thermoelectric modules

8/10/2019 Thermoelectric Modules

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Thermoelectric Modules: Principles and

Research

InterPACK 2011 Tutorial

Marc Hodes

Tufts [email protected]


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Outline1. Thermoelectric Effects

Seebeck Effect

Peltier Effect

Thomson Effect

Accompanying Irreversible Effects

2. Thermocouple Thermometry

3. Thermoelectric Modules (TEMs)

Construction

Benefits and Shortcomings

Applications

4. Analysis of Thermoelectric Modules

Controlled/Uncontrolled Side Formulation

Heat Conduction

Electrical Contact Resistance

TEMs Embedded in a Thermal Resistance Network

5. TEM Operating Mode Maps


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6. Techniques for Enhancement

Introduction

Optimal Pellet Geometry for Thermoelectric Refrigeration

Optimal Pellet Geometries for Thermoelectric Power Generation

Heat Pipe-TEM Assemblies

Non-Cartesian TEMs

7. Summary


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1. Thermoelectric Effects


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Thermoelectric Effects

Seebeck Peltier ThomsonSeebeck Experiment

Electrical energy may be reversibly converted into thermal energy and vice versa

by three thermoelectric effects.

Thermoelectr ic effects, i.e., the Seebeck effect, Peltier effect and Thomson effect

are named after the person who fi rst observed or predicted them.

Chronology.

1821: Seebeck observes compass needle deflect near loop formed by dissimilarconductors.

1835-1838: Pelt ier discovers Pelt ier effect and Lenz uti lizes it to reversibly freeze water

& melt ice.

1838-1850: Very litt le interest in thermoelectrici ty dur ing the era of electromagnetism.1851: Thomson predicts the existence of the Thomson effect.


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ThotTcold

e-s transport by electrostatic forces

thermal diffusion of e-sSeebeck Voltage

Seebeck voltage generated in (+)isolated conductor subjected to a

temperature difference.

Seebeck effectWhat is i t? Generation of a voltage gradient in electrically conductors

(including semiconductors) subjected to temperature gradients under opencircuit conditions.

Why does it occur? Thermal di ffusion causes a net flux of electrons (or

holes) along or against temperature gradients thereby generating voltage

gradients. At equilibrium, net flux of charge carriers due to electrostatic

forces balances that due to thermal diffusion.

How is it mathematically described? dV = dT, where V = voltage and =

Seebeck coefficient in V/K.

Additional Remarks

is + or - depending on materials scattering properties. It is low in metals, butmoderate in semiconductors, and temperature dependent.

The Seebeck effect is a bulk effect.

The Seebeck coeffic ient is a temperature dependent property.


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Similarities between Seebeck effect and p-n junctions.

Generate voltages in isolated mediums by diffusion, i.e., Seebeck voltage and

contact potential difference.

Cause transient current to f low in isolated medium.

Generated vol tage highest for semiconductors.

Differences between Seebeck effect and p-n junctions.

Seebeck vol tages arises due to thermal dif fusion, whereas contact potential

difference is due to mass diffusion (of electrons and holes).Seebeck voltage generated in uniform material, but contact potential difference

requires p- and n-type semiconductors.

Seebeck vol tage is bulk effect and contact potential dif ference interfacial effect.


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Peltier effect

What is it? Evolution or absorption of heat when current flows

through an interface between dissimilar conductors.Why does it happen? The electrical energy of charge carriers

comprising electrical current is material dependent.

How is it mathematically described? Q = I(21)T, where Q = rate of

heat absorbed in W, I = current in A and

1 and

2 are Seebeckcoefficients of materials that current flows into and out of,

respectively. Current direction is that of positive charge carriers.

Additional Remarks

The Peltier effect and Ohmic heating are unrelated.

The Peltier effect is an interfacial effect.

+-

I Metal 2

Metal 1

Heat absorbed by e-s-sHeat liberated by e-s2 >1


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Thomson effect

What is it? Evolution or absorption of heat as electric current flows

through a conductor subjected to a temperature gradient.

Why does it happen? The electrical energy of charge carriers

comprising a current is a function of temperature.

How is it mathematically described? dQ d dT

ITdx dT dx

Additional Remarks

Due to the additional term that the Thomson effect adds to the heat

equation, numerical solutions are necessary.

When TEMs operate in refrigeration mode, the Thomson effect may be

neglected, but it often must be accounted for when TEMs operate in

generation mode.

The Thomson effect is a bulk effect.

Irreversible effects accompanying thermoelectric effects

Heat conduction through finite temperature gradients.

Ohmic heating.


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Summary of Reversible and Irreversible Effects Pertinent to

the Analysis of TEMs

Seebeck coeffic ient () characterizes all 3 thermoelectric effects as shown without rigorous

proof by Lord Kelvin and confirmed after Onsagar reciprocity relations amongst transport

properties developed.

Representative values of relative Seebeck

coefficient (relative to Platinum) are shown in

the Table from Lascance (Electronics Cooling

Magazine, 12(4), 2006). It is much higher in

semiconductors (especially certain types)

than conductors. Electrical resistivity is also

much higher in semiconductors, however.


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Applications of Thermoelectric Effects

Thermocouple thermometry based on the Seebeck effect.

Cooling, heating and electric power generation based on thermoelectric

effects were a laboratory curiosity unti l the 1950s. After compound

semiconductors were developed for transistor applications, however,

Russian scientist Abram Ioffe improved their thermoelectric properties

such that thermoelectric refrigeration, precision temperature control and

power generation became commercially viable.


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Thermocouple ThermometryMost widely used & misunderstood temperature sensors.

Deceptively simple governing equations lead to misunderstandings.Thermocouples use Seebeck effect to measure temperature as

different conductors subjected to same temperature difference

produce different voltages. Output voltage for circuit in Figure is:

Reference

Junction

Voltmeter

Cu Wire

Co WireMeasurementJunction

Type T (Copper-Constantan)

Thermocouple Circuit

TjTmTR

( ) ( ) ( ) ( ) ( ) ( )R j R m j

m R j R R

T T T T T

Cu Cu Co Cu Cu CoT T T T T

V T dT T dT T dT T dT T T dT

+

-

Comments on circui t:

Reference junction must be isothermal. It may be ice bath or insulated body

(commonly a PWB) of known temperature as measured by, say, a calibrated thermistor.

Measurement junction (voltmeter) must be isothermal. If input terminals not at same

temperature, for example, errors usually result. Observable by touching an inputterminal.

Junct ion must be isothermal such that it does not produce any voltage. Otherwise,

temperature measurement impossible as Seebeck coefficient of junct ion is unknown.

(Junction is typically welded or solder joint of variable and unknown composition.)

Output voltage generated in regions of temperature gradients; , unlike in other temp.

sensors, junction is not the sensor.

Thermocouple wire must be homogeneous (not corroded, not strained, etc.); otherwise,

its Seebeck coeffic ient is unknown.

Sensit ivity of thermocouple [

V/oC] determined by difference in Seebeck coefficients(so called relative Seebeck coefficient) of two legs rather than their individual values.


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Tips on thermocouple measurements.

Beware of oxidation in thermocouples containing Nickel (types T, J, K, E & N) and mechanical

stresses changing Seebeck coeffic ient over time.

Type-T (copper-constantan) thermocouples common because component wires relatively free of

inhomogeneities; hence, calibration charts reliable. But, avoid them when conduction along copper

wire will cause signif icant measurement error.

Account for conduct ion errors and cal ibrat ion errors in uncertainty analysis.

