MINIATURIZED THERMOELECTRIC COOLER

y ,

Proceedings of IMECE’022002 ASME International Mechanical Engineering Congress & Exposition

November 17-22, 2002, New Orleans, Louisiana, USA

IMECE2002-32437

MINIATURIZED THERMOELECTRIC COOLER

Luciana W. da Silva and Massoud Kaviany∗

Department of Mechanical EngineeringUniversity of Michigan

Ann Arbor, Michigan [email protected], [email protected]

ABSTRACT

Vapor-deposited bismuth telluride (n-type) and an-timony telluride (p-type) films are used in a micro,column-type, patterned thermoelectric cooler. The opti-mum number of thermoelectric pairs and operating cur-rent are predicted. Such devices contain a number ofmetal/thermoelectric and metal/elecrical-insulator inter-faces. In the analysis, various interfacial resistances(phonon and electron boundary resistances and thermaland electrical contact resistances) have been included. Theboundary resistances cause a reduction in the thermal con-ductivity (desirable) and a reduction in the Seebeck coeffi-cient (undesirable) of the thermoelectric elements. The con-tact resistances reduce the overall device performance. Inthe fabrication, the stoichiometry of the deposited thermo-electric films, the patterned film deposition, and the selec-tion of the conducting connectors, are discussed. The ther-moelectric films are about 4 µm thick and are deposited onpatterned platinum (first trial layer for connectors), whichare in turn deposited on oxide coated silicon wafers. Thetop, suspended connectors that close the electrical circuitare bonded to the surface to be cooled. The non-uniformityof the composition in the thermoelectric films influences themeasured Seebeck coefficients. The analysis shows that acoefficient of performance of 0.38 is obtainable for a wirelessmicro sensor application.

∗Address all correspondence to this author.

NOMENCLATUREa unit cell dimension (A), side length (m)Ak surface area for conduction (m2)B emission constant (A/cm2-K2)c unit cell dimension (A)COP coefficient of performanced side width (m), barrier thickness (m)D diffusivity (m2/s)ec electronic charge 1.60210 × 10−19 (C)Eo potential barrier height (J)f frequency (Hz)hP Planck constant 6.626 × 10−34 (J-s)Je electrical current (A)k thermal conductivity (W/m-K)kB Boltzmann constant 1.381 × 10−23 (J/K)L thickness (m)L∗

te Lte/2δm mass (kg)n number density of primitive cells (m−3)N number of pairsP density of states (s/rad-m3), tunneling probabilityPe electrical power (W)q heat flux (W/m2)Q heat flow rate (W)Re electrical resistance (Ω)Rk conduction resistance (K/W)R∗ ratio of conduction resistancesSe energy conversion rate (W)T temperature (K)u velocity (m/s)

1 Copyright 2002 by ASME

Greek

αS Seebeck coefficient (V/K)γ ke/kp

δ electron-phonon cooling length (m)∆ϕ voltage (V)µ mobility (cm2/V-s)ρe electrical resistivity (Ω-m)τ transmission coefficient, relaxation time (s)ω angular frequency (rad/s)

Subscripts

b boundaryc cold, contactcc cold connectorD Debyee electronh hothc hot connectorj phonon modeJ Joulel loadmc metal connectorn n-type thermoelectric materialp phonon, p-type thermoelectric materialP Peltiersg solid-gassl solid-liquidte thermoelectric element

INTRODUCTIONFor local cooling of micro sensors and devices, thermo-

electric cooling is a suitable choice, since it does not requireany mechanical features and can be microelectronically in-tegrated. While the search for thermoelectric materialscompatible with solid-state electronics material continues,the tellurium alloys have the highest cooling performancearound room temperature. Thin films (700 nm) of telluriumalloys have been deposited by vapor deposition (Zou, et al.,2000a, 2001a, 2001b). Min and Rowe (1999) proposed amicro thermoelectric cooler where the thermoelectric thinfilms are grown on a very thin low thermal conductivity SiCmembrane (PECVD) to minimize the heat leakage effect.The current and heat flow parallel to the film plane. Thickfilms (10-50 µm) of tellurium alloys have been depositedusing electroplating for fabrication of thermoelectric cool-ers, where current and heat flow perpendicular to the filmplane (Fleurial, et al., 1997, 2000). Yao et al. (1999) haveexploited the optimal geometry and suitable materials, for

Qc (t)

Qk,h-c

ColdConnector

(Se,P)h

Se,J

(Se,P)c

(Se,P)h

Qc (t)

HotConnector

Sb2Te3(p-Type)

Contact andBoundaryResistances

Heat Sink

Bi2Te3

(n-Type)

Qk,h-1

Je

(−)

(+)

Sorption - BasedChemiresistorVapor Sensor(Load)

(Se,J)hb(Se,J)hb

(Se,J)cb

Rk,h-c

Ak = dte2

Lte

Column

Figure 1. RENDERING OF MICRO THERMOELECTRIC COOLER

USED WITH A MICRO VAPOR SENSOR. THE COLUMN-TYPE DESIGN

AND VARIOUS ENERGY CONVERSION MECHANISMS S AND HEAT

TRANSFER Q ARE ALSO SHOWN.

both thermoelectric legs and substrate, to increase the per-formance of this design.

Due to parasitic conduction heat transfer between hotand cold junctions, and the phonon and electron contactresistances, thin films (less than 1 µm) have not been usedin conventional column-type thermoelectric elements. Thissituation can be reversed, if thicker films are used. In vapordeposition, thicker films pose the challenge of concentrationvariation within the films and also peel-off. These challengesmay be met with co-evaporation of the alloy elements andby heating the deposition substrate.

Here, the column-type design of a layered-fabricatedmicro thermoelectric cooler is considered in a wireless vaporsensor application, as shown in Figure 1. The objective ofthe cooler is to lower the temperature of the sensor 20 Kbelow the ambient in few seconds, while using the minimumpower possible with a 3 V battery.

