Optimization of Thermoelectric Cooling for Microelectronics Robert A. Taylor and Gary L. Solbrekken University of Missouri E3402 Laferre Hall Columbia, MO 65211 USA Phone: (573) 882-5577 Email:
[email protected] ABSTRACT The electronics industry has traditionally cooled critical components using a simple fan/heat sink assembly. Each advance in IC fabrication technology has resulted in the need for a higher performance thermal solution, stressing the limits of conventional fan/heat sink technology. A possible solution to relieve the pressure being placed on future fan/heat sink technology is to incorporate thermoelectric (TE) cooling into the configuration. It has been established that when using TE technology in electronic applications the entire system needs to be optimized simultaneously. This study is an expansion of previous work as it provides an analytic expression for the TE element geometry that will minimize the junction temperature in an electronic application. Further, it is shown that a minimum junction temperature and a maximum COP can be simultaneously achieved by optimizing both the applied current and the TE geometry. Experimental measurements on commercial TE modules are presented that validate the 1dimensional thermal-electric models. The measurements precisely match predictions if temperature dependent material properties are used in the models. A model based case study suggests that up to ~100 W can be dissipated using a 0.4 K/W heat sink and an optimized bismuth-telluride TE module while maintaining a 85 oC junction temperature. KEY WORDS: COP, Geometry, Junction Temperature, TE, Boundary Resistance, Phonon NOMENCLATURE COP Coefficient of Performance I Electrical current (Amps) k Thermal conductivity (W/mK) L TE element length (m) N Number of TEC thermocouples Q Heat load (W) R Electrical resistance (Ohm) T Temperature (°C) W TE Input power (W) Z TE Figure of Merit (1/K) Greek Letters α Seebeck coefficient (V/K) ∆ Change in value Ψ Thermal resistance (°C/W) γ TE element geometry metric (m) ρ Electrical resistivity (Ohm-m)
0-7803-9524-7/06/$20.00/©2006 IEEE
Subscripts c TEC cold side h TEC hot side ha TE hot side to ambient hs TE hot side to heat sink j Junction jc Junction to case max Based on the maximum of given quantity min Based on the minimum of given quantity n N-type semi-conducting material opt Optimum p P-type semi-conducting material sa Sink to Ambient TE Thermoelectric Tj,min Minimum Junction Temperature I. INTRODUCTION Recently, there have been multiple studies that explore the use of thermoelectric (TE) refrigeration for electronic applications. Some of these studies seek to design TE systems in order to eliminate or reduce losses in efficiency and performance. Simons, et al completed a case study using conventional off-the-shelf TE modules applied to a server application [1]. The conclusion was that current TE materials cannot provide large enough COPs to be competitive with conventional vapor compression refrigerators. A similar finding was expressed by Phelan, et al [2]. A study by Bierschenk suggested that current materials can operate with COPs well above unity [3]. A study by Solbrekken, et al presented an operational envelope over which TE refrigeration provides a performance advantage over an air-cooled heat sink [4]. That study also presented a strategy for determining the operating current such that the junction temperature is minimized in the presence of a finite thermal resistance heat sink. A later study showed that an operating current can be chosen in order to design for optimum COP and the optimum junction temperature [5]. In addition to TE system optimization, research is being conducted to develop better TE materials. One researcher, Venkatasubramanian, demonstrated a significant increase of the figure of merit (~ 2.4) for superlattice materials [6]. Other researchers are also working on superlattice materials [7, 8, 9, and 10]. Ghamaty and Elsner are developing quantum-well materials while Skutterudites are being researched by Fleurial, et al [11, 12]. In each of the cases noted above, the material improvements are created by
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reducing the effective material thermal conductivity while not significantly altering the electric properties. This study takes an in-depth look into the optimization of an electronic system using TE refrigeration. It also demonstrates the intricate nature in which phenomena are intertwined in the overall TE system design. Each system parameter must be carefully considered before a truly optimum solution can arise. Experimental measurements are taken on commercial modules to validate the system modeling and to demonstrate the existence of a common optimum when both minimizing the junction temperature and maximizing the COP. II. THERMOELECTRIC OPTIMIZATION MODELING Including a TE module as part of an electronic cooling solution poses a variety of design questions that need to be answered. In particular, the geometry of the TE module and the operating conditions for that TE module are in the direct control of the design engineer. Conversely, system parameters such as the heat sink thermal resistance and junction temperature are many times set by product engineers. Therefore, it is in the best interest to select the TE module and operating current to optimize the performance of the integrated system. It has been demonstrated in previous studies that to properly optimize the system performance, the entire electronic system needs to be modeled in addition to the TE module [2, 4]. The system performance is optimized when the junction temperature is minimized while the TE module COP is maximized. As a way to benchmark the performance of a TE cooled system, a baseline model should also be defined. Note: The models assume 1-D heat flow and constant material properties.
