Analysis and optimization of a novel high cooling flux stacked T-shaped thermoelectric cooler Open Access

At the present time, the miniaturization and integration of electronic chips have increased significantly and excessive heat flow density has emerged as a key constraint on the stability and performance of chips.^1,2 To effectively address the thermal challenges posed by these advancements, the thermoelectric cooler (TEC) acts as a solid-state heat pump that is environmentally friendly, can remove heat using the Peltier effect, and has shown great application potential^3,4 in laser communication devices and computer processors. TEC can achieve excellent localized cooling density within a limited chip package volume, thus significantly improving the chip’s performance and lifecycle.^5–7 

The most effective approach to strengthening the performance of thermoelectric (TE) devices is through the exploration of high-efficiency TE materials.^8–11 Nonetheless, finding more promising TE materials that can meet the demands of industrial production is still challenging, and optimization of the configuration and structure of TE devices represents another viable approach to enhance performance.^12–15 

A proper device design can fully exert the material performance potential, which is well-established in the field of thermoelectric generators. For example, the beneficial geometric design of the TE legs includes the different width ratios of the P-type and N-type TE legs,¹⁶ I-shaped and Y-shaped TE legs,¹⁷ asymmetric pyramidal legs,¹⁸ cylindrical TE legs,¹⁹ and optimization of TE legs based on the genetic algorithm.^20,21 Similarly, a structural design is also essential for TEC. Optimizing the geometric parameters of rectangular TE legs is a straightforward and effective approach.^22,23 Due to the geometric temperature distribution that can alter TE material properties, the design of a variable cross-sectional trapezoidal-shaped leg is investigated;²⁴ similarly, the structural shapes of TE legs, such as trapezoidal, tapered, and X-shaped legs, have been comparatively analyzed.²⁵ Additionally, the segmented design²⁶ and the use of algorithms can optimize the single-stage²⁷ and two-stage²⁸ TEC. For two-stage TEC, optimizing the geometrical parameter configurations of TE legs for the upper and lower stages²⁹ or omitting the intermediate ceramic substrate of the two-stage TEC with the trapezoidal TE legs also are effective structural optimization methods.³⁰ 

From above, the optimal design of TE devices primarily focuses on the shape and size of TE legs based on π-shaped connections. Although previous studies have explored different connection forms, such as linear connection form³¹ and U-type single-arm TE element connection form design³² in the field of thermoelectric generators, the TEC differs from the thermoelectric generator; altering the TE element connection form, the path of operational current and heat conduction of the TEC will be significantly changed, and refrigeration performance and mechanical properties are also different.

As a result, the connection of TE elements and optimized configuration is also a critical structural parameter; there is still limited research in this area. In this paper, a new connection form of TE elements called stacked T-shaped thermoelectric cooler (STTEC) is explored, and the influence of different TE boundary conditions and altered structural parameters on the performance of STTEC was successively analyzed. The research results offer insights into the optimization of TEC structures.

The three-dimensional model of STTEC is shown in Fig. 1. To ensure the rationality of STTEC’s size design and facilitate optimization, the geometry dimensions of STTEC in this work were adopted from dimensions of current commercially available micro-TECs. The overall dimension is 2 × 2 × H (depending on the study) mm³ of STTEC. It includes 18 pairs of P-type and N-type TE legs, which have the same dimensions. Considering the dimensions of current commercially produced TE legs, the reasonable TE leg width of STTEC is 0.24 mm and the TE leg height is 0.3 mm. Furthermore, the T-shaped copper slices have a uniform thickness of W_Cu, and the height difference between the TE leg and the T-shaped copper slice is ΔH, measured in μm. The ceramic plate has a fixed thickness of 0.20 mm.

The principle of operation is shown in Fig. 1(a). STTEC starts to operate when current is supplied; the process involves the absorption and release of heat, denoted as Q_c and Q_h, respectively, measured in W. The temperature of the cold and hot ends is represented by T_c and T_h, respectively, measured in K.

The materials used were carefully selected, and the TE legs were made of Bi₂Te₃,³³ a promising commercial TE material commonly utilized at low temperatures. Copper slices were chosen as excellent conductors for the electrodes. As for the substrate material, aluminum nitride was chosen since it has excellent thermal conductivity and electrical insulation. Additionally, the TE properties and thermodynamics properties of materials can be found in Fig. 2 and Table I. Poisson’s ratio of the two types of Bi₂Te₃ is 0.23.

The contact effects between heterogeneous interfaces of the STTEC cannot be ignored. In this study, the contact resistance value was determined using the research of Chowdhury et al.³⁴ The specific contact effects are shown in Table II. To simplify the model, reduce computational costs, and maintain a level of accuracy, the solder layer is not considered.

