Accurate control of friction with nanosculptured thin coatings: Application to gripping in microscale assembly

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To cite this version :

Philippe STEMPFLE, Aurélien BESNARD, Nicolas MARTIN, Anne DOMATTI, Jamal TAKADOUM

- Accurate control of friction with nanosculptured thin coatings: Application to gripping in

microscale assembly - Tribology International - Vol. 59, p.67–78 - 2013

gripping in mi ros ale assembly PhilippeStempé

a)

,AurélienBesnard

b)

,Ni olasMartin

a)

,Anne Domatti

a)

,JamalTakadoum

a)

a)

InstitutFEMTO-ST(UMRCNRS6174-UniversitédeFran heComté-CNRS-ENSMM-UTBM),ENSMM26

Chemindel'Epitaphe,F-25030BesançonCedex,FRANCE

b)

LaBOMaP,ArtsetMétiersParisTe h deCluny,RuePortedeParis,F-71250 Cluny,FRANCE

Abstra t

ChromiumthinlmsweresputterdepositedimplementingtheGLan ingAngleDeposition(GLAD)method,

whi his athin lmdepositionte hniquewhere thein identvaporux - omposed ofatoms andmole ules

from gas phase- strikesonto thesubstrate at tilted angles

α

. Oriented hromium olumns were produ ed withvarious olumnangles

β

(from0to60°) loselylinkedtothesputteringpressureandin iden eangle

α

. Three sputteringpressuresof 0.11,0.40and0.53Pawereused. In iden eangle

α

ofthesputteredparti les wassystemati ally hanged from 0to 80°. Tribologi al propertieswere investigated as afun tion of these

operatingparameters. Resultsrevealthatthetribologi albehaviourisstrongly orrelatedwiththestru ture

and espe ially the growth me hanism of the lms, whi h are both linked with the operating sputtering

parameters. Thus,atthelowestsputteringpressure(0.11Pa),gradualvariationsofthetribologi alproperties

andwettabilityareobservedasafun tionofthein iden eangle

α

,whi hareinterrestingfortailoringsurfa es displayingagradientofwettability. In ontrast,athighersputteringpressures(>0.2Pa),lo alvariationsof

stati fri tion oe ient, wettability andlateral onta tstiness are systemati allyobserved asafun tion

ofthe olumnangle

β

-andthenthein iden eangle

α

. Basi ally,theseresultsenabletotailortribologi al properties by tuning the in iden e angle

α

in order to ontrol the transition from sti king to sliding in mi ro-gripping.

Keywords: MEMS,fri tion ontrol,nanos ulpturedthin oatings,mi ro-gripping,

1. Introdu tion

Inmi roassembly, two approa hes are urrently onsidered [1℄: (i) theself-assembly paradigm[2, 3, 4℄

in whi h surfa e ee ts are used to organize and assemble stru tures mainly up to a few mi rometers,

and (ii) the mi roroboti assembly [1, 5℄, based on the miniaturization of the a tuation, high resolution

mi romanipulatorsandgrippingdevi es(Fig. 1a),morededi atedtomesos opi sized omponents(between

a few mi rometers and a few millimeters). This one is well suitable for assembling MEMS omponents

where the main hallenging issues on ern the handling of small omponents (mainly down to about 10

µm). Currentresear h in this eld in ludes: (i) the development of new strategies to pi k up, to handle,

and to releasemi ro- omponentsasfor instan e mi roassembly in dry and liquid medium [6℄; and (ii) the

developmentof newtypesof surfa es [7,8,9,10, 11, 12,13℄, whi h would enableto ontrolseparately the

various omponentsoffri tiono urredin drymediummi roassembly. Inthisframework,whereasadhesive

omponents [14, 15, 16, 17℄ and apillary ee ts [1, 11, 13, 18℄ (see Fig. 1b) are generally ontrolled by

grafting self-assembly mole ules on grippers in order to redu e their surfa e tension [15, 19℄, me hani al

omponentsoffri tion-i.e stati anddynami fri tion oe ientsandespe iallystati todynani oe ient

ratio- ouldbe ontrolled bymeansofhighlyporousnanos ulpturedthinlms(Fig. 1 )purposelytailored

to a hievedesiredtribologi alproperties[9,13,20,21,22,23℄.

