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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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Operating Mode Map Example 1
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 .
Operating Mode Map Example 2
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Operating Mode Map Example 2
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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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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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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, ( 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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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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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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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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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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Optimal Pellet Geometries for
Thermoelectric Refrigeration Under
Thermal Resistance BoundaryConditions
Motivation
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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%.]
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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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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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Courtesy of Thermacore, Inc
Marcus and Fleischmans Flat Front Model of VCHPKey assumptions.
Steady-state.
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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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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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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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Preliminary/ Proof of Concept Experimental DataData from assembly in Fig. Heat
pipe & TEM of similar geometry to
those above.
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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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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.