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Article

Standard Reference Thermoelectric Modules Based on Metallic Combinations and Geometric Design

by
EunA Koo
1,
Hanhwi Jang
2,
SuDong Park
3,
Sang Hyun Park
1,* and
Sae-byul Kang
1,*
1
Korea Institute of Energy Research, 152 Gajeong-ro, Yuseong-gu, Daejeon 34129, Republic of Korea
2
Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
3
Energy Conversion Research Center, Korea Electrotechnology Research Institute, 12, Jeongiui-gil, Seongsan-gu, Changwon-si 51543, Republic of Korea
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2025, 15(18), 10273; https://doi.org/10.3390/app151810273
Submission received: 3 September 2025 / Revised: 18 September 2025 / Accepted: 19 September 2025 / Published: 22 September 2025
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Abstract

To establish a reliable thermoelectric module evaluation, a Standard Reference Thermoelectric Module (SRTEM) was developed based on stability. Open-circuit voltage (Voc) was selected as the key calibration parameter due to its consistent response to temperature differences (ΔT). The SRTEM consists of eight p–n thermoelectric couples composed of metallic thermoelectric materials—Ni90Cr10 (chromel), Cu55Ni45 (constantan), Fe64Ni36 (invar), and pure Fe—selected based on their thermoelectric properties, structural compatibility, and contact resistance. Among the tested combinations, the chromel–constantan pair exhibited the highest Voc of 55 mV at ΔT = 150 K. To increase Voc and expand the usable calibration range, leg-shape modification and substrate replacement were investigated. Module simulation revealed that replacing the rectangular-leg geometry with a double-hourglass (2H/G) structure could increase Voc by 20.2%. Furthermore, measurement of single-leg modules with substrates attached confirmed a 16.0% improvement in Voc for the 2H/G shape over the rectangular shape, consistent with the predicted enhancement due to increased thermal resistance. In addition, replacing the alumina substrate with a higher thermal conductivity material, such as AlN, increased ΔT across the legs and yielded a further 9.1% improvement in Voc. These results demonstrate the potential of the proposed SRTEM as a calibration standard for consistent thermoelectric module measurements.

1. Introduction

Thermoelectric modules (TEMs), which generate electricity from temperature gradients, have attracted growing attention as eco-friendly energy conversion devices. TEMs are being applied in various fields, including waste heat recovery and solid-state energy conversion. With the escalating urgency of climate change, the demand for TEMs is expanding across sectors such as industrial waste heat utilization, medicine, vehicles, and sensors [1,2,3,4,5,6].
In response to these growing demands, substantial research efforts have focused on improving the performance of TEMs, primarily by developing high-zT semiconductor materials. Conventional thermoelectric materials such as Bi2Te3-, PbTe-, and skutterudite-based compounds have been widely studied [7,8,9,10,11,12]. Their performance has been enhanced through strategies including nano-structuring, doping, and band engineering to increase energy conversion efficiency [13,14,15,16,17].
However, despite significant progress in material development, module-level research continues to face challenges due to the absence of standardized measurement protocols. Inconsistencies in measurement results across different experimental environments remain unresolved. Variations in test setups, heat source configurations, and interfacial contact conditions can cause deviations in output characteristics, even for identically fabricated TEMs. International round-robin tests have revealed considerable variation in key output parameters—such as output voltage and power—when identical TEMs were evaluated across different institutions, with reported deviations in maximum output power (Pmax) reaching up to 27.2% [18]. These results emphasize the urgent need for standardized techniques to ensure reliable TEM evaluation and enable interlaboratory data comparison.
To support the standardization of TEM measurements, the development of a Standard Reference Thermoelectric Module (SRTEM) is essential. Unlike conventional TEMs that are designed to maximize power generation, the SRTEM is mainly developed to provide stable and reproducible output for calibration purposes. It is designed to deliver highly consistent electrical output under identical thermal input conditions, minimizing the influence of experimental variability. As illustrated in Figure 1, the SRTEM provides a stable and reproducible reference output that facilitates system calibration and cross-validation, thereby contributing to the establishment of a reliable measurement platform. For this purpose, the SRTEM must be fabricated using materials with both mechanical robustness and thermal stability. Conventional thermoelectric materials often lack sufficient mechanical strength and exhibit environmental sensitivity, limiting their applicability in calibration [19,20,21]. To address these limitations, a previous study demonstrated the potential of Ni-based alloys by fabricating a reference module with improved mechanical stability, confirming its feasibility as an SRTEM [22].
This study presents the development of an SRTEM employing durable metallic thermoelectric materials and a geometrically modified leg shape. The SRTEM is designed to operate within the representative temperature range of commercial TEM applications (323–473 K), providing stable electrical output under defined thermal gradients. This study explores SRTEM devices constructed from different metallic thermoelectric material pairs, highlighting the promise of the chromel–constantan system. Particular attention is given to a novel hourglass-shaped geometry as a three-dimensional design strategy and to the interfacial characteristics of metallic materials with direct bonded copper (DBC) substrates, both of which underscore new pathways for enhancing metal-based SRTEM performance. Through these approaches, the developed SRTEM offers a practical platform for module-level evaluation and supports the establishment of a standardized TEM measurement framework.
This study explores SRTEM devices constructed from different metallic thermoelectric material pairs, highlighting the promise of the chromel–constantan system. Particular attention is given to a novel hourglass-shaped geometry as a three-dimensional design strategy and to the interfacial characteristics of metallic materials with direct bonded copper (DBC) substrates, both of which underscore new pathways for enhancing metal-based SRTEM performance.