By introducing reasonable assumptions, avoiding over-analysis and omitting the factors that have little impact on the results, and simplifying calculations, we have the following:

1. The electrical boundary conditions of TEC are the positive input constant current and the negative input constant current set to zero potential (as shown Fig. 1).

2. The impact of environmental factors is ignored; thus, all exterior surfaces of TEC are assumed to be adiabatic except for the cold and hot surfaces.

3. When calculating the cooling flux and COP, a constant temperature boundary condition is applied to two sides of TEC. The temperature of the hot side is 330.15 K, and the cold side has a common testing temperature that varies between 240.15 and 330.15 K.

4. When analyzing the minimum cold end temperature of TEC at optimal current, the temperature of the hot side is varied between 300.15 and 330.15 K, and the cold side has cooling loads that vary between 0 and 40 W/cm².

5. When conducting thermal stress analysis, the fixed constraint boundary condition is applied on the hot surface of TEC, while the other boundaries are free. Strain in the height direction and all shear deformations of the hot side surface are zero.

6. Anisotropic material properties are not taken into account.

The finite element method was utilized in this study, and the numerical results were computed by COMSOL Multi-physics 5.6 simulation software, which couples the three modules of current, solid heat transfer, and solid mechanics by three physical fields of electromagnetic heat and thermoelectric effects and thermal expansion; constructs the geometric model; sets the boundary conditions and delineates the mesh sequentially; and solves the multi-physics field by a steady-state study.

To verify the grid independence, three grid systems of STTEC were examined. As depicted in Fig. 3, the values of the cooling capacity calculated from the three grid cells were essentially the same, with the maximum error of numerical results less than 1%, thus confirming the grid’s independence. To save computational resources, a grid number of 35 048 was chosen.

According to Fig. 4, by comparing and analyzing the power consumption obtained from the two methods, the power consumption of the STTEC is P₁ = U × I. Moreover, according to the first law of thermodynamics, the electric power consumption can be solved as P₂ = Q_h − Q_c. The maximum deviation is (P₂ − P₁)/P₁ = 0.06% < 1%; thus, self-consistency is confirmed.

The simulation model of the commercial π-TEC (MS02702010L2) is depicted in Fig. 5. To confirm the model’s accuracy, a comparison should be made with the actual performance of the π-TEC. The dimensions parameters are shown in Table III, and the performance parameters obtained from the testing platform are shown in Table IV. The testing process for key performance parameters is as follows: first, the TEC is placed in a vacuum hood environment for extracting air, in which absolute pressure is less than 30 pa, and a constant temperature of 300.15 K is maintained at the TEC hot end by using the thermostatic water cooling system. Second, a controllable DC power supply is used to gradually increase the input current from 0.2 A at intervals of 0.1 A; by using the data detection and recording system, the maximum temperature difference (ΔT_max) and corresponding optimum current (I_op) are obtained. Finally, when measuring the maximum cooling capacity (Q_Cmax), the TEC cold end is additionally connected with a heating resistor block with adjustable power to maintain a constant temperature of 300.15 K and Q_Cmax and I_op are obtained by gradually adjusting the input current and analyzing the data.

The numerical results curve is depicted in Fig. 6, T_h is set to 300.15 K alone, and the maximum temperature difference (∆T_max) can be obtained. By setting both T_h and T_c to 300.15 K, the maximum cooling capacity (Q_Cmax) can be found, the optimum current (I_op) of the model is 1 A, Q_Cmax is 1.28 W, and ∆T_max is 68.3 K. The maximum error is 1.5% < 5% between the numerical results and test data. Considering acceptable experimental errors, the numerical model is valid.

To illustrate the design principle of STTEC, Figs. 7 and 8 show the temperature clouds (ΔT = 30 K, I = 0.5 A). In addition, according to the application scenario high-temperature conditions, T_h is set to a reasonable value of 330.15 K. From Fig. 7, we see that the π-TEC temperature distribution mainly varies along the direction of the leg height, while the temperature distribution of STTEC changes significantly along the direction of leg height and leg width.

From Fig. 8, the two TE legs of π-TEC are distinguished in temperature by 0.2 K at the same horizontal plane since the TE properties of the P-type and N-type legs are different, whereas the temperature of the horizontal section of the center of the STTEC varies alternately with a large temperature gradient and the temperature difference is 32 K. The principle that causes this phenomenon is because the STTEC has peculiar TE elements connection forms, it consists of T-shaped copper slices and two types of thermoelectric legs stacked alternatively in contact with each other, which significantly changes the current and heat transportation and facilitate the thermoelectric conversion, thus altered the temperature distribution of STTEC.

