IEEE TRANSACTIONS ON COMPONENTS, PACKAGING...

IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 1, NO. 9, SEPTEMBER 2011 1395

Ultrathin Thermoelectric Devices for On-ChipPeltier Cooling

Man Prakash Gupta, Min-Hee Sayer, Saibal Mukhopadhyay, Member IEEE, and Satish Kumar

Abstract— The efficient usage of thermoelectric (TE) devicesfor microelectronics cooling application requires investigationand remedy of various obstacles such as integration of thesedevices with electronic package, parasitic contact resistances,and utilization of appropriate current pulses. We develop acomputational model to investigate the effect of steady state andtransient mode of operation of ultrathin thermoelectric cooler(TEC) devices on hot-spot cooling considering the effect of crucialthermal and electrical contact resistances. Our analysis showsthat the transient pulses can be very effective in reducing the hot-spot temperature by 6–7 °C in addition to the cooling achieved bythe steady state current through the TEC device. We correlate theimportant characteristics of the transient temperature behaviorof hot-spot under the TEC operation such as the maximumtemperature drop (�Tmax), time taken to achieve �Tmax andtemperature overshoot after turning off pulse current with theelectrical and thermal contact resistances and Seebeck coefficientof the TE material. It has been observed that thermal andelectrical contact resistances play a very crucial role in theperformance of TEC devices as high values of these resistancescan significantly diminish the effect of Peltier cooling duringsteady state operation. The effect of these parasitic resistances iseven higher for the transient cooling of hot-spots by the pulsedcurrent through the TEC device. High Seebeck coefficient ofTE materials is desirable as it increases the figure of meritof TE devices. However, cooling capabilities of heat sink maybecome bottleneck to realize the benefits of very high Seebeckcoefficient as the back heat flow from the hot side to cold side ofTEC device diminishes the degree of cooling achieved by theseultrathin TECs.

Index Terms— Contact resistance, hot-spot, Peltier, thermoelec-tric, transient.

I. INTRODUCTION

THERMOELECTRIC (TE) devices have potential to makeimportant contributions in various applications such assolid-state cooling, waste heat recovery, refrigeration, and heatpumps which may help to reduce green house emissions andprovide cleaner forms of the energy generation [1]–[3]. These

Manuscript received September 23, 2010; revised March 25, 2011; acceptedMay 16, 2011. Date of current version September 21, 2011. This work wassupported in part by the National Science Foundation under Grant ECCS-1028569. Recommended for publication by Associate Editor M. Hodes uponevaluation of reviewers’ comments.

M. P. Gupta, M.-H. Sayer, and S. Kumar are with the WoodruffSchool of Mechanical Engineering, Georgia Institute of Technology,Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected];[email protected]).

S. Mukhopadhyay is with the Department of Electrical and ComputerEngineering, Georgia Institute of Technology, Atlanta, GA 30332 USA(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCPMT.2011.2159304

devices have great appeal for site-specific and on-demandcooling in microelectronic and optoelectronic devices [1], [4].The power distribution on a microelectronic chip could behighly non-uniform both on temporal and local scales, whichcould lead to hot-spots. The peak temperature on the chipdrives the system level cooling solution. The conventionalcooling solutions for the electronics devices are bulky and inef-ficient to handle localized high heat fluxes and hot-spots [1].Thermoelectric coolers (TECs) could be employed for theseapplications for an efficient removal of localized heat, whichmay boost the performance of semiconductor devices andincrease the operating life of electronic circuits [5]–[7].

Despite high appeal in terms of operational simplicity, usageof TE devices for various commercial applications is limiteddue to the low efficiency and high cost compared with theconventional technologies. A figure of merit ZT = σS2T/kexpresses the efficiency of TE materials where σ is the elec-trical conductivity, S is the Seebeck coefficient, k is the thermalconductivity, and T is the operating temperature [8]. A widerange of alloys and superlattices of different materials such asSiGe, Bi2Te3, Sb2Te3, and skutterudites have been rigorouslyinvestigated to improve the figure of merit, ZT [7], [9]–[11].The additional challenges for TEC usage in electronic coolingapplications are low heat-flux pumping capacity and non-disruptive integration with the electronic devices. High elec-trical and thermal contact resistances further degrade theperformance of these devices [1].

Significant efforts have been made in recent years to exploreTECs for cooling hot-spots in microprocessors. In a relatedstudy, Litivinovitch et al. have analyzed steady state coolingof hot-spot using both Si and SiGe superlattice TECs [12].They observed a maximum cooling of 4.5 °C at the hot-spot location using TECs. Additional cooling over steady statevalues can be achieved for a short period of time at hot-spotusing transient current pulses. Pulse cooling effect in TECs hasbeen known for few decades and has been studied extensivelyfor free standing TECs. This effect is attributed to the interplaybetween Peltier cooling (surface effect) and Joule heating (vol-ume or bulk effect) as the former effect is realized quicker atthe cold junction compared to the later. Diffusion time constantfor Joule heating in TEC devices can be order of magnitudehigher than that of Peltier cooling (∼10–20 μs). The differencein these two time scales can be utilized for the transient coolingon the chip as a lower than steady state temperature can beachieved momentarily at the colder surface [8].

Transient cooling performance of TECs depends on severalparameters such as the TE material, TEC geometry, pulse

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1396 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 1, NO. 9, SEPTEMBER 2011

current characteristics (shape, duration and amplitude) etc.Experimental and numerical investigation of the transient pulsemode cooling by TEC devices has been studied by Snyderet al. [8]. They explored various parameters such as currentpulse amplitude, thermal diffusivity, supercooled temperature,and time to reach the minimum temperature. A 3-D theoreticalmodel was proposed by Cheng et al. [13] to simulate transientthermal behavior of TECs. They found that the coefficientof performance (COP) (which is defined as the ratio of heatremoval from cold junction to energy consumed by TEC) ofTEC increases with increase in the cooling load for a givencurrent. Yang et al. [14] have performed a numerical analysisof transient response of TECs with and without a coolingload attached to the TEC. They suggested that the pulseduration should be chosen based on the characteristic timeconstants for efficient pulsed cooling. Thonhauser et al. [15]studied the influence of pulse shape during transient modeoperation and found that a quadratic pulse form is the mostefficient as it consumes less energy and prevents extensiveheating. An electrical analogue of the 1-D transient model ofTEC was proposed by Mitrani et al. [16] to study the pulsecooling using SPICE. They investigated the effect of pulseshape and magnitude on cooling and analyzed the associatedcharacteristic time constants. Harvey et al. [17] studied theeffect of managing individual thermocouples inside TEC onthe efficiency of TECs while cooling a chip. They suggestedthat significant gains in performances in terms of the energyefficiency can be realized using distributed control of TEC.