2. Experimental Section

2.1. Thermoelectric Materials for SRTEMs

High-purity (>99.9%) metallic thermoelectric materials were selected as candidates for the fabrication of SRTEMs. As shown in Figure 2, bulk ingots were synthesized via high-temperature melting and machined into rectangular bars with dimensions of 3 × 3 × 10 mm3 for property evaluation. Electrical conductivity and Seebeck coefficient were measured simultaneously using a commercial system (ZEM-3, ULVAC RIKO, Yokohama, Japan) under a low-pressure helium atmosphere, which minimizes outgassing and enhances contact between the sample and electrodes. Thermal diffusivity (α) was obtained using the laser flash method (LFA 467 HyperFlash, Netzsch, Selb, Germany) with disk-shaped samples (diameter: 12.7 mm, thickness: 1 mm). Specific heat capacity (Cp) was measured in parallel using a Pyroceram 9606 standard. The material density (Dρ) was determined via the Archimedes method, and thermal conductivity (κ) was calculated using the relation κ = α × Cp × Dρ.
The typical measurement uncertainty of the Seebeck coefficient, electrical conductivity, and thermal diffusivity is 7%, ±10%, and ±3%, respectively. However, we could not rule out the possible error in measuring the thermoelectric properties due to the sample-to-sample variation as a single specimen was measured. However, the measurement uncertainty on material property does not significantly affect the main conclusion drawn in this study, as the overall power output of the device is affected by numerous factors other than thermoelectric elements, such as electrodes, composition and working environment of solders, and the substrate.

2.2. Evaluation of Contact Resistance in Metallic Thermoelectric Materials

To evaluate the electrical contact properties of the bonded region, each metallic thermoelectric leg was joined to the Cu electrode surface of the direct bonded copper (DBC) ceramic substrate using Sn–Ag–Cu (SAC) solder paste. A customized scanning probe equipment was employed to measure interfacial resistance through a four-probe method [23]. The specific contact resistance (Rsc) was determined by multiplying the resistance variation (ΔR) at the bonded interface by the corresponding contact area (A), expressed as Rsc = ΔR × A.

2.3. Module Fabrication

Three SRTEMs were fabricated using different combinations of metallic thermoelectric materials. Each module consisted of 16 thermoelectric legs (8 p-type and 8 n-type) arranged in 8 pairs. The legs, with a bonding cross-sectional area of 3.00 mm × 3.00 mm, were mounted between two alumina substrates patterned with Cu electrodes (Ferrotec, Tokyo, Japan). Bonding was performed under vacuum at 573K using SAC solder paste (KZ-1354, Shenzhen, China). The SRTEM device was soldered under an applied pressure of 25 kgf in a 5 × 10−3 Torr vacuum chamber for 1800 s. The hot-side and cold-side substrates were prepared 30.0 × 30.0 × 1.0 mm3 and 30.0 × 35.0 × 1.0 mm3, respectively, with the extended cold side designed to facilitate external wiring during assembly. To evaluate the effect of substrate thermal conductivity, additional modules were fabricated using AlN substrates, while all other fabrication conditions and dimensions were kept identical to those of the alumina DBC modules.

2.4. Thermal–Electrical Measurement of SRTEMs

To characterize the electrical properties of the developed SRTEMs, measurements were conducted using a custom-designed evaluation system for TEMs. The experiments were carried out under a high vacuum environment (≤10−3 Torr) to minimize convective heat losses. The temperature gradient was established by maintaining the cold side (Tc) at 323 K via a water-cooled copper block, while the hot side (Th) was raised to 473 K using a cartridge heater attached to the upper block. For improved thermal interface conductivity, graphite sheets with a thickness of 0.5 mm and thermal conductivity of 5 W/m·K were placed between the module and both thermal contact surfaces. The test pressure of 40 kgf has been applied to the SRTEM device. Surface temperatures were tracked using platinum resistance temperature sensors (Pt100). The open-circuit voltage (Voc) and internal resistance (Rin) were subsequently recorded to assess the module’s performance.

2.5. Simulation of SRTEMs with Geometric Leg

To evaluate the effects of leg shape on thermoelectric performance, three-dimensional finite element method (FEM) simulations were conducted using the Heat Transfer Module of COMSOL (version 5.5) Multiphysics. Two module configurations were modeled: one with conventional rectangular legs and the other with geometrically modified double-hourglass (2H/G) legs. Material properties were assigned to match those of the fabricated modules, and the SRTEM geometries were constructed using the actual module dimensions. The hot and cold sides were fixed at 473 K and 323 K, respectively. From the simulated temperature distributions across the entire module, the Voc was calculated to compare the thermal resistance characteristics of the two leg geometries. The machinability of the proposed 2H/G legs was verified using wire electrical discharge machining (EDM) (AL600G, Sodick Gyeonggi-do, Korea).

3. Results

3.1. Measurement System for TEM Characterization

Measurement systems for evaluating the performance of thermoelectric generators can be broadly categorized into two types (Figure 3).
  • Type 1: This system establishes a temperature gradient across the TEM by contacting the hot side and the cold side and independently controlling their respective temperatures [24,25]. In this case, the open-circuit voltage (Voc) and maximum output power (Pmax) generated by the temperature difference (ΔT) are measured.
  • Type 2: This measurement system is based on the Type 1 configuration, with an additional heat flux meter (HFM) incorporated to directly quantify the heat flow (Qin) input to and output from the TEMs [12,22]. In this case, both the Voc and Pmax induced by the temperature gradient and the conversion efficiency (ηeff) can be measured.
For a detailed evaluation of the overall power generation performance of TEMs, including ηeff, it is necessary to employ a Type 2 system capable of analyzing Qin. In contrast, in many research and development contexts where the verification of only Voc and Pmax is sufficient, a Type 1 system is typically constructed and utilized. Due to its simple structure and straightforward operation, the Type 1 configuration is often widely used for TEM characterization, especially in industry and university labs [26,27,28,29,30].
In this context, the proposed SRTEM is intended to serve as a reference module for calibrating relatively simple Type 1 measurement systems that do not incorporate heat flow analysis.
Based on the performance results of the calibration SRTEM corresponding to the Type 1 thermoelectric measurement system developed in this study, further research will be conducted to extend its application to SRTEMs for Type 2 systems incorporating heat flux analysis.