If possible, attach portion of thermocouple upstream of junction to same surface as tip to reduce

conduction errors, e.g., wrap thermocouple around heat pipe at axial location where measuring temp.

Avoid bending thermocouple wires where temperature gradient present when possible. This is where

the Seebeck coefficient accuracy is most critical.

Avoid plac ing thermocouples near electrical noise, e.g., 60 Hz AC power lines and transformers. If

this is impossible use metal shielded thermocouples and ground shield.

As per Fig., due to low relative Seebeck coeff icients (LHS), voltages output by thermocouples arerather low (RHS). Care must be taken to account for voltage measurement uncertainties.

from www.omega.com

Relative Seebeck coefficient vs. temperature for commontypes of thermocouples from Traceable Temperatures by

Nicholas and White.


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Resistance based thermometry

Temp. determined by measuring sensors electrical resistance which = f(temp.).

Platinum resistance thermometers (PRTs).

Highest accuracy (approaching 0.001 K), precision & stability for 14 K T 1000 K.

Reqd sensor excitation causes self heating.

ThermistorsSemiconducting ceramic resistors made from metal oxides.

Extremely high (nonlinear) sensitiv ity over limi ted temp. range so excellent for control.

Pyrometry (Radiation Thermometry)

Non-contact temp. measurement based on Plancks distribution & objects emissivi ty.

Object surface = sensor; optical properties of surface reqd; line of sight very desirable.

Can make 10s of 1000s of temp. measurements at once (expensive capital investment).

Example niche applications of various temp. sensors

Thermocouple--Quiescent gas temp. if thermistor/RTD self heating problematic.

Platinum Resistance Thermometer--Thermocouple calibration over long period of time.

Thermistor--Precise temp. control of waveguide when very high temp. resolution reqd.

Pyrometer--Thermal image of entire circuit board. Too useful for moving/remote target.

Other Types of Thermometry


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2. Thermoelectric Modules


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TEMs are solid state devices used for cooling, heating or power generation.

In cooling and heating modes, thermoelectr ic materials generate a

temperature difference from an applied voltage difference.

In generation mode, thermoelectric materials generate a voltage difference

from an applied temperature difference.

Object or medium to be cooled, heated or both (during precision temperature

control) in thermal contact with controlled side substrate.

In generation mode, heat source mounted on control led side.

Heat sink mounted on uncontrolled side.

TEMs are about a 300 million USD/year industry.

Thermoelectric Modules

Single Stage TEM Bank of Single

Stage TEMs

Multistage TEM


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TEMs: Present and FutureAfter about 50 years, ZT for medium and high temperature materials increases from about 1

to about 3.Electrical contact resist ivit ies between thermoelectric materials and interconnects reduced

from about 10-9

m2 to about 10-11

m2.

Thermal management of 1300 W/cm2 hot spots on an IC demonstrated.

Every major automobile manufacturer investigating scavenging of exhaust heat usingthermoelectr ic modules. 5%-10% energy savings projected in 5 10 year time frame.

Another 3 fold leap in ZT would be genuinely disruptive; e.g., household refrigerators would

be solid state & portable power sources based on combustion and solid state heat-to-

electric ity conversion could become commonplace.

Evolution of ZT over time. 3.5 mm x 3.5 mm x 100 m

thick TEM soldered to

integrated heat spreader for IC.

Liquid-cooled auto exhaust

system for scavenging waste

heat utilizing low (Bi2Te3),

medium (PbTe) and high (SiGe)

temperature TE materials in 3

zone thermoelectric generator.


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Thermoelectric Module Construction

Controlled Side Ceramic Substrate(Component or Heat Source)

Electrical Interconnect

n-type Semiconductor

Pellet (- value of )

p-type Semiconductor

Pellet (+ value of )

RLExternal Leads to:

Resistive Load (RL) in Generation Mode

Bipolar Power Supply (in Cooling and Heating Modes)

DC-

+

+

-

Uncontrolled Side

Ceramic Substrate

(Heat Sink)


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Benefits and Shortcomings of TEMsBenefits

Solid state and no moving parts; therefore, compact, rugged, acoustically silent,reliable, long lasting and maintenance free. Nearly electr ically silent, low weight,

moderate cost, modular, environmentally friendly and work in any orientation.

Cascaded TEMs can refrigerate to temperatures < 100oC in 20oC ambient.

Configurable for localized cooling/heating.

Precise temperature control under transient condi tions by controlling current. Current

direction determines whether cool ing or heating is provided at controlled side substrate

and its magnitude controls rate thereof.

Tuneable operating/output voltages (to an extent).

Versatile. Same module can be used for cooling, heating and generation.

Shortcomings

Low thermodynamic effic iencies; e.g., 1/5 the coeffic ient of performance of a vapor

compression refrigerator. Also, cant pump heat over long distances as possible with

vapor compression systems.

Limited performance (heat flux in refrigeration mode, power output in generation mode).

Demand or output low voltage/high current (DC) power; therefore, significant

irreversibil ities due to conversion.

If TEMs had higher performance and efficiency, household refrigerators would besolid state. And they may be in the future.


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Representative TEM applications

Power generation from automotive waste heat. Exploits large exhaust gas-to-

ambient temperature dif ference as per US DOE Freedom Car Program.Precision temperature control of photonics. (Electronics have maximum

operating temperature, but photonics have specified operating temperature.)

Laser diodes in optical amplifiers.

Focal plane arrays in infrared cameras.

Portable (combined) refrigerators and warmers.

Heat (from radioisotopes)-to-electricity conversion on deep space missions.

Health; e.g., wireless vital sign monitoring and power generation for cardiac

pacemakers.

Seiko Thermic watch. Titanium-lithium-ion rechargeable battery powered by

heat from users wrist. 10 (series-wired 100 pellet) TEMs (+ booster circuit)

charge 1.5 V battery.

Power from gaseous or

liquid fuel in remote or

hostile environments; e.g.,

for cathodic protection

against corrosion of gaspipe lines. From Global Thermoelectric, Inc.s website


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3. Analysis of Thermoelectric Modules


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Cold/hot Sides versus controlled/uncontrolled Sides

of a TEMShortcomings of conventional approach in which cold and hot sides of aTEM are defined.

In precision temperature control applications, the component side of

a TEM often alternates between being colder and hotter than the other

side because of, e.g., changes in ambient temperature. This becomesa nuisance when analyzing TEMs over a range of operating

conditions.

Distinguishing between operating modes is problematic; e.g., when

work is being done on a TEM in order to pump heat against atemperature gradient, is it operating as a refrigerator or a heat pump?

Identical eqns should apply to TEM in all operating mode. To

accomplish this, one side of TEM must absorb heat due to Peltier

effect and the other release it for currents in positive dirn. Cold / hot sides of TEM should be determined by solving eqns;

they cant be arbitrarily imposed if the eqns are to be general.

Defining controlled and uncontrolled sides of a TEM solves the foregoing

problems.


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n = 1

n = 2

n = 3

n = N

VoVN

Controlled Side Subtrate

Uncontrolled Side Subtrate

Controlled/Uncontrolled Sides Framework

Cooled and/or heated component or medium is on the controlled side of TEM in

precision temperature control applications.

Either a heat source or a heat sink is on the controlled side in generation mode. This

determines the direction of current through the TEM.Current is + when posit ive charge carriers flow from thermocouple 1 to thermocouple

N. Thermocouples 1 and N have n-type and p-type pellets adjacent to their external

leads, respectively.

For + current, Peltier heating and cooling occur at controlled and uncontrolled sides of

TEM, respectively. Opposite is true for negative currents.