The preliminary experimental results show that ther-moelectric films of about 4 µm can be deposited. Using thisresult, we have modeled the flow of heat and electricity in-side the micro cooler, and made geometry and pair numberoptimization. In the model, the various boundary and con-


(AkRk)b,pp

Incident Phonon Wave

Reflection

Transmission

Phonon BoundaryResistance

e-

Potential Barrier Height Eo , J

Barrier Thickness d, m

(AkRk)b,ee

Electron BoundaryResistance

Phonon, Te (Lattice Vibration)

Mixed BoundaryResistances

e-Electron, Tce

(AkRk)b,pe and (AkRk)b,ep

(a)

(b)

(c)

Connector

Lte

ThermoelectricElement

c = 3 nm

a = 0.4 nm

CrystalStructure ofBi2Te3 andSb2Te3

Connector

Figure 2. THERMAL BOUNDARY RESISTANCES ASSOCIATED

WITH PHONON AND ELECTRON HEAT TRANSPORT AT THE

METAL/THERMOELECTRIC INTERFACE: (a) PHONON BOUNDARY

RESISTANCE, b) ELECTRON BOUNDARY RESISTANCE, (c) MIXED

BOUNDARY RESISTANCES.

tact resistances to the heat and current carriers (phononsand electrons) have been included. In the fabrication, thedeposition of patterned conductors on silicon wafers cov-ered with oxide, and the deposition of the thermoelectriccolumns over the conductors are reported and the currentchallenges are discussed.

SMALL-SIZE EFFECTS ON THERMOELECTRICTRANSPORT PHENOMENA

Heat is transferred across a continuous solid junctionby electrons and phonons. The thermal boundary resis-tances associated with the thermoelectric heat transportthrough ideally smooth interfaces are presented in Figure2. A phonon wave incident at the interface will be par-tially transmitted (and partially reflected) due to the mis-match of the acoustic properties of the two materials. Thisphonon wave reflection causes the phonon boundary resis-tance (AkRk)b,pp, as shown in Figure 2(a). A barrier acrossa metal/semiconductor contact associated with a thin oxidelayer forms a electronic potential barrier of thickness d andheight Eo, as shown in Figure 2(b). This barrier representsa resistance to the electronic heat transport across the inter-face, i.e., the electron boundary resistance (AkRk)b,ee. Heat

Phonon-ElectronNon-EquilibriumRegion

ThermalEquilibriumRegion

Te

Tce Tcp

Tp

Tp

Tp = Te

Te

TheThpConnector

δ

Lte

ThermoelectricElement

Lc

(AkRk)c and (AkRe)c

Contact Resistances

(a) (b)

Figure 3. (a) PHONON-ELECTRON NONEQUILIBRIUM NEAR TO THE

BOUNDARY DUE TO THE MISMATCH OF THE ELECTRON AND

PHONON BOUNDARY RESISTANCES. (b) THERMAL AND ELECTRI-

CAL CONTACT RESISTANCES.

can also be directly exchanged between phonons (on oneside of the interface) and electrons (on the other side). Theresistance associated with this heat transfer is the mixedboundary resistance (AkRk)b,pe, or (AkRk)b,ep, as shown inFigure 2(c).

Because the thermal boundary resistances of electronsand phonons are not the same, and due to ohmic heatingand Peltier cooling/heating, electrons and phonons can havedifferent temperatures adjacent to the interface and requirea distance δ (cooling length) to equilibrate. This phonon-electron nonequilibrium region is shown in Figure 3(a).

The thermal (AkRk)c and electrical (AkRe)c contactresistances, shown in Figure 3(b), are due to surface rough-ness and gap at the interface.

The boundary resistances, contact resistances, andcooling length, as well their effects on the thermoelectriccooler performance, are described below.

Phonon Boundary ResistanceThe phonon boundary resistance is due to the mismatch

of the properties of the two materials at an interface. Inour case, the interface is formed by a thermoelectric ma-terial (Bi2Te3 or Sb2Te3) and a conductor (metal connec-tor), which have different densities, Debye temperature andfrequency, and also a different speed of sound, providingresistance to the flow of phonons at the interface.

Two theories have been applied to the prediction ofthe phonon boundary resistance: the acoustic mismatchmodel (AMM) and the diffused mismatch model (DMM).A key assumption of the AMM is that no scattering occurs


at the interface. This is a reasonable assumption at verylow temperatures, where the phonon wavelength is longerthan other interface length scales such as defects and rough-ness. As the temperature increases the phonon wavelengthdecreases, compromising the AMM theory. The DMM as-sumes that all the phonon interactions with the boundaryare diffuse rather than specular.

Phelan (1988) showed that by using the Debye modelfor the phonon density of states, the DMM yields resultsslightly more in agreement with experimental data then theAMM. We will calculate the phonon boundary resistanceRk,b,pp using DMM and compare the results obtained fromthe measured and the Debye densities of states.

The physical system consists of a film (material te, ther-moelectric element) deposited on a substrate (material mc,metal connector). In a typical application, a net heat fluxq is caused by the increase of the film temperature Tte, rel-ative to the substrate temperature Tmc, due to the phononboundary resistance at the interface between the two dis-similar materials, which is given by

(AkRk)b,pp =Tte − Tmc

q. (1)

Phelan (1998) showed that q can be determined by con-sidering only one side of the interface and derived an expres-sion for q as a function of the phonon density of states Pp:

q =hPτte→mc

8π

∑j

up(te,j)× (2)

∫ ∞

ωp=0

Pp(ωp)ωp

[1

exp( hPωp

2πkBTte)− 1

exp( hPωp

2πkBTmc)

]dωp,

where hP is the Planck constant, j is the phonon mode(either longitudinal or transverse), up(te,j) is the speed of thephonon of mode j in material te, ωp is the phonon angularfrequency, kB is the Boltzmann constant, and τte→mc is thetransmission coefficient given by

τte→mc =

∑j

u−2p(mc,j)∑

j

u−2p(te,j) +

∑j

u−2p(mc,j)

. (3)

Equation (2) is numerically integrated to yield a valuefor q, which is substituted into equation (1) to determine(AkRk)b,pp.

Table 1. BULK PROPERTIES OF n- AND p-TYPE PAIR.

Property Bi2Te3 Sb2Te3

TD, K 165 160

a, A 4.38 4.25

c, A 30.36 29.96

αS, µV/K -228 171

k, W/m-K 1.45 1.70

ρe, Ω-m 10−5 10−5

Table 2. MICROSCALE PROPERTIES OF n- AND p-TYPE PAIR.

Property Bi2Te3 Sb2Te3

n, m−3 6.61×1026 7.11×1026

ωD, rad-s−1 2.16×1013 2.09×1013

up, m-s−1 6362 6007

τte→mc 0.76 0.74

The three phonon wave speeds, two transverse and onelongitudinal, were assumed to be equal. So, for material tewe have

∑j

u−2p(te,j) =

1u2

p(te,l)

+2

u2p(te,t)

=3

u2p(te)

. (4)

The phonon speed up is related to the Debye temper-ature TD and Debye angular frequency ωD through the ex-pressions

TD =hPωD

2πkBand ωD =

(6π2u3

pn)1/3

, (5)

where n is the ratio between the number of primitive cellsand the unit volume.

