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1. In

Aa solpotengrad[1].

Zmeria meit is

wherthe acond(W/m

Twastinterhigh[2].

Longinotti1, SMascolo2, andtran Italia, 2 Drresponding a

tract: The melopment of aied in a wide

ulate, optimizcially when dmeters and conew methodoer of Comsolmodern optimrithms. It ha

hin an industridevelopmen

erators (µTEprietary materi paper show

EG’s element y. Values osical variablefidentiality rea

words: Seebero-generator, frithm, multiob

ntroduction

A thermoelectlid state devicntial when it

dient due to th

ZT is a comit for thermoeeasure of theirdefined as:

re α is the Sabsolute temp

ductivity (S/mm*K)[1]. The possibilitte heat into elrest as a conh ZT values i

S. Di Marco1

d A. BuoscioDeltaTi Reseauthor: via Tib

main topic of an innovativerange of com

ze and improvdealing with

onstraints. ology is obtainl multiphysicmization appas been sucal research pr

nt of thermEGs) based ials. ws how this

geometry inof the thermes can’t be asons.

eck effect, therfinite element bjective optim

tric micro-gence, able to get is exposed e thermoelect

mmon dimenselectric (TE) mr thermodynam

Tk

ZT2σα

=

eebeck coeffiperature (K),

m), κ is the the

ty of using μlectricity has

nsequence of in a certain r

1, S. Pistilli1, olo*1 earch Consorburtina 1232, 0

this paper ise tool that camplex problem

ve system dehuge number

ned by joinings simulation

proach of genccessfully approgram focuse

moelectric mon innov

s tool optimn a simple oelectric mat

disclosed

rmoelectric analysis, gen

mization.

nerator (μTEGenerate an eleto a tempera

tric Seebeck e

sionless figurmaterials whicmic efficiency

T

ficient (V/K), σ is the ele

ermal conduct

μTEGs to conrecently regathe discover

range of mate

F. Costa1, M

rtium 00131 Roma -

s the an be ms, to esign rs of

g the with netic plied ed on

micro-ative

mizes case

terial for

etic

G) isectric ature

effect

re of ch is

y and

T is ectric tivity

nvert ained ry of erials

M. Giusti1, G

- Italy, antonie

Besides thigh efficienthe optimal g4].

For this rperformance a significantallows time materials andsuch as length/width

Accordindirections, stinto two cahorizontal strtransfers aloelements; whtransfers alon

This wortool for deselements bashorizontal str

2. Thermoe

2.1 Governin

Heat fluxmain quantiteffect simulat

where E is thHeat energy balance arethermoelectristationary cas

Expliciting thof electric po

. Gammariel

etta.buosciolo

the ZT of thecy µTEG, it

geometry of th

reason, simulaparameters byt part of µTand cost sav

d variations oshape, therand thermal cg to the diffetructures of μategories: veructures. In vong thickneshile in horiz

ng their surfacrk describes tsigning high sed on thin-firucture.

electric Mod

ng Equations

x Q and electrities of intertions [1]:

TJQ −α=EJ σ−σ=

he electric fieldconservation

e the goveric effect anse assume the

Q =⋅∇J =⋅∇

he thermoelecotential V, they

llo1, I. Gison

o@altran.com

e material, to is necessary

he µTEG’s el

ation of thermy numerical mTEG developving in assesof design parmoelectric

coupling. ferent heat traμTEGs can beertical structuvertical structuss direction zontal structuce [4]. the applicatioperformance

ilm TE mater

del

s

ic current fluxrest in therm

T∇κ−T∇σα

d. n and electrirning equatinalysis, that following for

EJ ⋅ 0=

ctric equationsy assume the f

n1, G. Latessa

fabricate to design ement [3,

moelectric methods is pment: it ssment of arameters,

material

ansferring e divided ures and ures, heat

of TE ures heat

on of the µTEG’s

rial, with

x J are the moelectric

ic current ions for

in the rm:

s in terms form:

a1,2,

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Thesin Mult

coefare c 2.2 G

Tcan micrthin subsbothshowcomp

Figu

The contaof mdirecintegabov

(( σ−α⋅∇ T( ∇σ−=

(−⋅∇

se equations aorder to btiphysics [5]. To simplify

fficient, elecconsidered ind

Geometry De

The model desbe manufac

roelectronics pfilm of TE

trate and twoh thermal andws the geompound structu

xm

Silico

AlumAirTherm

ure 1. Cross secmat

substrate is aacts are made

materials usedctly by a negrating all theve.