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Nomenclature, Conventions & Boundary Conditions

A single thermocouple TEM is shown for simplicity.

Current flow is + when posit ive charge carriers flow counterclockwise.

- +I Peltier-cooled csi-I Peltier-heated csi


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Assumptions

Constant properties for p-type and n-type semiconductor pellets

which form the thermocouple

p = positive # = -n, = electrical resistivity & k = thermal

conductivity. p,n is defined as (p -n).

L = length of each pellet and Ap = cross section.

Thermal/electrical effects due to electrical interconnects are not

considered.

Contact resistances are negligible.

1D heat transfer except for constriction/spreading resistances

associated w/ heat conduction between pellets and substrates.

Isothermal csi and usi. Also assume 1D current flow through themsuch that have uniform Peltier heating or cooling.

No Thomson effect because of constant Seebeck coefficients.

Insulated pellets, except at csi and usi.

Heat Conduction in a TEM


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2 2

2 20 subjected to at 0 and atc u

P

d T IT T x T T x L

dx kA

Control volume analysis to derive heat equation governing conduction in

the pellets:

Results is that the heat equation and boundary conditions are:


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Dimensional solution (temperature distribution)2 2

2

2 22 2

u cc

P P

I I L T TT x x T kA kA L

Dimensionless form of solution

2

c

u

2

T-T=

T

I=

2

c

u c

X X X

T

xX

L

R

K T T

and electrical resistance (R) and thermal conductance (K) of a

thermocouple are

2 2and P

P

L kAR K

A L

where


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Surface Energy Balances

Convention is that q is positive in the x-dirn; , positive heat flow

represents heat flow into the csi and out of the usi

Surface energy balances (SEBs) at csi/usi involve 3 terms

accounting for 1) heat conduction from/to substrates, 2) Peltier

cooling/heating & 3) heat conduction from/to pellets

General form of an SEB has no storage or generation terms, because

a surface contains no mass or volume. Hence:

E Ein out

Consider SEB at csi. In words, rate of heat transfer into csi (qc)

equals rate of Peltier cooling (Ip,nTc) at csi plus rate of conductive

heat transfer into the pellets (-kApdT/dx) at csi, i.e.,:

,

02c p n c p

x

dT

q I T kA dx

If current (I) is negative have Peltier heating at csi, but foregoing eqn.

sti ll applies


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Based on the temperature distr ibution in the pellets derived above,

the SEBs at the csi and usi become, respectively

2

,

2

,

( ) / 2

( ) / 2

c p n c u c

u p n u u c

q I T K T T I R

q I T K T T I R

Preceding SEBs fundamental to TEM analysis. If I is + have Peltier-

cooling at csi.

Differentiating qc expression w.r.t. I & setting result = to 0 yields

current (Imax

) for which qc is maximum. Hence:

,

max

p n cTI

R

2 2

,

,max ( )2

p n c

c u c

Tq K T T

R

where

2

2

p

p

LRA

kAK

L

qc,max = maximum heat rate that can be pumped out of controlled side ofTEM for a given Tc & Tu. It occurs at Imax.


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Maximum temp. difference TEM can create between its uncontrolled &

controlled sides in refrigeration mode [Tmax = (Tu Tc)max] occurs at

qc,max = 0 & is given by: 2 2,max

2

p n cTT

KR

A figure-of-merit (Z) for TEM may be defined such that the higher its

value, the larger the value of Tmax is. Hence:

2

,p nZ

KR

Consider why Z varies as it does with p,n, K and R

High Seebeck coeff. (p,n) leads to high Peltier cooling at csi &

Peltier heating at usi which is desirable to pump heat.

Low conductance (K = 2kAp/L) irreversible heat conduction

from uncontrolled ( hot ) side of TEM to controlled ( cold ) side.

Low electrical resistance (R = 2L/Ap) reduces irreversible Ohmic

heating.


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For case at hand geometry & k & of both pellets in thermocouple

are equal; , Z = p,n/(4k), a material property. z defined as 4Z, i.e.,

Z has units of K, but often non-dimensionalized by multiplying it by

T.

An important research task w/ regard to TEMs is to z in order to

qc,max & Tmax. An implication of this is that material scientists & solid

state physicists, as opposed to heat transfer specialists, receive

most of the funding to study TEMs & state-of-the-art heat transferanalyses arent as sophisticated as one might expect. Also ZT is an

overrated parameter as halving k does not in general have the

same effect as halving .

Coefficient of Performance (COP)

COP () quantifies thermodynamic efficiency of refrigerator & equals

ratio of rate of heat absorbed at refrigerated (controlled) side [qc] to

rate of work done on TEM:

cqW

2, p nz

k


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Overall energy balance on control volume around TEM shows rate of

work done on TEM = (qu - qc). Hence:

2

, ( )p n u cW I T T I R

It fol lows that the COP of a TEM is:

2

,

2,

( ) / 2

( )

p n c u c

p n u c

I T K T T I R

I T T I R

where 1rst term accounts for electrical work done on TEM to overcome

back emf generated by Peltier effects & 2nd term is due to electrical

resistance of TEM circuit.

In the limit as the figure-of-merit of the pellets approaches , the

COP of the refrigerator (TEM) is that at the Carnot limit, i.e.,

c

u c

TT T


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Surface energy balances at the controlled side interface (csi) and

uncontrolled side interface (usi) of a TEM when it has N thermocouples

become:

2

2

/ 2

/ 2

c c u c

u u u c

q N I T K T T I R

q N I T K T T I R

Pellets conductive heat fluxes at csi and usi in terms of are:

,

0

,

1

1

c cond P u c

x

u cond P u c

x L

dTq NkA NK T T

dx

dTq NkA NK T T

dx

where negative and positive qc,cond and qu,cond, respectively, imply

conduction out of the pellets and into the respective ceramic substrates.

where - and + qc and qu, respectively, imply heat transfer out of TEM.Rate of work done on an N-thermocouple TEM is:

2

2 ( )u c

I R

K T T

2

, ( )

TEM p n u cW N I T T I R

Di i l T Di t ib ti d I l i ti


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Dimensionless Temp. Distribution and ImplicationsMaximum pellet temp. tabulation

For = 0, no Ohmic heating or

Peltier effect; therefore, lineartemperature distribution.

For 0 < 1 and -1 , all

Ohmic heat conducted to csi &

usi, respectively.

For Ohmic heat

conducted to csi and other to

usi.

Detailed physical

interpretations of heat flow as

f(,I) follow from the analysis.

Ubiquitous statement in literature that the Ohmic heat is conducted to

the csi and the other to the usi at all condit ions is incorrect.

2I=

2 u c

R

K T T

c

u

T-T=

T cT

TEM Embedded in Thermal Resistance Network w/ Electrical


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qcpRcp-,c

Rcp-c

Ru-,u

T,c

T,u

Tc

Tu

Tcp

qc

qu

, ,

2 2

,

2 2

, , ,

2 2

,

( ) / ( ) /

( ) / ( ) / 2 / 2

( ) / ( ) / 2 /

(1)

(2)

2 (3)

(4)( )

cp cp c cp c cp c cp c

cp c cp c p n c u c ec R

u u u u p n u u c ec R

TEM p n u c ec R

q T T R T T R

T T R N I T K T T I R I R

T T R N I T K T T I R I R

W N I T T I R I R

Rcp-,c = Thermal resistance b/t cp & its local ambient.

N = Number of thermocouples in TEM.

I = current through TEM.

