Thermoelectric Refrigerators

A thermoelectric (TE) couple is built by joining electrically conducting n-type and p-type ma- terials at the top by metal (black bar) [34]. When the current flows in the direction shown in Fig. 1.17(A), the negatively charged electrons in the n-type material and the positively charged holes in the p-type material flow from the junction to the base, hence taking heat away from the junction. This is the fundamental concept behind the thermoelectric refrigerators discussed in this section. Similarly, as de- picted in Fig. 1.17(B), both types of carriers conduct heat to the cold base when the junction is heated, and a voltage difference is generated at the two base electrodes. This is the basis of thermoelectric gene- rators as further discussed in the next section.

Active Cooling Heat Source

Heat Sink Heat Rejection

e+ _e+

Fig. 1.17. Thermoelectric A) Cooler B) Generator [34]

Thermoelectric modules have the advantage of being compact, quiet, and having no moving parts [35]. They are controlled by current supplied to the thermoelectrics, similar to piezoelectric materials. The usefulness of thermoelectric materials is often characterized by the dimensionless product ZT, where Z is the thermoelectric figure of merit defined by equation (1-5), and T is the temperature in °K.

K Z • = ρ α2 (1-5)

ρ is the electrical resistivity, and K is the thermal conductivity.

Reference [36] analyzes the problem of thermoelectric cooling in context of power electronics and con- cludes cooling power densities up to and above 100W/cm2 may be achievable with Bi2Te3 based thin

film coolers of 20 micron leg lengths. [35] derives equations for chip temperature and allowable power dissipation with thermoelectric module augmentation. The conclusion from this study is that off the shelf thermoelectric modules may be used to provide cooling enhancement only for a limited range of powers. The figure of merit, Z, and the coefficient of performance, COP, need to be improved, given COP is defined using the following equations:

) . . . 2 . 2 . . .( . 2 K T G G I C T I N p Q = α − ρ − ∆ (1-6)

( )

Q

Q

COP=

/

where N is the number of thermoelectric elements,

G is the ratio of cross-sectional area to length of each thermoelectric element, I is the electrical current,

Tc is the cold side temperature in °K,

∆T is the temperature difference (Th-Tc) between the hot side and cold side of the thermoelec-

tric elements,

Qp is the heat pumping capacity of a thermoelectric module, and

Qte (or W) is the amount of heat dissipated by a thermoelectric cooling module, or the input

power to the thermoelectric module.

ZT from the off the shelf module in this analysis was 0.87 whereas COP was 0.84 as opposed to 1.9 to 3 observed in vapor compression systems.

Many refrigeration options for microelectronics are discussed in [37], among which thermoe- lectric refrigeration is the most viable due to its scalability to micron levels, competitive projected cool- ing capabilities, ease of control, and high reliability. Cost, on the other hand, continues to be the big inhibitor of this technology. An analysis using the simple model of Fig. 1.18 and parameters from a commercially available thermoelectric component reveal a better heat removal performance compared to a standard cooling fan for Q < 125W. Due to modest COP (< 1) of the thermoelectric module, i.e. low efficiency, Q+W >> Q in this model, and the system is much more sensitive to the value of R2 than

R1. The implication is that an excellent heat transfer capability is required between the hot side of the

Fig. 1.18. Thermal model of incorporating a refrigerator into electronic packaging [37]

Fig. 1.19 predicts the thermal performance of future thermoelectric coolers assuming material Z improvements, but otherwise no change in electrical resistivity and thermal conductivity. ZTroom is

expected to reach at least 2 or 3 by 2010 [37].

Fig. 1.19. Future performance of thermoelectric coolers [37]

A more recent comprehensive analysis [38] on thermoelectrically enhanced heat sinks advo- cates the use of today’s best bulk thermoelectric materials in optimum thermoelectric cooler (TEC) de- signs, instead of off the shelf components. For a given TEC geometry an optimum current exists based on the hot and cold side temperatures in order to optimize COP values up to 4 or higher in worst case operating conditions. Fig. 1.20 demonstrates this concept by plotting COP against current to the TEC for a selected element geometry and ∆T. ∆T must be less than 30 ºC in order to achieve a COP signifi- cantly higher than 1. The current required to produce the high COPs is 10-30% of Imax for a TEC. The graphs in Fig. 1.20 are generated using Micro Alloyed Materials (MAM) bulk Bi2Te3 thermoelectric

materials, which have higher figure of merit than the ones used in the plot of Fig. 1.19 from [37]. The authors of [38] also propose that the heat pumping capability of the material used in the plots of Fig. 1.19 could in fact be quadrupled if the element height was reduced by a factor of 4, which is a possible geometry with today’s technology. [39] suggests further COP improvements are attainable by spreading

small thermoelectric coolers to strategic locations such as hot spots and controlling them through a dis- tributed network.

Fig. 1.20. COP as a Function of Current and ∆T [38]

In light of leakage, pump reliability, noise, vibration, cost and size concerns associated with liquid cooling alternatives, thermoelectric design enhancement is an attractive method to scale the ther- mal management capability of air cooling to high powered electronics. The cost of thermoelectric mate- rials is still not comparable to the traditional air cooling solutions. Due to the small form factor of the thermoelectric modules, it is conceivable, however, that the cost can be reduced in the future as the pro- duction volumes increase. Therefore, thermoelectric cooling is a promising emerging technology from sustainability and efficiency perspective.