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[Raju Chetty](https://orcid.org/0000-0003-1072-8241), [Jayachandran Babu](https://orcid.org/0000-0002-1182-6655), [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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[Best practices for evaluating the performance of thermoelectric devices](https://mdr.nims.go.jp/datasets/be304bcd-6c38-4f59-8c26-923592849785)

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Best Practices for Evaluating the Performance of Thermoelectric DevicesRaju Chetty1†, Babu Jayachandran1†, and Takao Mori1,2*1International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba 305-0044, Japan.2Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan*Corresponding author: MORI.Takao@nims.go.jp† These authors equally contributed to this workIntroductionThermoelectric (TE) devices, which enable converting thermal energy into electrical energy and vice-versa, can play a crucial role in energy harvesting and thermal management for future society.1–4 The conversion efficiency () of TE devices is the ratio between the electrical output power (Pout) to the input heat flow (Qin) under a defined temperature difference, expressed by      (1)Recent advancements in the development of high-performance TE materials led to the realization of reported high conversion efficiencies and output power densities in laboratory-scale fabricated devices with engineered electrical contacts and variable geometries (cross-sectional area, height, number of TE elements, fill factor, etc.).5–8 The efficiency measurements of these TE devices are mostly carried out by customized instruments and test conditions due to the varying device dimensions, operating temperature range, etc.9 However, a lack of TE device measurement guidelines or standard test conditions (STC) and/or commercial reference devices leads to large discrepancies in the measurement results. For example, a recent international round-robin (RR) test performed at twelve laboratories from nine countries on commercial Bi2Te3-based TE devices revealed a significant standard deviation of maximum power output (~27%) and maximum efficiency (~26%).10 Moreover, the performance deviates from the manufacturer’s specifications by ~46%. Considering the possibility of partial influences from the TE material properties deviation for each device, the major deviations in performance were due to dissimilarities in measurement conditions and inaccurate measurement procedures. Recently, interlaboratory measurements on a Ni alloy-based TE device11, a prospective standard reference due to its structural, chemical, and thermal stability, reported a standard deviation of <1% for the power output and ~8% for the efficiency.12 Uniform guidelines were followed during the interlaboratory test, using custom-built systems which happened to have similar features. Thus, there is currently a dire need in this field to adhere to a set of standard practices to improve the measurement accuracy of TE devices. The standard practice should comprise adopting the right procedures in setting up the device, measurement of electrical power and heat flow, and validation of the measured performance parameters. We hope this commentary article sheds light on some of these issues related to TE device measurement and discusses the best practices to be followed in estimating and reporting the TE device performance. No official or standard measurement protocol for the TE device is available up to now. However, a sequential procedure for setting up and measuring of TE device is suggested.13 While installing the TE device, special attention must be taken care with the one-dimensional heat flow, thermal coupling at the interfaces, applied pressure, atmosphere, and positioning of temperature sensors to avoid possible measurement errors. A schematic of the TE device measurement system with a heat flow meter (HFM) is shown in Figure 1A. To ensure the one-dimensional heat flow, the heater, TE device, and heat flow meter are to be placed collinearly with each other. A strong thermal coupling is needed to transfer the heat from the heater to the TE device to the heat flow meter. This can be achieved by placing graphite sheets, and thermal grease at their interfaces via reducing the thermal contact resistance. The effect of applied pressure on the TE device is crucial to reduce the thermal contact resistances and, consequently the electrical output power. Figure 1B shows the ratio Pmax/Pmax0 as a function of applied pressure onto the Bi2Te3-based TE devices (TED1- 40 mm  40 mm, TED2- 20 mm  20 mm), where Pmax0 is the maximum output power when the minimum load (~1 kgf) is applied. This study reveals that the optimum pressure to achieve Pmax is ~0.5 MPa for TED1 and ~0.7 MPa for TED2. The threshold pressure