Tj
ψhs
Th
ψsa Ta
Qc Fig. 2. Baseline System Thermal Resistance Network ii.TE Model A sketch of a TE cooled system is shown in figure 3. The system is effectively the baseline configuration with a TE module placed between the heat sink and CPU. A thermal interface material (grease) is assumed to be placed between each of the material boundaries. The thermal modeling of the TE refrigerated system can aided with a resistance network, shown in figure 4.
Ta
Heat Sink
Th TE Module Tc
Interface Material Heat Source
Fig. 3. Sketch of a TE Cooled Electronic System.
Tj ψjc
Tc
ΨTE TE Unit
i. Baseline Model The baseline model assumed for this study consists of an air-cooled heat sink attached directly to a heat source (CPU) with a thermal interface material placed between the heat sink and heat source. Figure 1 shows this configuration.
Th
Ψhs
Ψsa
Ta
Qc + W
Qc W
Fig. 4. Thermal Resistance Network for TE Cooled System
Ta
Tj
Heat Sink Heat Source Interface Material Fig. 1. Baseline System Configuration
A thermal resistance network can be generated for the model. Figure 2 shows the simple one dimensional resistance network. Note that the heat flow, Qcpu, is the heat flow on the cold side of the TEC.
In figure 4, Ψjc and Ψhs are the contact interface (grease) resistances, and Ψsa is the thermal resistance of the heat sink. As implied by figure 4, the operation of the TE module requires external input work. That work is needed to drive heat against the natural temperature gradient. The TE module eventually converts the input work to heat which must be dissipated by the heat sink (as illustrated in figure 4 by the additional heat flow term through the heat sink resistance). This additional heat load limits the application of TE refrigeration relative to the baseline configuration, and is only captured through rigorous system level modeling. It is of general interest to establish the amount of heat that can be cooled by the TE refrigerator. This is found through an energy balance on the cold junction of the TE module, and is given by:
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Q c = 2 N α IT c − =
2 N α IT c L OMO N Electron Heat Pumping
−
∆T 1 2 I R TE − 2 ψ TE 1 2 2Nρ I − 2L N γ kO ∆N T OM 2 γ LOM ON Conduction Joule Heat Heating Leak
A γ= e L
Where:
I opt =
W =
NM ∆NT α IO 2LO Electron Heat Pumping
COPopt =
Using these equations along with knowledge of the interface and heat sink thermal resistance, the CPU junction temperature can be found: (4)
Here, the heat sink thermal resistance has been added to contact interface thermal resistance to obtain ψha. This is, ψha = ψhs + ψsa. iii. Maximizing the Coefficient of Performance The electric current applied to the TE module (see eqns. 1 and 2) can be independently specified. As such, the designer should choose the current that optimizes the overall system performance. One approach is to maximize the coefficient of performance (COP). The COP is found by simply dividing the eqn. 1 by eqn. 3. This results in the following:
1 2 ρ I − k γ∆ T 2 γ ρ α I∆ T + I 2 γ
α IT c − COP =
(6)
(
(5)
To maximize the COP the derivative of eqn. 5 is taken with respect to current and set equal to zero. To do this, the material properties (α, k, ρ), geometry (γ), and the temperatures (Tc and ∆T) are assumed to be constant. This process is relatively straightforward and can be found in many references, such as Angrist [13]. The resulting COP maximizing current is:
Th Tc
∆T 1 + 1 + ZTavg
)
(7)