Emailaddress: philippe.stempfleens2m. fr(PhilippeStempé

a)

,AurélienBesnard

b)

,Ni olasMartin

a)

,Anne Domatti

a)

,JamalTakadoum

a)

)

(b) apillaryee tsinmi ro-assembly:thehandledobje tremainsstu konthebaremi rogripper;( )nanos ulpturedthinlm

thatis oatedonthegripper'sngers anpreventthese apillaryee ts,andmoreoveritenablesto ontrolthetransitionfrom

sti kingtoslidingbytailoringitsmi roar hite ture

GLan ingAngleDeposition (GLAD)method=rstreportedin 1959[24℄andlaterbyRobbieetal [25℄

= is an attra tive physi al vapour deposition method to fabri ate omplex1D, 2D or 3D nanostru tured

olumnarthin lms[26, 27, 28℄in luding nanopillars[23, 27, 28, 29, 30℄, zigzagnano olumns [20, 31℄, and

nanospirals[32℄. Thismethodisbasedonthe hangeoflo ationofthevapoursour erelativetothe olumns

duringgrowth. Basi ally,thesour eisnotmovedbutratherthesubstrate,whi h anbetiltedor/androtated

alongits entralaxis(Fig. 2). Thus,twodegreesoffreedom anbeadjusted: (i)arotationaxisatanangle

α

, whi h allows to vary the in iden e angle of the parti les ux, and (ii) a rotaryaxisat an angle

φ

also alled azimuthalangle, whi h indire tlymodies theposition oftheparti lessour e. TheGLADte hnique

takesadvantageof the shadowingee t reated by atilted substraterelative to thenormal in iden e and

a hange ofthe material ux througharotationof thesame substrateduring thedeposition. As aresult,

byfavouringthedire tionalgrowthofthe olumns and ontrollingtheirstru ture,itis possibleto produ e

various kindsofnanoar hite ture(Fig. 3) displayingawideningspe trumofphysi o- hemi alpropertiesof

materials in ludingtheirstateofstress [29, 33,34℄, density[35℄, opti al[22℄, ele tri al [35℄and me hani al

behaviours[23,28,30,32℄. Besides,topography[22,27,36,37℄andwettabilityoflms analsobe ontrolled

bytheoperatingparameters-i.e sputteringpressure,in iden eangle

α

and olumnangle

β

.

So, the aim of this work is to study how these operating parameters an inuen e the stru ture, the

density, theme hani al properties and nally thetribologi al propertiesof GLAD lmsunder low onta t

pressure(150 MPa) and low velo ity (0.1mm/s) asmetin lassi almi roassembly grippers[1, 5,38℄. For

this purpose, hromiumthin lms(thi knessabout850nmandRMS: 8.7

±

3.6nm)weresputterdeposited implementing the GLAD method on sili on wafers by varying boththe sputtering pressure (from 0.11to

0.53 Pa) and the in iden e angle

α

of the sputtered parti les from 0 to 80°. Oriented hromium olumns were produ ed with various olumn angles

β

(from 0to 60°) losely linked to the sputteringpressure and in iden eangle

α

. Notethatthepanelofar hite turesprodu edbyGLADmethodisnotsolelyrestri tedto metalli ompounds,but erami s[39℄,andsemi ondu ting[40℄oralloyedmaterials[41℄ anbegrown. Thus,

hromiumallowsthe synthesizeof attra tive ompounds forme hani alperforman es, espe ially metalloid

materials su h as some hromium nitride phases

CrN

or

Cr

2

N

. However, in this work, pure hromium lms was preferred to alloyed materials orother omplex ompounds be ause the sputtering me hanisms

of parti les are largely simplied and easier to simulate in order to understand the possible relationships

vapour sour e ona substrateholder, whi h anbetilteda ordingtoan angle

α

ompared to the normaltothe substrate. Moreover,it anbeanimatedbyarotation

φ

alonganaxis entredonthesubstrate.