3.2. Selection of Primary Calibration Parameter

The SRTEM was designed not only to maximize electrical output power generation, but also to serve as a calibration reference for thermoelectric measurement systems (Type 1). Accordingly, the design focus was placed on ensuring reproducibility and accuracy as the primary calibration parameter, rather than on enhancing device output performance.
The thermoelectric device evaluation system first establishes a temperature gradient across the thermoelectric device to provide thermal input, whereby the test device generates an electrical output through thermoelectric conversion. In this thermoelectric conversion, Voc is the first electrical parameter to be measured directly and serves as the fundamental variable from which all subsequent performance metrics are derived. It is defined by the Seebeck relation, Voc = S·ΔT, where S denotes the Seebeck coefficient of the material and ΔT is the applied temperature difference (ΔT = Th − Tc).
Because Voc is determined solely by the intrinsic properties of the thermoelectric material and the imposed ΔT, it is inherently more robust against experimental variations. In contrast, the remaining parameters (such as output power) are obtained as secondary variables, which introduces cumulative uncertainty since their values are affected by the accuracy of Voc. As shown in Figure 4, several additional error propagations arise in the subsequent process of measuring and calculating the output power after the initial Voc measurement.
This error propagation comes from (1) the current measurement noise, which originates from the inherent sampling noise of the electronic load or source measure unit [31,32]; (2) the voltage drop and contact resistance variation, arising from wiring resistance and unstable electrical contacts under load conditions [33,34]; and (3) the self-heating of the load, caused by thermal drift due to resistive heating of the electronic load at higher power levels [35,36]. Consequently, the output power measurement inherently contains larger uncertainty than the direct Voc measurement.
Notably, Voc is the parameter that can be measured directly without the influence of current flow or load conditions. Governed primarily by S and ΔT, Voc is less sensitive to variations in circuit configuration, load sweep range, and contact resistance. Conversely, parameters such as Pmax and ηeff require calculation under specific load conditions and involve additional assumptions and heat flux measurement, making them more susceptible to interlaboratory variability.
Based on these minimized error propagation considerations, the Voc was selected as the primary calibration parameter for the SRTEM. The module was designed to ensure stable and reproducible Voc itself under consistent thermal boundary conditions. Stable thermoelectric materials were employed to minimize variability in the Seebeck response.

