Role of Thermal Conductivity for Thermoelectrics with Finite Contacts

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1 3 nd International Termal Condutivity Conferene 0 t International Termal Expansion Symposium April 7 May 1, 014 Purdue University, West Lafayette, Indiana, USA Role of Termal Condutivity for Termoeletris wit Finite Contats Yee Rui Ko, ko7@purdue.om Sool of Eletrial and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA Birk Nanotenology Center, Purdue University, West Lafayette, Indiana 47907, USA Kazuaki Yazawa Birk Nanotenology Center, Purdue University, West Lafayette, Indiana 47907, USA Ali Sakouri Sool of Eletrial and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA Birk Nanotenology Center, Purdue University, West Lafayette, Indiana 47907, USA ABSTRACT Te role of termal ondutivity in te performane of termoeletri (TE) devies as ompared to oter material properties su as Seebek oeffiient and te eletrial ondutivity will be disussed. A TE energy onversion system tat inludes termal ontats for te ot side and te old side wit finite eat transfer performanes is onsidered. Some of te trends in eletronis ooling appliations ave been desribed. In tis artile, te effet of material properties as a funtion of energy urrent flow diretion will be foused. TEs ave an advantage as solid-state eat energy onversion devies espeially for appliations wit spatial onstraints. A ommonly aepted appliation is te Peltier ooling of ig power or ig eat flux eletroni devies su as laser diodes (>1 W/mm ). Tese appliations lead to a limited eat transfer performane in bot ot and old ontats. Based on a generi one-dimensional model for TE systems, termal ondutivity appeared to be te most important property to be improved to get better energy onversion performane among tree TE properties inluding Seebek oeffiient and eletrial ondutivity. For TE ooling, termal ondutivity of te TE material is te most ost sensitive in terms of mass use of te material, for minimizing te power onsumption to pump te eat from te target devie at te onstrained temperature. Typially in eletronis, te devie temperature is onstrained, su as 65 o C 85 o C. Hene te maximum ooling to rea minimum target temperature is not always required. Aieving tis target temperature wit minimum eletrial power input for a given power dissipation from te target devie is required. Te differene in impat between termal ondutivity and te oter material properties is on te termal resistane of te TE element similarly to te energy arvesting system ase. By anging any properties, a oeffiient-of-performane (COP) of ooling yields te same as ZT remains te same. Tis artile will summarize te role of termal ondutivity as te termal resistane mat wit finite external ontats in te TE miroooler, wile relating te effets of te termal ondutivity, Seebek oeffiient, and eletrial ondutivity to te finite termal resistane of te TE miroooler. Keywords: termoeletri, miroooler, interfae, ontat, oeffiient of performane, ost, figure-of-merit (ZT), optimization. 1. INTRODUCTION Termal management is a key issue in eletroni iruit design. Te miniaturization of integrated iruit (IC) ips inreases te omplexity of termal management. One of te most ommon ooling metods is Peltier ooling wit termoeletri (TE) materials. TE ooling is widely used for ooling in temperature sensitive appliations, e.g. laser diodes (Zang, Anderson, & Lau, 003). Te TE miroooler provides a simple struture design and preise temperature ontrol for te eletroni IC. Despite te advantages, te TE miroooler is known to be a low effiieny ooling metod. Earlier studies (Ko, Yazawa, & Sakouri, 013, 014; Lee, Kim, & Kim, 010) sow te optimization of te oeffiientof-performane (COP) and te eat flux of te TE miroooler, by varying te material properties, module tikness, and drive urrent. However, te DOI: /