For Bi2Te3 and Sb2Te3, a hexagonal unit cell of dimen-sions a and c is taken to be the primitive cell. The numericalvalues of the lattice parameters a and c, as well the Debyetemperature (Rowe, 1995) used for determining the phononspeed and the transmission coefficient of material te (Bi2Te3

or Sb2Te3), are presented in Table 1. The material mc, as-sumed to be copper, has an average phonon speed equal to3,570 m/s (www.webelements.com). The results obtainedfrom equations (3) and (5) are presented in Table 2.


0 1 2 3 4 5

0.1

0.2

0.3

0.4

0.5

Bi2Te3[Experimental,(Rauh, 1981)]

Sb2Te3[Experimental,(Rauh, 1981)]

fp, THz

Pp,

TH

z-1

Bi2Te3[Debye Model]

Sb2Te3[Debye Model]

Figure 4. VARIATION OF DENSITY OF STATES Pp OF n- AND p-

TYPE PAIR, WITH RESPECT TO FREQUENCY.

The measured (Rauh, et al., 1981) and the Debyephonon density of states (DOS), Pp [THz−1], as a functionof the phonon frequency fp [THz] for the thermoelectricmaterials Bi2Te3 and Sb2Te3 are shown in Figure 4.

To establish Pp as a function of the angular frequencyωp and on a per unit volume basis (i.e., Pp given in[s/rad-m3]), as required by equation (2), the values shown inthe graph are divided by 2π and multiplied by the factor n,defined above. The Debye density of states Pp,D [s/rad-m3]is given by

Pp,D =ω2

p

2π2u3p

. (6)

From the areas below the curves of the Figure 4, onecan predict that the boundary resistances resulting fromthe Debye and the measured DOS will have the same orderof magnitude. This was verified and is shown in Figure 5,where we have assumed Tte − Tmc = 1 K.

For Tte equal to 300 K, the phonon boundary resistancesat the interfaces Bi2Te3/Cu and Sb2Te3/Cu, evaluated asa function of the experimental density of states, are 2.9 ×10−7 K/(W/m2) and 2.5 × 10−7 K/(W/m2) respectively.

Electron Boundary ResistanceThe electron boundary resistance in a thin boundary re-

gion is modelled using a potential barrier with rectangularshape (Bartkowiak and Mahan, 2001). The electrons can betransferred across this barrier by tunneling. Then, the elec-tronic boundary resistance is found from analogy with the

(AkR

k)b,

pp ,

K/(

W/m

2 )

Tte , K

Experimental DOS Sb2Te3

Debye DOS Sb2Te3

Experimental DOS Bi2Te3

Debye DOS Bi2Te3

0 50 100 150 200 250 300 35010-8

10-7

10-6

Tte - Tmc = 1 K

Figure 5. VARIATION OF BOUNDARY RESISTANCE (AkRk)b,pp OF

n- AND p-TYPE PAIR, WITH RESPECT TO TEMPERATURE.

thermal (electronic) conductivity given by the Wiedemann-Fanz law,

1(AkRk)b,ee

=π2

3T

(AkRe)b

(kB

ec

)2

, (7)

where (AkRe)b is the electrical boundary resistance givenby

1(AkRe)b

=4πe2

cmeP

h3P

[h2

PEo

8π2med2

]1/2

, (8)

me is the effective mass of the electrons in the barrier, Eo

is the potential barrier height, d is the barrier thicknessand P is the tunneling probability. Tunneling occurs if[h2

PEo/(8π2med2)]−1/2kBT 1.

For thick barriers the dominant transport mechanism isthermionic emission. Then, π2/3 in equation (7) is replacedby 2, and the electrical boundary resistance is given by

1(AkRe)b

=ecBTe−Eo/kBT

kB, (9)

where B = 120 A/cm2-K2, and Eo ≥ 2kBT (Mahan et al.,1998).

In order to choose between tunneling and thermionicemission, Eo and d should be estimated. It is known thatsilicon devices are likely to contain a thin (5 to 25 A) ox-ide layer between the metal and the semiconductor (Pier-ret, 1996), and that tunneling barriers in tunnel junctionsare typically 10 to 40 A thick oxides (Smith et al., 1980).


This indicates that tunneling may be the electron trans-port mechanism here, and therefore, we use equation (7) toevaluate the electron boundary resistance.

To estimate (AkRe)b, we assume that the potentialbarrier is thick enough (threshold) for thermionic emis-sion. In this limit Eo is equal to 2kBT . Then, from equa-tion (9), for room temperature, we have (AkRe)b equal to2×10−12 Ω-m2. Using this in equation (8), with me equalto 3.825×10−31 kg (effective mass of the electrons in aoxide layer) (Nassibian and Duong, 1985), and assuming[h2

PEo/(8π2med2)]−1/2 equal to 3 eV−1 (Bartkowiak and

Mahan, 2001), the tunneling probability P was found equalto 0.02. Lee et al. (1994) measured the electron transmis-sion probability across CoSi2/n-Si(111) interfaces and re-ported that for voltages drop across a 72 A thick junction,which were varied from 1 to 4 V, the tunneling probabilityvaried from 0.005 to 0.055. For a 25 A thick junction (un-der the same voltage drop variation), the tunneling proba-bility varied from 0.05 to 0.6. These results indicate that atunneling probability of 0.02, as found from equation (8), isreasonable for a barrier with d between 25 and 72 A. There-fore, (AkRe)b equal to 2×10−12 Ω-m2 is also reasonable fortunneling. Using this in equation (7), we have (AkRk)b,ee

equal to 2.7 × 10−7 K/(W/m2).

Total Thermal Boundary ResistanceThe total thermal boundary resistance Rk,b is given by

1Rk,b

=1

Rk,b,pp+

1Rk,b,ee

+1

Rk,b,ep+

1Rk,b,pe

. (10)

Assuming for simplicity that there is no direct heattransfer between electron and phonon subsystems acrossthe boundary, i.e., Rk,b,pe and Rk,b,ep → ∞, the total ther-mal boundary resistance is evaluated from equation (10)as a function of the phonon and electron boundary resis-tances only. Therefore, at the interfaces Bi2Te3/Cu andSb2Te3/Cu, the total thermal boundary resistances are 1.4× 10−7 K/(W/m2) and 1.3 × 10−7 K/(W/m2) respectively.In the micro cooler model we have considered (AkRk)b equalto 10−7 K/(W/m2) for both n- and p-type thermoelectricmaterials.

