Introduction

In recent years, the progress in microelectronics, photonics, and other high-density electronic systems has greatly amplified the need for efficient and compact cooling solutions. Traditional cooling methods, such as fan-based or liquid cooling systems, are often inadequate for micro-scale applications due to their size, noise, and passive cooling1,2,3,4,5,6. This has led to growing interest in thermoelectric cooling technology, which offers a solid-state, noise-free, fast-response, and highly reliable solution for precise temperature control in compact environments. Based on the Peltier effect7,8,9,10, a temperature difference can be generated across the junction of two dissimilar materials with the passing of an electric current. Therefore, thermoelectric coolers (TECs) have been used for the thermal management of electronics, i.e., pumping heat away from the localized hot spot to prevent the overheating of sensitive components11.

Miniaturized thermoelectric coolers with improved cooling power density and response speed are suitable for localized thermal management11,12. Since the discovery of Bi2Te3 alloys in the 1950s, commercial thermoelectric coolers have been exclusively based on these materials. Currently, the miniaturization of thermoelectric coolers has also been mainly focused on Bi2Te3-based coolers11,12,13,14,15,16,17,18,19,20,21,22. In addition, only a few compounds can achieve high thermoelectric performance around room temperature, such as MgAgSb23,24,25,26, SnSe27,28, Ag2Se29,30,31,32, PbSe-based materials33,34, and Mg3Bi2-based alloys35,36,37,38,39,40,41,42,43,44,45. Typically, the n-type Mg3Bi2-based materials have recently emerged as a promising candidate for thermoelectric cooling due to their relatively high zTs, low cost, and environmental friendliness39,42. Consequently, developing miniscale Mg3Bi2-based coolers capable of achieving substantial cooling temperature differences and high cooling power density is critical.

This study aims at the design and fabrication of miniaturized Mg3Bi2-based thermoelectric coolers. The optimal design of the miniscale cooler is realized by investigating the impact of leg geometry and contact layer on the cooling performance through simulations46,47,48,49,50,51. Experimentally, magnetron sputtering is employed to deposit ultrathin Cu layers onto the Mg2Ni layer, enabling the fabrication of miniscale thermoelectric coolers. The work seeks to advance design principles for miniaturized thermoelectric coolers and facilitate the development of high-efficiency, space-constrained thermal management solutions for next-generation electronics.

Results

Principles for the design of a miniscale thermoelectric cooling device

The performance of thermoelectric coolers, e.g., the maximum cooling temperature difference (ΔTmax) and cooling power (Qc), is jointly determined by the material properties and the device design. In this study, the performance of Mg3Bi2-based thermoelectric coolers is investigated by examining the effects of varying leg lengths, different ceramic materials, and varied electrical contact resistivities. The material properties used for the calculation are shown in Supplementary Fig. 1.

When the cooler operates at the optimal electrical current and reaches a steady state, the cooling power at the cold side is determined by Eq. (1),

$${Q}_{{{{\rm{c}}}}}=N\left[S{T}_{{{{\rm{c}}}}}I-\frac{1}{2}{I}^{2}R-K({T}_{{{{\rm{h}}}}}-{T}_{{{{\rm{c}}}}})\right]$$
(1)

where Tc is the cold-side temperature, Th is the hot-side temperature, N is the number of thermoelectric pairs, and I is the electrical current. In addition, S, R, and K are the Seebeck coefficient, the electrical resistance, and the thermal conductance of a thermoelectric pair consisting of an n-type leg and a p-type leg.