Figure3: ObservationbySEMofthe rossse tionof: a)in lined;b)zig-zag; )heli al olumnarstru tureof hromiumlms

2.1. Deposition ofthe nanos ulptured hromiumthinlms

Chromiumthinlmsweredepositedon(100)sili onsubstratesbyd magnetronsputteringfrom hromium

metalli target (purity 99.7 at.%). The metalli target was sputtered with a onstant urrent density

J

Cr

= 200 A.m

−2

in argon atmosphere. The substrates were grounded and kept at room temperature. Argonmassowratewasset onstantinordertorea hasputteringpressureof0.11,0.40or0.53Pa

(pump-ingspeedwasmaintainedatS =10

L.s

−1

). Thedepositiontimewasajusted inordertodeposita onstant

thi kness loseto900nm. Thislatterwas he kedafterdeposition byprolometry. Thehome-madeGLAD

substrateholderallowedanorientation hangeofthein iden eangleoftheparti lesux

α

from 0to90°. 2.2. Thin lms hara terization

2.2.1. Stru tureanddensity

The rystallographi stru turewasinvestigatedbyX-raydira tion(XRD)usingmono hromatized

CoK

α

radiationwith aBragg-Brentano onguration

θ/2θ

. TheDebye-S herrer methodwasusedto al ulatethe rystallitegrainsize. Columnangle

β

wasmeasuredfrom s anningele tronmi ros opy(SEM)observations onthefra tured ross-se tionofthelmsdepositedonsili onsubstrates. Densityofthelmswas al ulated

asafun tionof thein iden eangle

α

ofthesputteredparti ulesandforthethree dierentpressuresusing Paik'srelationships[44℄. Density

ξ

oforientedthinlmsprodu edbyGLAD, anberelatedtothein iden e angle

α

oftheparti lesuxby:

ξ =

ξ

α=0

°

1 + c tan (α)

(1)

where

ξ

α=0

°

isthedensityofthelm(

kg.m

−3

)

depositedatanin iden eangle

α = 0

°and

c

isa onstant, whi hisproportionaltotheratiooftheshadowingstepheighttothe olumnthi kness. Atrst,wesuppose

thatthedensityofthebulkmaterial

ξ

0

isthesameasthedensityofthelmdepositedatanin iden eangle

α = 0

° (i.e

ξ

0

= ξ

α=0

). Parameter

c

depends on thenature of thesputtered materials andthe deposition onditions,espe iallythesputteringpressure. Films'densityvs. in iden eanglewas omputedforthethree

involvedpressure: 0.11,0.40and0.53Pa(Fig. 4).

An abruptdropofthe density anbenoti edfor in iden eangleshigherthan60°where theshadowing

ee tattheatomi s alebe omessigni ant. Forgrazingin iden eangles(

α > 80

°

)

,ahighporousstru ture is obtainedsin ethe density ofthelmis fewtens% ofthe bulk. Consequently,to getsomeknowledge of

the lm's density, evolution as afun tion of the in iden e angle

α

allows some lose orrelations between stru tural hara teristi s(e.g. thegrowthofaporousar hite ture)andtuneableme hani al[28℄orele tri al

properties[35℄.

2.2.2. Topographi al analysis

Thinlms exhibit self-ane properties in a ertain range of s ales[36, 37, 45℄. Self-anity is a

gener-alization of self-similarity, whi h is the basi property of mostof thedeterministi fra tals [46℄: apart of

self-ane obje tis similar to whole obje t after anisotropi s aling. Thus, manyrandomly rough surfa es

areassumedtobelong totherandomobje tsthatexhibittheself-aneproperties[47,48℄. Fra talanalyses

of the self-ane random surfa es using AFM or prolometer are often used to study and ompare these

surfa es,whi hhavethesamethi knessandroughness[37, 49, 50,51℄.

Dierentmethods offra talanalysis arereported in theliterature[16,18, 37,45, 46, 48,49, 50,51, 52,

53, 54℄. Ea h one displays its systemati error but results obtained by any method provide informations

aboutthedegree of omplexity orfragmentationof thesurfa es [45℄. However, themeasurementa ura y

anstronglybeae tedbythe hosenmethod[49℄. Thus,in thiswork,fra taldimension(

D

f

)is omputed by using a ube ounting method [37, 49℄ -implementedwithin theSPM data analysissoftware Gwyddion

(http://gwyddion.net) - whi h is dire tly derived from the well-reliable box- ounting approa h [48℄. The

algorithm is based on the following steps: a ubi latti e with latti e onstant

l

is superimposed on the z-expandedsurfa e. Initially

l

issetat

X

2

(where

X

islengthofedgeofthesurfa e),resultinginalatti eof8 ubes. Then

S(l)

isthenumberofall ubesthat ontainatleastonepixeloftheimage. Thelatti e onstant

Paik'smodelfordierentsputteringpressures[44℄

l

isthenredu edstepwisebyfa torof2andthepro essrepeateduntil

l

equalstothedistan ebetweentwo adja entpixels. Theslopeofaplotof

log(S(l))

versus

log(

1

_/

_l

₎

givesthefra taldimension

D

f

dire tly(Fig. 5a).

