A general approach in evaluating and optimizing thermoelectric coolersRefroidisseurs thermoélectriques : une approche générale à l'évaluation et l'optimisation
Introduction
Thermoelectric coolers (TEC) have found applications in areas such as microelectronic systems, laser diodes, telecommunication, and medical devices. Recently there is an increasing interest in the use of TEC for enhanced cooling of high power components like microprocessors in both manufacturing test processes and user conditions. High cooling capacity TECs, in combination of air cooling or liquid cooling techniques, are being pursued to extend the conventional air cooling limits for high power dissipating microprocessors (Bierschenk and Johnson, 2004, Bierschenk and Gilley, 2006, Chein and Huang, 2004, Hasan and Toh, 2007, Ikeda et al., 2006, ITRS, 2006, Phelan et al., 2002, Sauciuc et al., 2003, Simons et al., 2005, Solbrekken and Yazawa, 2003, Taylor and Solbrekken, 2006). Compact in size and silent in operation, the TEC is easy to be integrated into a server or desktop computer system in comparison with the vapor compression cooling technology (Phelan et al., 2002).
In the design and development of TEC apparatus for microelectronic components, it is crucial to determine and optimize the TEC performance within the cooling system constraints. The widely used approach is the iterative method as is given in (Huang et al., 2000, Taylor and Solbrekken, 2006, Phelan et al., 2002, Hasan and Toh, 2007). The iterative method offers results based on TEC pellet thermoelectric properties, which is nonetheless tedious and time-consuming for designers to use in practice. Presented in the work by Taylor and Solbrekken (2006) are some semi-analytical solutions for the optimization of device temperature Tj associated with the electrical current and pellet geometry. It is noted that these semi-analytical expressions contain inter-dependent parameters such as ΔT and Tc, which essentially requires an iterative procedure for full closure. Simons and his co-workers presented some analytical solutions for electronics modules based on Mathcad (Simons and Chu, 2000, Simons et al., 2005;) and analyzed the TEC enhanced cooling performance for high power multi-chip modules with available commercial TECs. Due to computerized derivations in the absence of human simplification, their solution expressions were complicated in formulation and utilized only within the same group without verification by other researchers. It is worthwhile to point out that all the above mentioned predictive methods require prior knowledge of TEC pellet geometrical dimensions and thermoelectric properties including Seebeck coefficient, thermal conductivity, and electrical resistivity. These pellet properties vary with carrier concentration and manufacturing processes, and, as manufacturers’ proprietary information, are mostly not available to designers. A detailed discussion on the material properties variation versus carrier concentration and composition can be found in (Rowe, 1995). Lineykin and Beb-Yaakov (2007) provided a graphical approach to the design of TEC. Their method is essentially an iterative process, involving the fitting of parameters like heat sink side thermal resistance (Rha) to specific TEC performance metrics. Besides, the device side thermal resistance (Rjc) is not represented in their approach, which cannot be used to determine the performance metrics such as device temperature and cooling power directly under the condition of non-zero thermal resistance. It is noted that the existing optimization studies on TEC performance parameters and related thermal resistances with respect to electrical current for cooling microelectronic components are still limited or presented in a roundabout way. Verification of TEC analysis methodology and thermal performance across different researchers are also rarely reported in literature.
In this paper, a general approach in evaluating and optimizing TEC cooling systems are presented, with the cooling of microprocessors as an application example. Analytical solutions at both pellet and module levels including the thermal resistances at the hot side and cold side are presented in concise form with detailed derivation steps for ease of usage in practical design analysis. Apart from the conventional iterative methods, the present analysis approach is able to predict TEC performance metrics in a deterministic and straightforward manner provided that pellet level or module level parameters are known. In addition, the module level analysis, formulated with the TEC module parameters, is especially useful in optimizing TEC thermal performance in the absence of detailed pellet dimensions and thermoelectric properties. A TEC based cooling configuration for high power generating microprocessors is examined as a representative application scenario. Comparison with previous work is also conducted for cross-verifications of the present approach.
Section snippets
Analytical expression at pellet level
The present analysis starts with the basic one-dimensional thermal balance equations of the TECs, which are available in previous literature such as Rowe, 1995, Phelan et al., 2002 and Taylor and Solbrekken (2006). It is noted that the temperature effect on the thermoelectric properties, the effects of ceramic plates, and joining copper traces and electrical contact resistances, which are negligibly small, are not included in the present thermal balance model.
Cooling power absorbed at the TEC
Analytical expression at module level
It is known that the thermoelectric properties of TEC pellet materials such as bismuth telluride vary with carrier concentration depending on manufacturers’ processes. On the other hand, these details, together with the geometry factor G, are difficult to obtain directly from the manufacturers, who are inclined to protect their proprietary manufacturing materials and processes. To facilitate the optimization in the design and development stage, the analysis method based on TEC module parameters
Results and discussion on TEC optimization
Listed in Table 1 are the details of the TECs analyzed in this work. TEC 1 is a high power TEC, developed recently by a proprietary supplier. It has a nominal power dissipation of 330 W with a packing density of 263 pairs of thermoelectric pellets in a footprint of 50 mm × 50 mm. TEC 2 and TEC 3 are the existing TECs with traceable product specifications and thermal resistances, whereas the pellet details are also available in by Simons et al. (2005) and Hasan and Toh (2007), respectively. The
Conclusions
In this paper, a general approach in evaluating and optimizing TEC systems is presented. Analytical solutions including Rha and Rjc are presented for both Qc and Tj with respect to the operational current at both pellet level and module level in simplified formulation. As against the commonly used iterative procedure, the main feature of the present analytical method lies in the fact that the TEC thermal performance can be obtained in a straightforward and deterministic manner. Although Simons
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