Most of the studies based on the transient mode of operationhave been performed for free standing thick TECs wherecontact resistances are not crucial. Recently, TEC modulesmade of ultrathin (∼100 μm) Bi2Te3 based superlatticeshave been successfully integrated to the heat spreader of anelectronic package for site-specific localized cooling [1]. Thecooling capacity of TECs can be significantly improved byemploying these ultrathin TEC modules as it improves the heatpumping capacity and has the potential to be integrated on theactive side of the chip. Wang et al. [18] conducted numericaland experimental study for on-chip hot-spot cooling usingmini-contact TECs and observed that high thermal contactresistance can have detrimental effect to the extent that itcan completely nullify the cooling effect. Ju [19] performednumerical investigation of pulse cooling in 1-D TEC geom-etry to study the effect of contact electrical resistance onits performance. They observed that the intense localizedheating at the interface due to the electrical contact resistancesstrongly affects the minimum achievable temperature at thecold junction. The author further suggested that the impact ofelectrical contact resistance can be more pronounced for theTECs of length of the order of 100 μm or smaller.

The past studies on pulsed cooling are mostly based on the1-D geometries isolated from the realistic electronic package.A detailed study of the pulsed cooling in the context of use ofultrathin TEC modules on the active side of the electronicpackage considering the details of 3-D package and TECdevice has not been performed. Transient cooling by TECdevices involves two competitive effects, Joule heating andPeltier cooling. Peltier cooling is a surface effect, which helps

in reducing hot-spot temperature by removing heat from thecold junction. Whereas, Joule heating is a volumetric effectand it increases temperature not only within TEC but alsoat the hot-spot. The spatial difference between the origins ofthese two effects allows Peltier cooling effect to be realizedat the hot-spot location earlier than the joule heating effect.Short current pulses through TECs can help to extract theadvantage of this phenomenon. However, the effect of parasiticcontact resistances at the interface of TE material and metalliclayers inside an ultrathin TEC module and at the interface ofTEC module and package can significantly affect the TECperformance in a transient operation. A detailed investigationis required to quantify how these parasitic resistances degradethe TEC performance. The degree of Peltier cooling is directlyproportional to the Seebeck coefficient of TE material. How-ever, high temperature gradient across TE material can lead toback flow of heat and the range of desired Seebeck coefficientneed to be investigated. Finally, the high energy consumptionand low efficiency is one of the major obstacles for the TECemployment in the electronic cooling applications. It is crucialto explore whether ultrathin TECs provide any significantadvantage in reducing the power consumption. The goal ofthis paper is to address all important issues related with theultrathin TEC operation in the electronic package environmentdiscussed above.

In this paper, we develop a detailed 3-D thermal model ofthe electronic package and attached TEC devices to investigatethe effect of both steady state and transient mode of operationof TECs on hot-spot temperature. Our numerical model solvesfor the temperature distribution in the electronic package andTEC modules including the effect of thermal and electricalcontact resistances, which are very significant for the ultrathinTEC modules. We incorporated the effect of Peltier coolingand Joule heating inside the TEC module to analyze thetemperature reduction at hot spot on the chip for current pulsesof different magnitudes. Important contributions of this paperare listed as follows.

1) The effect of parasitic contact resistances for ultrathinTEC devices integrated with a 3-D electronic package isinvestigated for the steady-state and transient operationof TECs, which provides insights for the range ofacceptable or desired contact resistances in order toefficiently use these devices.

2) The important characteristics of the transient temper-ature behavior of hot spot under the TEC operationsuch as the maximum temperature drop (�Tmax), timetaken to achieve �Tmax and the temperature overshootafter turning off a pulse current have been investigatedand empirical correlations have been derived, whichcorrelate these characteristics with the vital parameterssuch as the amplitude of pulsed current, electrical andthermal contact resistances, etc. These correlations willprovide the guidelines for the design of current pulsesand control algorithms in order to facilitate smoothoperation of TECs.

3) The effect of Seebeck coefficient on pulse cooling hasbeen discussed, which describes the limits of high valuesof Seebeck coefficient to avoid excessive back heat

GUPTA et al.: ULTRATHIN THERMOELECTRIC DEVICES FOR ON-CHIP PELTIER COOLING 1397

flow. The energy analysis of TEC operation has beenpresented to explore the energy consumed for a specifiedheat removal by these ultrathin TEC devices and hencereveal the COP of these devices.

The rest of this paper is organized as follows. Section IIexplains the governing equations for the TEC operation,computational model, and the validation of the model againstpublished experimental measurements. In Section III, thekey parameters, their importance and their range of studyis described, which is followed by the results and analysis.Finally, Section IV concludes this paper.

II. COMPUTATIONAL METHODOLOGY AND VALIDATION

We develop a computational model which solves Fourier’sconduction equation in the electronic package and TEC mod-ule to analyze the effect of TEC device on temperaturereduction at hot-spot location on a chip. A schematic of theelectronic package, TEC module, and heat sink is shown inFig. 1. A 100 μm thick TEC module comprised of 7 × 7 p-ncouples is attached at the back side of the heat spreader. Thearea of the TEC device is 3.5 mm × 3.5 mm. The thickness ofthe TE layer of the TEC device is 8 μm; two metallic layersare attached on the both sides of this thin layer. We haveselected this geometry to compare and validate our modelingresults against the steady state experimental and computa-tional results in [1]. The reference values of electrical/thermalcontact resistances at the interface of superlattice–metal layer(10−11 �m2; 1 × 10−6 m2K/W) and at the interface of TECmodule-heat spreader layer (10−10 �m2; 8 × 10−6 m2K/W)are also obtained from [1]. These values of contact resistancesare considered in all simulations unless stated differently. Thedimensions and thermal conductivity of different componentsof the electronic package and TEC module are listed in Table I.Our computational domain includes heat spreader, thermalinterface material (TIM), chip, and TEC. In order to reducethe computational time of the simulation, the heat sink isrepresented by a convective heat transfer boundary condition atthe top of the spreader surface. A high heat flux (1250 W/cm2)source is located at the center of the bottom surface of chip(area 400 × 400 μm2), which generates a hot spot at the cen-ter. The rest of the bottom surface is considered as heat sourceof uniform heat flux of 43 W/cm2. These values of heat fluxesat the bottom of the chip are chosen in order to compare ournumerical results against the experimental observations in [1].