The maximum temperature difference of the thermoelectric cooler is expressed by Eq. (2),

$$\Delta {T}_{\max }=\left({T}_{{{{\rm{h}}}}}+\frac{1}{Z}\right)-\left(\sqrt{\left({T}_{{{{\rm{h}}}}}+\frac{1}{Z}\right)-{{T}_{{{{\rm{h}}}}}}^{2}}\right)$$
(2)

where the figure of merit of a thermoelectric pair (Z) is given by Eq. (3),

$$Z=\frac{{({S}_{{{{\rm{p}}}}}-{S}_{{{{\rm{n}}}}})}^{2}}{{[{({\kappa }_{{{{\rm{p}}}}}{\rho }_{{{{\rm{p}}}}})}^{1/2}+{({\kappa }_{{{{\rm{n}}}}}{\rho }_{{{{\rm{n}}}}})}^{1/2}]}^{2}}$$
(3)

When the temperature difference becomes zero, the cooling power reaches its maximum value (Qc, max), which is shown by Eq. (4),

$${Q}_{{{{\rm{c}}}},\,\max }=N\left(S{T}_{{{{\rm{c}}}}}I-\frac{1}{2}{I}^{2}R\right)$$
(4)

Considering the impact of electrical contact resistance (Re) and substrate thermal resistance (Rt) on the cooling performance, Eq. (2) can be rewritten as,

$$\Delta {T}_{\max }=\left({T}_{{{{\rm{h}}}}}+\frac{1}{{Z}_{{{{\rm{d}}}}}}\right)-\left(\sqrt{\left({T}_{{{{\rm{h}}}}}+\frac{1}{{Z}_{{{{\rm{d}}}}}}\right)-{{T}_{{{{\rm{h}}}}}}^{2}}\right)$$
(5)

where the updated figure of merit (Zd) is given by Eq. (6),

$${Z}_{{{{\rm{d}}}}}=\frac{Z}{\left[1+\frac{4{\rho }_{{{{\rm{e}}}}}}{L({\rho }_{{{{\rm{n}}}}}+{\rho }_{{{{\rm{p}}}}})}\right]}$$
(6)

where ρe is the electrical contact resistivity. In Eq. (6), it is assumed that the leg lengths (L) and cross-sectional areas of the n-type and p-type are identical.

The impact of substrate thermal resistance on the hot-side temperature is shown by Eq. (7), where Qh is the heat dissipation of the cooler, and Ts is the heat sink temperature.

$${T}_{{{{\rm{h}}}}}={T}_{{{{\rm{s}}}}}+{R}_{{{{\rm{t}}}}}{Q}_{{{{\rm{h}}}}}$$
(7)

The electrical contact resistance also affects the maximum cooling power, and Eq. (4) can be rewritten as,

$${Q}_{{{{\rm{c}}}},\,\max }=N\left[S{T}_{{{{\rm{c}}}}}I-\frac{1}{2}{I}^{2}(R+4{R}_{{{{\rm{e}}}}})\right]$$
(8)

Calculations on the performance of the Mg3Bi2-based cooler were conducted. Based on Eq. (5), the relationship between ΔTmax and leg length under different contact resistivities was calculated (Fig. 1a). As the length of the thermoelectric leg decreases, the ΔTmax diminishes, primarily due to the increased influence of irreversible losses associated with contact resistances at the interfaces. These losses become more pronounced as the leg length is reduced, leading to a significant reduction in cooling performance. This reduction becomes more pronounced as the interfacial electrical contact resistivity increases, and the disparity in ΔTmax is noticeable when the leg length is less than 1.0 mm. For a Mg3Bi2-based leg with dimensions of 1 × 1 × 1 mm3, the contact resistivity of 10 μΩ cm2 accounts for approximately 6.7% of the total internal resistance, further highlighting the critical role of minimizing contact losses in optimizing the performance of miniaturized thermoelectric coolers. According to Eq. (8), the large electrical contact resistance is also deleterious to maximum cooling power since the Joule heating caused by contact resistance becomes more significant at shorter leg lengths (Fig. 1b). The relationship between ΔTmax and leg length for different substrate materials, e.g., Al2O3, AlN, and diamond, is depicted in Fig. 1c. It is assumed that the thickness of ceramic materials is 500 μm and the electrical contact resistivity is zero. The results demonstrate that the choice of substrate material significantly impacts the thermal resistance, thereby influencing the ΔTmax of the thermoelectric cooler. Specifically, substrates with higher thermal conductivity exhibit mitigated degradation of ΔTmax, highlighting the critical role of substrate material selection for optimizing cooling performance.