for achieving the Pmax may vary based on the type of TE materials and devices. Thus, it is highly recommended to optimize the applied pressure before the actual TE device performance test. Mostly, the TE devices are measured under a high vacuum to reduce the convection heat losses. In principle, the oxidation-resistant TE device can be measured in an air atmosphere, which might result in an error in the heat flow measurement due to the convection heat loss. Thus, it is recommended to cover the TE devices with thermal insulation materials. The improper placement of temperature sensors at the hot side and cold side of the TE device strongly influences the TE device characterization. Thus, the positioning of the temperature sensors within the vicinity of TE devices is highly recommended.Measurement of Electrical Output Power Characteristics The electrical output power (Pout) and efficiency () are the important parameters for the TE device characterization. The voltage difference (V) develops across the device under a temperature difference (ΔT), which depends on the thermopower (α) of TE materials. The trade-off between the voltage developed and the electrical current (I) generated maximizes the output power (Pmax). For a finite ΔT, the voltage developed is maximum (Voc) when no load (I=0) is connected across the device. With an increase in current flow, the voltage drops linearly and becomes zero at the maximum permissible current (Isc). The V-I characteristics are generated by varying the current through the device from 0 to Isc. The variation of output power (P) is the product of generated V and applied I. The V-I, and P-I curves are generated by fitting linear and quadratic curves to the experimentally measured data points respectively. However, inside a TE device (shown in Figure 2A), the current flow causes the Peltier heat to be absorbed or liberated at the junctions, the Joule heat released from TE materials and the Thomson heat contributions disturb the steady state thermal conditions, lower the actual ΔT across the device and hence the voltage developed. The actual P-I curve deviates from the ideal quadratic trend in such conditions, leading to errors in Pmax estimation. A sufficient time interval is recommended between each measurement (delay time) to minimize these artifacts in V-I, P-I measurements. A too-short delay time can result in an overestimation of P (Figure 2B) whereas longer delay times increase the measurement time. Therefore, determining a sufficient delay time for each measurement condition is essential. The delay time can be influenced by the electrical and thermal resistances of TE devices, the heat capacity of the measurement system, atmospheric conditions, etc. A rapid measurement combined with a sufficient delay time between the data points is essential to estimate Pmax accurately. Recently, Kanno et al.14 suggested a non-linear current sweep technique (square root spaced) for the direct measurement of Pmax, which collects finely spaced data points around the Pmax region (shown in Figure 2C). Moreover, the common sources of errors in electrical power estimation of a TE device come from current source/ voltmeter measurements, electrical wire, lead resistances, etc. It is recommended to use periodically calibrated measurement instruments to avoid uncertainties and systematic errors with the measuring instruments. A four-probe arrangement is recommended to exclude the influence of wire resistance, even in cases where the TE device resistance is significantly larger compared to the wire resistance. The lead resistances at the soldered joints should be minimal to alleviate the electrical losses due to Joule heating. Standard soldering practices are recommended across all the contact junctions. For TE devices with contact leads at hot-side, the electrical joints should be fabricated with materials that can withstand and be stable at the target hot-side temperature. Good temperature stability (within 0.5°C/min) should be ensured between both the sides of TE device for accurate measurements of power output and heat flow. Heat flow measurementsInput heat flow (Qin) measurement with good accuracy is crucial for TE device characterization. A reference block or absolute method is usually used for the Qin measurement. A reference block method for measuring Qin is difficult due to the inevitable radiative heat loss under high-temperature conditions. Alternatively, Qin can be measured by the absolute method using a guarded hot plate (GHP), which is challenging due to various technical difficulties and economic issues. Thus, the reference block method is widely used for the measurement of output heat flow (Qout), thereby determining the Qin. Recently developed high-performance TE devices use a reference block method for evaluating the heat