3.3. Thermoelectric Properties of the Candidate Metallic Materials

To ensure the stability and reproducibility of the calibration parameter Voc, the SRTEM requires thermoelectric materials with high durability and long-term reliability. However, conventional commercial thermoelectric materials—while offering relatively high zT values such as Bi2Te3-based TEMs—often exhibit mechanical or chemical instability under repeated thermal cycling. Their powder-based consolidation processes (e.g., spark plasma sintering and hot pressing) may further introduce grain boundary defects and residual stresses, limiting long-term stability [37,38,39,40]. Therefore, in this study, a set of metallic thermoelectric materials with superior structural stability was investigated as candidate materials for the SRTEM. These metallic materials are typically produced through high-temperature melting processes and are known for their excellent mechanical and thermal stability [41].
Several metallic-based thermoelectric materials were shortlisted as candidate materials for application in the SRTEM. Ni90Cr10 (Chromel), a simple solid-solution alloy, was identified as a strong candidate due to its standardized fabrication process, which ensures minimal variability in physical properties among specimens. In addition, its high phase stability minimizes phase transition or precipitation issues, thereby providing excellent reproducibility—an essential requirement for SRTEM. From the perspective of stability, Cu55Ni45 (Constantan) was also considered. As a single-phase solid-solution alloy, it exhibits strong phase stability and maintains stable thermoelectric properties across a wide temperature range (from room temperature to above 600 °C) [42]. Alongside its favorable thermal characteristics, its chemical stability effectively suppresses oxidation and corrosion, making it a promising candidate for reliable and reproducible SRTEM applications.
Candidate materials were also assessed in terms of their thermal expansion behavior. In particular, Fe64Ni36 (Invar) demonstrates a nearly zero coefficient of thermal expansion in the range of ~20–300 °C, a unique characteristic that has already been validated through widespread use in precision instruments and watches, suggesting its applicability for SRTEM [43]. Finally, compared with powder-based materials, alloys that undergo melting processes generally provide higher reproducibility due to their compositional uniformity. Furthermore, in the case of single-element metals, even greater uniformity and reproducibility are expected. In this context, pure Fe, which not only exhibits intrinsic thermoelectric properties but also provides high mechanical strength and durability, was comparatively analyzed as a potential SRTEM candidate material.
Figure 5 presents the temperature-dependent thermoelectric properties of the candidate metallic materials. In Figure 5a, the Seebeck coefficients (S) are shown over the operating temperature range. Ni90Cr10 and Fe exhibit positive Seebeck values, indicating p-type behavior, while Cu55Ni45 and Fe64Ni36 show negative values corresponding to n-type characteristics. Ni90Cr10 and Cu55Ni45 demonstrate an increasing trend in S with rising temperature, which is consistent with the typical behavior observed in metals and degenerate semiconductors [44]. Among the materials, Cu55Ni45 exhibits the highest Seebeck coefficient, followed by Ni90Cr10. At an operating temperature of ~473 K (200 °C), the measured Seebeck coefficients were 23.8 µV/K for Ni90Cr10, −57.5 µV/K for Cu55Ni45, −1.3 µV/K for Fe64Ni36, and 0.66 µV/K for pure Fe. Fe64Ni36 shows a decreasing Seebeck coefficient as the temperature approaches its Curie point (~553 K), reflecting magnetic ordering effects [45]. In addition, near ~523 K, the Seebeck coefficients of both Fe64Ni36 and pure Fe approach zero, and their Seebeck polarity changes, leading to unstable thermoelectric characteristics. This instability makes Fe64Ni36 and Fe unsuitable as candidate thermoelectric materials for the SRTEM.
Figure 5b shows that most metallic candidates exhibit increasing electrical resistivity (ρ) with temperature, a typical characteristic of metallic conduction resulting from enhanced electron–phonon scattering. Nevertheless, their resistivity values remain significantly lower than those of conventional semiconductor-based thermoelectric materials, such as Bi2Te3 (typically >10 μΩ·m) [46]. This inherently low resistivity helps suppress internal joule heating and contributes to stable electrical output during repeated measurements.
Figure 5c presents the measured thermal conductivity (κ) as a function of temperature for the candidate metallic materials. Except for pure Fe, the alloy-based materials exhibit a gradual increase in κ with temperature, consistent with the behavior predicted by the Wiedemann–Franz law [47]. The measured κ values range from approximately 10 to 40 W/m·K, which is substantially higher than those of typical thermoelectric materials (<5 W/m·K). Pure Fe, as a single composition, inherently exhibits higher thermal conductivity. These elevated κ values can hinder the establishment of a sufficient ΔT across the module. To address this, thermal resistance may need to be increased through structural modifications or by applying appropriate thermal interface materials.
Figure 5d shows the calculated figure of merit (zT = S2/ρκ·T) for the candidate metallic materials. The solid gray line represents the typical zT range of conventional thermoelectric materials such as Bi2Te3-based materials [48]. All four metal-based candidates exhibit significantly lower zT values compared to the semiconductor reference. At the operating temperature of 473 K, the zT values were 0.036 for Ni90Cr10 (chromel), 0.14 for Cu55Ni45 (constantan), 6.75 × 10−4 for Fe64Ni36 (invar), and 4.95 × 10−4 for pure Fe, with constantan showing the highest value among the tested metallic materials. Although the overall zT values are relatively low, when considering module-level performance, all candidates can still be applied within the target operating temperature range as thermocouple couples such as chromel–invar, Fe–constantan, and chromel–constantan. The Fe–invar pair could also be fabricated, but its markedly lower zT compared to chromel–constantan makes it less favorable for SRTEM development.
Applsci 15 10273 g005
Figure 5. Thermoelectric properties of candidate metallic materials for SRTEM. (a) Seebeck coefficient S, (b) electrical resistivity ρ, (c) thermal conductivity ĸ, and (d) figure of merit zT over the operating temperature range (323–473 K). For comparison, the zT of commercial thermoelectric material (Bi2Te3) is also shown in (d) [48].
Figure 5. Thermoelectric properties of candidate metallic materials for SRTEM. (a) Seebeck coefficient S, (b) electrical resistivity ρ, (c) thermal conductivity ĸ, and (d) figure of merit zT over the operating temperature range (323–473 K). For comparison, the zT of commercial thermoelectric material (Bi2Te3) is also shown in (d) [48].
Applsci 15 10273 g005

3.4. Bonding Characteristics of Thermoelectric Elements

To enable the electrical integration of thermoelectric elements into a module, reliable bonding to the substrate and electrode is essential. Imperfect bonding can introduce additional interfacial resistance, which critically affects the overall module performance. Specifically, contact resistance arises at the interface between the thermoelectric leg and the Cu electrode, and is strongly influenced by factors such as surface roughness, bonding quality, and differences in material properties [49,50]. These interfacial issues may lead to degraded electrical and thermal conductivity across the joint.
Semiconductor-based thermoelectric materials such as Bi2Te3 typically require intermediate metallization layers (e.g., Ti or Ni) to ensure stable bonding [51,52,53,54]. In contrast, the metallic thermoelectric materials in this study were directly bonded to DBC substrates without such layers.
To evaluate contact resistance under realistic bonding conditions, four types of metallic thermoelectric legs—Ni90Cr10, Cu55Ni45, Fe64Ni36, and pure Fe—were bonded to substrates, as shown in Figure 6a. After bonding, the surface intended for measurement was polished to ensure uniformity. Contact resistance was then measured using a micro scanning probe system equipped with a spring-loaded tip (Figure 6b). The measurement setup, illustrated in Figure 6c, employed a four-point probe method to assess resistance variations across the bonded interface. For the SRTEM to ensure consistent calibration performance during repeated measurements, maintaining low and stable contact resistance is important.
The contact resistance measurements are summarized in Figure 7. Ni90Cr10 Cu55Ni45 and Fe64Ni36 exhibited contact resistances on the order of 10−7 μΩ·cm2, while pure Fe, as a single-element metal, demonstrated the lowest value at approximately 10−8 μΩ·cm2. Figure 7e presents the measured contact resistance of a Bi2Te3-based leg, which remained relatively high. In contrast, all metallic candidates consistently showed lower contact resistance, confirming their potential for reliable electrical connections in SRTEM applications. These values were achieved without the use of additional metallization layers, validating the feasibility of direct bonding between metallic thermoelectric legs and DBC substrates. The resulting low-resistance interfaces contributed to mechanically stable junctions, further supporting the use of metallic materials for robust and reproducible SRTEM fabrication.