2 94 MODELING impat of te finite interfae resistanes of te TE miroooler is not well understood. An analytial eletro-termal model based on te energy balane at te nodes along te eat flow to study te effets of te interfae resistanes of te TE miroooler is developed. To be onsistent, a similar analytial formulation is employed as presented in te earlier works (Ko et al., 013; Sau, Fedorov, Josi, Ziabari, & Sakouri, 01). Nomenlature A, area, m d, tikness of tin film/superlattie ooler, m F, fill fator, eat transfer oeffiient, W/m K I, urrent, A Q, eat flow, W q, eat flux, W/m S, Seebek oeffiient T, temperature W, power, W Greek symbols b, termal ondutivity, W/mK, effiieny, % s, eletrial ondutivity, 1/Ωm y, termal resistane, K/W Subsripts s, sample (IC iruit) a, ambient, old side, ot side m, miroannel side of silion substrate. MODEL Te effets of te interfae resistanes for bot te otside and old-side of te TE element wit various target ooling temperature, T and various material properties for te TE element as been presented. A set of temperature boundary onditions ave been applied to te model, wit IC temperature, T s = 100 o C and te eat sink temperature, T m = 74 o C. Beause te TE model operates at ambient temperature, T a = 7 o C, te material properties used in te model analysis are assumed to be onsistent wit te room temperature values. Te size of te TE miroooler in te analytial model is μm. Figure 1 sows tat termal iruit built for te TE miroooler. Te following set of equations an be formed based on te energy balane at te temperature nodes T s, T, T, and T m. Peltier ooling and Joule eating are ating on te nodes, T and T. Te equations ontain te termal ondutane, K, and te eletrial resistane, R, of te leg. Te external termal resistanes, y and y, are also onsidered in te model. were, and σs ZT = β (1) s Q = () + R Q STI = ( I K T T ) (3) ( ) R KT T STI = I Q (4) ( T T m) Q = (5) βfa K = d d R = σ FA (5a) (5b) Equations () and (5) sow te ooling eat flux, Q, extrated from te IC ip into te TE module and te waste energy, Q, pumped into te eat sink, respetively. Te termal ontats play an important role in Q and Q. Equation (6) an be formed by omparing Equations (3) and (4). Q Q = RI + SI ( T T ) (6) By substituting Equations () and (5) into Equation (6), T 1 RI T T s Ψ y = SIT 1 RI SIT T s Q : interfae T T k : TE leg sub : Termal Spreading in substrate +ΨRI Ψ SIT + T T m Figure 1. Termal network of te one-dimensional eletro-termal model for a termoeletri (TE) miroooler. Q 1ΨSI m (7)

3 Role of Termal Condutivity for Termoeletris wit Finite Contats 95 Substitute Equation () into Equation (3) and solve Equation (3) for T, T T s R SIT I Ψ + T = T + (8) K By substituting Equations (5a) and (5b) into Equations (7) and (8), te general formula for te optimum drive urrent, I, is found as: β 1 d d 3 I I σ FA T S d σ S FA d σ T T s Sd TSd + I S FA d σ T T T T s s βfa + T T m + + S FA d S σ σ FA d = 0 (9) Te drive urrent, I, obtained in te equation is te minimum drive urrent to mat te temperature boundaries applied in te matematial analysis. Matematia as been used to solve te tird-order equations to obtain te drive urrent from te above ondition. Subsequently, te drive urrent, I, obtained from Equaton (9) an be used in Equation (10) to alulate te required power for te devie. P = I R (10) Te required power of te devie is essential for determining te COP of te superlaties ooler (SLC). Te COP of te model is given by Equation (11) Q Q T T s COP P IR ( = = = IR ) (11) for y and y are sown in Figure. Te results sow te maximum aievable COP of te TE miroooler is similar wit same y value, altoug te y and y of te miroooler migt be different. Optimum tikness to aieve maximum COP is sifted to a smaller value if y is smaller, e.g., optimum tikness for y =1 wit y = 9 K/W is ~1.5 μm, wereas te optimum tikness of te miroooler for y = 18 K/W is ~.5 μm. Furtermore, Figure sows tat te maximum aievable COP for te lower y value is iger ompared to te TE miroooler wit a iger y value. Unless speifially mentioned in te figures, all te analyzed models below are for ZT = 1, wit te termal ondutivity, b = 1.5 W/ mk, eletrial ondutivity, s = /Ωm, and te Seebek oeffiient, S = V/K. =0.75 Ψ =9K/W =1 Ψ =9K/W =1.5 Ψ =9K/W =0.75 Ψ =1 Ψ Module Tikness, d (m) =1.5 Ψ Figure. Coeffiient-of-performane (COP) versus module tikness of te termoeletri (TE) miroooler wit different ombinations of y values. Figure 3 sows a omparison between models wit different y ratios wit a fixed value for te total =0.5 = = 3. RESULTS AND DISCUSSIONS Te ontat resistane is one of te most important parameters affeting te performane of te ot spot miroooler. However, te effets of te ontat resistanes to te TE miroooler performanes are not well understood. A relative ratio between eat sink resistanes (y ) to te ot-side resistanes (y ) in tis projet is defined. Figure sows te relationsip of te COP and module tikness of te TE models wit various y ratios. Beause te same y value migt onsist of different values for y and y, te analytial results of te model wit same y ratio but different values =1 = Module Tikness, d (m) Figure 3. Coeffiient-of-performane (COP) versus module tikness of te termoeletri (TE) miroooler wit total fixed ontat resistanes but different ombinations of y values.