Fig. 1: Calculated performance of the Mg3Bi2 alloys/(Bi, Sb)2Te3-based thermoelectric cooler.
Fig. 1: Calculated performance of the Mg3Bi2 alloys/(Bi, Sb)2Te3-based thermoelectric cooler.The alternative text for this image may have been generated using AI.
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a The relationship between the maximum cooling temperature difference and the leg length at different electrical contact resistivities. b Maximum cooling power density vs. leg length at different contact resistivities. c The relationship between the maximum cooling temperature difference and the leg length with different substrate materials. d The relationship between the temperature of the hot-side ceramic substrate and the leg length.

Furthermore, it should be noted that the temperature of the hot-side ceramic substrate is significantly influenced by the heat exchange capacity of the heat sink and contact thermal resistance dictated by the thermal grease. Experimentally, appreciable thermal non-uniformities can be observed in the ceramic substrate. Finite element simulations using COMSOL have been performed on the temperature distribution of the hot-side ceramic substrate with different leg lengths (Fig. 1d), and the simulation parameters are listed in Supplementary Table 1. The maximum temperature is localized at the interface between the electrode and thermoelectric legs, whereas the minimum temperature emerges at the peripheral region distal to the thermoelectric pairs. With the decreasing leg length, the temperature differential between the maximum and minimum values becomes notable, reflecting intensified thermal non-uniformity that directly compromises ΔTmax. The insets of Fig. 1d show the comparison of the temperature cloud diagrams between the Al2O3 and AlN substrates. Owing to the lower thermal conductivity, the Al2O3 substrate exhibits more pronounced thermal non-uniformity. To further miniaturize the cooler and reduce thermal resistance, 200 μm AlN substrates are taken into account, with the calculation and simulation results shown in Supplementary Fig. 2.

Contact layer design of the Mg3Bi2-based miniscale thermoelectric cooler

The design of the contact layer plays a pivotal role in the fabrication of the high-performance thermoelectric cooler. Previously, iron39, nickel52, and 304 stainless steel53, which are weldable and can realize a low contact resistivity, have been used as the contact layer for Mg3Bi2-xSbx. Compared to these metals and alloys, materials such as Mg2Ni54 and Mg2Cu55 have also been developed as contact layers and demonstrated good reliability. Mg2Ni, exhibiting the lowest electrical contact resistivity (~ 2 μΩ cm2)43,54 among Mg2Cu (~ 12 μΩ cm2)55, 304 stainless steel (~ 5 μΩ cm2), and Fe (~ 2 μΩ cm2)39,52,53,56, is chosen for this study. Since Mg3Bi2-based materials are prone to react with water, electroplating and chemical plating should be excluded from contact layer fabrication57,58. Therefore, the bonding between the contact layer and Mg3Bi2-xSbx is realized by sintering. It should be emphasized that Mg2Ni is unweldable, thereby an additional metallic layer on Mg2Ni is required for soldering.

Experimentally, a Mg2Ni layer was fabricated on Mg3Bi2-xSbx through a sintering process, followed by the deposition of a Cu thin film onto the Mg2Ni layer using the sputtering technique, i.e., Mg3.2Bi1.497Sb0.5Te0.003/Mg2Ni/Cu film. The contact layer structure is shown in Fig. 2a. The impact of contact layer thickness on the cooling performance has been investigated through finite element simulations. The results indicate that a thinner contact layer favors the optimal leg cross-sectional ratio between the n-type and p-type thermoelectric legs (An/Ap) approaching unity (Fig. 2b). This not only benefits the processing of the thermoelectric legs but also contributes to obtaining a higher cooling power density. On the other hand, based on the optimal leg cross-sectional area ratio, the disparities in ΔTmax due to different contact layer designs are compared in Fig. 2c. As the leg length decreases, a thinner contact layer can result in an improved ΔTmax, and a similar trend is also reflected in maximum cooling power (Supplementary Fig. 3). Considering the significant impact of contact layer thickness on the performance of miniaturized coolers, sputtering is employed to fabricate the metallization layer.