∇σα−∇σ TV)TV ⋅∇σα−∇

TV ∇σα−∇σ−

are transformebe implemen

fy the simuctric and therdependent from

escription

scribes a singlctured by stprocesses. It iE material do metallic cond electrical c

metry (not inure:

xp

gap

n substrate

minium

moelectric materi

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a silicon wafee of aluminiud in the simulew Comsol

e governing eq

) ) =∇κ− T ( )V∇−

) 0T =

ed to a weak nted in Com

ulation, Seermal conductim temperature

le TE elementtandard frontis constituted deposited ontntacts that worontacts. Figu

n scale) and

zszm

hs

ial

del (not in scaleion.

r, while the mm. The behavlation are defphysic inter

quations descr

form msol

beck ivity, e.

t that t-end by a to a rk as

ure 1 the

e) and

metal viour fined rface, ribed

2.3. Boundar

The follapplied in the

Heat exchang

- Hot - Cold

293.Electric exch

- Potecold

- Variside

Fi 2.4. ElectriMethod

The methpotential anapplication oconditions, inthis techniqucircuit and electric potecurrent (throuThe generatethe following

ry Conditions

lowing boune model:

ge surfaces: side, with a te

d side, with.15K

hange surfacesential ground rd side surface)iable potentiasurface)

igure 2. Bound

ic Power

hod, used to nd current,of two differn two differee it is possiblthe short ci

ential and theugh an optimied electric powg scheme:

s

ndary condit

emperature ofh a temper

s: reference at 0) l reference (o

dary surfaces.

Density Ev

evaluate the is realized

rent sets of ent runs. By le to simulate rcuit to evae amount ofized load) respwer is evalua

tions are

f 493.15K rature of

V (on the

on the hot

valuation

electrical by the

boundary means of the open

luate the f flowing pectively.

ated using

wherelemThot, the s

The

wherelemin thcircuThe

whertherm

The apprthe ifromand these

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Figure 3. Elec

re V is the opment, defined a

while I is thesame surface a

electric powe

load RP =

re Ri is the ment , evaluatehe open circuuit. Electric Powe

re S is the hmoelectric ele

(S =

physics useraise also the tinverse of the

m the heat excthe differencee:

= 1t TR

temperature ofixed as:

ctric power eval

pen circuit poas average va

e short circuit and integrated

∫∫ •=2S

JIr

er is:

iload R

VR ⎜⎜⎝

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internal resised as ratio betwuit and the cu

er Density is:

SPP load

d =

horizontal secement:

gapx2( m +⋅

ed in this mthermal resist

e ratio of the hchange surface of the nomin

∫∫−2

1

SColdHot TT

of the previou

Thot=493.15Tcold=293.15

luation scheme.

otential of thealue on the surcurrent flowin

d as follows:

dSnr

2

loadRV

⎟⎟⎠

⎞

stance of theween the pote

urrent in the s

ction area of

L)p ⋅

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∫ •2

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us named surf

5 K 5 K

.

e TE rface ng in

e TE ential short

f the

s to ough wing

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faces

All the matthermal condtemperature wafer, that isrepresented in

Figure 4.

3. Genetic A

μTEG’s by genetic altechnique thaproblems chasubjected to l 3.1. Optimiz

A generwritten in the

ma

c(x) ≤

A ·

l ≤ x ≤

First steprepresented criterion: thethe one with t

This choiprocesses of aims at the sa

terials used iductivity whic

variations, es more sensitin Figure 4.

Silicon thermatemperat

Algorithm

element optimlgorithm, an aat can be apparacterized bylinear or non-l

zation Problem

ric optimizatie following for

ax f(x) (object

such th

≤ 0 (non- line

· x ≤ b (linear

≤ u (lower and

p of the opby the defi

e optimum elethe higher powice is relatedthe microele

ame time to m

in the modelch is constantexcept for thive to this va

al conductivity vture.

mization is padvanced mathplied to solve y many paramlinear constrai

m Design

ion problem rm:

tive function)

hat:

ar constraints

r constraints)

d upper bound

ptimization dfinition of oement of the wer density.

d to the manuectronics indumaximize the

l have a t with the he silicon ariable, as

versus

performed hematical complex

meters and ints.

can be

s)

ds)

design is optimality μTEG is

ufacturing ustry: that

electrical

powreduwafe

Efuncalgor

S

identoptimfor eAt dthe uppedefinwhovariathe f

T

lineadescsubjeis co

3.2.