The operation of TECs is based on the interplay of Peltiercooling and Joule heating. Note the Peltier cooling is a surfaceeffect while the Joule heating is a volume effect. Heat isabsorbed at one side of the TEC module (cold-junction) whena TEC module is turned on and rejected at the other sideof the module (hotter junction). We incorporate the Peltiercooling effect by adding heat (∼S·I·Th) at the hotter sideand subtracting heat (∼S·I·Tc) from the colder side of thesuperlattice structures. Here, Th and Tc are the temperaturesof the hotter and colder junctions. The value of S is takenas 300 μV/K based on the experimental measurement in [1].The volumetric heat generation inside the TEC layer, at theinterface of the superlattice and metal layer and at the interface

Heat Sink

Heat Spreader

Chip

Substrate

TECTIM

Fig. 1. Schematic of an electronic package. Heat spreader, chip, TIM, chip,substrate, and TEC are shown.

TABLE I

DIMENSIONS AND THERMAL CONDUCTIVITY OF DIFFERENT

COMPONENTS OF THE ELECTRONIC PACKAGE

Component Thermal DimensionsConductivity(W/m-K)

Spreader 400 30 mm × 1 mm × 30 mmTIM 1.75 11 mm × 0.125 mm × 13 mmTEC-superlattice 1.2 3.5 mm × 0.008 mm × 3.5 mmChip 140 11 mm × 0.5 mm × 13 mm

of TEC module and heat spreader layer is considered byadding Joule heating terms (I2R) terms at the correspondingvolumes and layers. The thermal contact resistances at theseinterfaces are incorporated by adding an appropriate thermalresistor at the corresponding interfaces.

1) Governing Equations: The governing differential equa-tion for temperature distribution inside the electronic packageis represented as

∂2T

∂x2+ ∂

2T

∂y2+ ∂

2T

∂z2+ Q̇ = ∂T

α∂ t(1)

where

Q̇ ={

I 2

A2σkinside TEC

0 elsewhere.(2)

Here, T is temperature, α is thermal diffusivity, I is current,A is area of an element, σ is electrical conductivity, and k isthermal conductivity.

2) Boundary Conditions: Heat flux boundary condition isapplied at the bottom of the chip, which can be expressed as

−k ∂T∂y

= q ′′ where q ′′ ={

1250 Wcm2

at the hot spot

43 Wcm2

elsewhere.(3)

In addition, at the cold end of TEC

−k A ∂T∂y

∣∣∣∣y=y+c

=[−k A ∂T

∂y− SI T

]y=y−c

+ I 2 Relec . (4)

Here, the y coordinate is directed from TEC to the heatspreader, and y+c and y−c are locations just above and belowthe cold junction. S is Seebeck coefficient and Relec is contactelectrical resistance.


Convective Cooling

TEC

y

Chip

x

Heat Spreader

(a) (b)

(c) (d)

331 370 373 376 379 382 K345 360 375 387 K

342.5 386.2 386.8 387.3 K343 343.4 K

Fig. 2. (a) Temperature contours in a vertical cross-section of an electronicpackage are shown [only heat spreader, TIM, chip, substrate, and TEC isconsidered for simulations. Convective heat transfer boundary condition isapplied at the top of the spreader]. (b) Temperature contours on the bottomsurface of the chip. High heat flux (1250 W/cm2) source is located at thecenter of this surface of area 400 × 400 μm2 which generate a hot spotat the center. The rest of the surface has a uniform heat flux of 43 W/cm2.(c) Temperature contour at the cold side of TEC. (d) Temperature contour atthe hot side of TEC.

Also, at hot end of TEC

−k A ∂T∂y

∣∣∣∣y=y+h

=[−k A ∂T

∂y+ SI T

]y=y−h

+ I 2 Relec (5)

y+h and y−h are locations just above and below hot junction.

Finally, at the top surface of heat spreader

−k ∂T∂y

= h(T − T∞). (6)

Here, h is convective heat transfer coefficient and T∞ isambient air temperature, which is taken as 300 K.

The simulations are performed using the finite volumemethod-based commercial solver FLUENT. 200 K cells areconsidered for the simulations, grid independence tests verifythat these cells are sufficient for the further simulations.The temperature contours in a vertical cross-section of theelectronic package, on the chip bottom surface and at the coldand hot sides of TEC are shown in Fig. 2.

The computational model is validated by comparing the hotspot temperature at the bottom surface of the chip againstthe numerical results in [1], which was verified against theexperimental observations in [1]. The comparison is done withand without considering the contact thermal and electricalresistances at the superlattice–metal interface. An excellentagreement (within 2–3 °C) with the results in [1] for differentvalues of contact resistances validates the developed computa-tion model (Fig. 3). The maximum cooling (5.5 °C) at steadystate is achieved at the current amplitude of 3 A, which is alsoobserved in the experimental measurements in [1].

Tem

pera

ture

(˚C

)

Current (A)

100

0 2 4 6

110

120

130Num-1 (R

th � 0; R

elec � 0)

Num-p (Rth � 0; R

elec � 0)

Num-1 (Rth � 1 × 10−6 m2K/W; R

elec � 1 × 10−11 �m2)

Num-p (Rth � 1 × 10−6 m2K/W; R

elec � 1 × 10−11 �m2)

Fig. 3. Hot-spot temperature at the bottom surface of the chip is comparedwith the numerical results in [1], which was verified against the experimentalobservations in [1]. Here, ‘Num-1’ corresponds to the numerical results in [1]and ‘Num-p’ corresponds to the current simulation results.

III. RESULTS AND DISCUSSION

A. Range of Important Parameters

The important parameters investigated in this section arethermal (Rth) and electrical (Relec) contact resistances at theinterfaces of TE material and the metallic layers inside theTEC module and the Seebeck coefficient (S) of TE material.Thermal contact resistance is a very important parameter asit can be a major contributor of TEC total thermal resistanceleading to the bottleneck for effective heat removal from thehot side of the TEC module to the ambient which in turncan increase the temperature at the cold junction of TEC andat the hot spot. The range of the thermal contact resistancesconsidered in this paper is 1 × 10−7–7.5 × 10−6 m2K/W.These resistances are dependent on the fabrication processand can vary from one manufacturing process to the other.The range of Rth considered here is based on the typicalvalue of thermal contact resistances estimated in [1]. Theelectrical contact resistance at the TE-metal interface leads tothe Joule heating which can drastically diminish the effect ofthe Peltier cooling. In this paper, we consider the effectiveTE properties of the Bie2Te3 based thin film TE materialwhich makes Ohmic contact with the metallic layers insidethe TECs. The typical values of Relec measured in [1] usingtransmission line method is of the order of 10−11 �m2.However, these values are largely dependent on the fabricationprocess, so we consider Relec in the range of 10−12 �m2to 10−10 �m2. We have derived the empirical correlationsbetween the transient temperature characteristics at the hotspot and Rth/Relec values to provide guidelines for the futuredesign of TEC operation. Seebeck coefficient (S) is anotherimportant parameter investigated in this paper. High S valuesare desired in TE applications as the figure of merit ofTE materials is proportional to the square of S. Designingmaterials with high S and hence high figure of merit is veryactive research area in the materials science. However, highSeebeck coefficient can also have an adverse effect on hot-spot cooling as back heat flow in TEC device can diminish theeffect of Peltier cooling and so the investigation of effects ofS on the degree of achieved cooling is important. The value ofS for Bie2Te3 superlattice material is measured as 300 μV/Kin [1]. In this paper, it has been varied between 100 μV/Kto 400 μV/K to study the effect of extreme values during