Phonon-Electron NonequilibriumThe fact that electrons and phonons are in thermal

nonequilibrium causes the appearance of the length scaleδ (cooling length), which is the distance from the boundaryrequired for electrons and phonons to reach equilibrium, asshown in Figure 3(a).

The cooling length δ is estimated from the relation

δ2 = Deτe−p, (11)

where τe−p is the electron-phonon relaxation time and De

is the electron diffusivity given by the Einstein relation

De =kBµeT

ec. (12)

The mobility of the free carriers µe is reported by Zou etal. (2001b) as 75 cm2/V-s for Bi2Te3 and 173 cm2/V-s forSb2Te3. The electronic charge ec is equal to 1.602 × 10−19

C and the temperature T is assumed 300 K. Fleurial et al.(1988) determined the relaxation time τe−p for the n and p-type bismuth telluride thermoelectric materials as 4×10−13

s and 3 × 10−13 s respectively. Then the cooling length δwas found equal to 9 nm (De = 194×10−6 m2/s) and 12 nm(De = 447×10−6 m2/s) for Bi2Te3 and Sb2Te3 respectively.

Thermal Resistance of Thermoelectric ElementThe thermal resistance Rk,h−c of a thermoelectric el-

ement with length Lte, which takes into account theboundary phenomena, including phonon-electron thermalnonequilibrium, is given by (Bartkowiak and Mahan, 2001),

Rk,h−c

Lte

Akk

=R∗

e + R∗eR∗

p(1+γ)2

2R∗k

+ γL∗tecothL∗

te

(1+2R∗k)−1 + R∗

pγ2

γL∗tecothL∗

te + R∗eR∗

p(1+γ)2

2R∗k

, (13)

where γ = ke/kp,

R∗e =

Rk,b

Rk,b,e, R∗

p =Rk,b

Rk,b,p, R∗

k =Rk,b

Lte

Akk

, L∗te =

Lte

2δ, (14)

(Rk,b,e)−1 = (Rk,b,ee)

−1 + (Rk,b,ep)−1

, (15)

and

(Rk,b,p)−1 = (Rk,b,pp)

−1 + (Rk,b,pe)−1

. (16)

Note that Rk,h−c is greater than the bulk resistanceLte/(Akk) due to the thermal boundary resistances and thephonon-electron nonequilibrium. This increase in Rk,h−c

reduces the undesirable heat conduction from the hot tothe cold junctions.


δ , nm

(AkRk)b,ee = (AkRk)b,ee = 10-6 K/(W/m2)

(AkRk)b,ee =10-4 (AkRk)b,pp = 2.9 x 10-7

(AkRk)b,ee = 2.7 x 10-7 (AkRk)b,pp = 2.9 x 10-7

Bi2Te3Lte = 4 µm

1 10 3 10 4

Rk,

h-c

/(L

te /A

kk)

1

1.2

1.4

1.6

1.8

δ = 10 nm δ = Lte /2

10 2

Eq. (13)Eq. (17)

Figure 6. VARIATION OF THE THERMAL RESISTANCE Rk,h−c OF

THE THERMOELECTRIC ELEMENT, WITH RESPECT TO THE COOL-

ING LENGTH δ.

For Lte 2δ, equation (13) becomes

(Rk,h−c)i

Lte

Akki

= 1 +2(Rk,b)i

Lte

Akki

, (17)

where i = n, p (n- and p-type thermoelectric elements) andAk is the cross-sectional area. Note that the bulk thermalconductivity k is the sum of the phonon kp and electron ke

thermal conductivities.Based on the values we have estimated for the cooling

length and Lte = 4 µm, Lte/2δ = 222 (δ = 9 nm) and 167(δ = 12 nm), i.e., Lte/2δ 1, so equation (17) is valid forthe micro cooler model.

In Figure 6, the effect of δ on the thermal resistanceRk,h−c is presented. For δ Lte/2, equation (13) reducesto equation (17). Note that δ can affect Rk,h−c only whenRb,pp and Rb,ee are different. For the predicted bound-ary resistances [(AkRk)b,pp = 2.9 × 10−7 K/(W/m2) and(AkRk)b,ee = 2.7 × 10−7 K/(W/m2)] and cooling length(δ = 9 nm) of the Bi2Te3 thermoelectric element, the in-crease in Rk,h−c is only 10%. For (AkRk)b,ee greater than(AkRk)b,pp, the total thermal boundary resistance is dom-inated by the phonon contribution, i.e., (AkRk)b,pp is itsupper limit. In this case, the increase is about 20% (for δ= 10 nm). In the case where the electron and phonon con-tribution to the total thermal boundary resistance are thesame, but one order of magnitude higher than the predictedboundary resistances, the increase would be around 35%.

Seebeck Coefficient of Thermoelectric ElementBartkowiak and Mahan (2001) have reported that, for

δ Lte/2,

αS = αS,b +αS,bulk − αS,b

2k(AkRk)b

Lte+ 1

, (18)

where the boundary Seebeck coefficient αS,b is given by

αS,b =(

kB

ec

)π2

3kBT

[h2

PEo

8π2med2

]−1/2

, (19)

assuming that tunneling is the dominant electron transportmechanism across the metal/semiconductor interfaces.

Taking [h2PEo/(8π2med

2)]−1/2 equal to 3 eV−1

(Bartkowiak and Mahan, 2001), we found αS,b equal to22 µV/K. The bulk Seebeck coefficient is given in Table1 for the n- and p-type thermoelectric materials. Basedon the predicted boundary resistances, we found a reduc-tion of 10% in the bulk Seebeck coefficient. This reductionis undesirable since it decreases the thermoelectric energyconversion.

Further examination of small-size effect on the Seebeckcoefficient is underway, and the results will be later includedin the micro cooler model.

Thermal and Electrical Contact ResistancesThe thermal and electrical contact resistances at

metal/thermoelectric interfaces, and the thermal contact re-sistance at metal/electrical-insulator interfaces of the microcooler, reduce the device performance. The effect of thethermal contact resistance is a discontinuity of the temper-ature gradient at the interface in the presence of a heat flow.An electrical contact resistance increases the total electricalresistance of the circuit, and generates Joule heating at thejunctions.