The cooling flux can be used as one of the indicators of TEC, which is usually used to evaluate the cooling applicability for hotspot cooling; it is dependent on input current (I) and temperature difference (ΔT). From Fig. 9, under different operating conditions, the cooling flux increases with I but decreases once I exceeds the optimal current (I_op). In other words, the cooling flux is influenced by three terms representing different factors: the Peltier effect’s heat extraction of the TEC, the generation of Joule heat from the device’s internal resistance, and heat conduction due to temperature difference. When I is less than I_op, the increment of Peltier refrigeration is greater than Joule heat production. When I is at its optimum value (i.e., the peak of the cooling flux), the increments of Peltier refrigeration and Joule heat production are equal. As I is greater than I_op, the rate of increase of Joule heat production is more rapid than the Peltier refrigeration, with reduced cooling flux as a result. Furthermore, as ΔT increases, the Fourier heat conduction also enhances; therefore, the cooling flux shows a decreasing trend.

At the optimal current, the cooling fluxes of the two TECs are depicted in Fig. 10. From a temperature difference (ΔT) of 50–0 K, the increase in cooling flux of STTEC ranges from 17.2 to 101.6%. TEC is a device that pumps energy from an input current; due to the configuration of STTEC, which consists of alternating stacks with copper slices and two different TE legs, it allows for high current inputs and the Peltier effect is positively correlated with the input current, thus increasing cooling ability with better TE conversion efficiency of STTEC, resulting in better refrigeration performance. However, the stacked structure enhances the Fourier heat conduction effect and accelerates the decay of cooling flux, with the reduced cooling flux at ΔT greater than 50 K. Consequently, with actual low temperature difference cooling needs, STTEC can pump and move large amounts of heat.

The COP is also a performance index, which is shown in Fig. 11; the behavior of the COP is different from that of cooling flux. It decreases with the increasing temperature difference (ΔT) and input current (I) for two types of TECs; on the one hand, with the increase of ΔT, the enhancement of the cooling effect also increases the Fourier heat conduction and leads to the increase of heat loss so that the COP is reduced; on the other hand, with the increase of I, the increase of the cooling production of the Peltier is made and the COP tends to decrease due to the additional increase of the Joule heat. Moreover, due to the different ways of connecting the two kinds of TECs’ thermoelectric elements, their COPs under the same I and under the same ΔT are also different. Furthermore, the same cooling flux of two TECs is depicted in Fig. 12, ΔT decreased from 40 to 0 K, and the COP of STTEC increased from 5.1% to 358.5%. The STTEC has better cooling efficiency and energy utilization, but as the temperature difference increases to 50 or 60 K, the COP of STTEC has deteriorated. Due to the special characteristics of the STTEC structure, the current transfer is improved, and the conversion efficiency of TE elements is greatly enhanced at low temperature differences, consuming less power to achieve excellent cooling effects. For hotspot cooling of the chip, which does not require to be operated under extremely high ΔT, there is a significant advantage for STTEC.

In practice, the TECs are subjected to cooling loads depicted in Fig. 13, inputting optimal current (I_op); the cold surface temperature (T_c) keeps increasing linearly with the increase of cooling load; and STTEC has a lower temperature growth rate. Thoroughly, two types of TECs maintain low T_c at cooling loads below 11.5 W/cm², and the π-TEC has relatively lower T_c. Conversely, when the cooling load exceeds 12.9 W/cm², the STTEC outperforms the π-TEC in sustaining a relatively low cold-end temperature. When the cooling load is 40 W/cm², T_c of the STTEC is reduced by 46.6 K. This phenomenon can be explained as the T-shape structure optimized the path of current flow between the copper slice and the thermoelectric leg, which significantly reduces the internal resistance, and electric resistance is positively correlated with Joule heat. According to the working principle of TEC, its cooling performance is mainly determined by the combination of the unfavorable effect of Joule heat production and the favorable effect of Peltier cooling. Therefore, weakening the adverse effects of Joule heat production allows the Peltier cooling to dominate; the current is positively correlated with the Peltier cooling, and the increased current can be input to increase the cooling flux of the STTEC to effectively cool the loads.

As the hot surface temperature (T_h) is reduced from 330.15 to 300.15 K, the cooling load corresponding to equal T_c of π-TEC and STTEC is reduced from 12.9 W/cm² to 11.5 W/cm². Because the working principle of STTEC is to pump heat, improving the heat dissipation effect of the hot surface is more conducive to unleashing its refrigeration potential and achieving good cooling effects. To sum up, the STTEC proves to be effective in cooling hotspots with high heat flux density.

