equation is expressed as in Equation (7) using the value of maximum power generation efficiency ηmax and Th and Tc [24]2.2. Measurement apparatusFigure 2 shows a schematic diagram of the apparatus for this measurement. The apparatus consists mainly of a diode laser, thermography, variable resistor, voltmeter, chiller, cold plate, and PC. The diode laser with a wavelength of 455 nm was used for the thermal input to the thermoelectric device. The laser intensity value was set to be the actual intensity output from the laser as measured with a power meter, and the input shape of the laser was adjusted to match the shape of the module. A mode mixer was also used to ensure uniform heating within the surface. Th and Tc were determined by observing the side surface of the device with the thermography, sending the data to the PC, and then averaging the temperatures in the areas of aluminum oxide plates for the hot and cold sides, respectively. The cold side of the device was bonded to the cold plate, and the temperature on the cold side was controlled by the chiller. Then, the laser intensity to heat the module surface was set by the PC, and heat input was started. The laser-heated surfaces of the module and the observation surfaces of the thermography were coated with black paint (JAPAN SENSOR JSC-3). In this measurement, the optical absorbance at the laser wavelength (455 nm) and the emissivity near room temperature (corresponding to wavelengths around 10 µm) were set to 0.983 and 0.94, respectively, using the experimentally measured value obtained with the UV–Vis spectrophotometer (V-670, JASCO) and the catalog value [34]. After Th and Tc were stabilized within �0:1°C, the value of the load resistance was varied to find the maximum Pout. Qin was calculated from Equations (3)-(5) by substituting the values of Th and Tc. By repeating this process with different laser intensities, the η and ZT values at various temperature differences ΔT ¼ Th � Tc were calculated. This thermography is calibrated using a black plate with the emissivity of 0.94 before each measurement [35]. In addition, the temperature measurement is calibrated periodically by inter- measurement with a thermocouple coated with black paint.3. Measurement3.1. Verification sample and measurements conditionsThe module used in this study is the SINGLE-STAGE THERMOELECTRIC GENERATOR TG12–2.5, and its specifications are summarized in Table 1 [33]. It should be noted that the ZT value varies depending on the measured temperature range: 0.61, 0.72 and 0.79 at Th ¼ 110; 170; and 230°C, respectively, with the fixed ThermographyVoltmeterLoadResistanceLaserThermoelectric moduleFigure 1. The diagram of the simultaneous measurement of the power generation efficiency η and device figure of merit ZT.Figure 2. Schematic diagram of the measurement apparatus.Sci. Technol. Adv. Mater. 26 (2025) 3                                                                                                                                              N. NAKAMURA et al.Tc ¼ 50°C, indicating the large temperature dependence of the thermoelectric properties for the constituent thermoelectric legs.The experimental conditions were as follows: the cold plate temperature was set at 15°C and the laser power was varied from 1500 mW to 4500 mW in increments of 500  mW. Measurements were conducted in the atmosphere. An average value was taken from five measurements at each laser power setting.3.2. Temperature measurementsFigure 3(a) shows an example of the thermography image data at the laser power of 4500 mW, where Th and Tc are defined around the central area of aluminum oxide plates to eliminate the influence of heat loss near the edges. The standard deviation of the temperature was less than 0.4°C in all measurement conditions. Figure 3(b) showed the averaged line scan data in the direction of heat flow in the black area marked in Figure 3(a). Figure 3(c) shows ΔT        dependence of Qin calculated using the above data. As shown in Figure 3(a, b), the surface was homogeneously heated realizing a one-dimensional heat transport in Y-direction.3.3. Output power measurementWe characterized the maximum Pout with varying Rout under the application of Qin. Firstly, the DC internal resistance of the thermoelectric device Rin at each condition was calculated from the slope of the measured I-V curve, where I is tuned by changing Rout. The Rinvalue calculated from Figure 4(a) is 4.81 Ω, which is consistent with the catalog reference value in Table 1. Figure 4(b) shows the I dependence of Pout ¼ IVð Þ at various Qin values, where Rout for the maximum output condition at 1500 mW was 8.52 Ω, which is also confirmed to be close to the reference value of optimum η. Based on these data, Figure 