= Seebeck coefficient (p,n = pn)

K = Conductance of thermocouple (2kAp/H) where k, Ap & H = thermal

conductivity, pellet footprint/height, respectively.R = Electrical resistance of thermocouple (2H/Ap)

Rec-R = Electrical contact resistance of a thermocouple (4Rec-/AP)

Rec- Electrical contact resistivity

Tu = Temperature of usi.

T,u = Uncontrolled side ambient temperature.

= Rate of work done on TEM.

control

volume

TEM Embedded in Thermal Resistance Network w/ Electrical

Contact Resistance at Interconnects

TEMW

n n np pp

DC-+

+-

RL

(1) Energy balance at control point (cp)

(2) Surface energy balance at controlled side pellet-

substrate interface (csi)

(3) Surface energy balance at uncontrolled side pellet-

substrate interface (usi)

(4) Energy balance on control volume around TEM

qcp = Power dissipated at cont rol point (cp).

Tcp = Temperature of control point .

Tc = Temperature of csi.

Rcp-c =Thermal resistance between cp & csi.

T,c = Controlled s ide ambient temperature.

csi

usi


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3. Operating Mode Maps

TEM Operating Modes


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TEM Operating Modes4 primary operating modes

Generation, when < 0, i.e., TEM does work on an external load.

Cooling. qc > 0, heat transfer from controlled side substrate into csi.

Heating. qc < 0, heat transfer from csi into controlled side substrate.

Neutral. qc = 0, no heat transfer between csi & controlled side

substrate.

Numerous sub-modes within the primary modes.

Refrigeration is a sub-regime of cooling only possible when Tc < Tu.Heat pumping is a sub-regime of heating only possible when Tc > Tu.

Coefficients of performance only exist in refrigeration/heat pump modes.

Operating mode maps are plots which provide the operating mode as f(I).5 separate operating mode maps, depending on the relative magnitude of

Tc and Tu, are required to capture all possible operating modes.

Terms l ike thermoelectric cooler (TEC) are misnomers in sense that

any thermoelectric module (TEM) can operate in all operating modes.

TEMW

Operating Mode Map Example 1


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0 < Tu Tc < Tmax.

is the coefficient of performance in

refrigeration mode.

= qc/

qc,max corresponds to the maximum rate of

heat transfer into the csi in refrigeration

mode. It occurs at Imax.qc,idle corresponds to rate of heat transfer into

csi when TEM in open circuit configuration. It

occurs at I = 0.

max corresponds to the maximum COP in

refrigeration mode. It does not occur at Imax.It occurs at Iopt.

In effic ient heating mode both the Peltier

effect and Ohmic heating result in heat

transfer to the csi. Conversely, in inefficient

heating mode there is Peltier cooling at thecsi.

Short circuit mode occurs at I = Ish. qc is

lower at I = Ish than at I = 0 because of Pelt ier

heating at the csi.

Many more observations can be made.

TEMW .



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Tu Tc > Tmax.

Refrigeration sub-mode is impossible

because qc < 0 for all I.

Peltier-reduced heating sub-modecorresponds to case when qc,idle < qc < 0.

This means there is heat transfer from the

csi into the controlled side substrate, but

at a lower rate than if the TEM simply

operated in open circuit mode, i.e.,

conventional 1D heat conduct ion.

Range of currents over which TEM

operates in generation mode is larger

than when Tu Tc < Tmax than when Tu

Tc Tmax because of higher temperature

difference across i t.

Operating Mode Tabulation


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Operating Mode Tabulation

Given Tc, Tu and I, the Table provides the primary operating mode and sub-mode.

An ExampleCalculation Example: Precision Temp Control of an


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An Example

Reconfigurable optical add drop modules (ROADMs) are analog devices that route light containing information

(voice, video, and/or data) amongst optical fibers in telecommunications networks. Light from incoming optical

fibers travels along waveguides (often silica) fabricated on a large die (often silicon) and is routed to the

appropriate outgoing fiber by various optical components. ROADMs use thermooptic phase shifters to locally

heat the waveguides in order to change their temperature. Since the index of refraction of the waveguides is

temperature dependent, the phase of the light traveling through them may be controlled. This phase control in

combination with interferometers enables light to be switched between different paths. Integrated on the same dieas the heat-dissipating thermooptic phase shifters, however, are temperature-sensitive optical components, e.g.,

optical filters, which must be maintained within narrow operating temperature ranges (e.g., 1oC) to function

properly. In order to maintain the die at constant temperature except in the vicinity of the thermooptic phase

shifters as, for example, the ambient temperature changes, it may be mounted on a heat spreader which, in turn,

is mounted on a TEM.

Calculation Example: Precision Temp. Control of an

ROADM

Consider a ROADM switch that dissipates 10 W of heat & must be maintained at 75oC at ambient temps. between

5oC & +65oC A th TEM l t d h 71 th l ( 2 0 10 4 V/K 1 25 10 5 k


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5oC & +65oC. Assume the TEM selected has 71 thermocouples (p = -n = 2.010-4 V/K, = 1.25 10-5 m, k =1.5 W/(mK), Ap = 1.96 mm2, & L = 1.14 mm) & 30 mm x 30 mm x 0.75 mm-thick alumina substrates [k = 36.0

W/(mK)]. Assume the switch is thermally insulated from its environment except thru a layer of conductive epoxy

(R = 1.710-5

m2

W/K) attaching it to TEMs controlled side substrate. The uncontrolled side substrate isconnected thru a layer of thermal grease (R = 2.58 10-5 m2K/W) to a heat sink w/ a thermal resistance of RHS.What is the optimal value of RHS insofar as the TEM requiring the least amt. of electrical power? Do not consider

voltage conversion losses. You may neglect electrical contact resistance at the interconnects in the TEM in the

analysis.

Schematic of problem:

Solution approach: For a given value of RHS, the maximum TEM


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43

pp g HS,

power for Peltier cooling/heating at the csi corresponds to T,u =+

65o

C/-

5o

C. Hence, at the value of RHS for which TEM power isthe same for Peltier cooling & heating at the csi at foregoing

conditions, the maximum power that must be supplied to the

TEM for the switch to operate in ambients between 5oC and

+65oC is a minimum. Optimal value of RHS is determined byplotting TEM power required vs. RHS on the same graph for the

foregoing conditions to determine when these 2 powers are

equal.

Such a plot may be made by solving the balance eqs., i.e.,


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44

p y y g q

, ,

2,

2

, , ,

2

,

( ) ( ) SEB at cp

( ) [ ( ) / 2] SEB at csi

( ) [ ( ) / 2] SEB at usi

W=N[ ( ) ] overall energy balance

cp cp c cp c cp c cp c

cp c cp c p n c u c

u u u u p n u u c

p n u c

q K T T K T T

K T T N I T K T T I R

K T T N I T K T T I R

I T T I R

Consider each variables value in balance eqns.:

qcp = power dissipated by the switch = 10 W

Kcp-c = thermal conductance between control point (switch) &

csi, i.e., inverse of thermal resistance of conductive epoxy

attaching switch to TEM in series w/ 1D & constriction

resistances thru controlled side substrate & its 14.4 W/K.

Tcp = control point temperature = 75oC

Tc = csi temperature = unknown #1.

Kcp-,c = 0 as switch thermally insulated from environment

except thru TEM

T,c is irrelevant (switch doesnt transfer q to its local ambient)


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45

, ( q )

N = # of thermocouples in TEM = 71

I = current supplied to TEM = unknown #2

p,n = p n = 4.010-4

K = thermal conductance of each thermocouple = 2kAp/L =5.1210-3 W/K

R = electrical resistance of each thermocouple = 2rL/Ap = 1.46

10-2

Ku-,u = thermal conductance between usi & its local ambient.

