An effective method of evaluating the device-level thermophysical properties and performance of micro-thermoelectric coolers

doi:10.1016/j.apenergy.2018.03.027

Applied Energy

Volume 219, 1 June 2018, Pages 93-104

https://doi.org/10.1016/j.apenergy.2018.03.027 Get rights and content

Highlights

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A three-dimensional numerical model of micro thermoelectric cooler is developed.
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The joint impact of boundary and size effects on TE properties is discussed.
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A comparison between the numerical and reported experimental results is conducted.
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The impact of interfacial resistances on cooling performance of TEC is discussed.
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The cooling capacity and optimal working condition of the micro TEC is analyzed.

Abstract

Despite the success of achieving thermoelectric materials with high figure of merit, precisely evaluating the performance of micro-thermoelectric coolers remains challenging at the microdevice level because of various interfacial effects and device construction. This study develops a method for the effective evaluation of the device-level thermophysical properties capturing various interfacial and size effects, and establishes a three-dimensional numerical model to evaluate the cooling performance of micro-thermoelectric coolers. The model is validated by the reported experimental data. The impact of interaction between boundary and size effects is captured in the investigation of Seebeck coefficient, thermal conductivity and electricity resistivity of the thermoelectric materials at the device-level. Contact resistances are also considered in analyzing the cooling performance. Results indicate that the device-level figure of merit decreases by 5–18.1% with decreased thermoelectric element thickness from 20 μm to 5 μm. The boundary effects considerably weaken the cooling performance of the microdevice, and a higher heat flux corresponds to a greater impact of boundary effects. Cooling temperature increases by 6.1 K due to the boundary effects when heat flux is 300 W/cm², while the temperature difference decreases by 17.1%. Finally, the three-dimensional numerical model is performed to evaluate the cooling performance and optimal working condition of the micro-thermoelectric cooler. At heat flux of 300 W/cm² and 200 W/cm², the minimum cold side temperatures of 310.7 K and 287.3 K are predicted to be achieved at 11 μm/20 mA ( $H_{te} / I$ ), 15 μm/16 mA, respectively.

Introduction

Thermoelectric cooler (TEC) is widely used in electronic devices, refrigerators, air conditioning systems, photovoltaic equipment, medical instruments and industrial fields due to its numerous advantages, such as compact size, no moving part, environmentally friendly and temperature control capability [1], [2], [3]. Recent advance in fabrication techniques have enabled the fabrication of microdevices [4]. Thin-film micro-TEC has got more attention for its potential application in the on-demand localized cooling of microelectronic and optoelectronic devices [5]. Recognizing the importance of the thermophysical properties of materials evaluated by the figure of merit (ZT) to TECs, many researchers have been devoting themselves to developing new thermoelectric (TE) materials to improve ZT [6]. However, when TE materials with high ZT are fabricated into thin-film microdevices, the effective thermophysical properties at the device level are diminished, and the practical cooling performance is severely limited by interfacial effects [7]. For practical applications, the practical cooling performance of micro-TECs has also been investigated [8].

The low efficiency of common bulk TE materials has limited the applications of TECs [9]. Recent developments in nanotechnologies have led to significant ZT enhancement [10], [11], [12], and considerable efforts have been made to explore low-dimensional TE materials with high efficiency. Low-dimensional materials and nanostructures, such as quantum wells, super lattices (SLs), quantum wires, and quantum dots, offer new ways to improve ZT by manipulating the electron and phonon properties of materials [13], [14]. Venkatasubramanian et al. [15] reported that Bi₂Te₃/Sb₂Te₃ SLs with a period of 6 nm fabricated by MOCVD technique had a maximum ZT of 2.4 at 300 K. Harman et al. [16] presented PbTe/PbSeTe based quantum dots SLs with an intrinsic ZT value of 2.0 at 300 K. However, the measured operating device thermoelectric ZT declined to 1.6 at the system level because of extraneous or parasitic factors. Despite the success of achieving TE materials with high ZT, the ZT of micro- TECs made of high ZT materials is typically lower than expected, presumably because of the fabrication of TE couple, various interfacial effects, and device construction [7], [8], [16], [17].