4 96 MODELING of te ontat resistanes. Te ratio of te ontat resistanes, y, is te deisive parameter for te COP of te TE miroooler. Te lower te resistanes ratio, y, te iger te performanes of te TE miroooler (COP). As mentioned earlier, TE miroooler is known to be a preise temperature ooling metod for laser diode ooling appliations. However, tese ooling appliations often require a lower target ooling temperature ompare to oter IC ips. In earlier studies (Lee, Yoon, & Kim, 001), researers found tat lower ooling eat flux, Q, is required to aieve te low T. Yet, te analytial results in Figure 4 sows tat te key parameter to aieve low target temperature, T, is not, in fat, beause of te ooling eat flux, Q, as sown in te earlier studies. Te key fator for a low ot side temperature, T, is ontrolling te ratio of y. A relatively good eat sink must be designed to aieve te low ot side temperature, T. Figure 4 also sows tat a low y ratio will improve miroooler performane. For example, if te target ot-side temperature, T = 85 o C, te COP of te model an be more tan doubled (from 6.3 to 13.9) if y is dereased to 1/10 ompared to y at 10 μm. miroooler wit y = 0.1 and y = 1. Te effets of te single material property, termal ondutivity, and eletrial ondutivity, and Seebek oeffiient are also sown in Figure 5. For y = 1, te urrent density dropped wit te improvement of te ZT value for anges in any of te TE properties. For te y = 0.1 models, te urrent density for te Seebek oeffiient and eletrial ondutivity improvement models ad a similar beavior to te y = 1 models; te urrent density dropped wit an inrease in te ZT value. However, if te termal ondutivity is redued in te y = 0.1 TE miroooler, te urrent density beame larger ompared to te referene model wit ZT = 1. Figure 5. Current density versus module tikness of te termoeletri (TE) miroooler wit different y = 0.1 and y = 1. Figure 4. Coeffiient-of-performane (COP) versus module tikness of te termoeletri (TE) miroooler wit different y values and a ot-side target temperature, T. To analyze te impat of a single material property to te TE miroooler performane, te models wit a fixed ZT value wit different ombinations of material properties are examined (Ko et al., 013, 014) For example, to find te impat of inreasing ZT from 1 to, we an derease b to alf, inrease s to double, or inrease te Seebek oeffiient to sqrt. times ompared to te ZT = 1 model. Figure 5 sows te urrent density versus module tikness of te TE Figure 6 sows te eletrial power onsumed by te TE mirooolers wit y = 0.1 and y = 1 wit variations of a single material property. Altoug te urrent densities between te eletrial ondutivity and Seebek oeffiient improvement models are different, te eletrial power onsumptions for tese models are similar. Te effets of te single material property to te eletrial power of te TE mirooolers sow different trends for y = 0.1 and y = 1. For te y = 1 models, te eletrial power of te all termal ondutivity dependent, eletrial ondutivity dependent, and Seebek oeffiient dependent models derease wit an inrease of te ZT value. For example, te eletrial power onsumed by te ZT = 1 model is 0.7 W, ZT = wit b dependent onsumed 0.3 W and ZT = 3 wit b dependent onsumed 0. W for a 10-μm module tikness. On te oter side, eletrial ondutivity and Seebek oeffiient dependent models for bot y = 0.1 and y = 1 ave te same eletrial power onsumption trend similar to te b-dependent