F[1D & spreading resistances thru uncontrolled side substrate;

(known); grease layer resistance (known) & RHS (unknown #3)T,u = uncontrolled side ambient temp. = -5oC (heating mode)

and +65oC (cooling mode).

Wdot = rate of work done on TEM = unknown #4

.

Soln. of balance eqs. for 4 unknowns yields rate of electrical work


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46

done on TEM as f(RHS) for refrigeration & heating mode per plot.

. TEM

Peltier Cooling at cs i

Peltier Heating at csi

As per the preceding graph, the minimum reqd TEM power


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47

occurs when heat sink sized such that its resistance is 1.5 oC/W.

Additional Comments

Circuit packs containing ROADMs have limited power budget.

If power reqd for thermal management , more optical

functionality may be included on device.

When device temp. = 75oC in 5oC ambient, corresponding

80oC temp. difference makes it difficult to insulate device well

enough that Kcp-,c may be considered 0.The Thomson effect & fact that properties of pellets are

f(temp.) have been neglected which could cause 10-20%

error in analysis..

Techniques for Enhanced Performance & Efficiency


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48

q yImproved high Z thermoelectric materials.

High (magnitude) Seebeck coefficients to maximize reversible thermoelectric effects.

Low k and electrical minimize (irreversible) heat conduction through fini te

temperature gradients and bulk Ohmic heating, respectively.

Electron-transmitting/phonon-blocking superlattices (stacks of nm-scale layers of

conventional thermoelectric materials, e.g., Bi2Te

3), enable decrease of k with modest

increase of

.

2

, /( ) p nZ k

Extracted from DARPA

Report by L. Dubois


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49

Fabrication improvements

Decreased interfacial Ohmic heating via reduced electrical contact resistiv ity atelectrical interconnects a la thin f ilm TEMs fabricated by semiconductor processing

techniques.

Elimination of solder fillets at interconnects such that Peltier effects are confined to

bottom/top of pellets.

Those covered here

Pellet geometry optimization

Novel thermoelectr ic assemblies

Non-Cartesian-geometry TEMs

The above techniques for enhancement are complimentary.


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50

Optimal Pellet Geometries for

Thermoelectric Refrigeration Under

Thermal Resistance BoundaryConditions

Motivation


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51

Optimizing the height and cross-sectional area of the pellets in a TEM may

Increase performance, i.e., maximum heat f lux dissipated by component attached to it(q cp) for specified temperature drop below ambient and vice versa.

Increase efficiency, i.e., coefficient of performance (), for specif ied performance

below maximum performance (where effic iency is fixed).

Tune the operating voltage of TEMs to reduce DC-DC power conversion losses.

Optimization has been accomplished, under the assumptions that

There is no thermal resistance between heat source and csi, where Peltier cooling

occurs, i.e., the thermal resistance of the TEM substrates, etc. are neglected.

All heat from heat source enters TEM, i.e., exchange of heat with the local ambient is

neglected.

Uncontrol led side of a TEM is subjected to isothermal BC, i.e., there is no thermal

resistance between it and the fluid which cools it . This is usually unrealistic as air-

cooled heat sinks are generally attached to the uncontrolled side of a TEM.

The motivation of this work is to develop an optimization algorithm in which the3 assumptions above are relaxed and to perform the analysis with flux-based

quantit ies rather than rate-based ones for the sake of generality.

TEM Operating in Refrigeration Mode and Thermal


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52

qcp

(finite or 0)

Rcp-,c(finite or

)

Rcp-c

(finite or 0)

Ru-,u(finite or 0)

T,c

T,u

Tc

Tu

Tcp

qc

qu

controlvolume

p p pn nn

DC- +

csi

usi

Resistances Coupling TEM to Surroundings

Relevant temperatures

T,c, prescribed ambient temperature on controlled side of TEM

Tcp, temperature of control plane. A prescribed quantity such that,

e.g., photonics component mounted to TEM, maintained at its

operating temperature.

Tc, temperature of control led side interface (csi) between pellets andinterconnects, where Peltier cool ing occurs. Not prescribed.

Tu, temperature of uncontrol led side interface (usi) between pellets

and interconnects, where Peltier heating occurs. Not prescribed.

T,u, prescribed ambient temperature on TEMs uncontrolled side.

Flux based quantities

R cp-,c, thermal resistance between control plane and controlled

side ambient.

q cp, prescribed heat flux generated by component attached to TEM.

R cp-c, prescribed thermal resistance between control plane and csi .q c, heat flux into csi . Not prescribed.

q u, heat flux out of usi . Not prescribed.

R u-,u, prescribed thermal resistance between usi and local ambient.

Possible assumptions on key parameters:

Governing EquationsSurface energy balances Variables


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53

Surface energy balances

Control plane

csi

usi

Variables

K = thermal conductance (1/thermal

resistance)

= pellet packing density

p,n = Seebeck coefficient of thermocouple

k = pellet thermal conductivity

= current flux through pellets

Rec- = electrical contact resistiv ity at

interconnects

Current f lux rather than current appears in above eqns;

, performance & efficiencyindependent of pellet cross-sectional area, which may be varied to tune operating voltage

of TEM to that of source.

Optimization Objective: Determine pellet height (H) and current flux () corresponding to

maximum performance or efficiency for specif ied performance below maximum one when

Tcp,

p,n, k,

, Rec-, T,c, T,u and thermal resistances (conductances) prescribed.

csi and usi surface energy balances are used to express Tc and Tu in terms of and H.

Then expressions for qcp and WTEM as f(, H) and prescribed parameters follow.

Coeffic ient of performance defined as'' ''/ .c TEM q W

qcp

may be subst ituted for qc

in

expression, except when Rcp-

,c

0, when cooling

efficiency (CE) defined as '' ''/ .cp TEM CE q W

Flux-based rate of work done on TEM from

overall energy balance

Heat & Work Flux Eqns and Optimization Procedure


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54

Performance optimization procedure

Define (numerical) function qcp,max(H) as maximum performance at relevant corresponding to

q/ = 0.

Numerically maximize qcp,max(H) with respect to H.

Efficiency optimization procedure for specified qcp < qcp,max

Based on parabolic-like dependence of qcp,max(H) on H determine, lower and upper values of H

(denoted by Hl & Hu, respectively), which accommodate specified performance at an appropr iate .

Define (numerical) funct ion WTEM

(H) for Hl

H

Hu, where corresponding

follows from setting

q cp(,H) = q cp at given H.

Numerically minimize WTEM(H) with respect to H in order to determine H and which maximize .

Same procedure appl ies to s impler cases, e.g., when, successively, Rcp-,c , Rcp-c 0,

Ru-,u 0 and Rec- 0 in example below to place in relative context the irreversibili ties

associated with the various thermal resistances and Ohmic heating at the interconnects.

Effect of Pellet Cross-Sectional Area (AP)


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55

The preceding equations and plot of

performance (q cs), effic iency (

) and voltageper unit TEM footprint (VTEM) versus current (I)

for selected values of pellet cross-sectional

area (AP) show that

q cs,max and (q cs) are independent of AP,

i.e., maximum performance and efficiencyat a specif ied performance are

independent of AP.

Maximum values of q cs and occur at

different currents.

Operating current and voltage

corresponding to specified qcs are

directly and inversely proport ional,

respectively, to AP.