Thermal Contact Resistance. Lahmar et al. (2001)performed an experimental investigation on the thermalcontact resistance between gold coating and ceramic sub-strates, and showed that thermal treatment increases sig-nificantly the adhesion and reduces the thermal contactresistance between the two materials. The contact resis-tance decreased from 10−7 to less than 10−8 K/(W/m2)after thermal treatment.

Orain et al. (2001) set up a measurement techniquefor determining the thermal conductivity of dielectric thinfilms. It was reported that for films thicker than 1 µm,the film thermal conductivity is equivalent to the value forthe bulk material. For thinner films, a drop in the con-ductivity was observed, revealing the importance of thefilm/substrate contact resistance. The effect of the layer-ing technique and the nature of the metal and substrate


on the contact resistance was also presented. Contacts ofAu/Al2O3 and Au/SiO2 formed by evaporation had resis-tances estimated on the order of 1 to 2×10−7 K/(W/m2).

Based on the above results we have assumed a ther-mal contact resistance (AkRk)c of 10−7 K/(W/m2) for thepredictions from the micro cooler model.

Electrical Contact Resistance. In macroscopic ther-moelectric devices, electrical contact resistance (AkRe)c be-tween the semiconductor and metal electrodes has been re-ported to typically be between 10−8 and 10−9 Ω-m2, whenstandard techniques for making a junction (such as solder-ing or hot pressing) are used (Goldsmid, 1986; Ilzycer, etal., 1980). However, films with micron or submicron thick-ness are produced using thin-film growth techniques (e.g.,evaporation or sputtering), and the resistances are expectedto be much smaller.

If it is assumed that there is no gap in the contactzone, then the electrical contact resistance (AkRe)c is thatbetween the two materials at the interface (for example,Bi(Sb)-Te/metal). Choosing the highest electrical resistiv-ity between these materials, which is 10−5 Ω-m (for Sb2Te3

and Bi2Te3, as presented in Table 1), and estimating thelength of the contact Lc equal to 100 nm, it would result in(AkRe)c equal to 10−12 Ω-m2.

Equation (7) expresses the relation between the ther-mal (electronic contribution) and electrical resistances:(AkRk)b,ee and (AkRe)b when used for boundary resis-tances, or (AkRk)c,e and (AkRe)c when used for contactresistances. For bismuth telluride, the electron thermal con-ductivity ke is estimated to be 25% of the bulk thermal con-ductivity k (Bartkowiak and Mahan, 2001). Assuming thesame contribution for the thermal contact resistances, wehave (AkRk)c,e = 0.25 (AkRk)c. Then, from equation (7),for T = 300 K, (AkRe)c is equal to 1.8×10−13 Ω-m2.

Jaeger (1988) has reported electrical contact resistancesfor a variety of aluminum-silicon systems, which range from10−5 to 10−10 Ω-m2 as a function of annealing temperature.

Under well-controlled laboratory conditions, measuredelectrical contact resistance between Si and Pt have beenreported to be 5×10−12 Ω-m2, and between Si and Al, 1 to2×10−11 Ω-m2 (Wolf, 1990). Si/metal is not a type of elec-trical contact found in the thermoelectric cooler, but this isconsidered a good indication that the electrical resistivityof the Bi(Sb)-Te/metal contact can be less or equal than2 × 10−11 Ω-m2, since the electrical resistivity of Si (10−4

Ω-m) is higher than the resistivity of the thermoelectric el-ements.

Until we measure the electrical contact resistance of theBi(Sb)-Te/metal contacts, (AkRe)c equal to 2×10−11 Ω-m2

is assumed for the model calculations.

FILM THICKNESS CONSIDERATIONSThe thermoelectric element thickness is limited by the

film deposition process. From the model analysis it wasverified that the aspect ratio Lte/dte affects the device per-formance, and that aspect ratios on the order of unity aredesirable for dte between 7 and 11 µm.

Zou et al. (2000b, 2001b) has reported the growth of p-type Sb2Te3 and n-type Bi2Te3 thin films (700 nm) withhigh Seebeck coefficient by means of co-evaporation. Anumber of other techniques have been used to grow Bi(Sb)-Te thin films, such as flash evaporation (Damodara Dasand Selvaraj, 2000), sputtering (Stark and Stordeur, 1999),pulsed laser deposition (Yamasaki, et al., 1998) and molec-ular beam method (Nurnus, et al., 2000). However, theseprocesses often require either long material preparation pe-riods or relatively complicated and expensive equipment. Incomparison, co-evaporation offers the advantage of a shortfabrication process time and requires simpler equipment,resulting in much lower fabrication costs. Moreover, it iscompatible with microdevice fabrication process.

Using direct evaporation of compounds we have de-posited 4 µm thick Bi2Te3 and Sb2Te3 films. However, thestoichiometry of these films is not constant along the thick-ness, resulting in non-desirable thermoelectric properties,as will be discussed in subsequent section. The evaporationset up is being modified to allow the co-evaporation of theelements and the deposition of films as thick or thicker than4 µm that would have high Seebeck coefficients. Therefore,the model predictions are based on Lte equal to 4 µm.

GEOMETRY OPTIMIZATIONThe heat flow path in the micro thermoelectric cooler

is shown in Figure 1 and the various parameters used in themodel are indicated in Figure 7. The surface convectionand the radiation heat transfer between the heat sink andthe vapor sensor are neglected as the conduction resistancesof the films are much smaller than the surface radiation re-sistance and the air conduction resistance (all in parallel).It is also assumed that the Joule heating in the thermoelec-tric material is equally split between the top and bottombounding surfaces. So, at the cold junction,

Qc + Qk,c−h = (Se,J)c + (Se,J)cc + (Se,P)c, (20)

and at the hot junction,

Qh + Qk,h−c = (Se,J)h + (Se,J)hc + (Se,P)h. (21)


Heat Sink, ksink

Load(Vapor Sensor)

nkn

pkp

n

Cold Connector, cc

Hot Connector, hc Tc

Th(Rk,b)n

Rk,c3 Re,c3

Thermoelectric Element, te

di

Li

ai

i = te, cc, hc

Je

-Qc (t)

Qh T

(Rk,b)p

Tl

ElectricalInsulation

ElectricalInsulation

Figure 7. VARIOUS PARAMETERS OF THE MICRO THERMOELEC-

TRIC COOLER.

Qk,h−c is the heat transferred from the hot to the coldsurface by conduction,

Qk,h−c =Th − Tc

Rk,h−c= −Qk,c−h. (22)

The thermal resistance Rk,h−c is given as a function of thenumber of pairs Nte by

1Rk,h−c

= Nte

[1

(Rk,h−c)p+

1(Rk,h−c)n

], (23)

where (Rk,h−c)i is given by equation (17). The total ther-mal boundary resistance (AkRk)b was taken to be equalto 10−7 K/(W/m2) for both n- and p-type thermoelectricmaterials, as discussed in a previous section.