Time (s)

�T (

˚C)

0 0.02 0.04 0.06 0.08 0.1

1 A

3 A

6 A

8 A

–5

–10

0

–15

Fig. 4. Hot-spot temperature change with time after turning on TEC deviceat different current amplitudes.

steady-state and transient operation. For the parameters andtheir ranges discussed above, we analyze both steady stateand transient operation of TECs and investigate the effect ofamplitude of current pulses and the energy consumption inTEC devices.

B. Transient Response of Hot Spot

The lower response time for the Peltier cooling compared tothe Joule heating can allow high amplitude transient currentpulse through the TEC device to reduce the temperature atthe hot-spot below the steady state operation of TECs. Thistransient mode operation of TECs may lead to very efficienton-demand cooling of hot spots in the microelectronic chips.We first investigate the change in hot-spot temperature withtime after turning on the TEC device at different currentamplitudes. Lower values of current amplitude demonstrate thedominance of Peltier cooling effect due to the relatively lowJoule heating. For low values of current amplitudes (≤3 A),the hot-spot temperature stabilizes and achieves its steadystate values in less than 0.1 s. For higher amplitude currents(≥6 A), Joule heating becomes significant and can counterthe Peltier cooling effect. This suggests that temperature athot spot should reduce first due to Peltier cooling, reach aminimum value and subsequently increase when Joule heatingeffects is realized at the surface, which is typically realizedslower than the Peltier cooling. The numerical results confirmthis behavior as the maximum cooling does not correspondto the steady state values but at some intermediate time (e.g.0.03 s for I = 8 A), Fig. 4. It should be noted that the effectis realized at the hot spot on the chip bottom surface, which islocated 0.5 mm away from the location of the colder side ofTE superlattice. This clearly indicates that TEC can be utilizedfor the additional transient cooling at the hot spot.

We next explore the effect of transient current pulses onPeltier cooling by applying pulses of different magnitudes (Ip)on top of the constant current (Imin) through the TEC deviceand investigate the characteristics of transient temperaturebehavior at hot spot in response to the pulsed current throughthe TEC. The transient current pulses of period 0.06 s areapplied after the system temperature reaches to their steadystate values at constant current of Imin. Here, Imin = 3 A

Time (s)

Time (s)

(b)

(a)

Cur

rent

(A

)

Pulse amplitudeI

p

Imin

= 3A

0

5

10

15

Cur

rent

(A

)

0

0 0.05 0.1 0.15

5

–5

10

–10

15Current pulse � 6 ACurrent pulse � 9 ACurrent pulse � 12 ACurrent pulse � 15 ACurrent pulse � 18 A

Fig. 5. (a) Shape of the current pulse for Ip = 4 × Imin = 12 A.(b) Temperature drop at hot spot with time subjected to a pulsed currentof 0.06 s duration for different values of IP . The current pulse is appliedafter the system reaches steady state at Imin = 3 A.

is the current magnitude, which provides maximum steadystate cooling (Tss) (see Fig. 3). The shape of the currentpulse is shown in Fig. 5(a). Fig. 5(b) shows the change inadditional cooling (�T = T − Tss) achieved at hot-spotlocation with time for transient current pulses of differentmagnitudes (defined as Ip in the figure). After reachingminimum temperature at the hot spot, temperature starts risingand overshoot in temperature over the steady state values isobserved even though the current pulse amplitude is changedback to Imin = 3 A. Three important characteristics of theobserved transient cooling at hot-spot location subjected totransient pulse is the maximum temperature drop (�Tmax), thetime taken to achieve maximum temperature drop (tmin), andthe temperature difference (�Tovershoot) between peak valueof the temperature attained at hot spot after the pulse currentis turned off and the steady state temperature (Tss). Next,we derive and analyze the empirical correlations for thesetemperature characteristics of transient cooling for currentpulses of different amplitudes.

1) Empirical Correlations: The empirical correlations fortransient temperature characteristics are important as they canprovide guidelines for the design of the current pulses in orderto facilitate smooth and energy efficient operation of TECs.The time (tmin) taken to achieve maximum temperature dropat hot spot during pulse cooling decreases as the current pulseamplitude is increased which means higher IP corresponds tofaster cooling [Fig. 6(a)]. An expression for tmin is derived


using linear approximation of 1-D heat equation for TECin [8], i.e., tmin ∼ [IP/Imin + 1]−2. Our numerical data areproportional to a slightly changed expression [IP/Imin + 2]−2.This difference can be attributed to the fact that tmin in ouranalysis corresponds to the location of hot spot, which is awayfrom TEC cold junction and our analysis corresponds to a3-D system while expression for tmin in [8] corresponds tothe temperature at cold junction of an isolated TEC. �Tmaxincreases with increasing IP due to the augmented Peltiercooling but soon attains a peak value of 6 °C correspondingto Ip = 12 A and subsequently �Tmax starts decreasing asthe increasing Joule heating effect with increasing currentdiminishes Peltier cooling effect at hot spot, Fig. 6(b). Theseresults suggest that higher values of IP (>12 A) are notfavorable as they bring down �Tmax and reduce the coolingduration as well.