Conclusion: Tuning AP matches TEMoperating voltage to that available in the

absence of DC-DC power conversion to the

extent possible, but it does not affect

performance or effic iency.

Effect of Pellet Height (H)


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56

q

cs,max and

(q

cs) are dependent on H, i.e.,maximum performance and effic iency at a

specified performance depend on H.

Peak performance occurs at H = Ho because

decreasing H reduces performance once

interfacial Ohmic heating dominates bulkOhmic heating.

Refrigeration impossible when H < Hmin due to

interfacial Ohmic heating.

Operating current and voltage (nonlinearly)

decrease and increase, respectively, withincreasing H for a specified performance

Conclusions: At maximum performance H =

Ho. Below maximum performance, proper Hcorresponds to maximum efficiency. This

is more important than selecting H which

minimizes DC-DC power conversion losses.

Baseline Conditions for Sample CalculationFixed


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57

Fixed

p,n

= 0.0004 V/K, m, k = 1.5 W/(mK). (Bi2

Te3

properties at 300K)

Tcp = 290 K, T,c = T,u = 310K

= 50% (typical of commercial module with dense packing)

Varied

K cp-,c = 250 W/(m2K), corresponding to efficient gas-phase forced convection. (Subsequently set

equal to 0.)

K cp-c = 2000 W/(m2K), corresponding to thermal contact between rough surfaces (i.e., component

and TEM substrate) at moderate pressures. (Subsequently set equal to .)

K u-,u = 1000 W/(m2K), representative of a forced convection heat sink of larger footprint than TEM.

(Subsequently set equal to .)

Rec- = 10-9

m2, typical of a conventional TEM. (varied between 10-11 and 10-8

m2 and also setequal to 0.)

Peak Performance as a Function of Rec-


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58

Reducing Kcp- from baseline value (250 W/(m2K)) to 0 increases performance by 0.5 W/m2

for all Rec- as i t implies that heat into TEM exclusively from that generated at control plane.

Increasing Kcp-c from baseline value (2000 W/(m2K)) to

modestly increases performanceas Rcp-c is a relatively unimportant thermal resistance in TEMs.

Increasing Ku-,u from baseline value (1000 W/(m2K)) to

dramatically increases

performance by lowering temperature of the usi.

When Kcp-

0, Kcp-c

and K u-,u

, performance

1/Rec-. Otherwise, reducing itbelow a threshold value is of no benefit as other irreversib ilit ies dominate.

H and Corresponding to Peak Performance as a

Function of R


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59

Function of Rec-

Peak H and independent of K cp-,c as peak heat f lux into TEM (qc) independent of it.

Effect of Kcp-c on optimum H and is modest.

Ku-,u to dramatically optimal H as, because usi temp. it may be brought closer to csi

to

bulk Ohmic heating. Optimal

dramatically

as interfacial heating at usi i rrelevant.

When Kcp- 0, Kcp-c and Ku-,u , H and Rec- and 1/Rec-, respectively.

Otherwise, asymptot ic limits for optimal values reached below threshold Rec-.

Maximum Performance and Corresponding as f(H)


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60

Plot is for baseline conditions.

Range of H values (each with a corresponding

) accommodate given performance belowpeak one (i.e., q cp < qcp,peak), where H and are fixed, as shown in plot.

Minimum and maximum values of H that accommodate specified performance denoted by

Hl and Hu, respectively.

H-peak yields maximum

for specified qcp and found by (numerically) differentiatingWTEM(H) in range Hl H Hu and setting result equal to 0.

Hl, Hu, Ho, H-peak & Hopt and Corresponding s as f(q cp)


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61

Plots are for baseline conditions.

Ho corresponds to that necessary for peak performance, i.e., 0.76 W/cm2.

Subscript opt denotes conditions pertaining to maximum for specified H.

The smaller qcp is relative to qcp,peak, the more important it is to properly size pellet height.

At q cp,peak, Hl = Hu = Ho = H-peak.

At, e.g., 26% of q cp,peak, (Hl), (Hu), (Ho) and (Hopt) are 8%, 28%, 65%, and 85% (or 15%) of (H-peak).

Clearly it is crucial to optimize H to maximize . Reducing heat flux into TEM to extent

possible is also crucial.`

ConclusionsA procedure has been provided to compute (unique) pel let height in and current flux thru a

f


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62

TEM operating in refrigeration mode corresponding to maximum

Performance, i.e., heat flux generated by a component attached to it and maintained ata specified temperature drop below ambient temperature or vice versa.

Efficiency, i.e., coeff icient of performance, for a specified heat flux generated below

the maximum one for a specified temperature drop.

The following variables have been accounted for

Thermal resistance between component and interface in TEM where Peltier cooling

occurs.

Thermal resistance between component and ambient (as not all heat generated by

component is conducted into TEM it is mounted too)

Thermal resistance between interface in a TEM where Peltier heating occurs and

ambient.

Electrical contact resistance at interconnects in TEM.

The formulation is on a flux basis and shows that current flux rather than current

determines performance and effic iency, imply ing that pellet cross-sectional area (ornumber of pellets) may be tuned to match (to an extent) TEM operating voltage to a power

supplys output vol tage.


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63

Optimal Pellet Geometry for Generation

Mode

Objectives

Increase performance, i.e., maximum output power for specified thermal boundary

diti d l d i t


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64

conditions and load resistance.

Increase efficiency for specified performance below maximum performance (whereperformance is f ixed).

Additional comments

Same assumptions as in refrigeration mode.

Effic iency (

) and output power ( ) defined as

Formulation based on effective footprint of TEM (Ae = 2NAP) because of the importance

of matching electrical resistance of TEM to that of load. (Flux based quantities are

irrelevant.)

Optimizations must yield a (positive) integer number of pellets.Optimization is considerably more complicated than for refrigeration mode because H

and N must be optimized simultaneously.

2csand /q , respectively.g L gW I R W gW

Effect of Number of Pellets (N)Maximum performance and efficiency at specified

performance are independent of N but N tunes load


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65

performance are independent of N, but N tunes load

resistance corresponding to specified performance.

Permissible pairs of N and H exist only at discrete N.

TEMs electrical resistance is too high to accommodate

load at sufficiently high N and can be too low to

accommodate load at sufficiently low N.

Effect of Pellet Height (H) and Optimum Performance

Peak performance occurs in the limit as H 0 A TEM can not output higher power than


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66

Peak performance occurs in the limit as H 0. A TEM can not output higher power than

Wg, peak at any load resistance.RL must be RL corresponding to specified performance at N = 1 in the limi t as H 0.

Maximum performance for a specified load occurs in the limit as H 0 at the nearest

integer number of pellets corresponding to N = (RLAe/Rec-)1/2. This is evident as curves for

arbitrary H are embedded within those for H 0.

Efficiency OptimizationN corresponding to maximum effic iency for specified load resistance and performance

follows from insertion of H(N) expression into that for effic iency and differentiation


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67

follows from insertion of H(N) expression into that for effic iency and differentiation.

In general result is non-discrete # of pellets;

, use nearest integer # below or above it.

When optimization yields significantly less than one pellet, efficiency is considerably

reduced by operating a single pellet TEM, the best alternative.

Optimum H does not correspond to operation at I corresponding to maximum efficiency

(when RL =

NR), but somewhere between it and maximum possible H.Implementation at temperature pertinent to energy scavenging in electronics (Bi2Te3pellets, RL = 5 , Wg = 1 W, Tc 100

oC, Tu = 20oC, Rec- = 10

-9

m2, Ae = 625 mm2). As per

plots, at optimum N = 118.5, H = 3.40 mm and

= 3.28%, nearly the limit of Bi2Te3.