Qc and Qh are the heat transferred from the load (vaporsensor) to the cold surface and from the hot surface to theheat sink respectively:

Qc = −Tl − Tc

Rk,c−land Qh =

Th − T∞Rk,h−∞

. (24)

At the cold side,

1Rk,c−l

= Nte1

Rk,c1 + Rk,cc + Rk,c2, (25)

and at the hot side,

1Rk,h−∞

= Nte1

Rk,c3 + Rk,hc + Rk,c4 + Rk,sink. (26)

Note that the thermal contact resistances between thethermoelectric elements and connectors are (Rk,c1)−1 =(Rk,c3)−1 = 2Ak(k/L)contact and between the connec-tors and the electrical insulator films are (Rk,c2)−1 =Acc(k/L)contact and (Rk,c4)−1 = Ahc(k/L)contact, where(k/L)contact was assumed equal to 107 (W/m2)/K, as dis-cussed in a previous section. The thermal resistances of theconnectors are (Rk,i)−1 = (Ak/L)i, where i = cc, hc, andthe thermal resistance of the heat sink (including the elec-trical insulator film), which was assumed an infinite solid,is (Rk,sink)−1 = ln(4ahc/dhc)/(πksinkahc) (Kaviany, 2001).

(Se,P)c is the Peltier cooling at the cold junction and(Se,P)h is the Peltier heating at the hot junction, given by

(Se,P)c = −NteαSJeTc and (Se,P)h = NteαSJeTh, (27)

where αS = αS,p − αS,n is the sum of the Seebeck coeffi-cients of the n− and p−type materials and Je is the electriccurrent flowing along the thermoelectric elements and metalconnectors.

(Se,J)c and (Se,J)h are the portions of the Joule heating(generated in the thermoelectric elements) assigned to thecold and hot junctions respectively. Note that the Jouleheating generated at the metal/thermoelectric contacts isalso being considered,

(Se,J)c = (Se,J)h =12Je

2Re,h−c +12Je

2Re,c. (28)

The electrical resistance of the thermoelectric elements is

Re,h−c = Nte

(ρe,pLte

Ak+

ρe,nLte

Ak

), (29)

where ρe is the electrical resistivity. The contact electricalresistance is

Re,c =4Nte(AkRe)c

Ak, (30)

where (AkRe)c was taken to be equal to 2×10−11 Ω-m2, asdiscussed in a previous section.

(Se,J)cc and (Se,J)hc are the Joule heating generated inthe cold and hot connectors respectively, given by

(Se,J)i = Je2Re,i , where i = cc, hc , (31)

and

Re,cc = Nte

(ρea

dL

)cc

; Re,hc = Nte

(ρea

dL

)hc

+Re,pads. (32)


(AkRk)b = 10-7 K/(W/m2)(AkRk)c = 10-7 K/(W/m2)(AkRe)c = 2 x 10-11 Ω-m2

Qc = -15 mWLte = 4 µmT - Tl = 20 KT = 298 K

dte = 11 µm

9 µm

7 µm

dte = 11 µm

9 µm

7 µm

∆ϕ ,

V

0

2

4

6

8

10

12

Nte

0 50 100 150 200 250 3000

J e ,

mA

5

10

15

20

25

30

(a)

(b)

∆ϕ = 3 V

Figure 8. VARIATION OF REQUIRED (a) VOLTAGE AND (b) CUR-

RENT, WITH RESPECT TO NUMBER OF PAIRS.

Note that Re,pads is the electrical resistance between thecontact pads and initial thermoelectric structures of thecooler device. Based on measurements of preliminary fab-ricated structures, we have estimated Re,pads equal to 50Ω.

Therefore, the total electrical resistance of the devicecan be expressed as

Re = Re,h−c + Re,cc + Re,hc + Re,c, (33)

and the total power consumed as

Pe = ReJe2 + (Se,P)h + (Se,P)c = ∆ϕJe, (34)

where ∆ϕ is the voltage required.The coefficient of performance is given by

COP = −Qc

Pe. (35)

The calculations were performed as a function of thethermal and electrical properties of the thermoelectric ma-terials (Zou, et al., 2001b) presented in Table 1.


dte = 11 µm

9 µm

7 µm

NteP

e , m

W

0

4

8

12

16

20

24

0 50 100 150 200 250 300

dte = 11 µm

9 µm7 µm

Qc = -15 mWLte = 4 µmT - Tl = 20 KT = 298 K

0

0.1

0.2

0.3

0.4

CO

P

Pe, min = 40 mW

COPmax = 0.38

(a)

(b)

Figure 9. VARIATION OF (a) POWER REQUIREMENT AND (b) CO-

EFFICIENT OF PERFORMANCE, WITH RESPECT TO NUMBER OF

PAIRS.

In Figure 8 it is shown the current and voltage requiredas a function of the number of thermoelectric pairs, for Tl−T∞ = 20 K, Qc = −15 mW, Lte = 4 µm and Ak = dte

2. For∆ϕ = 3 V, the micro cooler will need 20 to 40 thermoelectricpairs, as indicated by the shadowed area.

The device power requirement and coefficient of perfor-mance are shown in Figure 9. Note that the voltage re-striction requires the micro cooler to work below optimumconditions. The minimum dimension dte = 7 µm has beenchosen due to the limitations on the minimum feature size(3 µm) obtained in the micro fabrication process. This isa safe choice and therefore, we will be working on reduc-ing this limit since it would improve the device operationalconditions.

The definition of the cross-sectional area of the thermo-electric elements (i.e., dte

2) is a compromise between reduc-ing the conduction heat transfer (a small area is desirable)and reducing the resistance to the flow of electrons (a largearea is desirable), which causes the undesirable Joule heat-ing generated in the system. Both, conduction and Jouleheating, increase with the number of pairs, causing the de-crease in the device performance.