Asimu

er and to muce the probaer level. Electrical powtion, called rithm theory:

:f

Second steptification of mized and theeach variable. design level sothers are va

er and lower bned. Referringse geometry able and fixedfollowing tabl

VARIA

NAME

xm

xp

gap

zm

Table 1: Sum

FIXNAME

hs

zs

L

Table 2: Su

Third step is rar and non linribed in this pected to the f

onnected to ma

x

Optimization

A genetic algoulates the proc

minimize the ability of def

wer density fitness func

/W(A4

I*V:

p is repref all variable definition of

some parametariables to bebounds of eachg to the deschas been sho

d parameters aes:

ABLES TO OPT

LOWER BOUND 10 µm

6 µm

4 µm

1 µm

mary of variabl

ED PARAMETE

ummary of fixed

represented bynear constraintpaper the chofollowing lineanufacturing r

xp - gap > 2µm

n Algorithm

orithm is a hecess of natural

area in ordefect occurrenc

is the objection in gen

)cm2

sented by les that canf variability ra

ters are fixede optimized; h variable mucribed case sown in Figurare summarize

TIMIZE

UPPER BO

60 µm

10 µm

5 µm

6 µm

les to optimize

ERS VALUE

500 nm

375 µm

20 µm

d parameters

y the definitiots. In the exam

oice of variablear constraint,requirements:

m

euristic searchl selection [6]

er to ce at

ctive netic

the n be anges

d and also

ust be study re 1, ed in

UND

m

m

on of mple les is , that

h that .

The algorithmfeasible popunew populatio

At each individual ocomputing itscalled parentcreate the nexSome of the ithat have highelite individpopulation.children fromchanges to a of parents. The algorithmcriteria is metcumulative chfunction over 3.3. Optimiz

μTEG’sby interactioMathWorks LiveLink moThe geneticMatLab, wcalculation isMultiphysicselement elecevaluates μTdescribed in PAt each generby genetic ainto ComsolComsol simu 4. Results

The resullist of variabdensity.

Table 3 initial values (optimized de

Setting thgeometry, thcurrent densiin the followi

m starts by crulation; then itons.

step, the aof the curs fitness values, based on thxt population.individuals inher fitness areduals are p

Then the m the parentsingle parent

m stops when t. In this case hange in valuer 50 generation

zation Tool

element optimon of Coms

MatLab, thdule.

c algorithm while electris performed b: the first o

ctric potentialTEG’s elemenParagraph 2. ration, for eac

algorithm, Mal model’s paulations to eva

lt of the genebles that maxi

shows the d(project desig

esign). hese optimal vhe thermal ity change as ing maps (Fig

eating a randot creates a seq

algorithm scorrent populae and selects mheir fitness, in

n the current pe chosen as elipassed to t

algorithm ts by makingor by combin

one of the stoit stops whene of the fitnesns is less than

mization is psol Multiphyhrough the

is implemeical power by two runs oone evaluates l and the secnt electric cu

ch individual patLab sets nearameters andaluate fitness f

etic optimizatiimize electric

difference betwgn) and the fin

values in the mdistribution shown in Tab

gure 5-7).

om initial quence of

ores each ation by members, n order to

population ite. These the next produces

g random ning a pair

opping n average s

n 1e-6.

performed ysics and

Comsol

ented in density

f Comsol μTEG’s

cond one urrent, as

processed ew values d invokes function.

ion is the cal power

ween the nal values

model, the and the

ble 3 and

V

Tablbefor

Figuon th

Figuthe T

Variable

xm

xp

gap

zm

le 3: Comparire and after opti

re 5. Heat maphe TE material).

re 6. Heat mapTE material).

