Basics Tec1

8/2/2019 Basics Tec1

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PRINCIPLES OF THERMOELECTRIC COOLING

1. INTRODUCTION

The operation of thermoelectric coolers is based on the phenomenon known as Peltier

effect. This is observed when an electric current flows across a junction of two dissmilar

conductors . The junction region is then found to absorb or evolve heat depending upon thedirection of current flow. In the circuit made of two conductors 'A' & 'B', one of the two junctions

will get heated while the other will be cooled. Electric current, thus, pumps heat out of one

junction, which is consequently cooled and deposits it into the other junction which gets heated.The phenomenon is completely reversible and a reversal of the current direction will interchange

the role of hot and cold junctions.

Peltier effect is one of the three thermoelectric effects which are thermodynamically

interrelated. These are known as Seeback, Peltier and Thomson effects and the threecorresponding thermoelectric coefficients are defined as follows fig. [ 1.1 ].

T1> T2

Fig 1.1

(i) Peltiercoefficient ( ) ; It is the ratio of the rate of heat absorbed or evolved(Q) at ajunction to the current (I) flowing across the junction ,

that is,

= Q/I 1.1(a)

VA

B

B

T1

T2

A

B

B

TC

I

TH


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(2) Seebeck coefficient ( AB): The two junctions are maintained at different temperatures a

thermo emf operates around the circuit giving rise to a closed circuit current or open circuit

voltage. This thermo emf measured as open circuit voltage (V) divided by the temperature

difference between the two junctions is known as Seeback Coeffcient. Thus

=

V

T T H C

3.1 b

AB = V/( TH-TC ) 1.1(b)

(3) Thomson Coefficient (): While the first two coefficients and have been defined for a pair ofconductors A & B, the Thomson coefficient is defined for the individual conductors A & B

separately. When an electric current (I) flows in a conductor across which a temperature gradient(dT/dx) has been maintained parallel to the direction of the current flow, there is reversible

absorption or evolution of heat along the conductor. This is known as Thomson effect. Thomson

Coefficient () is defined as the rate of heat absorbed or evolved per unit length, current andtemperature gradient. That is

1.1c/.

/

dxdTI

dxdQ=

The three coefficients are related thermodynamically through the Kelvin relations given

below :

AB = T . AB 1.2a

A-B=T. dAB/dT 1.2b

Absolute values of Seeback & Peltier coefficients are also defined for individualconductors when the other conductor of the pair is taken to be a superconductor. In that case these

relations can be expressed as :

= T 1.2c

= T. d/dT 1.2d


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2. Basic Thermoelectric Cooler :

The functioning of a thermoelectric cooler can be discussed with reference to a single

thermocouple structure shown in fig 1.2.In a preliminary analysis the Thomson Coefficient (),

being comparatively small in magnitude, is neglected. The two legs of the thermocouple areusually chosen to have n & p type conductivities since their Seeback & Peltier Coefficients have

opposite signs resulting in additive thermo-electric effects.

Fig 1.2

The basic equation for heat pumping in an elementary TE module such as the one shown infig 1.2 expresses the net heat (QC) pumped out per second at the cold junction at temperature (TC)

as the balance of Peltier extracted heat ( ABI) and the heat input originating from joule heating

and thermal conduction from the hot to the cold end. Equation 1.3 represents this relationship.

Q = AB.I- [I2 R/2 +K(TH - TC }] 1.3

Here 'R' is the total electrical resistance offered by the two legs and 'K' is their combined thermal

conductance. Both R & K contain dimensional parameters for lengths (l1 & l2) and areas of cross

section (A1 & A2) for the two legs. Explicit relations for 'R' & 'K' are of the type.

P N

+

TH

TH

TC

QC

V

I


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R = l/A and K= A/l 1.3a

where , are the material specific parameters known as electrical resistivity and thermalconductivity respectively.

For heat balance considerations the total joule heat (RI2) is equally divided between thecold & hot junctions. This division can be analytically justified.