Fig. 2: The design of n-type Mg3.2Bi1.497Sb0.5Te0.003 thermoelectric leg.
Fig. 2: The design of n-type Mg3.2Bi1.497Sb0.5Te0.003 thermoelectric leg.The alternative text for this image may have been generated using AI.
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a Schematic view of the leg structure, including pre-circuited AlN ceramic plate, Cu electrode, Sn42Bi58 solder, sputtered Cu layer, Mg2Ni contact layer, and Mg3Bi2-based materials. b Simulated maximum temperature difference as a function of the cross-section area ratio of the n- and p-type legs (An/Ap) with different contact layer thicknesses. c Simulated maximum temperature difference as a function of the leg lengths with different contact layer thicknesses. d Scanning electron microscopy image of the Mg3.2Bi1.497Sb0.5Te0.003/Mg2Ni/Cu film/Sn-Bi solder/Cu electrode junction, the corresponding EDX mapping, and the interfacial electrical contact resistance.

Based on the simulations, the optimized thermoelectric legs feature an overall dimension of 1 × 1 × 1 mm3. Within this structure, the Mg3Bi2-xSbx layer has a thickness of ~ 0.9 mm, and the Bi2Te3-based layer has a thickness of 1.0 mm. The n-type Mg3.2Bi1.497Sb0.5Te0.003/Mg2Ni/Cu film/Cu electrode joint is soldered, and interfacial contact resistivity and elemental mapping results are shown in Fig. 2d. The electrical contact resistivity between the Mg2Ni and the Mg3.2Bi1.497Sb0.5Te0.003 is 1.0 μΩ cm2. The energy-dispersive X-ray spectroscopy (EDX) mapping confirms the absence of significant elemental diffusion at the interface, while clearly identifying the presence of the sputtered Cu film. The electron probe microanalysis (EPMA) point analysis results show the atomic proportion of Mg in Mg3.2Bi1.497Sb0.5Te0.003 remains at 60%(Supplementary Table. 2). Regarding the apparent presence of Sb in the Sn-Bi solder layer, this artifact arises from the close spectral proximity between the Sn and Sb characteristic peaks in EDX (Supplementary Fig. 4), and the EPMA results (Supplementary Table. 3) confirm the absence of Sb in the solder layer. In addition, the interfacial shear strength of the thermoelectric joint has been characterized (Supplementary Fig. 5). Scanning electron microscopy (SEM) image and EDX results of the sheared interfaces between solder and Mg2Ni, and between Mg2Ni and Mg3.2Bi1.497Sb0.5Te0.003 are shown in Supplementary Figs. 6–9, respectively.

Performance of the Mg3Bi2-based miniscale thermoelectric cooler

The fabrication process of the Mg3Bi2-based miniscale thermoelectric cooler is illustrated in Supplementary Fig. 10. The miniscale cooler was integrated through vacuum reflow soldering, with the assembly held at 453 K for 30 s and subsequently cooled in the furnace. This process is designed to minimize the formation of defects such as voids in the solder layer, while also ensuring compatibility with thin copper films within a narrow soldering window.