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4. Energy Efficient Thermoelectric Heat

Pipe Assembly for PrecisionTemperature Control

Need for Precision Temperature Control of

Photonics Components


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69

Electronic components (memory, ASICs, etc.) meet performance & reliability specs

over wide range of operating temperatures; e.g., Intel Atom (bare die) processor

requires 0 85oC case (die) temperature.

Photonic components (laser diodes, optical amplifiers,etc.) require precision temperature control; e.g., JDSU

2745 pump lasers operate at 45 2oC.

Minimizing total power for specified network throughput is a primary objective in

telecommunications. This requires transfer of bits in optical domain with minimaltransfer to electrical domain, i.e., photonics components.

Emerging all-optical network (AON) poised to enable less power hungry network

that accommodates growth and cost reduction requirements. Hence, reduced

power precision temperature control of photonic components is important.

Heat Pipes and Variable Conductance Heat PipesHeat Pipes


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70

Evaporator

Section

Condenser

Section

Optional Adiabatic Section

Operation: Evaporation drives vapor to condenser section and condensate returned by

capillary forces in liquid-saturated wick.

Benefits: Passive, reliable and silent. Effective conductances 10 100X that of Cu rod

achievable. May transport large quanti ties of heat.

Shortcomings: Substantial radial thermal resistance of liquid-saturated wick. At heat

loads beyond performance limits assume effective conductance of wall/wick annulus.

Ubiquitous in electronics cooling to transport heat to and spread heat within air-cooled

heat sinks.

Wick

A

A

Section A-A

Heat pipe-heat

sink assembly for

CPU courtesy o f

Thermacore, Inc.

Variable Conductance Heat Pipes (VCHP)

Differ from standard heat pipes as, because of non-condensable gas (NCG) presence,

their effective conductance increases with heat load & ambient temperature such that


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71

p

they provide some degree of temperature control.Operation. No condensation in vapor + NCG region as saturation temp = ambient temp;

, active and inactive condenser regions. Vapor flow carries NCG to inactive region.

Moveable vapor-vapor + NCG front passively regulates evaporator temp; e.g., as qevapor pressure increase decreases NCG volume thereby increasing active portion of

condenser. Act ive control by heating vapor + NCG reservoir to expand NCG & decreaseactive condenser length improves performance.

Shortcomings. Cant provide sub-ambient temperature control, slow transient response;

, in general, inappropriate for precision temperature control of photonics.

VAPOR REGIONVAPOR + NCG

REGION

-

+

Heat In

MOVEABLE

FRONT

Fins

Heated Reservoir

EVAPORATOR ADIABATIC CONDENSER (Lc)

ACTIVE (La) INACTIVE (L ia)

TEM-Based Precision Temperature ControlState-of-the-art.

Fi d t h t i k TEM b t l ti l l d ll d i bl h


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72

Fixed geometry heat sinks on TEMs, but relatively large and small ones desirable when

operate in cooling and heating modes, respectively.

Heat sink size not optimized, but should be such that maximum TEM power minimized.

Then fraction of power budget for telecommunications devoted to thermal management

is minimized.

TEM,max vs. H over permissible H range at typical ambient temp extremes (-5 and

65oC) when usi-ambient thermal resistance (Ru-,u) optimized for each H plotted in

Fig. [qcp = 10 W, Tcp = 55oC, TEM footprint = 30 x 30 mm2 and = 30%.]


73/88

73

Outside permissib le H range cant maintain Tcp in +65o

C ambient.At sufficiently high H, Ru-,u = 0 to minimizeTEM,max when T = 65

oC; otherwise its fini te.

Minimum TEM = 3.82 W at H = 1.13 mm and Ru-,u = 0oC/W.

Maximum TEM significantly reduced by simultaneously optimizing H and Ru-,u.

Very significant further power reductions achievable by control ling Ru-.u.

TEM-VCHP Assembly for Reduced Power Precision

Temperature Control


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74

VAPOR VAPOR + NCG

-

+

MOVEABLE

FRONT

n p n p n

Al Plate to Mount TEM

on and Embed VCHP in

No moving parts are required.Extremely large heat s ink may be used as at low ambient temp and/or high heat load fins

may be turned off on demand. (Passive operation of VCHP also highly beneficial.)

Heated NCG reservoir requires very modest power (< 1 W, say) and permits control of flat

front between pure vapor and vapor + NCG region, where fins are turned off.

EVAPORATOR ADIABATIC CONDENSER (Lc)

ACTIVE (La) INACTIVE (L ia)

VCHP PrototypeStainless steel insert reduces conduction from (heated) reservoir into condenser section

such that they may be maintained at different temperatures.


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75

Courtesy of Thermacore, Inc

Marcus and Fleischmans Flat Front Model of VCHPKey assumptions.

Steady-state.


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76

Flat front divides condenser into active region of length (La) where pure vapor exists & inactiveregion of length (Lia = Lc La) where vapor + noncondensible gas exist.

Total p in pure vapor (in evaporator, adiabatic section & active region of condenser) and vapor + gas

(in inactive region of condenser & reservoi r) is psat(Tvc), where vc is vapor core.

Negligible axial conduction in wall & wick; , step changes in temperature and vapor concentration

at flat front separating pure vapor from vapor + NCG regions in condenser.Thermal equilibr ium between inactive region of condenser and reservoir and ambient such that

vapor pressure in these regions is psat(T), where T is the ambient temperature.

Governing equations

Newtons Law of Cooling relates heat load (q) to overall heat transfer coefficient (Uvc-) between

vapor core within active length of condenser and ambient. vc vc a vcq U P L T T

Gas mass (m) such that all in reservoir (condenser fully open) when component mounted to

evaporator dissipates max heat load (qmax) at max ambient temp (T,max). Then NCG volume (Vg) =

reservoir volume (Vr) and for ideal gas mixture

,max,max

,

sat set sat r

g

p T p T V

m R T

where Tset is Tvc reqd for component mounted to VCHP to operate at its setpoint temp and accounts

for component-vapor core Rth. qmax = Uvc-PvcLc(Tset T,max) dictates reqd value of (Uvc-Pvc).

,max

,max( )

sat set sat or r

vc vc vc cv sat vc sat v

p T p T TV Vq U P T T L

A p T p T T A

Follows that Tvc for arbit rary heat load and ambient temp may be computed from:

Integration of TEM and VCHP Models for TEM-VCHP

Assembly ModelRequires determination of mg such that condenser ful ly open when qcp = qcp max and To = Tmax


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77

Requires determination of mg such that condenser ful ly open when qcp qcp,max and To Tmaxin presence of TEM.

Requires eqn for Ru-,u in form that accounts for VCHP rather than fixed resistance heat sink.

General expression for Ru-,u:

, , , 1/u u u e e wall e wick vc vc a

u vc

R R R R U P L

R

Substituting an expression for La based on ideal gas law, preceding eqn becomes:

,

1

/

u u u vc

g

vc vc c r v

sat vc sat

R RmR T

U P L V Ap T p T

Setting q from usi to vc equal to that out of usi based on surface energy balance at usi:

22

2 2

, , / 2 / 22 2

u vc ec Rp n c u c vc u u vc p n c u c ec R

u vc

T T I RI RN I T K T T T T NR I T K T T I R I R

R

,

2 2

,

1

// 2 / 2

u u u vc

g

vc vc c r v

sat u u vc p n c u c ec R sat

R R

mR TU P L V A

p T NR I T K T T I R I R p T

Combining preceding eqns yields Ru-,u expression in terms of standard unknowns that govern TEM,

i.e., I, Tc and Tu. (Saturation pressures must be evaluated from saturation data for working fluid.)