flow. Therefore, this article is focused on discussing the best practices in evaluating the Qout by the reference block method. An oxygen-free copper block with high thermal conductivity is commonly used as a heat flow meter (HFM) to improve homogeneity on the coupling interfaces at the cold side of TE devices. The output heat flow (Qout) can be evaluated by Fourier’s law of heat conduction,   (2)where Aref is the cross-sectional area, κref is the thermal conductivity, Lref and ΔTref are the distance and the temperature difference between two thermocouples inserted in the reference block, respectively. Then, the input heat flow (Qin) can be evaluated by    (3)Where Qloss corresponds to the heat loss due to the convection and radiation (shown in Figure 3A). Avoiding the sources of errors in measuring the output heat flowOne-dimensional heat flow within the heat flow meter is crucial to measure the Qout using the reference block method. Thus, the cross-sectional area of the reference block and the TE device should be the same to ensure one-dimensional heat flow, otherwise, the heat loss from the bottom of the TE device leads to the underestimation of the Qout and results in an overestimation of the conversion efficiency. Figure 3B shows that the Qout is underestimated when the cross-sectional area of the TE device (ATE device) is greater than the cross-sectional area of the heat flow meter (AHFM) which is mainly attributed to the heat loss from the TE device to the surroundings. In another case, the Qout is overestimated when the cross-sectional area of the TE device (ATE device) is less than the cross-sectional area of the heat flow meter (AHFM) due to the additional heat from the heater reaching the HFM as shown in Figure 3C. Another systematic error comes from the uncertainty of the κref. Thus, the measurement of κref with good accuracy is essential as the Qout evaluation directly depends on it. Precise information such as thermal conductivity evaluation method, uncertainty, purity, materials quality, and manufacturer of the reference block is essential in estimating the Qout (Figure 3D). An overestimation or underestimation of Qout using κref data can be avoided or reduced by measuring the temperature-dependent κref relative to the certified standard reference material (SRM) with an estimation of error percentage through repetitive measurements. Another essential source of error in evaluating the Qout is the measurement of temperature difference in the heat flow meter. It is important to measure the ΔT without any fluctuations under the steady state conditions. The homogeneity of heat flow in the reference block can be maintained by an accurate measurement of temperatures using the temperature sensors. Thus, the sensitivity of temperature sensors plays a crucial in determining the ΔT (Figure 3E). For example, Kanno et al.14 reported that there is a significant difference in the uncertainty of the Qout between the uncalibrated (~6.2 W) and the calibrated (~0.4 W) temperature sensors. The calibration of temperature sensors with good accuracy is the best practice to avoid the underestimation or overestimation of the ΔT, then Qout. The insertion of temperature sensors into the middle of the HFM by filling the drilled holes with thermal grease can minimize the temperature irregularities at the points of measurement and the uncertainty in the ΔT (Figure 3E). Recently, Kanno et al.14 reported that the quick measurements before reaching thermal stabilization (steady state) lead to an overestimation of conversion efficiency by up to 27%. It was reported that the measurements performed with too short a delay time resulted in the overestimation of P and underestimation of Qout. Thus, the optimization of delay time after applying electrical current to achieve steady state conditions prior to performing the heat flow measurements is crucial to minimize error.Heat loss due to radiation and convectionHeat loss plays a predominant role in evaluating TE device conversion efficiency; therefore, care must be taken in estimating the Qloss contribution to the TE device. Generally, the Qloss consists of radiative and convective heat loss to the atmosphere (Figure 3A). The Qloss due to convection can be avoided by performing the measurements under a high vacuum. If the measurement is performed in air, the convection loss can be reduced by covering the TE device with thermal insulation materials (e.g., glass wool). The Qloss due to the radiative heat flow can be mitigated by filling gaps in the TE device using fillers such as glass wool, aerogel, etc. However, the relatively low density of filler materials limits them to serve as perfect radiation shields. The Qloss due to the radiation can also be reduced by increasing the active surface area (filling factor) of the TE device. Recently, Kanno