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AbstdeveapplisimuespeparamThe powthe algorwiththe genepropThisµTEstudyphysconf
Keywmicralgor
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
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,
COMSOL Multiphysics® Simulation Integrated into Genetic Optimization
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
tion of the modterial compositi
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
The are f
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 ⎜⎜⎝
⎛+
iload RR =
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 ⋅
model allowtance (Rt), throheat flux, flowes (Thot and Tnal temperatu
∫ •2
dSnq rr
us named surf
5 K 5 K
.
e TE rface ng in
e TE ential short
f the
s to ough wing
Tcold), re of
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
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