The cooling performance of the Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale thermoelectric cooler is measured by the homemade system59, and the setup for this characterization is shown in Fig. 3a. The measured cooling temperature differences, cooling power, and coefficient of performance (COP) are shown in Figs. 3b–f. The Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale cooler achieved maximum cooling temperature differences of ~ 59.0 K, ~ 69.9 K, and ~ 81.1 K at hot-side temperatures of 300, 325, and 350 K, respectively (Fig. 3b). The cooler exhibits a nearly linear relationship between the cooling power and the cooling temperature difference for varying electrical currents (Fig. 3c) at the hot-side temperature of 300 K. The electrical-current-dependent cooling power at different cooling temperature differences is shown in Fig. 3d. At the current of 1 A and the temperature difference of 10 K, the COP is approximately 2.3 (Fig. 3e). At a hot-side temperature of 300 K, the cooler can achieve a maximum cooling power density of ~ 5.7 W cm−2. Compared to the previously reported Mg3Bi2-based coolers38,55,60, our results demonstrate a significantly improved cooling power density, benefiting from the miniaturization of the thermoelectric cooler (Fig. 3f). This high cooling power density is essential for localized thermal management of electronics. The measurement uncertainty of cooling power has been analyzed, and it is less than 3.6% (Supplementary Figs. 11–13). The detailed cooling performance of this miniscale cooler at hot-side temperatures of 325 K and 350 K is shown in Supplementary Figs. 14 and 15. Correspondingly, the steady-state cooling performance of the miniscale cooler is simulated, and the impact of thermal radiation is considered (Supplementary Fig. 16)61. To evaluate the stability of the cooler, the cyclic cooling performance of the device has been characterized (Fig. 3g). At the hot-side temperature of 300 K, the cooler was subjected to cyclic currents of 1 A and 3 A (i.e., electrical current densities of 1 A mm−2 and 3 A mm−2) for 270 h (~ 3000 cycles). After the cycling test, the cooler maintained ~ 98.3% of its original performance under the electrical current density of 3 A mm−2.

Fig. 3: Thermoelectric cooling performance of the Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale device.
Fig. 3: Thermoelectric cooling performance of the Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale device.The alternative text for this image may have been generated using AI.
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a The setup for characterizing the cooling performance of the Mg3.2Bi1.497Sb0.5Te0.003/(Bi, Sb)2Te3 cooler. b The relationship between electrical current and cooling temperature difference at the hot-side temperature of 300, 325, and 350 K, respectively. c The relationship between cooling power and cooling temperature difference at the hot-side temperature of 300 K. d The relationship between cooling power and electrical current under different cooling temperature differences. e The relationship between COP and electrical current at the hot-side temperature of 300 K. f The comparison of the maximum cooling power density among different Mg3Bi2-based coolers38,55,60. g Cyclic cooling performance of the miniscale device.

In addition to the large cooling power density, the miniscale thermoelectric cooler can also realize a rapid response for cooling. Herein, the transient cooling performance of the Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale cooler was measured. For the transient cooling performance characterization, the cooling temperature difference generated over time was recorded immediately after applying an operating electrical current. In practical applications, the cooling performance of the device varies with thermal loads. Therefore, the transient cooling performance under varying thermal capacitances was characterized using custom-designed thermal capacitance samples, as detailed in Supplementary Fig. 17. The relationship between the response time and the cooling temperature difference is calculated through a time decay function model, as shown in Eq. (9)62.

$$\frac{\Delta T-\Delta {T}_{{{{\rm{Steady}}}}}}{\Delta {T}_{{{{\rm{Initial}}}}}-\Delta {T}_{{{{\rm{Steady}}}}}}=a\cdot {e}^{\frac{-t}{\tau }}+c$$
(9)

where ΔTSteady is the steady-state temperature difference, ΔTInitial is the initial cooling temperature difference, τ is the response time constant, and t is the response time. The transient cooling performance of the miniscale cooler under the thermal capacitance of 0 J K−1, 0.27 J K−1, and 0.80 J K−1 has been characterized (Supplementary Figs. 18 and 19). These results show the response time constant increases with larger thermal capacitance, indicating the cooling response will undergo appreciable changes under operational conditions.