T-shaped copper slices are a key element for conducting heat and current, and the geometrical variation has an important effect on the STTEC’s cooling performance. In addition, changes in the geometric dimensions could alter the thermodynamic properties of the STTEC, which may reduce the reliability of the device.²³ To accurately identify the location where the maximum thermal stress occurs, the maximum von Mises thermal stress on the surface of the thermoelectric leg at the contact interface between the copper slices and the thermoelectric leg characterizes the thermal stress level as an output.

As shown in Fig. 14(a), optimal current (I_op) decreases with the increasing height difference between the TE leg and the T-shaped copper slice (ΔH) and I_op increases slightly with the increase of copper slice thickness (W_Cu), reaching its maximum value at W_Cu = 50 µm, and then slowly decreases. Figure 14(b) depicts that at the optimal current, the thermal stress decreases with the increase of ΔH. When ΔH < 50 µm, the STTEC has high-level thermal stresses, and the thermal stress is beyond yield stress (112 Mpa) for thermoelectric legs of Bi₂Te₃ materials;³⁵ it has low reliability. That is, when ΔH < 50 µm, the STTEC has an enhanced optimal current for thermoelectric conversion and a boost in the local temperature gradient and thermal stresses; the STTEC has easily localized fractures and cracks, which cause failure. However, as ΔH > 80 µm, the thermal stress is at a low level and effectively decreases with the increase of W_Cu because increasing W_Cu can ease thermal stresses at heterogeneous interfaces due to mismatched coefficients of thermal expansion.

As shown in Fig. 14(c), increasing the height difference (ΔH) or the copper slice thickness (W_Cu) can decrease and then increase the cold end temperature (T_c) at the optimum current (I_op). This phenomenon can be explained as reducing ΔH increases I_op and not only promotes the Peltier effect cooling but also promotes the Fourier conduction of hot and cold sides caused by the temperature difference, reducing cooling performance as a consequence. Moreover, large ΔH leads to a significant reduction of I_op, so it is inhibited by the Peltier effect cooling. Therefore, the cold-end temperature is increased. In addition, W_Cu of appropriate size can improve thermoelectric conversion and heat transfer on the respective cold and hot parts, both too thin and too thick, which can reduce cooling performance. Consequently, there exists an optimal minimum cold end temperature of 283.4 K, and the size parameters of the copper slice are W_Cu = 50 µm and ΔH = 80 µm, and the corresponding thermal stress is 93.74 Mpa. Considering only cooling performance, it is an optimal T-shaped copper sheet size parameter. Furthermore, when the copper sizes are W_Cu = 60 µm and ΔH = 100 µm, T_c is 284.9 K, and the thermal stress is 76.53 Mpa and T_c is decreased by 1.5 K, but the thermal stress is reduced by 18.4%, the cooling performance was maintained at a high level, and the reliability is greatly improved of STTEC. The parametric design methods are of significant theoretical and practical meaning.

In this paper, we present a new Bi₂Te₃-based stacked T-shaped thermoelectric cooler (STTEC), composed of T-shaped copper slices and two types of thermoelectric legs stacked alternatively in contact with each other. The influence of performance is investigated using the method of coupling multiple physical fields. The key findings are as follows:

1. The STTEC significantly increases optimal current by changes in the heat and current transportation, and its cooling performance advantage over π-TEC increases with the decreasing temperature difference. STTEC’s cooling flux increases by 101.6% at the temperature difference of 0 K. At the same cooling flux, the STTEC’s COP is 3.58 times higher and STTEC is suitable for application scenarios where the temperature differences are not extreme.

2. The STTEC is less sensitive to cooling loads and advantageous for cooling high loads compared to π-TEC and maintains a lower cold-end temperature by 46.6 K; improving the heat dissipation condition can lead to greater improved cooling performance of STTEC. In practice, STTEC cools high heat flow density hot spots with great advantages.

3. The medium size of the T-shaped copper slice can improve the cooling performance of STTEC, and increasing the thickness of copper slices and height differences is beneficial to improve reliability. A combination of cooling performance, thermal stress levels, thicker T-shaped copper slices of 60 µm, and the larger-sized height difference of 100 µm is the superior choice. In summary, while developing the STTEC to meet actual demands, the design factors must be carefully evaluated and chosen to get a synthesized performance.

This research was funded by the Zhengzhou Collaborative Innovation major Project: development and industrialization of new high-performance semiconductor refrigeration materials and components (Grant No. 18XTZX12005).

The authors have no conflicts to disclose.

Shengchao Yin: Conceptualization (equal); Data curation (equal); Methodology (equal); Writing – original draft (equal). Huadong Zhao: Funding acquisition (equal); Supervision (equal). Jingshuang Zhang: Investigation (equal); Methodology (equal). Cheng Li: Funding acquisition (equal); Visualization (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.