Sin e resultsof fra tal analysis an strongly beinuen ed by the tip onvolutionof the AFM analysis

(Digital Instruments Nanos ope III Dimension 3000), this one was he ked beforehand [49, 51℄. Besides,

fra tal's results were also ompared on largers ales by using a phaseshifting interferometri prolometer

ATOSMICROMAP570 (

λ

=520nm,spatialandverti alresolutionsare0.5µmand0.02nm,respe tively) in orderto omputethesystemati error: around3%. (Fig. 5b). Finallyaveragevalueof

D

f

was omputed from data ompiledfromthewholeAFMandinterferometri pi tures.

2.3. Nanotribologi al setup

Inthiswork,tribologi alexperimentsare arriedoutformodellingthetwo riti alstepsofmi rogripping

(i.e., pi k-upandrelease,respe tively)whensliding and/oradhesiono urbetweenthehandledobje tand

the gripper [1, 38 ℄. So, the experimental devi e is a ball-on-dis nanotribometer manufa tured by CSM

Instruments (Switzerland) [55℄. Fig. 6 displays the link between the mi rogripping (Fig. 6a) and the

tribologi al test (Fig. 6b): (i) the gripper is modelled by the atsample, whi h is oated by the various

GLAD lms; (ii) thehandled obje t is modelled bya

Si

3

N

4

ball whi h is gluedon the pin. Besides, the latteris mountedonasti lever(Fig. 6 ), designedasafri tionlessfor etransdu er(K

x =265.1Nm -1 ;K z =152.2 Nm -1

). During thetest, theballis loaded ontotheat samplewithapre isely known for e using

losed loop. Thefri tionfor e isdeterminedbymeasuringthedee tion oftheelasti arm(lowloadrange

downto50µN).Theloadandfri tionresolutionsareabout1µN.

AsshowninFig. 7,thenanotribometerissetwithinagloveboxinorderto ontrolboththetemperature

(22°C) andtherelativehumidity(RH35%) andso,anyadditional apillary ee tsthat ouldo urduring

thetests. Thenormalload(10mN)andtheball'sdiameter(

φ 4 mm

)area urately hosenforlimitingthe onta tpressureat 150MPa,whi hisusuallymetinmi rogripping[e.g.,1℄.

Alltestsare arriedoutinlinearre ipro atingmodebothin thedire tionparallel andperpendi ular

to the orientation of the olumns, with and against the tiltaxis of the olumns, in orderto noti eany

ee tofthe olumnangleonthefri tionbehaviour. AsreportedinFig. 8,twokindsoftestsare arriedout

Figure5: Examplesofthefra taldimensionassessmentsfor hromiumlmsdepositedwith

α

=

80°andsputteringpressureof 0.11Pa arriedouton(a)anAFMmap(1µm):

D

f

=2.21and(b)aninterferometri prolometermap(320µm):

D

f

=2.28

Figure6: Linkbetweenthemi rogrippinggeometry(a)andthenanotribologi altest(b): Thegripperismodelledbytheat

sample oatedbytheGLADlm;thehandledobje tismodelledbytheballgluedonthe antilever( )

Figure8:Tribologi altests: a)ingrossslipregimeformeasuring

µ

s

and

µ

d

onthewholeof y lesb)inabsen eofsliding,the assessmentoftheslopeof

F

T

= f (δ)

when

δ < a

(with

a

,thehertz onta tradius)givestheaveragelateral onta tstiness

k

L

ˆ (i)Whentheos illationamplitudeis greatlyhigherthanthe onta tradius(i.e

δ

±0.5 mm),agross slipregimeisobserved(Fig. 8a)leadingtoassessboththeaveragestati (

µ

s

)anddynami (

µ

d

)

fri tion oe ient,andalsotheratio

µ

s

µ

d

parti ularlyinterestingto ontrolthetransitionfromsti kingtosliding

inmi roassembly. Theaveragevalueoffri tion oe ientsare omputedby onsideringallthe y les

ofthetribologi altests. Besides, possiblewear analsobeassessed. Forthiskindoftest, thesliding

velo ityandthenumberof y lesare: 0.1mm.s -1

and10 y les,respe tively.