Empirical formulae for tmin and �Tmax are expressed by (7)and (8), these correlations give a close fit to the numerical data,which relate tmin and �Tmax to current pulse ratio (IP/Imin)when other parameters are kept constant

tmin = 0.8(

IpImin

+ 2)−2

(7)

�Tmax = 7[

1 − exp(

1 − IpImin

)]. (8)

It is interesting to note that this paper is focused on thecooling of hot spot located below the cold end of TEC at somedistance inside 3-D electronic package and yet the empiricalexpression for �Tmax and tmin are similar to that obtained bySnyder et al. [8] who performed the study for free standing 1-D TEC. Temperature overshoot (�Tovershoot) is the temperaturedifference between peak value of the temperature at hot spotafter the pulse current is turned off and Tss; it increases as thecurrent pulse magnitude is increased [Fig. 6(c)]. Pulsed currentduration also affects �Tovershoot significantly. Results suggestthat current pulse should be turned off just after achieving�Tmax in order to minimize �Tovershoot.

C. Thermal Contact Resistance Effect

In this section, we analyze the effect of thermal contactresistance at the interface of TE material and metallic layersin a TEC device for both steady and transient operation ofTEC. The analysis also provides insights for the range ofacceptable or desired contact resistances for the efficient usageof TEC devices. Since, the Peltier effect originates at thesurface, the role of contact thermal resistances during TECoperation becomes very important as these contact resistancesin ultrathin TEC device can significantly degrade the perfor-mance. A significant variation in these resistances is possibledepending on the fabrication process and attachment methodof TEC devices with the electronic package. We analyzed theeffect of these resistances by changing the thermal contactresistance (Rth) in the range of 1 × 10−7–7.5 × 10−6 m2K/W;the typical value of contact resistance estimated in [1] is1 × 10−6 m2K/W. The degree of cooling achieved by applyingsteady state current through the TEC is shown in Fig. 7(a).The maximum achievable cooling at hot spot decreases from

1 2 3

(a)

(b)

(c)

4 5 6

Ip/I

min

Ip/I

min

t min (

s)�T

max

[˚C

]

0

0.02

0.04

0.06

0.08

0.1

Fit to

Numerical

Numerical

0.8I

p

Imin

+ 22

Ip

Imin

1 –7 1 – exp[ ]

01 1.5 2 2.5 3 3.5 4

2

4

6

8

Ip/I

min

�Tov

ersh

oot [

˚C]

0

2

2 3 4 5 6

Pulse duration 0.4 sPulse duration 0.6 sFitted curves

4

6

8

10

Fig. 6. (a) Time to reach minimum temperature (tmin) at hot-spot locationfor current pulses of different magnitudes and duration 0.04 s. (b) Variation ofmaximum temperature drop (�Tmax) at hot spot subjected to current pulsesof 0.04 s duration. (c) Temperature overshoot at hot spot subjected to pulsedcurrent of two different durations (0.4 s and 0.6 s). Imin = 3 A.

5.5 °C to 4 °C when Rth is increased from 1 × 10−7 m2K/W to7.5 × 10−6 m2K/W. The maximum cooling corresponds to thedifferent current amplitudes for different Rth . Decreasing Rthallows applying high amplitude currents in order to achievebest cooling at the hot spot, Fig. 7(a).

1) Transient Cooling and Empirical Correlations: Theeffect of Rth on the additional cooling achieved by theapplication of transient pulses is even worse. The additionalcooling (�T ) achieved by applying a pulsed current of Ip =12 A and 0.04 s duration is shown in Fig. 7(b). We analyze thetransient thermal characteristics of this additional cooling, tmin,�Tmax, and �Tovershoot as function of Rth . The time to reach


0

0 2 4

(a)

(b)

�T (

˚C)

6

Rth � 7.5 × 10−6 m2k/w

Rth � 2.5 × 10−6 m2k/w

Rth � 1 × 10−6 m2k/w

Rth � 1 × 10−7 m2k/w

Current (A)

0 0.05 0.1 0.15

7.5 × 10–6

5 × 10–6

2.5 × 10–6

1 × 10–6

1 × 10–7Rth(m2K/W)

Time (s)

−2

−4

−6

5

�T (

˚C)

0

−5

–10

Fig. 7. (a) Steady-state (I = 3 A) temperature drop at hot spot for differentthermal resistances at superlattice–metal interface. (b) Temperature drop at hotspot with time subjected to a pulsed current of 0.04s duration. The thermalresistances at superlattice–metal interface corresponding to different curves areshown in the figure. The current pulse is applied after the package reachessteady state at Imin = 3 A. Ip = 12 A.

maximum cooling (tmin) decreases with increasing contactthermal resistances [Fig. 8(a)]. An empirically determinedcorrelation given by (9) shows an exponential relationshipbetween tmin and Rth when all other parameters are keptfixed. The increase in Rth accompanies with decrease inmaximum temperature drop (�Tmax). �Tmax decreases from6.5 °C to 1 °C when Rth is increased from typical valueof 1 × 10−6m2K/W to 7.5 × 10−6 m2K/W, but increasesby 3 °C when Rth is decreased from 1 × 10−6m2K/W to1 × 10−7 m2K/W, [Fig. 8(b)]. Clearly, an order of magnitudeincrease in Rth (from 10−6m2K/W to 10−5 m2K/W) almostnullifies the Peltier cooling. This underlines the requirementof low parasitic resistances for the efficient utilization ofTEC during transient pulsed cooling. However, decreasing Rthvalues lower than 1 × 10−7 m2K/W does not provide anyfurther significant increase in �Tmax indicating the maximumdesired value of Rth . The empirical correlation between �Tmaxand Rth given by (10) also shows an exponential relationship,which can be used to estimate the effect of the parasiticresistances on the degree of cooling. The RT in (9) and (10)can be considered as characteristic parasitic thermal resis-tance constant of the interface. Higher values of contactthermal resistance also augment �Tovershoot. For pulse currentmagnitude (12 A) and duration (0.4 s), �Tovershoot increasesby 0.8 °C when Rth is increased from 1 × 10−6 m2K/W to

0.03

0.025

0.02

0.015

Fit to

τT � 0.03s, R

T � 5 × 10–6 m2K/W

�TmaxT

� 8˚C, RT � 5 × 10–6 m2K/W

0.01

0.005

t min (

s)�T

max

[˚C

]

0 2 4

(a)

(b)

6

Numerical

8

Thermal Resistance (×10–6 m2K/W)

00

2

4

6

8

10

2 4 6

Numerical

Fit to

8

Thermal Resistance (×10–6 m2K/W)�T

over

shoo

t (˚C

)

01.5

2

2.5

3

2 4

(c)

6

Numerical

8

Thermal Resistance (×10–6 m2K/W)

τT 1 – 0.167exp –( )][ RthR

T

�TmaxT

exp –( )RthRT

Fig. 8. (a) Variation of tmin for different thermal contact resistances.(b) Maximum temperature drop at hot spot for different thermal contactresistances. (c) Temperature overshoot at hot spot. Pulsed current of 12 Ais used for 0.04 s duration. Imin = 3 A.