et al.14 suggested that estimating the maximal radiative loss for the finite TE device area can be good practice for comparing various TE devices with minimal uncertainty.Effects of TE Material’s Properties, Electrical Contacts on Device Performance MeasurementA reliable performance measurement needs a TE device with good physical, thermal, and chemical stability. Degradation of TE device performance during the measurement can occur due to deteriorated thermoelectric properties of materials and electrical contacts. At elevated temperatures, many TE materials were reported to undergo microstructural evolutions, chemical element volatilization, thermal hysteresis due to chemical rearrangement, etc.15,16 A carefully designed contacting /joining method is essential to minimize the electrical and thermal contact resistances. Under large temperature gradients, interatomic diffusion between contact layers and TE materials can poison the device's performance. Thus, an effective diffusion barrier layer is necessary for many materials to preserve long-term stability and performance. The structural failures due to mechanical stresses, thermal expansion mismatch, fatigue, etc. must be carefully considered as the TE device usually mounts under compressive loading. Oxidation issues also need to be taken care of as many practical TE devices are designated to work in the open air. Passivation strategies to protect the TE materials from these external environments, such as ceramic fillings, and vacuum packaging would also be helpful in reducing parasitic thermal losses as discussed in Figure 3A. We have summarized the key issues in TE device characterization and general practices to avoid the sources of errors in electrical output power and heat flow measurement, thereby estimating conversion efficiency. Repeatable measurements following the general practices under the same test conditions improve the data reliability. Validation of high-performance TE devices by performing inter-laboratory tests under similar experimental conditions is a best practice for measurement reliability. Any deviation during the tests can be correlated with the thermal stability of TE materials and electrical contacts, which helps to formulate future studies towards the commercialization of TE devices.Acknowledgment: Support from JST Mirai Program Grant Number JPMJMI19A1 is acknowledged.References1. Mao, J., Liu, Z., Zhou, J., Zhu, H., Zhang, Q., Chen, G., and Ren, Z. (2018). Advances in thermoelectrics. Adv Phys 67, 69–147. 10.1080/00018732.2018.1551715.2. Petsagkourakis, I., Tybrandt, K., Crispin, X., Ohkubo, I., Satoh, N., and Mori, T. (2018). Thermoelectric materials and applications for energy harvesting power generation. Sci Technol Adv Mater 19, 836–862. 10.1080/14686996.2018.1530938.3. 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Avoiding errors in efficiency measurements of high-performance thermoelectric generator modules: Toward best practices for materials researchers. Materials Today Physics 36, 101171. 10.1016/j.mtphys.2023.101171.15. Zheng, Y., Tan, X.Y., Wan, X., Cheng, X., Liu, Z., and Yan, Q. (2020). Thermal Stability and Mechanical Response of Bi2Te3-Based Materials for Thermoelectric Applications. ACS Appl Energy Mater 3, 2078-2089. 10.1021/acsaem.9b02093.16. Gorskyi, P. V. (2022). Typical mechanisms of degradation of thermoelectric materials and ways to reduce their impact on the reliability of thermoelectric modules. Physics and Chemistry of Solid State 23,505-516. 10.15330/pcss.23.3.505-516. Figure captions:Figure 1. TE device installation for power generation and efficiency measurement A. Schematic of the TE device measurement system with a heat flow meter (HFM).B.  Effect of pressure on the maximum electrical output power (Pmax). The values of Pmax are normalized to the maximum power obtained when the minimum pressure was applied (Pmax0) to show the increment in power when the pressure is increased.Figure 2. Influence of electrical current on the output power measurementA. Schematic representation of Joule, Peltier, and Thomson heat release or absorption during the current flow inside TE device.B. Effect of delay time on the electrical output power (c) Direct measurement of maximum electrical output power with a non-linear current sweep. Reproduced with permission.14Figure 3. Influence of heat loss on the output heat flow measurementA. Schematic of heat transfer and loss mechanisms inside the TE device. B. Underestimation of Qout due to the cross-sectional area mismatch (ATE device > AHFM) of TE device with heat flow meter. C. Overestimation of Qout due to the cross-sectional area mismatch (ATE device < AHFM) of TE device with heat flow meter.D. Essential specifications of the heat flow meter materials. E. Influence of temperature sensor positioning on Qout.