PROJECT VALUE 55 μm

7 μm

4 μm

6 μm

ing Parameter imization

p before optim.

p after optimiza

OPTIMIZVALUE10 μm

7.36 μm

4 μm

2.12 μm

values compa

mization (detail

ation (detail vie

ZED E

m

m

m

arison

view

ew on

Figure 7. Eloptimization (d

Figure 8. Eoptimization (d The behaviouand optimizeTable 4:

FEATURE

Horizontal are

Electric Potenti

Electrical Curre

Heat flux

Electric Powgenerated (Pl

Electric PowDensity (Pd

lectrical curredetail view on t

Electrical curredetail view on t

ur of the two med design) ca

E PROJVAL

a (S) 2280al (V) 57.80ent (I) 5.75

435.18wer

load) 0.08

wer d) 3.64 W

nt density mthe TE material

ent density mthe TE material

models (projean be summ

JECT LUE

OPTV

0 μm2 4

0 mV 69

mA 7.

8 mW 274

mW 0.

W/cm2 25.8

ap before ).

map after ).

ect design marized in

TIMIZED VALUE

80 μm2

9.92 mV

.10 mA

4.33 mW

12 mW

86 W/cm2

F

Madiffe

si

Therm

Elec

The

Tablbehav

IpowhighmodlosseA Telectone.

TpresehourmachprocFiguinto conv

5. C

Tof inthe oIt haand to

FEATURE

ax temperature erence at the two ides of the TE

materialmal conductivity

trical resistance

ermal resistivity

le 4: Comparviour

In optimum μer density am

h value is relatdel, that doesnes due to thermE element intrical power d

The computaented in the prs of run-timhine: 16GByessor.

ure 8 shows generations o

verges to the o

Figure 8. F

Conclusions

This paper aimnteraction of optimization aas been develohas been appldemonstrate

PROJECT VALUE

146.8 K

2.96 mW/K

10.05 Ω

2.30 K/W rison table o

μTEG’s elemmounts to 2ted to the usan’t take in accmal interfaces

n a real devicdensity lower t

ation time, tprevious tabl

me on a stanyte RAM a

the fitness fuof genetic algoptimum value

Fitness Function

ms at demonsmulti-physics

approach of goped as a genlied on this c

that the

OPTIMIZVALUE

178.4 K

K 1538.17 mW

9.85 Ω

3.65 K/Wof the two m

ment the elect5.8 W/cm2.

age of a simplcount any kins and packagine can producthan the estim

to obtain ree, is less than

ndard workstaand Xeon 3

function evolugorithm: it quie.

n Evolution

strating the pos simulation

genetic algoritneral purpose ase study in ose optimiza

ZED E

K

W/K

Ω

W model

trical This

lified nd of ng. ce an mated

esults n 12 ation GHz

ution ickly

ower with hms. tool

order ation

techniques cimprove the μ

Numericademonstrativ

More gencontribution tdevice modeaccount andtechnical con 6. Referenc 1. A. F. Iofand ThermsupplementedInfosearch ltd2. C. J. VineiG .KanatzidiBig EfficienAdvanced Ma3. C. Gould and Mechan(Ed.), ISBN: 4. H. BottnerInternational(2002) 5. S. P. Yushand K. C. Koof Thermoelthe COMSOL6. KalyanmoyUsing Evolu(2001) 7. Acknowl

This wocollaborationauthors are gMilano Bicdiscussions ahaving inspvision and str

can drive thμTEG’s elemeal results me and completnerally, this tto device desi

els have manyd many comnstraints.

ces

ffe, Semicondmoelectric cd for the Ed, (1957) is , A. Shakouis, Nanostructncy Gains fatererials, 22,and N. Shamnical System978-953-307-

r, Proceedingsl Conference

hanov, L. T. Goppenhoefer,lectric PhenomL conference iy Deb, Multi-utionary Alg

ledgements

ork was can of several tegrateful to Prcocca Univeand to Dr. G. pired this resrong belief.

he design toent performanmust be cotely theoreticatool can be a igners, especiay variables to

mplex geome

ductor thermocooling, ReEnglish ed.

uri , A. Majumtured Thermofrom Small , 3970–3980, (

mmas, Micro Ems, Kenichi

-027-8, InTecs ICT '02. Twee on Thermo

Gritter, J. S. CMultiphysics mena, Proceein Boston, (20-objective Optgorithms. Wi

arried out eams. In partirof. D. Narduersity for Storto, ERG

search with lo

o greatly nces. onsidered al.

precious ally when o take in etrical or

oelements, ev. and London,:

mdar , M. oelectrics: Features, (2010)

Electronic Takahata h, (2009) enty-First oelectrics

Crompton Analysis

edings of 11) timization iley, UK

under a cular, the ucci from technical SpA, for ong term