7.5 × 10−6 m2K/W [Fig. 8(c)]. Rth has significant impacton all transient temperature characteristics and so requiresa significant attention in order to keep its value as low aspossible

tmin = τT[

1 − 0.167 exp(

RthRT

)], τT = 0.03s,

RT = 5 × 10−6m2K/W (9)�Tmax = �TmaxT exp

(− Rth

RT

), �TmaxT = 8 °C,

RT = 5 × 10−6m2K/W. (10)

D. Electrical Contact Resistance Effect

The electrical contact resistances at the superlattice–metalinterface can drastically reduce the achieved cooling at the


�T (

˚C)

–10

–5

0

5�T

(˚C

)

–10

–5

0

10

5

20 4 6

0.02 0.040 0.06

(b)

(a)

0.08 0.1

Current (A)

Time (s)

Relec

= 10–12 �m2R

elec = 10–11 �m2

Relec

= 5×10–11 �m2R

elec = 10–10 �m2

Relec

= 1×10–11 �m2R

elec = 3×10–11 �m2

Relec

= 5×10–11 �m2R

elec = 10–10 �m2

Fig. 9. (a) Steady-state (I = 3 A) temperature drop at hot spot for differenceelectrical resistances at superlattice–metal interface. (b) Temperature drop athot spot with time subjected to a pulsed current of 0.04 s duration. Theelectrical resistances at superlattice–metal interface corresponding to differentcurves are shown in the figure. The current pulse is applied after the packagereaches steady state at Imin = 3 A. Ip = 12 A.

hot-spot location. The effect of these resistances for pulsedcooling can be more pronounced as these resistances lead tothe Joule heating at the interface of superlattice–metal wherePeltier cooling is the most effective. The effect of electricalcontact resistances is analyzed by changing their values (Relec)in the range of 10−11–10−10 �-m2 which are chosen based onthe experimental measurements in [1]. The degree of coolingachieved by applying steady-state current for these differentvalues of Relec is shown in Fig. 9(a). When Relec is increasedfrom 10−11 �m2 to 10−10 �m2, the maximum achievablecooling at hot spot is reduced from 5.5 °C to 3.5 °C. Variationof Relec from 10−12 �m2 to 10−11 �m2 results in very littleimprovement in cooling showing that an attempt to decreaseelectrical resistances lower than 10−11 �m2 will not be muchbeneficial [see Fig. 9(b)].

1) Transient Cooling and Empirical Correlations: Theeffect of increasing Relec on additional cooling (�T ) achievedunder the application of pulsed current is shown in Fig. 9(b).A 0.04 s long pulse with Ip = 12 A and steady-state currentof Imin = 3 A is applied for different values of Relec atthe interface. As observed for the case of thermal contactresistances, tmin decreases with increasing Relec [Fig. 10(a)].The numerical data for tmin fit well to the empirically deter-mined exponential correlation [see (11)], which relates tminto Relec when other parameters are kept fixed. The maximumtemperature drop �Tmax decreases from 6.5 °C to 1.5 °C when

Relec is increased from 10−11 �m2 to 10−10 �m2 [Fig. 10(b)].The numerical data for �Tmax follow the empirical correlationgiven by (12) where �TmaxE is the maximum temperature dropwhen there is no electrical contact resistance at the interfaceand RE is the characteristic contact electrical resistance ofthe interface, which can serve as a useful indicator for thetolerable limits of Relec . It can be inferred from the results thatincreasing contact electrical resistance significantly degradesPeltier cooling resulting in lower values of both tmin and�Tmax

tmin = τE exp(

− RelecRE

), τE = 0.029s,

RE = 7 × 10−11 �m2 (11)�Tmax = �TmaxE exp

(− Relec

RE

), �TmaxE = 7.5 °C,

RE = 7 × 10−11 �m2. (12)The higher values of contact electrical resistance also aug-

ment �Tovershoot. For pulse current magnitude (12 A) andduration (0.4 s), �Tovershoot increases by 4 °C when Relecis increased from 10−11 �m2 to 10−10 �m2 [Fig. 10(c)].The effect of electrical contact resistances on temperatureovershoot is much higher than the effect of thermal con-tact resistances [see Figs. 8(c) and 10(c)] indicating that asignificant discretion is required to select the current pulsesconsidering the effect of crucial electrical contact resistancesin order to minimize the temperature overshoot.

E. Seebeck Coefficient Effect

We next analyze the effect of Seebeck coefficient (S) onsteady state and transient operation of TEC while keeping thecooling capability of heat sink unchanged [∼constant h in (6)].Seebeck coefficient (S) of TEC devices has significant impacton the Peltier cooling at the hot-spot location as amount of heatremoved from the colder side of the superlattice structures isproportional to the value of Seebeck coefficient. High S valuesare desired in all TE applications. However, high Seebeckcoefficient can have an adverse effect on hot-spot cooling asback heat flow in TEC device can diminish Peltier coolingeffect. To quantify the effect, we first investigate the degree ofcooling achieved at hot-spot for different steady-state currentsand for different values of Seebeck coefficient in the range of100–400 μV/K [see Fig. 11(a)]. We observe 2–8 °C coolingat hot-spot location as we change Seebeck coefficient from100 μV/K to 400 μV/K. It can be noticed that the effect ofincreasing Seebeck coefficient is countered by back heat flow,which can be more pronounced for higher amplitude current(I >4) due to larger temperature difference between cold andhot ends of TEC [Fig. 11(a)]. It has been observed that forcurrent amplitudes greater than 6A, the increased values ofS can instead degrade Peltier cooling if cooling capability ofheat sink remains same (∼ constant h). The effect of increasingSeebeck coefficient on additional cooling (�T ) achieved underthe application of a pulsed current is shown in Fig. 11(b). A0.04 s long pulse with Ip = 12 A and steady-state currentof Imin = 3 A is applied for different values of Seebeckcoefficient. We observe additional cooling (�Tmax) of 1 °C


0.03

0.025

0.02

0.015

Fit to

RE � 7 × 10–11 �m2

0.01

0.005

t min (

s)

0 2 4 6

(a)

(b)

(c)

Numerical

108Electrical Resistance (×10–11 �-m2)

τE exp –( )RelecR

E

Fit to

0 20

2

4

6

8

4 6

Numerical

108

Electrical Resistance (×10–11 �-m2)

�TmaxE

exp –( )RelecRE

τE � 0.029 s

RE � 7 × 10–11 �m2

�TmaxE

� 7.5˚C�T

max

[˚C

]

0 20

2

4

6

8

4 6

NumericalFitted curve

108

Electrical Resistance (×10–11 �-m2)

�Tov

ersh

oot [

˚C]

Fig. 10. (a) Variation of tmin for different electrical contact resistances.(b) Maximum temperature drop at hot spot for different electrical contactresistances. (c) Temperature overshoot at hot spot. Pulsed current of 12 A isused for 0.04 s duration. Imin = 3 A.

to 7 °C when S is increased from 100 μV/K to 400 μV/Kbut tmin and �Tovershoot also increases with increasing S [seeFig. 11(b)].