For practical applications, thin-film microdevices fabricated with high ZT TE materials have also been investigated. Goncalves et al. [18] presented flexible micro-TECs made of ultrathin (10 μm) Bi₂Te₃/Sb₂Te₃ TE elements. However, the tested maximum temperature difference of 5 K between the cold and hot sides of the device was much lower than the simulated value (18 K). Bulman et al. [19] reported the experimental results of thin-film SL thermoelectric modules, demonstrating an external temperature drop of 55 K under a heat pumping capacity of 128 W/cm². The measured average ZT₃₀₀ for the best SL devices was 0.75, which was much lower than that of the materials (2.4 in p-type and 1.2 in n-type). Da Silva et al. [20] measured the performance of a column-type micro-TEC made of Sb₂Te₃/Bi₂Te₃ with an average thickness of 4.5 μm. The average temperature drop achieved was approximately 1 K. Owoyele et al. [21] proposed a novel TEC architecture that employed thin-film TE elements on a plastic substrate in a corrugated structure. They showed that parasitic heat transfer through the substrate in the C-TE module is a source of performance losses, which can be minimized by proper thickness selection. To theoretically analyze the performance of micro-TECs, Ju et al. [22] proposed a modified definition of ZT capturing the contact resistances and boundary Seebeck effect, in which the contact resistances were simply connected into TE elements in series. They found that contact resistances considerably influence the performance of TE refrigerators. Da Silva et al. [7] developed a one-dimensional theoretical model to analyze the effects of electron and phonon boundary resistances on increasing thermal conduction resistance and decreasing Seebeck coefficient of TE elements, however, the effects of interfacial resistances on the electrical resistance of TE elements was not yet considered. Kong et al. [4] performed a three-dimensional analysis of the cooling performance of micro-TECs under controlled temperature differences considering the non-equilibrium between electrons and phonons at the TE/metal interfaces. Many researchers noticed that contact resistances (originated in the fabrication process) exerted severe adverse effects on the cooling performance of micro-TE devices [17], [23], [24], [25]. Nevertheless, boundary resistances and boundary Seebeck effect have received limited attention. In view of the inevitable interfacial and size effects, numerical methods still face challenges in forecasting the performance of micro-TECs.

It can be noted from the above analysis that the joint impact of interfacial and size effects on the thermophysical properties of TE materials at the device level and the cooling performance of microcoolers has remained largely unexplored. And, the numerical methods for estimating the performance of micro-TE devices still need to be further developed. Thus, this study developed a method based on coupled Boltzmann equations and Wiedemann–Franz (W-F) law to evaluate the device-level thermophysical properties and performance of micro-TECs capturing various interfacial (e.g., contact, boundary) and size effects. First, the numerical results were validated using the reported experimental data. Then, the joint influence of electron and phonon boundary resistances, boundary Seebeck and size effects on the Seebeck coefficient, thermal conductivity and electricity resistivity of TE materials at the device level were assessed. To investigate the influence of interfacial and size effects, sensitivity analyses of boundary resistances, contact resistances and thickness of the TE element were also conducted. Finally, a three-dimensional numerical model was performed to predict the cooling performance and optimal working condition of the micro-TEC. The contact resistances were considered in analyzing the cooling performance of micro-TE devices under various operating conditions.

Section snippets

Numerical modeling

This study aimed to develop an effective three-dimensional numerical model for analyzing the device-level thermophysical properties and predicting the cooling performance of micro-TECs. The flowchart of the three-dimensional numerical model is shown in Fig. 1. A numerical model based on the coupled Boltzmann equations, W–F law, and boundary and size effects was firstly built to evaluate the thermal thermophysical of TE materials at the microdevice level. Then, the numerical model was introduced

Case study

To validate the presented model, a reported micro-TEC with experimental and numerical results was selected [19], [30], and a model with the same structure and geometrical dimensions was built, as shown in Fig. 3. It consists of a single couple of n-type and p-type Bi₂Te₃ SL elements with in-plane dimensions of 250 μm × 500 μm and a thickness of 7.5 μm. The diameter of the circular contacts (Cu post) between the TE elements and the metal leads is 180 μm. Each element has one such circular

Practical cooling performance of micro-TEC

To ascertain the influence of contact resistances and boundary effects on the practical cooling performance of the microcooler, calculations were carried out when the hot surface of the microcooler was set constant temperature of 350 K, and typical heat flux (e.g., 100 W/cm², 200 W/cm² or 300 W/cm²) were applied on the cold surface of the microcooler.

Fig. 9 shows the effects of contact resistances on the cooling performance at TE element thickness and heat flux respectively equaling to 6 μm and

Conclusion

This paper developed an effective method for estimating the device-level thermophysical properties and cooling performance of micro-TECs capturing interfacial and size effects. It found that both boundary and size effects weaken the figure of merit of the thermoelectric material at the device level. And R_e,b has the greatest effect on the figure of merit, followed by R_k,b,p. This phenomenon is more obvious for smaller H_te, which suggests that the thickness of thermoelectric element should be

Acknowledgement

This work is jointly supported by the Natural Science Foundation of China (Grant Nos. 51506060 and 51376068) and the Fundamental Research Funds for the Central Universities (2016YXMS048). The supports are gratefully acknowledged.

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An effective method of evaluating the device-level thermophysical properties and performance of micro-thermoelectric coolers

Highlights

Abstract

Introduction

Section snippets

Numerical modeling

Case study

Practical cooling performance of micro-TEC

Conclusion

Acknowledgement

Energy Convers Manage

Energy Convers Manage

Int J Heat Mass Transf

Appl Energy

Int J Heat Mass Transf

Renew Sustain Energy Rev

Appl Energy

Appl Therm Eng

Appl Energy

Appl Energy

Phys Rep

Prog Mater Sci

An exhaustive experimental study of a novel air-water based thermoelectric cooling unit

Appl Energy

On-chip cooling by superlattice-based thin-film thermoelectrics

Nat Nanotechnol

Recent developments in thermoelectric materials

Int Mater Rev