It should be emphasized that when using the optimum COP approach, the temperature difference across the TE module, ∆T, is held constant. (Note: ∆T could be varied as part of an iteration process, however.) ( When the optimum COP current is used in a system configuration, such as that shown in figure 3, the heat sink thermal resistance needs to be calculated. For a given cooling load, Qc, the required heat sink thermal resistance is [3]:
1 ) − Ta COPopt 1 Q c (1 + ) COPopt
Th − ψ hs Q c (1 +
ψ sa =
(3)
Heating
T j = Ta + (Qc + W )ψ ha − ∆T + Qcψ jc
)
Tc 1 + ZTavg −
The temperature difference across the TE, ∆T, is defined as Th- Tc. In eqn. 1, it is assumed that the Seebeck coefficient for the n-type and p-type materials is the same. Eqn. 2 refers to the area of one TE element divided by the length of that element. The input work, or electric power, used by the TE must overcome the Seebeck voltage as well as the Joule heating.
2Nρ + I γN L O MO Joule
(
The corresponding optimum COP is:
(1)
(2)
2
α∆Tγ ρ ZTavg + 1 − 1
(8)
The COP maximization process just reviewed assumes that the TE module geometry has been defined. However there is no reason to not optimize the geometry for a given system. This optimization is commonly neglected in TE application studies. The TE geometry that maximizes the COP was derived using a very similar method to the current optimization study. A partial derivative of the COP (eqn. 5) is taken with respect to the geometry parameter, γ. Similarly, all other parameters are assumed to be constant. After setting the derivative equal to zero and some algebra, the solution can be given as the following:
(− kαI∆T )γ 2
2
+ (−2kρ∆TI 2 )γ
+ (αρ Tavg . I 3 ) = 0
(9)
Using the quadratic equation, we can solve eqn. 9 for an optimum geometry. It can be seen that as long as all the parameters are positive, this equation will always have two real answers. In every model tested one root is negative (hence, unrealistic), leaving a single optimum geometry. These optimum equations (eqn. 6 and eqn. 9), used simultaneously will define a module that operates at an optimum COP with respect to applied current and geometry. It should be noted that eqns. 6 and 9 are not independent. The solution process requires that either the current or geometry to be initially guessed. Using the guessed parameter, the second parameter is solved for using the corresponding equation. The optimized second parameter can then used to solve for the first parameter. This iterative process is repeated until the parameters converge. iv. Minimum Junction Temperature In a system where thermal performance is the primary goal, the optimum current can be found by
485
1.2
0.8
The TE module geometry can also be optimized to minimize the junction temperature, just as was done to maximize the COP. The partial derivative of the junction temperature, eqn. 4, is taken with respect to γ and set to zero. After some algebraic manipulation the solution is:
(I ρ )(2 Nαψ 2
γ opt =
ha
I − 1)
Q 2 αITc − (2 Nαψ ha I − 1) + 2 Nkρψ ha I 2N
305 300
COPopt, COP @ Tj,min
0.6 295 0.4 290
0.2 Tj,min, Tj @ COPopt
0 3
(11)
310
COP opt COP for Tj min Tj for COP opt Tj Min.
1
(10) COP
αρ ρ [2Nψ hs ]I 2 + [− − 2Nψ haα 2Tc − 4Nψ hakρ]I γ γ + [αTc − 2Nψ hakγα∆T ] = 0
For the junction temperature minimizing approach, heat load (Qc), thermal resistance (ψha), γ, and material properties are held constant. At a current of nearly 8A it can be seen that the maximum COP and the minimum junction temperature are both realized. It turns out that at the common optimum operating current all other system parameters are exactly the same. This point could be considered to be a true optimum.