3.5. Thermoelectric Output Performance of Fabricated SRTEMs

Three SRTEMs were fabricated using the following p–n type material combinations—Ni90Cr10–Fe64Ni36 (chromel–invar), Fe–Cu55Ni45 (Fe–constantan), and Ni90Cr10–Cu55Ni45 (chromel–constantan)—as shown in Figure 8a–c. The thermoelectric output performance was evaluated under steady-state conditions with the hot-side temperature fixed at 473 K and the cold-side temperature maintained at 323 K. The resulting output voltage and output power as a function of electrical current are presented in Figure 8d–f. For the chromel–invar module, the open-circuit voltage (Voc) was measured as 31.0 mV and internal resistance (Rin) of 255 mΩ (Figure 8d). The Fe–constantan module exhibited a Voc of 45.0 mV and an Rin of 255 mΩ (Figure 8e). The chromel–constantan module showed the highest output with a Voc of 55.0 mV and a low Rin of 36 mΩ (Figure 8f). Specifically, three SRTEM devices were fabricated for each material combination, and the Voc measurements exhibited differences within 3%, demonstrating a high degree of reproducibility.
These results are consistent with the relative Seebeck coefficient of the metallic thermoelectric materials (Figure 5a). Invar and Fe, on the other hand, possess ZT values that are two to three orders of magnitude lower than those of chromel and constantan, which accounts for the significantly small Voc observed in their modules compared with the chromel–constantan combination.
Based on the fundamental device-level performance analysis of the SRTEM, it was anticipated that materials such as Invar and Fe would offer advantages arising from their thermal expansion coefficient characteristics or compositional uniformity. However, the fabricated devices exhibited performance that was significantly lower, confirming that their applicability to SRTEM is relatively inferior compared to chromel–constantan-based SRTEM.
Among the tested modules, the chromel–constantan exhibited the highest Voc and stability. However, the Voc values of all tested SRTEMs were relatively close to the lower detection limit of standard thermoelectric measurement equipment. In principle, the Voc of the SRTEM should be comparable to that of the typical thermoelectric devices to be measured, so that the calibration can be properly performed within the corresponding voltage range and the offset accurately extracted. The chromel–constantan SRTEM shown in Figure 8f exhibited a Voc of 55 mV, which is still considerably lower than that of conventional ceramic thermoelectric modules (3 × 3 cm2). Nevertheless, this value is above the lower detection limit of 1 mV for the voltage measurement instrument (Kikusui PLZ164WA, Yokohama, Japan) employed in the thermoelectric characterization system and thus falls within the measurable range.
Such a low Voc characteristic, however, clearly indicates the need for substantial improvement, particularly when measurement uncertainty is taken into account. This reduction in performance was anticipated to some extent, given that metallic thermoelectric materials generally possess relatively low ZT values. Even so, in order to fully exploit the most critical properties of metallic thermoelectric materials for SRTEM applications—namely, their superior stability and reproducibility—it will be essential to enhance their limited device-level performance through structural optimization. This constitutes a central direction for the continued development of metal-based SRTEMs. For practical calibration applications, particularly in interlaboratory comparisons where reproducibility and resolution are critical, higher Voc values are desirable to ensure sufficient signal-to-noise ratio and minimize relative uncertainty. Therefore, strategies to further increase Voc are necessary to enhance the applicability of metallic SRTEMs as reliable reference modules.

3.6. Thermoelectric Leg Geometry on Simulated Thermoelectric Output

Metal-based SRTEMs exhibited relatively low Voc due to the inherently low thermoelectric properties of metallic materials. However, to ensure effective calibration within the typical measurement range of conventional TEMs, it is desirable to increase Voc beyond the current levels. One promising strategy to achieve this is by enhancing the internal temperature difference (ΔT) across the thermoelectric legs through geometric modification.
The thermoelectric performance of SRTEMs composed of metallic thermoelectric materials can be further enhanced through geometric modification of the thermoelectric legs. While conventional TEMs typically employ rectangular leg shapes, modifying the leg geometry increases the thermal resistance, resulting in a larger ΔT across the legs [55,56,57,58]. For metallic materials with inherently high thermal conductivity, this approach is effective, as increasing ΔT can compensate for the low Seebeck coefficient and thereby improve the Voc. Building on previous studies that explored hourglass and trapezoidal shapes, this work introduces a more complex double-hourglass (2H/G) shape (Figure 9a) designed to further increase ΔT [59,60]. The high mechanical strength of metallic thermoelectric legs allows the fabrication of such intricate shapes, which are generally infeasible with brittle thermoelectric materials.
To evaluate the effect of geometry on thermoelectric performance, finite element method (FEM) simulations were conducted under steady-state conditions, with hot-side and cold-side temperatures maintained at 473 K and 323 K, respectively (Figure 9). All geometries were simulated using the same dimensions as the fabricated modules. The output voltage and power of the rectangular and 2H/G shapes were compared, and the results are summarized in Table 1 and Figure 9.
The enhancement in 2H/G SRTEM is shown through the comparison of two geometrically different modules. The simulation of the module with a 2H/G shape showed improvements in Voc by 5.2% (chromel–invar), 11.0% (Fe–constantan), and 20.2% (chromel–constantan) relative to the simulation of the module with a rectangular shape (Figure 9d). These improvements support the role of geometric design in not only enhancing performance but also achieving more precise and reproducible Voc outputs for calibration purposes.
The fabrication feasibility of the 2H/G shape was demonstrated using EDM. As shown in Figure 10, 2H/G legs were successfully manufactured, confirming the practical applicability of the proposed design in SRTEM production. To evaluate the thermoelectric characteristics of rectangular and 2H/G-shaped geometries at the single-leg level, test samples were fabricated as shown in Figure 11a. Each Constantan single leg was bonded to an alumina DBC substrate, identical to those employed in the SRTEM process, thereby enabling measurement of the voltage across both ends.
As in Figure 11, the hot- and cold-side temperatures were maintained at 473 K and 323 K, respectively, and the resulting Voc was measured. As shown in Figure 11b, the 2H/G-shaped thermoelectric leg exhibited a Voc of 5.8 mV, whereas the rectangular thermoelectric leg of the same height produced approximately 5.0 mV. The single-leg performance measurements confirmed that the 2H/G-shaped leg demonstrated a significant 16.0% increase in Seebeck voltage compared with the rectangular leg. This result is consistent with the observation in Figure 9d, where the 2H/G-structured SRTEM device exhibited a 20.2% enhancement in Voc.
These findings clearly indicate that even for thermoelectric legs of identical material and height, a three-dimensional geometric design such as the 2H/G shape can effectively increase thermal resistance, thereby offering a direct pathway toward performance enhancement of metal-based SRTEM devices.