Similar to the steady-state operation, values of Seebeckcoefficient higher than 400 μV/K is not favorable for Peltiercooling using transient current pulses. We notice that thevalues of Seebeck coefficients, after which further increasein their values lead to decrease in Peltier cooling, are higherfor high convective heat transfer coefficients (better coolingby heat sink). Therefore, in order to crop the benefits ofhigh Seebeck coefficients, high cooling capability is required.Bi2Te3 based superlattices used in [1] for TE materials have Svalues of the order of 300 μV/K. The conventional air coolingsolutions for electronic packages are reaching their limits andit may become bottleneck to realize the benefits of furtherimprovement in S values of the TE materials.

Current (A)

Time (s)�T

(˚C

)�T

[˚C

]

S = 100 μV/KS = 200 μV/KS = 300 μV/KS = 400 μV/K

S = 100 μV/KS = 200 μV/KS = 300 μV/KS = 400 μV/K

0

0

−2

−4

−6

−8

−10

5

0

–5

–10

1 2 3

(a)

(b)

4 5 6

0 0.02 0.04 0.06 0.08 0.1

Fig. 11. (a) Steady-state temperature drop at hot spot for different values ofSeebeck coefficient of TEC. (b) Temperature drop at hot spot with time sub-jected to a pulsed current of 0.04 s duration. Different curves correspond to dif-ferent values of Seebeck coefficient as shown in the figure. The current pulseis applied after the package reaches steady state at Imin = 3 A. Ip = 12 A.

F. Energy Analysis for TEC Operation

This section explores the amount of heat removed fromthe hot-spot as well as total heat through the cold side ofTEC and the energy consumed in TEC device operation fordifferent current amplitudes; this analysis can be further usedto estimate the COP of Peltier cooling using these ultrathinTEC devices. The COP of TECs is defined as the ratio of theamount of heat removed from the hot spot to the amount ofenergy supplied to TEC. The amount of heat removed fromthe hot spot is defined as the difference of total heat from thebottom of TEC module with hot-spot on the chip and withouthot spot on the chip. This is different from the total heat (Qin)passing through the cold side of TEC module. The decreasingtrend of COP with increasing current is shown in Fig. 12(a).

The energy supplied to TEC (�Q) increases parabolicallywith increasing current [Fig. 12(b)]. However, the heat passingthrough the colder side of TEC (Qin) does not increasemonotonically with current. It achieves a maximum valuecorresponding to 12 A current and then decreases because ofthe back heat flow as a consequence of the larger temperaturedifference between the hot and cold sides of TEC. The valueof Qin , �Q, and COP corresponding to the point of maximumsteady-state cooling (∼3 A current) are 11.8 W, 0.6 W, and 1.7,respectively. A high value of COP is noted here compared tothe typical experimental values because �Q accounts only forthe TEC power consumption, however, there might be somelosses in the peripheral circuit elements which would lower theCOP. Results suggest that the rate of energy taken out by TEC


Current (A)(a)

(b)

CO

P

10

5

10

15

2 3 4 5 6

Current (A)0

0

20

40

60

80

8

10

12

14

16Numerical

Quadratic

Qin(W

)

�Q

(W)

5 10 15

Fig. 12. (a) COP variation with current. (b) Variation of energy removed(Qin ) from the colder side (left axis) and energy consumed (�Q) by TEC(right axis) against current.

from the hot-spot is nearly 1 W and it increases slightly withincrease in current. Since the power dissipated at the hot spot is2 W, it suggests that only half of it is taken out by TEC. Duringpulsed cooling, the maximum temperature drop is observedfor 12 A current. This current amplitude also correspondsto the maximum heat removal from the cold side as furtherincreasing current lead to decreased Qin [Fig. 12(b)]. Thepresent energy analysis shows that the TEC-based coolingis energy efficient only for low values of the currentamplitudes.

IV. CONCLUSION

In summary, we developed a computation model to analyzethe cooling of hot spots on-chip using an ultrathin Peltiercooler, which is attached at the bottom side of the heatspreader. We investigated the effect of both steady stateand transient mode of operation of TEC for hot-spot tem-perature reduction. The analysis shows that transient pulsescan be very effective to reduce the hot-spot temperature by6–7 °C in addition to the cooling achieved by the steady-statecurrent pulse through the device. The efficient utilization ofthese pulses for transient cooling operation requires a carefuloptimization of shape and duration of the pulse. We observethat the effect of additional transient cooling can be diminishedto 1 °C if the thermal or electrical contact resistance isan order of magnitude higher than the currently estimatedvalues from recent experimental measurements. It was noticed

that the Peltier cooling is enhanced by the increased valuesof Seebeck coefficient both for the steady state and pulsedcooling. However, the cooling effect of increasing Seebeckcoefficient is countered by the back heat flow, which can bemore pronounced for the higher values of current (I >4A) dueto the larger temperature difference between the cold and hotends of TEC. In order to further enhance the energy efficiencyof the Peltier cooling on a chip, a dynamic control mechanismis required which is under investigation.

REFERENCES

[1] I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan,R. Mahajan, D. Koester, R. Alley, and R. Venkatasubramanian, “On-chip cooling by superlattice-based thin-film thermoelectrics,” NatureNanotechnol., vol. 4, pp. 235–238, Apr. 2009.

[2] R. Mahajan, C.-P. Chiu, and G. Chrysler, “Cooling a microprocessorchip,” Proc. IEEE, vol. 94, no. 8, pp. 1476–1486, Aug. 2006.

[3] T. M. Tritt and M. A. Subramanian, “Thermoelectric materials, phenom-ena, and applications: A bird’s eye view,” MRS Bullet., vol. 31, no. 3,pp. 188–194, Mar. 2006.

[4] A. Majumdar, “Thermoelectricity in semiconductor nanostructures,”Science, vol. 303, no. 5659, pp. 777–778, Feb. 2004.

[5] T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, “Quantumdot superlattice thermoelectric materials and devices,” Science, vol. 297,no. 5590, pp. 2229–2232, Sep. 2002.