5
7 9 Current [A]
Junction Temperature [K]
minimizing the junction temperature. Here, the partial derivative of eqn. 4 is taken with respect to current. For this partial derivative it is assumed that all parameters in eqn. 4, except I, are constant. The resulting equation is set equal to zero and solved for an optimum operating current. As noted by Solbrekken et. al, this optimum current is found by taking the smallest positive root of [4]:
285 11
13
Fig. 5. COP and Junction Temperature Tj,min: Qc = 21 W, ψha = 0.6 K/W, N*γ=0.213 m, ∆T = 0-75 K COPopt ∆T = 51.16 K, Tc =292.7 K, N*γ=.0213 m, Qc=2-30 W
If current or the electrical resistivity approaches zero, the optimum geometry becomes zero - that is, infinitely tall. An interesting mathematical anomaly predicts that as 2 Nαψ sa I → 1 , the optimum γ will again approach zero. It is also possible for the optimum geometry to be infinitely short and thin if the denominator becomes small. Here again, eqn. 10 and eqn. 11 are not independent and an optimum is found through iteration. That is, either the current or geometry must be guessed and substituted into eqn. 10 or 11. The solution is then iterated until convergence.
When the two approaches align, as in Figure 5, they do so at a certain heat load and heat sink thermal resistance. It is possible to find the optimum current at different heat loads. Figure 6 shows that as the heat load increases, the minimum junction temperature occurs at a higher current. The junction temperature, Tj, and the cold side of the TE module, Tc, also increase at each heat load. We can see that the Tj surpasses 85oC at approximately 21 Amps (about 97 Watts). 380 375
III. OPTIMIZATION RESULTS i. Comprehensive Optimization For the overall electronic cooling system, there are nine system variables (not counting material properties) and five system equations (eqns 1-5), leaving four unknowns. Those 4 degrees-of-freedom can then be selected or they can be set through the optimization equations. If we assume that we want BOTH the maximum COP and the minimum junction temperature, we can use both current optimization equations and set them equal to one another. Additionally, the two geometry optimization equations can be set equal to one another. The next sections illustrate parametric studies for such a process. (Note: Thermal resistance is consistently held at ψha = 0.4 K/W, when applicable in these studies.) ii. Operating Current Comparison A comparison between the COP maximizing current and the junction temperature minimizing current was introduced in previous work [5]. To illustrate that both optimization strategies can result in the same design, a parametric study was completed. Figure 5 shows the junction temperature and COP trends as a function of current while holding certain parameters constant. For the COP maximizing approach, Tc-Th, γ, and material properties are held constant.
Optimum Current
370 Tj [K]
365 360 Tj, 80 W Tj, 100 W Tj, 120 W Optimum Current 85oC
355 350 345 340 10
15
20
25
30
Current [Amps]
Fig. 6. Junction Temperature for COPopt and Tj,min Approaches Tj,min: Qc = 80, 100, 120 W, ψha = 0.4 K/W COPopt: ∆T = 29.84, 21.54, 13.36K, Tc = 328.88, 340.1, 350.03 K. For both: N*γ = 0.883, 1.369, 2.417 m Figure 7 shows that COP actually increases with increasing heat loads. This is due to the fact that ∆T must decrease to in order to align the Tj with the Tj,min approach.
486
4
Optimum Current
3
COP
Along the same lines, we can explore the impact of γ on COP. This is done by plotting the optimum COP (using Iopt) for various geometries. Figure 9 shows the results of this relationship. (Note: 0.2*Iopt is plotted to fit within the plot scale) We can see that there is no global optimum for COP when the temperature difference is set (Tc is held constant at 340 K), but rather a larger value of γ is needed for higher heat loads.