Comparison of TEM-VCHP Assembly to TEM with

Fixed Resistance Heat SinkKey features of TEM.


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78

y

30 mm x 30 mm footprint.

Conventional Bi2Te3 pellets are utilized.

Pellet packing density is 31%.

Key features of FVCHP

10 cm condenser section and 17.7 cm3 reservoir.

Wick is s intered Cu power (keff = 40 W/(mK)).

2930 W/(m2K) overall heat transfer coefficient accounts for air-

side heat transfer with extended surfaces.

Component setpoint temp, Tcp, is 55

o

C and its powerdissipation (qcp) ranges ranges from 0 to 10 W.

Ambient temperature range is -5oC to 65oC.

TEM pellet height optimized to consume minimal power at

harshest cooling condit ion, i.e., qcp = 10 W and T = 65oC.

Comparison is relative to TEM-fixed resistance heat sink

assembly where H and Ru- optimized for minimum

maximum TEM power consumption.

Results shown in Figure.

Maximum power consumpt ion reduced by 25%, i.e., from 7.8 W to 5.3 W.

Average power consumption reduced by 53%.


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79

Preliminary/ Proof of Concept Experimental DataData from assembly in Fig. Heat

pipe & TEM of similar geometry to

those above.


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80

VCHP evacuated & refil led w/out

adding noncondensable gas for

TEM-constant conductance heat

pipe (CCHP) results.

At highest heat load (10 W) power

for TEM-CCHP and TEM-VCHP

assemblies similar.

Below harshest cooling condition,

TEM-VCHP assembly reduces

TEM power by up to about 2/3.

Schematic of TEM-LMS Assembly & LMS Prototype

Galinstan [Tmelt = -19oC, k = 16.5 W/(mK)] is pumped at arbitrary mass f low rate thru 0.61 mm

thick channels in FR4 substrate via magnetohydrodynamic body force.


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81

DC+ Electrode - Electrode

TEM

Low Resistance

Heat Sink

Galinstan Flow Channel

Permanent Magnet

Buried Copper Traces

FR4 Substrate

A A

Precision

Temperature

Controlled

Photonic

Component

Top View of Assembly Section A-A

Heat from

TEM

LMS

VARIABLE

R I

Heat Sink

CONST

R

TCold T THot

I

Courtesy of Rockwell Collins, Inc

Convective resistance to/from Galinstan very low as high k and low channel hydraulicdiameter; therefore, TEM-ambient thermal resistance controlled by sensible temp rise of

Galinstan, i.e., its variable mass f low rate.

Conclusions on Reduced Power Precision

Temperature Control


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Complimentary approaches are necessary to s ignif icantly reduce the TEM power reqd forprecision temperature control of photonics and include.

Development of improved thermoelectric materials.

Reduced electrical contact resistances at semiconductor-conductor interfaces in TEMs.

Realization of high pellet packing densit ies in TEMs.

Pellet geometry optimization.

Use of variable resistance heat sinks that do not compromise reliability, i.e., do not

have moving parts.

TEM-VCHP assemblies, which were shown to reduce average TEM power condit ion

over representative operating temp and heat load ranges by 53%.

TEM-LMS assemblies.


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Non-Cartesian TEMs for On-Chip Hot

Spot Thermal Management

On-Chip Hotspot Thermal Management Using Silicon

TEMs (Shakouri and Bar-Cohen et al.)


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Concept: Exploi t the inherent difference in Seebeck coefficient between metalelectrodes ( essentially 0) and doped Silicon.

Current flows from electrode into inactive side of Si chip above hot spot. Peltier

absorption eliminates hotspot. Current flows into inactive region of Si

(generating limited amount of Ohmic heat due to spreading & modest electr ical

resistivity of doped Si) & out ring electrode where Peltier heat released.

Eliminated 3oC hotspot for typical microprocessor conditions.

Hot Spot Thermal Management Using a Lateral Geometry

Thermoelectric Module (TEM)Problem: Dense transistor c lusters on ICs cause problematic high heat flux/temperature


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hot spots.State-of-the-art: Electr ic designers forced to use multi -core designs to increase IC speed.

Innovation: Lateral geometry TEMs and novel use of them to accommodate hot spots.

Benefits : Provide parallel cooling path in the region of a hot spot on an IC without any

moving parts. Can be integrated on to the die, into the heat spreader or into the base of theheat sink.

Heat-Out

Heat-In

Heat-Out

Heat-Inheat spreader

to heat sink

to coldregionof die

substratedie

heat sink

Lateral geometry TEM

Standard cool ingconfiguration for

microprocessor package

On chip hot spot mitigation

via insertion lateralgeometry TEM. Additional

cooling path provided whi le

primary one undisturbed.

Collaborators: S. Krishnan, C. Jones and O. Malis of Bell Labs.

6. Summary1) Thermoelectric effects and modules have been introduced physically and

mathematically.


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2) Operation of and proper use of thermocouples has been discussed.

3) A means to classify the operating mode of a TEM has been provided.

4) The height of the semiconductor pellets in a TEM operating in refrigeration mode

corresponding to maximum performance (heat flux for a specified temperature drop

below ambient) has been derived.5) An algorithm to optimize the height and cross-sectional area of the semiconductor

pellets in a TEM operating in refrigeration mode for maximum coefficient of performance

and favourable operating voltage, respectively, for a specified performance below the

maximum one has been discussed.

6) An algorithm to simultaneously optimize the height and cross-sectional area of thesemiconductor pellets in a TEM operating in generation mode for maximum performance

or efficiency for a specified performance below the maximum one has been discussed.

7) A novel TEM-variable conductance heat pipe (VCHP) assembly to increase the effic iency

of a TEM providing precision temperature control over a widely varying ambient

temperature range has been introduced.

8) A custom VCHP for use in a TEM-VCHP assembly for precision temperature control has

been discussed.

9) Non-Cartesian TEMs for on-chip hot spot mit igation have been introduced.

References

1) Hodes, M., Optimal Design of Thermoelectric Refrigerators Embedded in a Thermal

Resistance Network. To appear in IEEE Transactions on Component and Packaging

T h l i


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Technologies.

2) Zhang, R., Brooks, D., Hodes, M., Manno, V., van Lieshout, M., Optimized

Thermoelectric Module-Heat Sink Assemblies for Precision Temperature Control, Proc.

InterPack 2011, Paper #52019.

3) Hodes, M., Optimal Pellet Geometry for Thermoelectric Power Generation, 2010, IEEETransactions on Component and Packaging Technologies, 33(2), p. 307.

4) Hodes, M., Optimal Pellet Geometry for Thermoelectric Refrigeration, 2007, IEEE

Transactions on Components and Packaging Technologies, 30(1), pp. 50-58.

5) Hodes, M., On One-Dimensional Analysis of Thermoelectric Modules (TEMs), 2005, IEEE

Transactions on Components and Packaging Technologies, 28(2), pp. 218-229.

AcknowledgementsPeople

Dave Brooks, MS Candidate.


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Martin Cleary, Postdoctoral Fellow.

Vincent Manno, Professor.

Corey Melnick, Undergraduate Research Assistant.

Matt van Lieshout, MS Candidate.

Gennady Ziskind, Visit ing Professor.

Rui Zhang, MS Candidate.

Funding

Tufts University.

Wittich Sustainable Energy Research Initiation Fund.

thermoelectric modules

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