Another equation of interest in this connection relates the totalinput electrical power (W) to

the cooling power (Q) obtained from the device. A coefficient of performance ( ) is defined as :

= Qc/W 1.4

Here W is made up of two parts, one appearing as joule heating (RI2) and the other used in

overcoming the Seeback voltage generated in the thermocouple as a consequence of thetemperature difference between the hot and cold ends. Thus

W= RI2 + AB(TH - TC}I 1.5

It is seen from equations 1.3, 1.4 & 1.5 that the cooling power (QC), temperature lift T (=

TH-Tc) and coefficient of performance ( ) are all functions of the input current (I) which has to

be optimized for a particular application. Using the Kelvin relation we write AB = Tc . AB.

We then have the following equations.

1. Maximum cooling power ( Using dQ / dI = 0 : eqn 1.3)

Qm = (Tc)2/2R-K(TH-TC) (1.6)

Iq= Tc/R (1.6a)

The corresponding coefficient of performance

q= [ZTc -(TH - TC)]/ ZTHTC (1.7)

2. Max coefficient of performance ( Using d /dI=0 : eqn 1.4 & 1.5)


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2/)(TTWhere,

9.1.)11(

)(=

1.811

/1

Hm C

m

CHAB

opt

m

CHm

CH

C

m

T

ZTR

TTI

ZT

TTZT

TT

T

+=

++

++

+

=

3 . Maximum temperature lift ( Using d(T)/dI = 0 : eqn 1.3}

()m= ( TH-TC)m = ZTc2/2 , where Z =

2/R 1.10

The optimum current to obtain ( T)m

Iopt= Tc/ R 1.11

.The voltage applied across the cooler for any current I is given by

V = IR + (TH -TC ) 1.12.The quantity 'Z' appearing in equations 1.4 - 1.11, contains material related parameters

( ,K ,R). This is called the figure of merit for the thermocouple as it determines the ultimateperformance of the TE cooler from the material point of view.

Since 'Z', as defined above, also depends on the dimensions of the thermoelements through

R & K (eqn 1.3a), it can be further optimized by minimizing the product K.R.

It can be shown that KR is minimum when

When the thermoelement dimensions are chosen such that this equation is satisfied , the

expression for the optimized figure of merit (Z) becomes

pn

np

np

pn

AlAl

=


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1.13)( 2

2

ABBA

AB

kkZ

+

=

Since the thermocouples are usually fabricated from materialshaving comparable thermoelectric properties except for the sign of the

Seeback coefficient (AB) , it is useful to define 'Z' for individual materials

independently as follows :

Z = 2/k 1.14

Here parameters , & k pertain to one material alone ( beingmeasured with reference to a common metal usually copper). In a rigorousanalysis of thermoelectric devices, however, the complete expression for Z

has to be used.The material parameter Z as defined in eq. 1.13 is known as the

thermoelectric figure of merit for the material and determines its potential forthermoelectric applications. All efforts in material development are directedat improving Z.

The materials used in thermoelectric coolers are Bi2Te3 based semiconductor alloys with Sb

partially replacing Bi to give p-type material and Se partially replacing Te to give n type materialrespectively

We see that the three parameters , ( or ) and which together decide the figure ofmerit of the material , are not independent and are also strongly temperature sensitive. At a given

temperature they are all related to the carrier concentration (n) of the material as can be seen in the

fig (1.2a). It can be seen that while and rise with the carrier concentration , the thermoelectricpower falls , and the figure of merit Z has a broad maximum around a concentration n 1 X 1019 /cm3 and therefore these alloys are heavily doped.

. The preferred alloy compositions forsingle stage coolers have been those , where the

maxima in Z fall near the room temperature. The adjustment of the carrier concentration in

these alloys is done using dopants ( such as I in n-type alloys) or by stoichiometric deviations( such as excess Te in p-type alloys).