For a given load, as the number of pairs increases,


30

20

10

010-8 10-7 10-6 10-5

T

- T

l , K

AkRk , K/(W/m2)

Boundary

Contact

T

- T

l , K

30

20

10

010-13 10-12 10-11 10-10 10-9

(AkRe)c , Ω-m2

(AkRe)c = 2 x 10-11 Ω-m2

(AkRk)b = 10-7 K/(W/m2)(AkRk)c = 10-7 K/(W/m2)

Qc = -15 mWNte = 30dte = 9 µmLte = 4 µm∆ϕ = 3 V


(a)

(b)

Figure 10. VARIATION OF LOAD TEMPERATURE DECREASE T∞ −Tl, WITH RESPECT TO (a) THERMAL (BOUNDARY AND CONTACT)

AND (b) ELECTRICAL RESISTANCES.

the current needed in the system to achieve the desirable(T∞ − Tl) is decreased, since each thermoelectric pair re-ceives a smaller portion of the load. This has a positive ef-fect on the reduction of the power required [equation (34)],which when combined with the negative effect of the elec-trical resistance, results in a minimum power and maximumcoefficient of performance, as observed in Figure 9.

Having defined the number of pairs as a function ofthe voltage, the effect of the thermal and electrical resis-tances on the reduction of the vapor sensor temperaturewas explored and is shown in Figure 10. The assumed re-sistances are also shown. The total thermal boundary resis-tance is a function of the boundary resistances of phonons(estimated using DMM) and electrons (estimated assum-ing electron tunneling and using the Wiedemann-Franz lawat the boundaries), while the electrical contact resistancewill depend on the well-control of fabrication conditions. Itis shown that increasing the electrical and thermal contactresistances by one order of magnitude will deteriorate thecooling performance (T∞ − Tl). Therefore, it is the impor-tant to fabricate films with low contact resistances.

In Figure 11(a) the effect of the film thickness on the

0

T

- T

l , K

Lte , µm


dte = 11 µmQc = -15 mWNte = 30∆ϕ = 3 V

9 µm

7 µm

5

10

15

20

25

30

0 2 4 6 8 10 12 14 16 18 20

T

- T

l , K

(a)

(b)

0

5

10

15

20


αS /αS, bulk

0.4 0.5 0.6 0.7 0.8 0.9 1


δ = 10 nm

3 Κ

Figure 11. VARIATION OF LOAD TEMPERATURE DECREASE T∞ −Tl, WITH RESPECT TO (a) THERMOELECTRIC ELEMENT LENGTH

AND (b) REDUCTION IN SEEBECK COEFFICIENT.

device cooling performance is presented. The optimum val-ues observed are due to the opposite effects of increasingthe electrical (undesirable) and conduction (desirable) re-sistances of the thermoelectric elements. The model pre-dictions are based on Lte = 4 µm, which has been, so far,a fabrication limit, as discussed previously. Based on theresults shown, we will work towards increasing the thermo-electric film thickness to Lte dte.

In Figure 11(b) the effect of the reduced Seebeck coeffi-cient on the cooling performance is presented. Preliminarypredictions have resulted in a reduction of 10% on the See-beck coefficient (for a cooling length δ equal to 10 nm),which would correspond to a decrease of 3 K in cooling ca-pability.

FABRICATIONBased on the predictions from the thermoelectric cooler

model, a device has been designed to cool a vapor sen-sor with dimensions 1500 × 1500 × 50 µm3 by 20 K, infew seconds (load of 15 mW), using a battery of 3 V. Thefabrication process has begun and the hot connectors and


Sb2Te3

Bi2Te3

p-type n-type

SiO2

TiPt

Si

20 µm4 µm

600 µm

0.12 µm

Pt

(a)

(b)

Figure 12. Sb2Te3 AND Bi2Te3 THERMOELECTRIC ELEMENTS ON

Pt FILM PATTERN (HOT CONNECTORS). (a) SKETCH SHOWING

THICKNESSES OF THE FILMS. (b) SEM SHOWING FABRICATED

STRUCTURES.

thermoelectric elements have been deposited. As follows,the fabrication steps will be described and the results sofar obtained from the thermoelectric film deposition will bepresented.

The substrate used for device fabrication is a 4 in. sil-icon wafer, 500 µm thick, which is the micro cooler heatsink. A layer of silicon oxide (SiO2) is grown on top ofthe Si wafer for electrical insulation, and photoresist (PR)is spun, for subsequent alignment and exposure of the firstmask that defines the pattern of the hot connectors andelectrical connectors (pads). Platinum has been evaporated(on top of a thin layer of Ti for adhesion) as the first layerof connectors. However, the actual device will have thePt replaced by a low electrical resistivity and high thermalconductivity material (copper or gold). A new photolithog-raphy process defines the area (exposure of a second mask)where the n-type (or p-type) thermoelectric element (TE)will be formed. Once the thermoelectric film is deposited,the PR is removed, leaving the first TE on top of the hotconnectors. This process is repeated (exposure of a thirdmask) for the deposition of the p-type (or n-type) TE. TheSb2Te3 and Bi2Te3 columns deposited on the Pt pattern areshown in Figure 12.

In Figure 13, two different geometries and configura-tions of the thermoelectric cooler are shown, with the n-

Ti/Pt

Sb2Te3

7 µmBi2Te3

Pad200 x 200 µm2

Sb2Te3

Bi2Te3

Ti/Pt

40 µm

(a)

(b)

Figure 13. TOP VIEW OF Sb2Te3 AND Bi2Te3 THERMOELECTRIC

ELEMENTS ON Pt FILM PATTERN, WHERE (a) Nte = 50, dte = 7µm and (b) Nte = 15, dte = 40 µm.

and p-type columns deposited on Pt film pattern. Besidesthe optimum geometry, we have designed and we are fab-ricating micro thermoelectric coolers with up to 300 pairsand with different cross-sectional areas of the columns.

In Figure 14, the steps needed to be completed in thefabrication process are presented. A contact area is definedon top of each TE by exposure of a fourth mask [Figure14(a)]. After developing the PR, a thin Ti/Cu layer is de-posited by sputtering. A new photolithography process isrequired for exposure of the fifth mask that defines the areawhere copper (the metal that forms the cold connectors) willbe deposited [Figure 14(b)]. The thin Ti/Cu layer works asan electrode for the electrochemical deposition of a thickerlayer of copper that closes the electrical circuit of the ther-moelectric cooler [Figure 14(c)]. A contact area on top ofthe cold connectors needs to be opened (exposure of a sixthmask) for deposition of SnPb that will bond the micro coolerto the vapor sensor, as shown schematically in Figure 15.