3 2 2 1 1 0 10
15
20 Current [Amps]
25
25.00
30
90
20.00 COP, Current [A]
Fig. 7. COP for COPopt and Tj,min Approaches Tj,min: Qc = 80,100,120 W, ψha = 0.4 K/W COPopt: ∆T = 29.84, 21.54, 13.36 K, Tc = 328.88, 340.1, 350.03 K For both: N*γ = 0.883, 1.369, 2.417 m
iii. Module Geometry Optimization From the previous discussion, it is apparent that the TE geometry and the heat load are related to one another at optimum operating conditions. To further explore the role of γ in influencing the COP and junction temperature, the junction temperature minimizing current, eqn. 10, is plotted against γ in Figure 8. Here, we can see that there is indeed a value of γ that minimizes the junction temperature. That particular geometry then has the feature of providing a global temperature minimum for a given heat load and heat sink thermal resistance. In the figure where the heat load is assumed to be 75W and the heat sink thermal resistance is assumed to be 0.4 K/W, this happens when the current is approximately 17 amps and γ ~ 0.0141 m. It is interesting to note from the figure, however, that the degradation in performance for larger than optimum values of γ is relatively small.
0.2*Iopt COPopt Q
15.00
70 50
10.00
30
5.00
10
0.00 0.000
-10 0.005
0.010 0.015 Gamma [m]
0.020
Fig. 9. Impact of Geometry on System Performance – COPopt ∆T = 20 K, I = Iopt, Tc = 340 K It is useful to compare an optimized system with the baseline design of Figure 1. Figure 10 shows this comparison using the optimized current and geometry of eqns. 9 and 10. Therefore, each Tj,min point on the curve denoted with diamonds is analogous to the minimum Tj,min point of Figure 8. The optimum γ and the COP for the optimized TE design are also plotted in Figure 10. For each point the heat sink thermal resistance is held at a constant value of 0.4 K/W. 100
450
Gamma COP Tj,min Tj_baseline
10 Gamma [m], COP
In figures 6 and 7 it should be noted that at higher heat loads the element geometry is also different, shifting to larger values of γ for higher heat loads. An increasing value of γ could be interpreted as a thinning the elements. Using this interpretation one would conclude that in the limiting case of infinitely high heat loads, the TE elements become so ‘thin’ that they effectively disappear and the resulting system reverts to the baseline configuration of Figure 1.
354
100
110
400
1
350
0.1
300
0.01
250
Tj [K]
COP, 80 W COP, 100 W COP, 120 W Optimum Current
4
Heat Load [W]
5
0.001
350
COP Tj_min Current Tjmin
10
348 346
1
0 Tj [K]
COP, Current [Amps]
352 40
60 80 100 Heat Load [W]
120
140
200 160
Fig. 10. Optimized System Performance for Tj,baseline vs. Tj,min Ta = 30oC, ψha = 0.4 K/W, I and γ Optimized – Note Log Scale
344 342 340
0
0.003
20
0.008
0.013
0.018
Gamma [m]
Fig. 8. Impact of Geometry on System Performance – Tj,min Qc = 75 W, I = ITjmin, ψha = 0.4 K/W
In the figure it can be seen that the TE enhanced configuration has a lower junction temperature then the baseline configuration for heat flows up to about 64 W. Above 64W the baseline configuration has a lower junction temperature. This cross-over is due to the interfacial resistance between the CPU and heat sink, ψjc = 0.2 K/W. If this value is reduced, the cross-over point shifts right making
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TE refrigeration applicable at larger heat loads. An earlier study [5] showed that, in the limit (ψjc = 0 K/W), a TE system can always provide a lower junction temperature than a heat sink alone. This implies that in a TE system we can operate at a minimum junction temperature, a maximum COP, and an optimum geometry while out performing a heat sink alone design to a heat load cross-over point that is dependent on the contact resistance. Furthermore, these optimizing equations can predict each of these parameters including the module geometry.