3.7. Effect of Substrate Material on Thermoelectric Performance

The thermal conductivity of the substrate plays a role in establishing a sufficient ΔT across the thermoelectric legs, which directly affects the Voc. As ΔT must be reliably maintained to ensure an accurate and reproducible Voc value, the thermal transfer capability of the substrate is a supplementary design parameter in SRTEM development. Commercial TEMs typically employ alumina substrates due to their moderate thermal conductivity and cost-effectiveness [61]. Alternatively, AlN substrates offer higher thermal conductivity (around 180 W/m·K) than alumina substrates (around 25 W/m·K), which can enhance ΔT across the thermoelectric legs and consequently improve Voc [62,63]. To evaluate this effect, SRTEMs using chromel–constantan legs were fabricated with two substrate types—alumina and AlN—while maintaining identical module dimensions, leg geometries, and fabrication processes. The chromel–constantan combination was selected due to its demonstrated durability and stability in Voc, making it suitable for isolating the influence of substrate material. The fabricated modules are shown in Figure 12a.
Electrical output was measured under steady-state conditions with a hot-side temperature of 473 K and a cold-side temperature of 323 K. The I–V curves of the two modules are presented in Figure 12b. The AlN-based module exhibited a Voc of 60.0 mV and an Rin of 37 mΩ. The alumina-based module showed a Voc of 55.0 mV and an Rin of 36 mΩ. Compared to the alumina-based module, the AlN-based module showed an increase of 9.1% in Voc. The internal resistance remained nearly identical, indicating that the observed improvement is primarily attributed to the difference in substrate thermal conductivity rather than variations in electrical contact or thermoelectric materials.
These results demonstrate that high thermal conductivity substrates such as AlN can facilitate more efficient heat transfer to the thermoelectric legs, increasing ΔT and improving Voc. While the choice of thermoelectric materials remains the primary factor in module performance, these findings indicate that substrate properties can also contribute to the stability and consistency of output characteristics. Therefore, substrate selection, in conjunction with reproducible metallic thermoelectric materials, supports the development of reliable SRTEMs for standardized calibration.

4. Discussion

This study aimed to develop a Standard Reference Thermoelectric Module (SRTEM) with a focus on durability and stability. In contrast to conventional thermoelectric modules designed to maximize output power, the proposed SRTEM prioritizes open-circuit voltage (Voc) as the primary calibration parameter, due to its direct measurability, linear dependence on ΔT, and low sensitivity to experimental variations.
To ensure stable Voc, metallic thermoelectric materials with high durability and mechanical stability were selected as candidates. Four alloys—chromel, constantan, invar, and Fe—were investigated, and three thermoelectric couples [chromel–invar, Fe–constantan, and chromel–constantan] were assembled into SRTEMs for comparative evaluation. Among these, the chromel–constantan couple demonstrated the most favorable characteristics for SRTEM development. Its relatively high and stable Seebeck response was designed to enable consistent Voc, and the low contact resistance at the bonded interface supported stable electrical transfer. In addition, the compatibility of the two alloys with DBC substrates allowed durable bonding without additional metallization layers, in contrast to semiconductor-based thermoelectric legs (e.g., Bi2Te3 and PbTe) that are prone to fracture and interfacial degradation. As a result, the chromel–constantan SRTEM achieved a Voc of 55 mV at ΔT = 150 K. These results support chromel–constantan as a candidate for long-term stability and reproducibility in SRTEM applications. However, the relatively low Voc compared to semiconductor-based TEMs clearly highlights the need for further intensive improvement, which this study addressed by proposing two additional strategies to enhance the Voc response of metallic SRTEMs.
First, to further improve the accuracy of the calibration parameter, leg geometry was modified via finite element simulations. The results showed that adopting a double-hourglass (2H/G) shape increased thermal resistance and enhanced ΔT, leading to a 20.2% increase in Voc compared to the rectangular shape. This improvement was further supported by the direct measurement of single-leg modules with substrates attached, which exhibited a 16.0% increase in Voc.
Second, the effect of substrate material was investigated. Substrate thermal conductivity was found to influence the ΔT across the thermoelectric legs. A comparison between modules fabricated with alumina and AlN substrates revealed that the higher thermal conductivity of AlN improved heat transfer across the module, resulting in a 9.1% increase in Voc. While the effect of substrate material is secondary to that of the thermoelectric legs, this enhancement supports the overall reliability and effectiveness of the SRTEM design for standardized calibration.
Beyond the two approaches to Voc enhancement demonstrated in this work, further improvement of SRTEM performance can be expected through a variety of research strategies. From a structural perspective, optimizing the fill factor of the current, non-optimized SRTEM design alone is anticipated to yield a clear increase in Voc, while multilayered cascade device structures could also provide significant gains. From a materials perspective, beyond the reported chromel and constantan pair, the development of hybrid alloys with varied compositions is expected to further enhance Voc performance.
Through this study, we compared the characteristics of SRTEM devices fabricated from various combinations of metallic thermoelectric materials and confirmed the relative superiority of the chromel–constantan pair. Notably, we demonstrated for the first time that adopting a three-dimensional geometrical approach with an hourglass-shaped leg, rather than a simple rectangular leg, can effectively enhance the performance of metal-based SRTEM devices. Furthermore, we conducted the first analysis of the electrical contact characteristics between metallic thermoelectric materials and DBC substrates, confirming that metallic thermoelectric materials form excellent interfacial junctions suitable for application in SRTEM devices. The possibilities of further enhancement in SRTEM device performance were confirmed through 3D leg geometry optimization (e.g., 2H/G design) and substrate material improvement. These results from the chromel–constantan-based SRTEM (for Type 1 evaluation) could be extended to develop an SRTEM for the Type 2 thermoelectric evaluation system, which includes heat flux measurement for comprehensive thermoelectric device characterization. Further parameter-estimation techniques could be studied to facilitate model-based identification of the proposed SRTEM [64,65].
In this study, candidate thermoelectric materials were analyzed and reported within the preliminary performance range of the prototype SRTEM. However, based on these findings, long-term repeatability experiments on an optimized full-device-level SRTEM should be conducted over a sufficiently extended research period, and the resulting performance analyses should be reported. Furthermore, interlaboratory round-robin tests are required to compare SRTEM performance across research institutions, and standardized calibration protocols should also be established and documented as part of subsequent investigations.