A cross-sectional view of Bi2Te3 film deposited by the


PRPRPR

SiSiO2

TiPt

PR PR

PRPRPR

Si

Ti/CuCu

4 µm

600 µm

0.12 µm

Si

1.25 µm

(a)

(b)

(c)

Figure 14. STEPS TO BE COMPLETED IN THE FABRICATION PRO-

CESS: (a) CONTACT OPENING FOR Ti/Cu, (b) CONTACT OPENING

FOR Cu, AND (c) STRUCTURE THAT WILL BE BONDED TO THE VA-

POR SENSOR.

direct evaporation of the compounds is shown in Figure16(a). The film stoichiometry was examined by energy dis-persive X-ray analysis (EDX) and it was observed that theatomic ratio between tellurium and bismuth is not uniformalong the thickness. This is caused by the large difference inthe temperatures at which the elements evaporate or sub-limate during the deposition process, as presented in Table3 (Graper, 1987). A similar result was obtained for theSb2Te3 film, whose cross-sectional view can be seen in Fig-ure 17. Note that, for both films, the stoichiometry mea-sured in an area that covers Lte is close to the expectedvalue of 1.5 for both compounds. This means that all ma-terial evaporated or sublimated from the thermal sourcewas deposited on the wafer, but Bi2Te3 or Sb2Te3 were notformed (also verified by crystal structure analysis using X-Ray diffraction). The effect of this noncongruent stoichiom-etry along the film thickness is seen in the poor values of themeasured Seebeck coefficients for these films. As previouslydiscussed, co-evaporation of the elements will be used withsubstrate heating control.

The cross-sectional view of the Bi2Te3 film, after be-ing polished and ion milled, is shown in Figure 16(b). Theintention was to have a closer examination of the interfacebetween the thermoelectric element and the connector. Thepolishing started with silicon carbide papers (600 and 1200grit) and finished with lapping silicon carbide films (5 and1 µm). It was verified along the process that both thermo-

Si

SiO2(ElectricalInsulation)

SnPb(Solder)

Sb2Te3(p-Type)

SiO2(ElectricalInsulation)

Vapor Sensor

Si Wafer (Heat Sink)

50 µm

1 µm

6 µm

600 µm

Cu

Bi2Te3(n-Type)

Pt(Replaced byAu or Cu)

Figure 15. PLANNED BONDING OF THE MICRO COOLER TO THE

VAPOR SENSOR.

Table 3. MELTING (Tsl) AND EVAPORATION/SUBLIMATION (Tsg)

TEMPERATURES OF THERMOELECTRIC ELEMENTS, FOR p =10−6 Torr.

Element Tsl, oC Tsg, oC

Bi 271 410

Sb 630 345

Te 452 207

electric materials are soft compared with the Pt film and theSi wafer, and that under stress, the adhesion of the thermo-electric film can be compromised. No gaps were observedat the Bi(Sb)-Te/Pt interface, and in general, it seemed asgood as the interface of Si/Pt. However, no conclusionsregarding contact resistances can be inferred yet.

The material selection for the cold and hot connec-tors (metals) is also based on the thermoelectric mate-rials. Efforts will be made on increasing adhesion atthe metal/thermoelectric interfaces (decrease contact resis-tances), and avoiding diffusion of the metal into the thermo-electric materials (maintaining thermoelectric properties).

SUMMARYThe thermal resistance of the thermoelectric elements

increases with the thermal boundary resistance, while theSeebeck coefficient may decrease. The phonon boundary


500 nm

Lhb = 180 nm

ThermoelectricElement (Bi2Te3)

(a)

(b)

Heat Sink (Si)

2 µm

Lte = 3.5 µm, (Bi2Te3)

Hot Connector (Pt)

Heat Sink (Si)

At% TeAt% Bi

= 15

At% TeAt% Bi

= 1.5

At% TeAt% Bi

= 0.2

At% TeAt% Bi

= 1.5

Hot Connector (Pt)

Figure 16. CROSS SECTIONAL SEM OF Bi2Te3 FILM DEPOSITED

ON Pt FILM, (a) NOT PROCESSED AND (b) POLISHED AND ION

MILLED.

2 µm

Hot Connector (Pt)

Heat Sink, (Si)

Lte = 4.5 µm, (Sb2Te3)

At% TeAt% Sb

= 2.8

At% TeAt% Sb

= 1.6

At% TeAt% Sb

= 0.4

At% TeAt% Sb

= 1.3

Figure 17. CROSS SECTIONAL (not processed) OF Sb2Te3 FILM DE-

POSITED ON Pt FILM.

resistances estimated by the DMM theory, using the mea-sured and Debye density of states, are similar, and in agree-ment with that in literature. The electrical boundary resis-tance was estimated assuming electron tunneling and us-ing the Wiedemann-Franz law at the boundaries. As thethermoelectric film is much thicker than the cooling length,the phonon-electron nonequilibrium adjacent to boundariesdoes not affect the thermal resistance. The reduction in theSeebeck coefficient, due to boundary effects, will be includedin the model.

Thermal and electrical contact resistances are detri-mental to the device performance. To date, both resis-tances were estimated using experimental results available

in literature, however, measurements of these resistancesare planned. Well-controlled fabrication conditions are thekey to obtaining low contact resistances.

The length of the thermoelectric element Lte = 4 µmhas been limited by the film deposition technique. We havefound that the aspect ratio Lte/dte of the columns should bearound unity in order for the micro cooler to provide optimalcooling. As dte is constrained by the fabrication processto be greater than or equal to 7 µm, we plan to increasethe film thickness, while obtaining desirable thermoelectricproperties.

From the device modeling we have predicted (for ∆ϕequal to 3 V) that a device with number of pairs Nte equalto 30, Lte equal to 4 µm and dte equal to 7 µm, can decreasethe vapor sensor (load Qc equal to 15 mW) temperature by20 K, with a power required Pe equal to 48 mW, electricalcurrent Je equal to 16 mA, and coefficient of performanceCOP equal to 0.3.

In the fabrication, besides the improvements neededin the film deposition process that will lead to a uniformspecies distribution and low contact resistances, the reduc-tion of the minimum feature size (dte currently equal to 7µm) will be pursued, with the goal of 3 µm (which is achiev-able in integrated-circuit fabrication processes).

ACKNOWLEDGMENTThis work was supported by the Engineering Research

Center Program of the National Science Foundation underAward Number EEC-9986866, at the University of Michi-gan’s Wireless Integrated Micro Systems (WIMS) Centerand by the Conselho Nacional de Desenvolvimento Cien-tifico e Tecnologico - CNPq, Brazil (LWDS). The authorsare also thankful to Professors K. Wise and T. Zellers forthe help on the design, as well to Dr. D. McGregor and A.DeHennis for the help on the fabrication process.

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