4(c, d) show the open-circuit voltage and maximum Pout versus ΔT at each laser output. Here, since all the measurements were performed around room temperature, the open-circuit voltage is proportional to ΔT, and the maximum Pout increases in proportion to the square of ΔT with neglecting the temperature dependence of thermoelectric properties of the constituent thermoelectric legs.4. Error analysis and experimental results4.1. Error analysisWe describe the error analysis procedure in detail. The relative uncertainty of Qin takes into account the uncertainty in Qlaser, α, A, Th and variations in the heat transfer coefficient h, which ranges from 7 to 15 W/m2 K under natural air-cooled environment. Meanwhile, the relative uncertainty of the Pout includes the variable resistance value and the uncertainty in the V measurement. From the law of error propagation, the relative uncertainties are, respectively, expressed by the following equations: Based on these equations, the relative uncertainty of η is given by In the steady-state heat flow method using HFM (hereinafter, referred to as the conventional method) [36], Qin is expressed as where Qout represents the heat flow from the cold side of the module, k is the thermal conductivity of HFM, and Tu, Tb are the temperatures at the hot and cold Table 1. Specifications of sample module [33]. The load resistance for optimum η and ZT values are measured in Th ¼ 110; 170; 230°C and Tc ¼ 50°C.Ceramic Area Module Hight AC ResistanceLoad Resistance for Optimum η ZT30 mm × 30 mm 3.94 mm 4.47–5.69 Ω 10.47, 9.68, 8.75 Ω 0.61, 0.72, 0.79Sci. Technol. Adv. Mater. 26 (2025) 4                                                                                                                                              N. NAKAMURA et al.side temperatures in HFM. Therefore, the relative uncertainty of η for the conventional method is expressed as: It should be noted that it is assumed that the uncertainty due to Pout is negligibly small in the conventional method. The relative uncertainty of ZT is calculated from the following equation: Figure 3. (a) Thermographic image of the side surface of the thermoelectric module when 4500 mW is applied, (b) line scan data in the direction of heat flow in the black area marked in (a), (c) Qin as a function of T .Sci. Technol. Adv. Mater. 26 (2025) 5                                                                                                                                              N. NAKAMURA et al.ΔT used as the horizontal axis when graphing η and ZT includes the measurement error of each temperature measurement method. The uncertainty of each parameter together with the temperature measurement error for each temperature measurement method is summarized in Table 2.4.2. Experimental results and discussionTo confirm the validity of the proposed method, we performed a comparative measurement of η and ZT using the conventional method using HFM developed by the National Institute of Advanced Industrial Science and Technology (AIST) [36]. The measurement conditions were adjusted to maintain Tc at 15°C for both the proposed and the conventional methods. Figure 5(a) shows that the η values of the same device obtained by the proposed and conventional methods. Due to the effect of Carnot efficiency, η monotonically increases as ΔT increases. Importantly, the η values clearly match between these methods within a margin of error. As a possible reason for the slight difference between these methods, it should be noted that the conventional method uses the temperatures of the heat source and sink for Th and Tc, which may cause an estimation of larger ΔT in the conventional method by including contact thermal resistances. The measurement uncertainty of the proposed method is within 3% at ΔT ¼ 4K whereas that of the conventional method is 19% at ΔT ¼ 5K, ensuring the higher reliability of our method even in the low Qin condition.Figure 5(b) shows the comparison of the ZT values between the proposed and conventional methods and also the catalog values of the same device. As a result of Equation (2) excluding the contribution of the Carnot efficiency from η, the ZT values are almost constant regardless of ΔT in our measurement range. The ZT values for the two methods agree with each other within the error bar. In our method, the standard deviation is less than 2% and the relative error is less than 12% even at low heat flow input, whereas the Figure 4. Thermoelectric generation properties obtained by the proposal method. (a) I-V diagram at 1500 mW laser power, (b) the output power for the current at each laser power condition, (c) the open-circuit voltage at each temperature difference, and (d) maximum Pout.Sci. Technol. Adv. Mater. 