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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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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
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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.
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1398 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND
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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
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GUPTA et al.: ULTRATHIN THERMOELECTRIC DEVICES FOR ON-CHIP
PELTIER COOLING 1399
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
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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
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GUPTA et al.: ULTRATHIN THERMOELECTRIC DEVICES FOR ON-CHIP
PELTIER COOLING 1401
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
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1402 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND
MANUFACTURING TECHNOLOGY, VOL. 1, NO. 9, SEPTEMBER 2011
�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
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GUPTA et al.: ULTRATHIN THERMOELECTRIC DEVICES FOR ON-CHIP
PELTIER COOLING 1403
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
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1404 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND
MANUFACTURING TECHNOLOGY, VOL. 1, NO. 9, SEPTEMBER 2011
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.
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GUPTA et al.: ULTRATHIN THERMOELECTRIC DEVICES FOR ON-CHIP
PELTIER COOLING 1405
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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