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3. Effect of the Contact Resistance

Under ideal conditions, the size of the thermoelements can be reduced to any limit withoutaffecting the performance of the cooler module. This can be appreciated by examining eq. (1.3 )

& (1.5) reproduced below :

Qc = ITC- IR- K(TH - TC) 1.3

W =IR + (TH - TC) I 1.5

In these expressions 'R' & 'K' are the only dimension - dependent - parameters and these

remains unchanged by keeping l/A (ratio of the length to the area of cross section ofthermoelements) unchanged. For example by reducing l & A by half , R & K remain unchanged

although the volume or mass of the thermoelement becomes 1/4. For a given current I, therefore,

the cooling capacity 'Qc' & input power 'W' remain unchanged provided 'R' & 'K' are maintained

constant. The limitation on dimensions arises as a result of the contact resistance appearing at the

electrical contacts between the thermoelements and the metal links. For small sized

thermoelements the contact resistance becomes comparable to the resistance of the thermoelement.

The joule heating I2R caused by the contact resistance Rc acts as a built in heat load on the

cold stage and can become comparable to the heat load RI2/2 generated by joule heating in the

thermoelement and affecting the heat balance at the cold stage as considered in eq. (1.3). A good

Fig 1.2


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fabrication technology aims at keeping I2Rc


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Fig 1.3Fig 1.4

Now ,according to eq. 1.4, the maximum temperature lift [ ( T)m=ZTc / 2 ] depends upon Tc and also on the figure of merit 'Z' which falls

with decreasing temperature. Therefore, ( T)m for higher stages of a

cascade (operating at lower average temperature) decreases withtemperature due to decrease in both Tc and Z. So adding more and more

stages results in diminishing returns and the gain obtained by increasing thenumber of stages beyond 5 or 6 is not very significant with the thermoelectricmaterials available at present.

The average value of 'Z' for TE materials used in commercial

devices is 2.5 x 10-3K-1 For single stage coolers this gives ( T)m 67 K

(eq 1.4) for the heat sink at 300 K. This value corresponds to zero heat load

(Qc = 0) and therefore zero efficiency ( = Q/W = 0). The maximum heat

pumped by single stage coolers can be of the order of tens of watts using as

many as 127 couples connected thermally in parallel.

The performance parameters of thermoelectric coolers are normally

specified in terms ofTmax ( with Q=0) , Qmax ( with T =0) , Imax ( the current

for Tmax ) and Vmax ( the voltage applied across the cooler at Tmax . Therefore

N PP P P NNN

P

N

P

P

P

N

N

N

N

P

N

P

N

P

N

P

N

P

N

P

N

P

N

P

N

P

thermoelements

Alumina


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a load line of the type ( fig 1.5 ) can be drawn from which the maximum heat

pumped ( Q) at intermediate temperatures T < Tmax can be estimated.

Fig 1.5

For specific applications ,where the heat to be pumped (Q) along with

the temperature (T ) to be maintained is known , one can design a cooler for

optimum performance. The optimization can be in terms of either the

maximum heat pumped or the maximum efficiency ( c.o.p). Other design

constraints can be the voltage ( or current) supply available , the space

available for mounting the cooler , heat sink considerations etc,It has already been mentioned that for higher temperature lifts , a

cascaded structure is required, where the required temperature lift is suitablydivided over different stages. The structure has to be optimised in terms of thenumber of thermocouples per stage, current, dimensions of thethermoelements (thermocouple legs) and of course, the reliability and cost.5A Design of single stage coolers :

The theory of a basic thermoelectric cooler and the terms and equations related to itsdesign and operation have been discussed briefly.

The design of single stage TE cooler modules essentially means that for any application

where the heat load (Qc) , the hot side temperature (TH) , the cold side temperature (TC) and thefigure of merit Z of the material are known , the optimised structure of the TE Cooler has to be

determined in terms of the number of thermocouples (N) , their dimensions and the operational

characteristics of the module like Imax , Vmax (the current and voltage for maximum heat

pumping / cooling ) etc. Any design constraints like the current / voltage available , spaceavailable etc will also have to be taken into consideration .