26 (2025) 6                                                                                                                                              N. NAKAMURA et al.relative error for the conventional method is about 24%. These results indicate that the proposed method is promising for accurate ZT measurements with small temperature differences, which was difficult to achieve with the conventional method.5. ConclusionWe have developed a simple and accurate measurement method using a laser and thermography to simultaneously evaluate the power generation efficiency η and the device figure of merit ZT of thermoelectric devices. The η and ZT values estimated from the proposed and conventional methods agree with each other within the margin of error. The error analysis reveals that the proposed method shows higher accuracy than the conventional method; the results for the proposed method show an uncertainty of less than 3% for η and less than 12% for ZT with the small temperature difference of 4 K. The proposed method has the versatility to evaluate thermoelectric devices with various dimensions, providing a simpler and more adaptable measurement method. By reducing the complexity of the evaluation process of thermoelectric devices, this method will significantly contribute to the design and optimization of thermoelectric applications including energy harvesting, where efficiency measurements at small temperature gradients are essential.AcknowledgmentsThe authors thank H. Ohshima for technical support.Disclosure statementNo potential conflict of interest was reported by the author(s).FundingThis work was supported by ERATO “Magnetic Thermal Management Materials” [No. JPMJER2201] from Japan Science and Technology (JST) and Grants-in-Aid for Scientific Research (KAKENHI) [No. 24K17610] from Japan Society for the Promotion of Science (JSPS).Data availability statementThe data that support the findings of this study are available from the corresponding authors upon reasonable request.Table 2. Uncertainty budget of the evaluation of each parameter at laser power of 1500 mW.Uncertainty components Relative standard uncertaintyProposed method efficiency u(η)/η 3.0%Proposed method figure of merit u(ZT)/ZT 11.4%Heat flow measurement Heat transfer coefficient, W/m2/K 3.4%Emissivity of the surface 1.0%Laser absorption 1.0%Module area, m2 1.0%Laser intensity, W 1.0%Temperature measurement Thermography, K (proposed) 1.0°CThermocouple, K (conventional) 0.5°CAtmosphere, K (proposed) 1.0°CElectric power measurement Electrical resistance, Ω 1.0%Voltage measurement, V 1.0%Figure 5. Comparison of the proposed method with the conventional method. (a) The power generation efficiency and (b) ZT value as a function of the temperature difference.Sci. Technol. Adv. Mater. 26 (2025) 7                                                                                                                                              N. NAKAMURA et al.References[1] Borhani S, Hosseini M, Pakrouh R, et al. 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An integrated approach to thermoelectrics: combining phonon dynamics, nanoengineering, novel materials development, module fabrication, and metrology. Adv Energy Mater. 2019;9(23):1801304. doi: 10.1002/ aenm.201801304Sci. Technol. Adv. Mater. 26 (2025) 9                                                                                                                                              N. NAKAMURA et al.https://doi.org/10.1016/j.compscitech.2016.12.006https://doi.org/10.1016/j.compscitech.2016.12.006https://www.coherent.com/content/dam/coherent/site/en/resources/datasheet/materials/single-stage-thermoelectric-generator-tg12-2.5-ds.pdfhttps://www.coherent.com/content/dam/coherent/site/en/resources/datasheet/materials/single-stage-thermoelectric-generator-tg12-2.5-ds.pdfhttps://www.coherent.com/content/dam/coherent/site/en/resources/datasheet/materials/single-stage-thermoelectric-generator-tg12-2.5-ds.pdfhttps://www.japansensor.co.jp/manage/wp-content/uploads/2015/03/blackpaint.pdfhttps://www.japansensor.co.jp/manage/wp-content/uploads/2015/03/blackpaint.pdfhttps://doi.org/10.1007/s10765-022-03109-7https://doi.org/10.1007/s10765-022-03109-7https://doi.org/10.1002/aenm.201801304https://doi.org/10.1002/aenm.201801304 Abstract Abstract 1. Introduction 2. Measurement principles and setup 2.1. Measurement principles 2.2. Measurement apparatus 3. Measurement 3.1. Verification sample and measurements conditions 3.2. Temperature measurements 3.3. Output power measurement 4. Error analysis and experimental results 4.1. Error analysis 4.2. Experimental results and discussion 5. Conclusion Acknowledgments Disclosure statement Funding Data availability statement References