predicted optimum to demonstrate the ability of the analytic model to predict junction temperature and COP. In the second set of experiments, the junction temperature is held constant by varying the heat sink thermal resistance as suggested by eqn. 8, while the TE current is varied. The estimated heat loss through the insulation is between 1.0 and 1.5 W. It should be noted that the temperature measurement uncertainty at a 95% confidence level is estimated to be 1.2 K. Wind Tunnel
iv. Optimization Conclusions The above discussion suggests that, any arbitrary application of a single optimizing approach will not necessarily provide the global optimum for both COP and temperature. In previous studies, the geometry optimization in the context of a system has been neglected using primarily offthe-shelf designs for their analysis. It has been shown here that it is possible to improve the overall system performance if one goes through the additional effort of optimizing the geometry. III. EXPERIMENTAL TESTING All the aforementioned models assume 1-D heat flow (air gaps between TE elements conduct no heat) and that the TE material properties are independent of temperature. Experimental measurements are taken on off-the-shelf modules to test the modeling assumptions and to observe the simultaneous-optimal point of operation (see Figure 5). The test bed was built the University of Missouri as part of an undergraduate research project [14]. The test bed consists of a flow bench/duct system, as shown in figure 11 .The test assembly based on the model in Figure 3 was placed in the duct, as shown in Figure 12. Note: The heat sink was characterized in a previous study to provide a relationship between the heat sink thermal resistance and air velocity [14].
Heat Sink Plexi-Glass Duct Flow Bench
Heat Sink
Heater Placement Insulation
TE Module
Fig. 12. Experimental Test Section When the initial raw data was compared with the analytic models there was a significant discrepancy. However, when temperature dependent properties as quoted by D. M. Rowe were applied to the model, the predictions were much closer to the measurements [15]. Figures 13 and 14 compare the analytic predictions with the experimental junction temperature measurements. The ‘_M’ and ‘_EX’ designation in the legend denote the model and the experimental data, respectively. For both the Tjmin and COPopt models, it can be seen that the experimental data closely follows the predicted trends. Further, the measurements are within experimental uncertainty of the model predictions, validating the efficacy of the derived models. For the COPopt model, current, heat load, and heat sink thermal resistance must be changed to achieve the target temperature, 286K for the case shown in Figure 13. The heat sink thermal resistance and heat load are relatively difficult to control, and hence there is a larger deviation between the measurements and predictions as seen in the Tj of the COPopt model. Also, in the COPopt experiments, higher currents cannot be tested as the required heat sink thermal resistance is smaller then was feasible with the current heat sink. The lower current bound was chosen to be sufficiently far enough away from the optimum point in Figure 13.
Heater/TE Assembly
Fig. 11. Flow Bench Test Facility. The first set of experiments is intended to validate the Tj optimum current for a given thermoelectric module. To do this, the thermoelectric cold side, Tc, is measured with a thermocouple. The input heat, Qc, and the air velocity - and thus the heat sink thermal resistance - are held constant. The input current to the thermoelectric module is varied around the
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Fig. 13. Comparison Between Experimental and Predicted Junction Temperature Recall from Figure 5 that there is one optimum point in which both methods align for a given module and a given heat sink. For the TE module tested (N*γ = 0.337 m), the heat load and heat sink thermal resistance predicted at the optimum point is 15.5 W and 0.6 K/W. Indeed it can be seen from figure 13 the current that minimizes the junction temperature is about 3.5A (triangles). At the same time, from figure 14 it can be seen that the current that provides the maximum COP (diamond symbols) is also about 3.5A. This finding does demonstrate that for a given TE geometry and heat flow there is an optimum current that will simultaneously maximize the COP and minimize the junction temperature.
dominant. Therefore it will be necessary to integrate those contact effects with the current modeling methodology in order to optimize small-scale systems. Finally, though not specifically addressed in this study, TE material improvements will expand the envelope over which TE cooling technology will be an effective solution. V. REFERENCES 1. Simons, R. E., and R. C. Chu. “Applications of Thermoelectric Cooling to Electronic Equipment: A Review and Analysis,” Sixteenth IEE Semi-Therm, March 21-23, 2000. 2. Phelan, P.E., V.A. Chiria, and T-Y T Lee, “Current and Future Miniature Refrigeration Cooling Technologies for High Power Microelectronics,” IEEE Transactions on Components and Packaging Technologies, Vol. 25, No. 3, 2002. 3. Bierschenk, Jim and Johnson, Dwight “Extending the Limits of Air Cooling with Thermoelectrically enhanced Heat Sinks,” Marlow Industries, Inc. Dallas, TX, 2004. 4. Solbrekken, G. L., K. Yazawa, and A. Bar-Cohen, “Chip Level Refrigeration Of Portable Electronic Equipment Using Thermoelectric Devices,” Proceedings of InterPack 2003, Maui, HA, Jul 6-11, Paper IPACK2003-35305.