There are normally two approaches to this , namely maximum heat pumping and

maximum efficiency (coefficient of performance - c.o.p). Maximum heat pumping requires

Q

T

Q max

Tmax


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that the module operate at the current Iq that pumps the maximum amount of heat over a

specified temperature differential with an efficiency q which is less than the maximum c.o.p

max given by equation (1.8 ). The current for max c.o.p , I ,is generally less than that for

maximum heat pumping for a given T. Again , for a given temperature difference T the heat

pumped at maximum c.o.p (Q ) is always less than Qmax .Therefore given a heat load Q and

T , the choice between designing for max and Qmax depends on whether economy in poweror economy in space is desired.

For specific applications , a cooler can also be designed to operate at any efficiency

which is between q and max . This can happen if there is a restriction on the poweravailable to to pump a certain amount of heat Q.

5B. Design of T.E. Cascades

The general principles involved in the design of TE cooling cascades canbe appreciated with reference to fig(1.6) which schematically shows a cascade

of two stages A1 & A2 operating with efficiencies 1 & 2 with power inputs

W1 & W2 respectively.

aa

FIG 1.6

The heat (Qc) extracted per second at the source by A2 is given by :

Qc= 2W2 1.15

The heat (Qm) rejected per second at the intermediate temperature Tmby A

2

and extracted by the lower stage A

1

is given by

Qm = Qc + W2 =Qc(1 + l/ 2) [from eqn 1.15]

Qm/Qc = 1 + 1/ 2 1.16

Qc

Qc (1+1/ 1)

Qc (1 +1/ 1) (1 +1/ 2)

A2

A1W1,

1

W2,


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Finally the heat (Qh) rejected per second at the sink at temperature This given by :

Qh

= Qm

+ W1

= Qm

(1 + 1/1) since

m= Q

m/W

1

substituting for Qm from eq. (1.15)

Qh = Qc(1 + 1/ 2)(1 + 1/ 1) 1.17

The total input power in the two stages is (W1 + W2) and it is used to

extract heat 'Qc' per second at the source. The overall efficiency A of the

two stage cascaded assembly is therefore :

A = Qc/(W1 + W2)

= Qc/(Qh - Qc) since Qh = Qc + W1 + W2

= [(1 + 1/ 2)(1 + 1/ 1)-1]-1 using eq. (1.17) 1.18

A simple extension of this analysis to an n-stage cascade gives the

following expression for A

A = [(1 + 1/ n)(1 + 1/ n-1)...(1+1/ 2)(1+1/ 1)-1]-11.19

If all the stages are assumed to be operating with the same efficiency

the expression for A condenses to

A = [(1+1/ )n-1]-1 1.20

Fig. (1.7) gives a typical representation of the variation of m with

temperature lift (T) for multistage cooler modules.

It can be seen from fig 1.7 that for T


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is twice as efficient as the two stage module. For obtaining T 100 K athree stage module is, therefore, essential.

For estimating the required number (N) of thermocouples in different

stages eq. (1.16) can be used. This expresses the ratio of heat capacities oftwo successive stages. It is easily appreciated that the cooling capacityrequired for the lower stage has to be more because the heat required to bepumped by it is the sum of the heat pumped by the upper stage and thepower fed into that stage. The TE cooling cascades therefore have apyramidal structure with successively lower stages having more and morenumber of couples.

To a first approximation, (ignoring the variation of 'Z' with temperature),the cooling capacity of a single stage module can be taken as proportional to

the number of couples (N) in that modules. Taking = 0.5, equation (1.16)

gives the ratio of cooling capacities or the ratio of number of couples in thetwo successive stages as 3 i.e. N increases by a factor of 3 for successivelower stages .

In a rigorous analysis , however the factors affecting the performance ofa cascaded cooler , like the temperature variation of the thermoelectricproperties , thermal resistance between various stages , contact resistancedue to each of the solders used etc have to be taken into account.