5 Role of Termal Condutivity for Termoeletris wit Finite Contats 97 Figure 6. Eletrial power versus module tikness of te termoeletri (TE) miroooler wit y = 0.1 and y = 1. models for y = 1. Te eletrial power for te S dependent and s dependent also derease wit an inrease in te ZT values. However, te b-dependent models for y = 0.1 sow a dissimilar trend. Te eletrial power onsumption inreases wit an inrease in te ZT value. Te effets of te single material properties to te COP ave been divided into two figures. Figure 7(a) sows te COP versus module tikness for te Seebek oeffiient and eletrial ondutivity dependent models, wereas Figure 7(b) sows te effets of te termal ondutivity redutions to te COP of te TE models. Figure 7(a) sows tat COP of te Seebek oeffiient and eletrial ondutivity dependent models wit y = 0.1 and y = 1. Bot of te y = 0.1 and y = 1 sow tat COP will inrease wit te improvement of te Seebek oeffiient and eletrial ondutivity of te models. For example, COP of te S- and s-dependent model inrease from 19.5 to 43.8 to 68.1 for ZT = 1 to ZT = to ZT = 3, respetively, for y = 1 at 1 μm TE tikness, wereas COP of te ZT = 1,, and 3 are 13.9, 9.4, and 44.8, respetively, at te 10-μm TE tikness for te y = 0.1. Figure 7(b) sows te COP versus TE module tikness wit inrement of te termal ondutivity wit y = 0.1 and y = 1. Inrement of te termal ondutivity sows exatly opposite effets for y = 0.1 and y =1. Te COP inreases from 6.3 to 7.3 to 7.7 at 10 μm TE tikness wit dereasing termal ondutivity from 1.5 to 0.75 to 0.5 W/mK, respetively, wit y = 1. Te trend for te y = 0.1 model is ompletely reversed. Te COP derease from 13.9 to 10.7 to 9.9 wit te β-dependent models wit ZT = 1,, and 3. Te results sow tat, for te design wit an extremely low eat sink termal resistane, te TE miroooler is not required. Figure 7. Coeffiient-of-performane (COP) versus module tikness of te termoeletri (TE) miroooler wit y = 0.1 and y = 1 for te (a) eletrial ondutivity and Seebek oeffiient improvement and (b) termal ondutivity derement. 4. CONCLUSION An analytial model to examine te effets of te ontat resistane on te performane of te TE miroooler on a otspot by using a new defined ontat resistane, y relation as been developed. Te ontat resistane ratio, y, must be arefully onsidered in te low target temperature, T, appliation. Te design of te ontat resistane ratio, y, is also essential to te material properties seletion for te TE miroooler. Higer ZT models migt ause lower COP if te y as not been arefully onsidered. Te purpose of tis artile is to understand te effets of te materials properties and interfae ontat to te performane of te TE miroooler. However, it is ard to just vary one property (espeially 3 times) and keep oter transport properties unanged in pratial.

6 98 MODELING REFERENCES Ko, Y. R., Yazawa, K., & Sakouri, A. Impat of material properties on ooling COP of integrated termoeletri mirooolers. In Proeeding of te Interpak013, San Franiso, 013. Ko, Y. R., Yazawa, K., & Sakouri, A. Cooling eat flux, COP, and ost optimization of integrated termoeletri miroooler wit variation of termoeletri properties. In Proeeding of te ITHERM014, Orlando, 014. Lee, K. H., Kim, H., & Kim, O. J Effet of termoeletri and eletrial properties on te ooling performane of a miro termoeletri ooler. Journal of Eletroni Materials, 39, Lee, H. J., Yoon, J. S., & Kim, C Numerial analysis on te ooling of a laser diode pakage wit a termoeletri ooler. Heat Transfer Asian Resear, 30(5), Sau, V., Fedorov, A. G., Josi, Y. K., Ziabari, A., & Sakouri, A. (01). Energy effiient liquid-termoeletri ybrid ooling for ot-spot removal. In Proeeding of te 8t Semi-Term Symposium, San Jose. Zang, J., Anderson, N. G., & Lau, K. M AlGaAs superlatties mirooolers. Applied Pysis Letter, 83(), 334.

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