Figure 4 shows the comparison of the transient cooling dynamics between the miniscale cooler and the regular-sized cooler, both fabricated using Mg3.2Bi1.497Sb0.5Te0.003 and Bi0.4Sb1.6Te3. (The geometric data of the regular-sized cooler and its cooling performance are shown in Supplementary Table 4 and Supplementary Fig. 20, respectively.) The miniscale cooler exhibits a much more rapid response than that of the regular-sized cooler (Fig. 4a). There is a notable difference in cooling speeds between the miniscale cooler (~ 65.4 K s−1) and the regular-sized cooler (~ 15.7 K s−1) when I/Imax = 1.0 (Fig. 4b). Compared to the regular-sized cooler, the response time constant of the miniscale cooler can be reduced by a factor of ~ 7, e.g., it is ~ 12.6 s for the regular-sized cooler and only ~ 1.8 s for the miniscale cooler when I/Imax = 1.0 (Fig. 4c). Correspondingly, the simulated transient performance of coolers is shown in Supplementary Figs. 21–23. Subsequently, the miniscale cooler was employed to cool the central processing unit (CPU) of the microcontroller (Fig. 4d). Under the ambient temperature of 295 K and natural convection cooling in air, the CPU stabilized at a steady-state temperature of ~ 300 K when the miniscale cooler was deactivated (TEC off). Infrared thermal imaging revealed a localized hot spot proximal to the CPU within the microcontroller, as evidenced by the inset of Fig. 4d. With the miniscale cooler operating at an electrical current density of 3 A mm−2 with a power consumption of 2.4 W and a COP of 0.39, the CPU temperature was effectively reduced to 273 K. The miniscale Mg3Bi2-based cooler effectively achieves localized cooling, as shown in the infrared thermal imaging (the inset of Fig. 4d).

Fig. 4: Comparison of the transient cooling performance between the Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale and regular-sized thermoelectric coolers.
Fig. 4: Comparison of the transient cooling performance between the Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale and regular-sized thermoelectric coolers.The alternative text for this image may have been generated using AI.
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Comparison of (a) the transient cooling effect, (b) the cooling speeds, and (c) time constants between the miniscale cooler and the regular-sized cooler. d The localized cooling on the CPU by the miniscale cooler.

Discussion

To sum up, we report the miniaturization of the Mg3Bi2-based thermoelectric coolers, including optimization of the thermoelectric leg length, interfacial electrical contact resistance, the thermal conductivity of the ceramic substrate, and contact layer design. The n-type thermoelectric legs with a copper layer (< 3 μm), a Mg2Ni layer (50 μm), and an Mg3(Bi, Sb)2 layer (900 μm), with a cross-sectional area of 1.0 × 1.0 mm2 were prepared. The contact resistivity of the n-type thermoelectric joint was only 1 μΩ cm2, and AlN was selected as the substrate material to minimize the thermal resistance. At a hot-side temperature of 300 K, this miniscale cooler achieved a maximum cooling temperature difference of ~ 59.0 K and a cooling power density of ~ 5.7 W cm−2. At 350 K, these values increased to ~ 81.2 K and ~ 7.4 W cm−2, outperforming the state-of-the-art Mg3Bi2-based coolers. The Mg3.2Bi1.497Sb0.5Te0.003/Bi0.4Sb1.6Te3 miniscale cooler achieved the time constants of ~ 1.8 s, ~ 12 s, and ~ 30 s and maximum cooling speeds of ~ 65 K s−1, ~30 K s−1, and ~20 K s−1 under the thermal capacitances of 0.0 J K−1, 0.27 J K−1, and 0.80 J K−1, respectively. After 270 h of continuous operation (approximately 3000 cycles), the cooler maintains its original cooling performance. In addition, this miniscale cooler was used to successfully achieve the localized cooling of the CPU in the microcontroller. Our results demonstrate that the miniaturized Mg3Bi2-based coolers are promising for localized electronic thermal management.