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Preparation of Thermoelectric material

The materials used in thermoelectric coolers are Bi2Te3 based semiconductor alloys with Sb

partially replacing Bi to give p-type material and Se partially replacing Te to give n type materialrespectively.The index of quality of the material is called the figure of merit Z ,which is defined as

Z= 2 / , where is the Seebeck coefficient , is the electrical resistivity and is the thermal

conductivity of the material . (Eqn. 1.14 , Appendix ). These materials have been in use for more

than three decades now and the highest values reported in literature for the figure of merit Z are 3 -

3.5 X 10 -3 / K. Commercial thermoelectric coolers however are made using material with a figure

of merit > 2.5 X 10 -3 / K.

We have from literature the approximate compositions of the p-type and the n-type alloys

which have been found to give the highest figure of merit as:

Bi 0.5Sb 1.5Te 3+ for p-type and Bi2Te 2.7 Se 0.3 for n type thermoelectric material.

It has however been seen that different workers have preferred minor variations of these.

Divergent techniques ranging from single crystal growth to powder metallurgy are used to produce

device grade material . At SSPL , preparation of thermoelectric material has been done using

Vertical Directional freezing technique. Facilities have been set up for the synthesis and growth

of Bismuth Telluride based alloys..Measurement apparatus for the evaluation of the thermoelectric

properties , and at room temperature have been set up. The figure of merit of the

prepared material at room temperature can thus be determined.


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Fabrication of a Thermoelectric Cooler

The schematic diagram of the structure of a basic thermocouple is

shown below.

The steps involved in the fabrication of a thermoelectric cooler can be

broadly classified as follows :

(i) Preparation of the patterned substrates.

(ii) Preparation of the thermoelements.

(iii) Development of jigs and fixtures .

(iv) Development of solders and soldering procedures.

(v) Assembly of cooler modules.

(vi) Cascading and testing.

Preparation of patterned substrates.

The alumina substrate (0.5- 1 mm thick) , which provides electrical

insulation as well as mechanical support to the thermoelements , holds the

copper pads ~25 m thick which provide the electrical interconnections. These

Alumina Substrate

PP NN

Cu pads

Thermoelements

Barrier layer (Ni)

Solder


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pads can be constructed on the alumina substrates using combination of

screen printing ,electroplating and photolithography. The resistance of the Cu

pads , their adhesion to the alumina substrate , as well as their capability of

withstanding repeated thermal cycling within the temperature range of

operation of the cooler are the important issues here. While plating thick

copper it is required that the flatness of the copper layer over the whole

substrate be held to within a tolerance of a few microns. For cascaded

coolers , the substrate has to be metallized and patterned on both the sides.

At SSPL , we have followed the process sequences given below.

(i) Cr / Au by evaporation followed by Cu plating and Photolithography

using a suitable mask.

(ii) Cr / Au by evaporation followed by Photolithography and Selective

plating of Cu on to the Alumina substrate upto the required thickness.

We have found that the second process sequence yields Cu pads

with better adherence. We have achieved upto 30 m thick well adherent Cu

pads on alumina substrates using this .

The suitability of the Cu pads arre tested by the ability of Cu pads

to withstand thermal cycling and prolonged operation.

Preparation of the thermoelements :

Making electrical contacts to the thermoelectric material is a very

important step in the fabrication process . A thin layer of Ni is normally used

to make electrical contacts to the thermoelectric material .The layer of Ni not

only improves the solderability of the material but also acts as a barrier for the

diffusion of Cu into the thermoelectric material.

Our aim is to deposit adherent ~3 m thick Ni layer on TE slices. The

procedure followed for preparation of the thermoelements is as follows:

1. After obtaining the ingot, it is sliced into sections of the required

thickness.


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2. The slices are lapped and polished to obtain the exact thickness as per

the design.

3. Electroless Ni deposition followed by electroplating of Ni on TE slices

upto~3 m is done.