Fig. 14. Comparison Between Experimental and Predicted COP One notable result of the measurements is that the COP can achieve values of 1.0 and larger for input currents of 2.0A and smaller. This reinforces the previous claims that TE COP values well above unity are possible if the ∆T is small enough. IV. CONCLUSIONS This study took an in-depth look into system optimization. It was shown that current as well as geometry can (and must) be optimized in order to achieve a design which is optimized for minimum temperature and maximum COP. It was also shown that there are four optimization equations that can be used to optimize the entire system: two for current and two for geometry. It was then shown through experimentation that these optimum currents could indeed be set equal to each other. This validated the existence of an optimum point for the given geometry and heat sink thermal resistance. The results of this study demonstrate the intricate nature in which system performance is heavily dependent on TE design and operation. Each parameter must be carefully considered before an optimum solution can arise. Since TE devices are very sensitive to boundary conditions, a slight error could mean significant deviation from that optimum. The current analysis was conducted based on macroscale modeling. It is expected that for micro-meter scale TE devices that electrical and thermal contact effects will become
5. Taylor, R. A. and Solbrekken, G. L., “An Improved Optimization Approach for Thermoelectric Refrigeration Applied to Portable Electronic Equipment,” InterPack, 2003, San Francisco, CA, July 16-22. 6. Venkatasubramanian et al., “High ZT High ZT pBiTe/SbTe BiTe/SbTe Superlattice” RTI, Nature, Volume11, Oct. 2001. 7. Chen, G., T. Zeng, T. Borca-Tasciuc, D. Song, “Phonon Engineering in Nanostructures for Solid-state Energy Conversion,” Materials Science and Engineering A, Vol. 292, 2000, pp 155 – 161. 8. Dresselhaus, M. S., T. Koga, X. Sun, S. B. Cronin, K. L. Wang, and W. Chen, “Low Dimensional Thermoelectrics,” Proceedings of the 16th International Conference on Thermoelectrics, pp. 12 - 20, 1997. 9. Fan, X., Croke, C., J.E. Bowers, A. Shakouri, et al., “SiGeC/Sisuperlattice micro cooler,” Applied Physics Lett. Volume 78, Number 11, 2001. 10. Solbrekken, Gary, Zhang, Yan, Bar-Cohen, Avram, and Shakouri, Ali, “Use of Superlattice Thermoionic Emission for ‘Hot Spot’ Reduction in a Convectively-Cooled Chip” InterPack, 2002. 11. Ghamaty, S., and N. Elsner, “Development of Quantum Well Thermoelectric Device,” Proceedings of the
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17th International Conference on Thermoelectrics, Baltimore, MD, August 30 - September 2, 1999. 12. Fleurial, J. P., A. Borshchevsky, T. Caillat, and R. Ewell, “New Materials and Devices for Thermoelectric Applications,” Proceedings of the 32nd Intersociety Energy Conversion Engineering Conference, July 27 – August 1, Honolulu, Hawaii, (2), pp. 1080 – 1086, 1997. 13. Angrist, S. W., Direct Energy Conversion, 4th ed., Allyn and Bacon Inc., Boston, 1982. 14. Scheel, Kasey, “Heat Sink Characterization,” University of Missouri Undergraduate Thesis [Internal Document], September 2005. 15. Rowe, D.M. “The Thermoelectric Properties of Heavily Doped Hot-Pressed Germanium-Silicon Alloys,” Journal of Physics D: Applied Physics, Vol. 2, 1497-1502.
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