5. Conclusions

This study developed a Standard Reference Thermoelectric Module (SRTEM) with an emphasis on reproducibility and durability rather than power maximization. Metallic thermoelectric materials were investigated, and the chromel–constantan couple was identified as the most stable candidate. In this framework, open-circuit voltage (Voc) was established as the primary calibration parameter because of its reproducibility and quantitative relation to the applied temperature difference.
Furthermore, device-level strategies, including three-dimensional leg geometry and substrate material selection, were shown to enhance the reliability of Voc as a calibration parameter. These findings confirm the feasibility of designing metallic SRTEMs that can provide consistent and stable outputs for use in measurement standardization.
Overall, this work lays the groundwork for metallic SRTEMs to serve as reference devices in thermoelectric research. Future studies should include extended durability evaluations, interlaboratory testing, and the development of standardized calibration protocols to fully establish their role in thermoelectric measurement systems.

Author Contributions

Conceptualization, E.K. and S.H.P.; methodology, E.K. and S.H.P.; software, E.K. and S.P.; validation, E.K. and S.H.P.; formal analysis, E.K. and H.J.; investigation, E.K. and H.J.; resources, S.-b.K. and S.H.P.; data curation, E.K.; writing—original draft preparation, E.K.; Writing—review and editing, S.H.P.; visualization, E.K.; supervision, S.H.P.; project administration, S.H.P.; funding acquisition, S.-b.K. and S.H.P. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Korean Ministry of Trade, Industry and Energy, grant numbers 2021202080023D and RS-2025-07982969.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
TEMThermoelectric Module
SRTEMStandard Reference Thermoelectric Module
αThermal Diffusivity
CpSpecific Heat Capacity
DρMaterial Density
κThermal Conductivity
CTECoefficient of Thermal Expansion
TMAThermomechanical Analyzer
LLength
DBCDirect Bonded Copper
RscSpecific Contact Resistance
ΔRResistance Variation
AArea
VocOpen-Circuit Voltage
PmaxMaximum Output Power
RinInternal Resistance
FEMFinite Element Method
2H/GDouble-Hourglass
EDMElectrical Discharge Machining
ThHot-Side Temperature
TcCold-Side Temperature
Qin Heat Flow Input
ηeffConversion Efficiency
ΔTTemperature Difference
EMFElectromotive Force
SSeebeck Coefficient
ρElectrical Resistivity
zTFigure of Merit