[6] A. Shakouri and Z. Yan, “On-chip solid-state cooling for integratedcircuits using thin-film microrefrigerators,” IEEE Trans. Comp. Packag.Technol., vol. 28, no. 1, pp. 65–69, Mar. 2005.

[7] R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O’Quinn, “Thin-film thermoelectric devices with high room-temperature figures ofmerit,” Nature, vol. 413, pp. 597–602, Oct. 2001.

[8] G. J. Snyder, J.-P. Fleurial, T. Caillat, R. Yang, and G. Chen, “Super-cooling of Peltier cooler using a current pulse,” J. Appl. Phys., vol. 92,no. 3, pp. 1564–1569, Aug. 2002.

[9] J. Hone, I. Ellwood, M. Muno, A. Mizel, M. L. Cohen, and A. Zettl,“Thermoelectric power of single-walled carbon nanotubes,” Phys. Rev.Lett., vol. 80, no. 5, pp. 1042–1045, Feb. 1998.

[10] K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K.Polychroniadis, and M. G. Kanatzidis, “Cubic AgPbm SbTe2+m : Bulkthermoelectric materials with high figure of merit,” Science, vol. 303,no. 5659, pp. 818–821, Feb. 2004.

[11] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D.Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M. S. Dresselhaus, G.Chen, and Z. Ren, “High-thermoelectric performance of nanostructuredbismuth antimony telluride bulk alloys,” Science, vol. 320, no. 5876, pp.634–638, May 2008.

[12] V. Litvinovitch, P. Wang, and A. Bar-Cohen, “Superlattice μTEC hotspot cooling,” IEEE Trans. Comp. Packag. Technol., vol. 33, no. 1, pp.229–239, Mar. 2010.

[13] C.-H. Cheng, S.-Y. Huang, and T.-C. Cheng, “A 3-D theoretical modelfor predicting transient thermal behavior of thermoelectric coolers,”Int. J. Heat Mass Transfer, vol. 53, nos. 9–10, pp. 2001–2011, Apr.2010.

[14] R. G. Yang, G. Chen, A. R. Kumar, G. J. Snyder, and J.-P. Fleurial,“Transient cooling of thermoelectric coolers and its applications formicrodevices,” Ener. Convers. Manage., vol. 46, nos. 9–10, pp. 1407–1421, Jun. 2005.

[15] T. Thonhauser, G. D. Mahan, L. Zikatanov, and J. Roe, “Improvedsupercooling in transient thermoelectrics,” Appl. Phys. Lett., vol. 85,no. 15, pp. 3247–3249, Oct. 2004.

[16] D. Mitrani, J. Salazar, A. Turó, M. J. García, and J. A. Chávez, “Tran-sient distributed parameter electrical analogous model of TE devices,”Microelectron. J., vol. 40, no. 9, pp. 1406–1410, Sep. 2009.

[17] R. D. Harvey, D. G. Walker, and K. D. Frampton, “Enhancing perfor-mance of thermoelectric coolers through the application of distributedcontrol,” IEEE Trans. Comp. Packag. Technol., vol. 30, no. 2, pp. 330–336, Jun. 2007.

[18] P. Wang, B. Yang, and A. Bar-Cohen, “Mini-contact enhanced ther-moelectric coolers for on-chip hot spot cooling,” Heat Transfer Eng.,vol. 30, no. 9, pp. 736–743, 2009.

[19] Y. S. Ju, “Impact of interface resistance on pulsed thermoelectriccooling,” J. Heat Transfer, vol. 130, no. 1, pp. 014502-1–014502-3,Jan. 2008.


Man Prakash Gupta received the B.Tech. andM.Tech. dual degrees in mechanical engineeringfrom the Indian Institute of Technology, Kanpur,India, in May 2009. He has been pursuing the Ph.D.degree from the School of Mechanical Engineer-ing, Georgia Institute of Technology, Atlanta, since2009.

His current research interests include electron-ics cooling and electro-thermal modeling of carbonnanotube-based composites.

Min-Hee Sayer received the Undergraduate degreein nuclear and radiological engineering and mechan-ical engineering from the Georgia Institute of Tech-nology, Atlanta, in May 2010. He is currently pur-suing the Masters degree in nuclear engineeringwith an emphasis on radial force balance analysisbetween L-mode and H-mode plasma.

Saibal Mukhopadhyay (S’99–M’07) received theB.E. degree in electronics and telecommunicationengineering from Jadavpur University, Calcutta,India, in 2000, and the Ph.D. degree in electricaland computer engineering from Purdue University,West Lafayette, IN, in 2006.

He is currently an Assistant Professor with theSchool of Electrical and Computer Engineering,Georgia Institute of Technology, Atlanta. Prior tojoining the Georgia Institute of Technology, he waswith IBM T. J. Watson Research Center, Yorktown

Heights, NY, as a Research Staff Member. He has co-authored over 100 papersin refereed journals and conferences and been awarded five U.S. patents. Hiscurrent research interests include analysis and the design of low-power androbust circuits in nanometer technologies and 3-D circuits and systems.

Dr. Mukhopadhyay received the National Science Foundation CAREERAward in 2011, the IBM Faculty Partnership Award in 2009 and 2010, theSemiconductor Research Corporation (SRC) Inventor Recognition Award in2008, the SRC Technical Excellence Award in 2005, and the IBM Ph.D.Fellowship Award for the period 2004–2005. He has received the Best inSession Award at SRC Technology Conference in 2005 and the Best PaperAwards at the IEEE Nano in 2003 and the International Conference onComputer Design in 2004.

Satish Kumar received the B.Tech. degree inmechanical engineering from the Indian Institute ofTechnology, Guwahati, India, in 2001, and the M.S.degree in mechanical engineering from LouisianaState University, Baton Rouge, in 2003. He alsoreceived the M.S. degree in electrical and computerengineering and the Ph.D. degree in mechanicalengineering from Purdue University, West Lafayette,IN, in 2007.

He joined the George W. Woodruff School ofMechanical Engineering, Georgia Institute of Tech-

nology (Georgia Tech), Atlanta, as an Assistant Professor in 2009. Prior tojoining Georgia Tech, he was with IBM Corporation, Austin, TX, where hewas responsible for the thermal management of electronics devices. He isauthor or co-author of over 40 journal and conference publications. His currentresearch interests include thermal management, atomistic transport models fornano-structures, flexible-electronics, and thermo-electric coolers.

Dr. Kumar was a recipient of the Purdue Research Foundation Fellowshipin 2005.

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