Methods

Material preparation

Mg3Bi2-based polycrystalline samples are prepared by using magnesium (Mg turnings, ZNXC, 99.995%), bismuth (Bi shots, ZNXC, 99.999%), antimony (Sb shots, ZNXC, 99.999%), and tellurium (Te ingots, ZNXC, 99.999%) as raw materials. The raw materials were weighed according to the nominal composition of Mg3.2Bi1.5-xSb0.5Tex. The weighted elements are loaded into the stainless jar in the glove box, and ball milled for 8 h (SPEX Mixer 8000 M). The obtained powder is filled in the graphite mold and then sintered at 1053 K with a force of 43 MPa for 2 min. The cylindrical graphite mold has a height of 120 mm, an outer diameter of 60 mm, and an inner diameter of 12.7 mm. Following the filling of the graphite mold with powder, two cylindrical plungers were employed to compress the powder from both ends.

Composition and microstructure characterization

The phase identification of the sample is performed by X-ray diffraction (XRD, XtaLAB Synergy, Rigaku), and the whole profile of the XRD patterns of Mg3.2Bi1.5-xSb0.5Tex is refined by the Le Bail method63, which is shown in Supplementary Fig. 24. The composition of Mg3.2Bi1.497Sb0.5Te0.003 was characterized by the electron probe X-ray micro-analyzer (EPMA, JXA-iHP200F, JEOL). The microstructure of the sample is characterized by scanning electron microscopy (SEM, Crossbeam350, ZEISS), and the elemental distribution is identified by energy-dispersive X-ray spectroscopy (EDX, Crossbeam350, ZEISS). The SEM and EDX characterization of the Mg3.2Bi1.497Sb0.5Te0.003 is shown in Supplementary Fig. 25.

Thermoelectric properties characterization

The Mg3Bi2-based materials and commercial p-type (Bi, Sb)2Te3 were cut into bar-shaped samples for simultaneous electrical resistivity and Seebeck coefficient measurement from 300 to 523 K on a commercial apparatus (CTA-3, Cryoall) under a helium atmosphere. The Mg3Bi2-based materials and commercial p-type (Bi, Sb)2Te3 were cut into disks with dimensions for the measurement of thermal diffusivity from 300 to 573 K (LFA 457, Netzsch). The density of the sample is measured by the Archimedean method. The thermal conductivity above 300 K is calculated by the product of thermal diffusivity, specific heat (calculated based on the Dulong–Petit law), and density. The thermoelectric properties below 300 K were characterized by the thermal transport option of the physical properties measurement system (DynaCool PPMS, Quantum Design).

Contact-layer preparation

The sintered Mg3.2Bi1.497Sb0.5Te0.003 disk with a diameter of ~ 12.7 mm and a thickness of 1.2 ~ 1.4 mm was polished to 0.7 ~ 1.0 mm. The raw elements of magnesium (Mg ingots, ZNXC, 99.995%) and nickel (Ni powder, ZNXC, 99.99%) were weighed according to the composition of Mg2Ni in the glovebox. These elements were sealed in the Nb tube and then encapsulated in the quartz tube. It was heated up to 1223 K in 3 h, maintained at this temperature for 24 h, and then quenched in water. The ingot of as-prepared Mg2Ni was ball-milled into powders. The junction of Mg2Ni/Mg3Bi1.497Sb0.5Te0.003/Mg2Ni is prepared by spark plasma sintering of the Mg2Ni powder/Mg3Bi1.497Sb0.5Te0.003 disk/Mg2Ni powder together at a temperature of 643 K and the applied pressure of 30 MPa for 5 min. Then, copper layers were sputtered onto the Mg2Ni layer, and the disk of Cu/Mg2Ni/Mg3Bi1.497Sb0.5Te0.003/Mg2Ni/Cu was prepared. The contact layer of the p-type (Bi, Sb)2Te3 leg (RusTec LLC) was electroplated in a Ni(SO3NH2)2 solution after acid etching by HNO3 (65−68%).