4. The slices are then tinned with the appropriate solder using a suitable

technology.

5. Each slice is then sectioned into thermoelements having a cross-section

as per the design.

6. Surface preparation of the cut ingot has to be done carefully as any

mechanical damage is likely to increase the thermoelement resistance

and affect the performance of the cooler . Tight dimensional tolerances

have to be maintained during the sectioning process so as to ensure

that there is minimum departure from the A/ l ratio required as per the

design.

Development of jigs and fixtures

Suitable mechanical jigs have to be designed for the precise placement

of the thermoelements on the substrates when they are soldered. These jigscan have a cellular structure and may be designed so that they are removable

after the soldering process. As the size of the thermoelements as well as the

distance between them decreases to 1mm and less , the design of these jigs

becomes more and more complex .

At SSPL , we have designed and fabricated jigs for the assembly of

thermoelectric coolers to suit our integration processes .

Development of solders and soldering procedures

Our aim is to develop solders with a range of melting points and

procedures to perform the soldering. The soldering procedures evolved have


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to be such that electrically perfect and mechanically stable joints must be

made , as subsequent repair and rework of such joints is extremely difficult.

At SSPL , we have synthesised solders of melting points 139oC(Bi 58 , Sn

42) and 118oC (In 52 , Sn 48) . The melting points of these solders have been

measured using DTA. These solders are used for TE cooler fabrication.

The contact resistance at the ends of the thermoelements is a very

important technological parameter and has to be measured accurately for

each of these solders . Therefore a measurement set-up for the evaluation of

contact resistance has been developed and measurements performed on test

samples soldered using each of these solders.


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Assembly of cooler modules

Suitable fixtures have to be designed for aligning and holding the substrate and the jig

loaded with the thermoelments during the soldering process. The following procedure can be

followed for TE cooler assembly.

For single stage coolers , the thermoelements are first soldered on to the base alumina

Patterned substrate on a temperature controlled soldering station in Argon atmosphere. The jig

may then be removed and the top plate will be soldered after suitable alignment.

For multistage cooler assembly at least three to four different solders with graded melting

points need to be used . First the individual stages will be assembled using the solder of a higher

melting point (as in the case of single stage TE coolers). The different stages can then be soldered

on top of each other by heating them in a temperature controlled work station in Ar atmosphere.

Suitable fixture for holding the stages together while soldering will be designed and fabricated.

The assembled coolers are tested in a suitable setup. Tests for

performance degradation after thermal cycling are also done.

Heat sinks

The design of suitable heat sinks is a very important part of the development of any

system using thermoelectric coolers . The heat pumping capability of the thermoelectric module

is significantly influenced by the efficiency of the heat sink. The hot side of the module must

interface with an efficient heat removal system to achieve useful temperature differential across the

module.

Natural convection, forced convection and liquid cooled are three of the most common

types of heat sinks. Thermal resistance varies among the different types and sizes of sinks with

natural convection being the least efficient and liquid cooled the most efficient. The

majority of thermoelectric cooling applications use forced convection heat sinks with

thermal resistance values (RQ) ranging from 0.10/W to 0.5/W.

Using TE Coolers.


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Thermoelectric modules can be mounted in the desired system for an application by a

variety of methods including: mechanical clamping, epoxy bonding, and direct solder bonding.

The individual requirements of the application will determine which method is most appropriate,

however, mechanical clamping is by far the most common. Thermoelectric modules are relatively

strong in compression and weak in shear. Whichever method of installation is used, it is

important to avoid excessive mechanical loading of the module. Thermal resistance occurs at each

interface of an assembly and affects the overall system performance. In mechanically-clamped

systems, the recommended flatness of interface surfaces should be within 0.001. Even with this

degree of flatness, interface materials must be used to fill in the small thermal gaps; typical choices

include silicone-based thermal grease, graphite foil, and thermally-conductive pads. Special care

must be taken to ensure that uniform pressure is applied during installation.


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