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Figure 1. Schematic of the interlaboratory calibration process using the Standard Reference Thermoelectric Module (SRTEM). Prior to calibration, measurements show deviations (σ) among laboratories due to differences in test environments. Calibrating the systems to the reference values provided by the SRTEM enables consistent and reproducible results across laboratories.
Figure 1. Schematic of the interlaboratory calibration process using the Standard Reference Thermoelectric Module (SRTEM). Prior to calibration, measurements show deviations (σ) among laboratories due to differences in test environments. Calibrating the systems to the reference values provided by the SRTEM enables consistent and reproducible results across laboratories.
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Figure 2. Metallic thermoelectric legs of various compositions, cut for performance evaluation.
Figure 2. Metallic thermoelectric legs of various compositions, cut for performance evaluation.
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Figure 3. Photographs of measurement systems for TEM characterization: (a) Type 1: simple configuration for measuring ΔT and electrical output (Voc and Pmax); (b) Type 2: extended configuration with an additional heat flux meter (HFM), enabling measurement of Voc, Pmax, Qin, and ηeff.
Figure 3. Photographs of measurement systems for TEM characterization: (a) Type 1: simple configuration for measuring ΔT and electrical output (Voc and Pmax); (b) Type 2: extended configuration with an additional heat flux meter (HFM), enabling measurement of Voc, Pmax, Qin, and ηeff.
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Figure 4. Schematic of the TEM evaluation system. While Voc is directly measured under open-circuit conditions, additional errors arise during current and resistance measurements for parameter evaluation, leading to error propagation in derived metrics such as output power.
Figure 4. Schematic of the TEM evaluation system. While Voc is directly measured under open-circuit conditions, additional errors arise during current and resistance measurements for parameter evaluation, leading to error propagation in derived metrics such as output power.
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Figure 6. (a) Metallic thermoelectric leg bonded to a DBC substrate. (b) Photograph of contact resistance measurement using a micro scanning probe. (c) Schematic of a four-probe system employing a scanning probe for contact resistance evaluation.
Figure 6. (a) Metallic thermoelectric leg bonded to a DBC substrate. (b) Photograph of contact resistance measurement using a micro scanning probe. (c) Schematic of a four-probe system employing a scanning probe for contact resistance evaluation.
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Figure 7. Resistance profiles measured across the bonding region for metallic thermoelectric materials: (a) Ni90Cr10, (b) Cu55Ni45, (c) Fe64Ni36, and (d) Fe. (e) Comparison of resistance profiles with commercial Bi2Te3 and metallic thermoelectric material.
Figure 7. Resistance profiles measured across the bonding region for metallic thermoelectric materials: (a) Ni90Cr10, (b) Cu55Ni45, (c) Fe64Ni36, and (d) Fe. (e) Comparison of resistance profiles with commercial Bi2Te3 and metallic thermoelectric material.
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Figure 8. SRTEMs fabricated with three material pairs and their thermoelectric output characteristics: (a,d) Chromel–invar, (b,e) Fe–constantan, and (c,f) chromel–constantan. Three modules for each type have been fabricated. Output was measured under steady-state conditions (Th = 473 K/Tc = 323 K).
Figure 8. SRTEMs fabricated with three material pairs and their thermoelectric output characteristics: (a,d) Chromel–invar, (b,e) Fe–constantan, and (c,f) chromel–constantan. Three modules for each type have been fabricated. Output was measured under steady-state conditions (Th = 473 K/Tc = 323 K).
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Figure 9. (a) Proposed double-hourglass (2H/G) leg shape. Temperature distribution for two modules with (b) rectangular and (c) 2H/G legs, showing improved ΔT and Voc in the 2H/G shape. (d) Comparison of Voc for three metal-based SRTEMs, with rectangular legs and 2H/G legs (simulated). In all three SRTEMs, heat resistance-modified (2H/G legs) modules are expected to show higher Voc than basic rectangular modules.
Figure 9. (a) Proposed double-hourglass (2H/G) leg shape. Temperature distribution for two modules with (b) rectangular and (c) 2H/G legs, showing improved ΔT and Voc in the 2H/G shape. (d) Comparison of Voc for three metal-based SRTEMs, with rectangular legs and 2H/G legs (simulated). In all three SRTEMs, heat resistance-modified (2H/G legs) modules are expected to show higher Voc than basic rectangular modules.
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Figure 10. Fabricated thermoelectric legs at actual size using EDM: rectangular shape and 2H/G shape, both made from metallic thermoelectric material.
Figure 10. Fabricated thermoelectric legs at actual size using EDM: rectangular shape and 2H/G shape, both made from metallic thermoelectric material.
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Figure 11. (a) Single thermoelectric voltage test sample of the rectangular leg and the double-hourglass (2H/G) leg, and (b) the open-circuit voltage (Voc) characteristics at 473 K (Th) and 323 K (Tc).
Figure 11. (a) Single thermoelectric voltage test sample of the rectangular leg and the double-hourglass (2H/G) leg, and (b) the open-circuit voltage (Voc) characteristics at 473 K (Th) and 323 K (Tc).
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Figure 12. (a) SRTEMs with chromel–constantan legs on alumina (left) and AlN (right) substrates, and (b) I–V characteristics of both devices. At ΔT = 150 K (Th = 473 K, Tc = 323 K), the AlN-based SRTEM exhibits a higher Voc (60 mV) compared to the alumina-based SRTEM.
Figure 12. (a) SRTEMs with chromel–constantan legs on alumina (left) and AlN (right) substrates, and (b) I–V characteristics of both devices. At ΔT = 150 K (Th = 473 K, Tc = 323 K), the AlN-based SRTEM exhibits a higher Voc (60 mV) compared to the alumina-based SRTEM.
Applsci 15 10273 g012
Table 1. Simulated and measured Voc of SRTEMs with different thermoelectric leg shapes and material combinations.
Table 1. Simulated and measured Voc of SRTEMs with different thermoelectric leg shapes and material combinations.
Material Combinations
Leg Shape Chromel–
Invar		Fe–
Constantan		Chromel–
Constantan
RectangularMeasured31.0 ± 0.9 mV45.0 ± 1.4 mV55.0 ± 1.7 mV
Simulated34.1 mV52.6 mV63.1 mV
Double-hourglassSimulated35.9 mV58.4 mV75.9 mV
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Koo, E.; Jang, H.; Park, S.; Park, S.H.; Kang, S.-b. Standard Reference Thermoelectric Modules Based on Metallic Combinations and Geometric Design. Appl. Sci. 2025, 15, 10273. https://doi.org/10.3390/app151810273

AMA Style

Koo E, Jang H, Park S, Park SH, Kang S-b. Standard Reference Thermoelectric Modules Based on Metallic Combinations and Geometric Design. Applied Sciences. 2025; 15(18):10273. https://doi.org/10.3390/app151810273

Chicago/Turabian Style

Koo, EunA, Hanhwi Jang, SuDong Park, Sang Hyun Park, and Sae-byul Kang. 2025. "Standard Reference Thermoelectric Modules Based on Metallic Combinations and Geometric Design" Applied Sciences 15, no. 18: 10273. https://doi.org/10.3390/app151810273

APA Style

Koo, E., Jang, H., Park, S., Park, S. H., & Kang, S.-b. (2025). Standard Reference Thermoelectric Modules Based on Metallic Combinations and Geometric Design. Applied Sciences, 15(18), 10273. https://doi.org/10.3390/app151810273

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