Device fabrication

The n-type Cu/Mg2Ni/Mg3Bi1.497Sb0.5Te0.003/Mg2Ni/Cu disk was cut into legs by wire cutting (with the protection of oil) in a dimension of ~ 1.0 × 1.0 × 1.0 mm3. The p-type Ni/Bi0.4Sb1.6Te3/Ni pellets were cut into legs by sand-wheel slice cutting in water in a dimension of ~ 1.0 × 1.0 × 1.0 mm3. The contact resistance of the thermoelectric leg is characterized by the homemade four-probe setup. The n- and p-type thermoelectric legs were soldered (Sn42Bi58, melting point 412 K) onto the ceramic plate deposited with copper and nickel metals by the one-step reflow method performed with the reflow oven (SRO 714, ATV). First, the vacuum reflow soldering furnace is evacuated to 10 Pa, then nitrogen (N2) is introduced, followed by another evacuation to 10 Pa. Nitrogen is continuously introduced to maintain the pressure in the furnace at 350 Pa, with a nitrogen flow rate of 6 slm. Then, the furnace temperature is increased from room temperature to 383 K at a heating rate of 1 K s–1 and held at 383 K for 2 min. After that, the temperature is raised to 453 K and held for 30 s. When the temperature is raised to 453 K, the chamber is sealed and evacuated to 10 Pa. Finally, nitrogen is continuously introduced as the temperature cools down to room temperature, with a cooling rate of approximately 0.5 K s–1. Using the same method, regular-sized thermoelectric coolers are fabricated, with their relevant parameters listed in Supplementary Table 4.

Simulation of the cooling performance

The cooling performance of the thermoelectric coolers was simulated by finite element analysis software COMSOL Multiphysics based on the thermoelectric properties of the n-type Mg3Bi1.497Sb0.5Te0.003 and the p-type Bi0.4Sb1.6Te3. The simulation parameters are shown in Supplementary Tables 1, 4 and Supplementary Fig. 1. In the construction of the simulation model for the miniature-sized cooler, two different n-type thermoelectric leg connection layer structures are considered, which are shown in Fig. 2a,c. For the thermoelectric legs prepared using multiple sintering processes, the contact layer thickness is designed to be 150 μm, and the metallization layer thickness is 100 μm. For the thermoelectric legs prepared using a combination of sputtering and sintering processes, the contact layer thicknesses are designed to be 50, 100, and 150 μm, with the metallization layer omitted. All simulated cooler models exclude the soldering layer.

Characterization of the cooling performance

The thermoelectric cooling performance characterization system mainly consists of three parts: the power supplies, the hot-side temperature control system, and the electrical and thermal measurement system. To ensure good thermal contact between the device and the heat sink during testing, a thermal paste is applied to the heat sink surface, and pressure is applied to the top of the cooler59.

For the steady-state cooling performance test, both the direct method and the extrapolation method are used. In the direct method, temperature data is directly read from the hot and cold sides of the cooler to obtain the cooling temperature difference. In the extrapolation method, a reference sample with a matching geometric size is fixed above the cooler, and a heater is fixed on top of the reference sample to provide a thermal load. By adjusting the current and thermal load, the cooling temperature difference and cooling power can be obtained. Combining the input power, the COP can be calculated. To ensure steady-state conditions, the temperature difference between the hot-side temperature and the set value should be less than 0.1 K within 90 s, and the variation in the temperature difference between the hot and cold sides should be less than 0.15 K within 30 s59.

For the cyclic reliability testing of the cooler’s cooling performance, two distinct electrical currents were alternately supplied to the thermoelectric cooler. Upon reaching a steady state at each operating current, the power supply switches to the next current to drive the cooling cycle. This alternating continuous operation between two different currents assessed the cooler’s operational reliability by monitoring changes in its achievable cooling temperature difference.

For the transient cooling performance characterization, the hot and cold-side temperatures are adjusted using a water-cooling temperature control system. The temperature difference between the hot-side temperature and the set value must be less than 0.1 K within 90 s, and the temperature difference between the hot and cold sides must be less than 0.15 K within 30 s to meet the initial conditions for the transient cooling performance test. Afterward, the set current is applied, and the temperature changes at the hot and cold sides are recorded. The insulating material is placed above the TEC to provide insulation while applying pressure.