ˆ (ii)Whentheos illationamplitudeislowerthanthe onta tradius(

δ

±10µm),noslidingiso urred (Fig. 8b). So, the oatingis just submittedto ashear test, that enablestoassess thelateral onta t

stiness asreportedbyMindlinetal [56℄. Thevariationsofthelatterwiththesputteringparameters

(in iden eangle

α,

sputteringpressure)provideinformationsabouttheme hani alpropertiesoflms. Thelateral onta tstiness istheslopefromthefri tionfor evs. displa ement(Fig. 8b). Inthis ase

thevelo ityandthenumberof y lesare5

µm.s

−1

and10 y les,respe tively.

3. Resultsand dis ussion

3.1. Morphology andstru tureofGLAD thinlms

As expe ted by thestru tural zone model proposedby Thornton[57℄, lmsdeposited a ordingto our

deposition onditions and with a perpendi ular in iden e of the parti les ux (

α = 0

°

)

exhibit a typi al olumnar mi rostru ture. This kind of morphology orresponds to the transition zone of the Thornton's

modelsin ethesputteringpressurewas0.11,0.40and0.53Paandthesubstratetemperaturewasafewtens

ofthe hromiummeltingpoint(2173K).Columns onsistofinverted one-likeunits appedbydomes. Films

produ edwiththeseoperating onditionsappearasaquitedensestru turewith olumnswidth loseto100

nm. Theyaremoreorlessseparatedbyvoidedboundariesthatarefewnanometreswide. Asimilar olumnar

stru ture wasprodu ed forlms preparedat sputteringpressureof 0.11, 0.40and 0.53Pa. In reasing the

in iden e angle

α

of the parti les ux, in lined olumns be ome separated and a mu h moreporous and brousstru tureisprodu edasthein iden eangle

α

in reasesandthesputteringpressureredu esdownto 0.11Pa. Itisalsoworthofnoti ingthatthe olumn angle

β

isinuen edbythesputteringpressure(Fig. 9 ).

Asthein iden eangle

α

tendsto90°,the olumnangle

β

asymptoti allyrea hes24°for0.53Pawhereas

β

tendsto35° for0.40Paand

β

rea hes60°for0.11Pa. Thus,forthethree sputteringpressures,

β

versus

α

well follows the empiri al tangent rule (

tanα = 2 tan β

) up to an in iden e angle

α

lose to 60°, as ommonlyobservedforseveral ompounds[58℄. Afterwards,asaturationofthe olumnangle

β

o urs. Itis mainly attributedto themeanfreepathofthesputteredparti lesand thesputteringemission(the angular

Figure 9: Evolutionof the olumn angle

β

vs. in iden eangle

α

in hromium thinlms deposited by sputtering for three dierentargonpressures. Columnangle

β

saturates loseto24and35°forsputteringpressureof0.53and0.40Pa,respe tively

Figure10: Typi alSEMviewsofthe fri tiontra kafterslidingforthreesputteringpressures: (a)0.11 Pa,(b)0.40Paand

( )0.53Paandforthesamein iden eangle

α

= 75

°(horizontalslidingdire tion)

to the target material. Due to enhan ed ollisions between sputtered parti les and argon atoms, ux of

hromiumatoms impinging on the growing lm be omes less dire tional[60℄. Theangular distribution of

sputtered hromium in oming from the target surfa e is spreadleading to a more randomizedux rather

thanpureballisti and onsequently,asaturationofthe olumnangle

β

( f. Ÿ3.6). 3.2. Tribologi al propertiesof GLAD thinlmsin grossslip regime

3.2.1. Evolutionof theaverage dynami fri tion oe ientwith the sputteringparameters

In ontrast to what waspreviously observedby Abreu et al [21℄ and Lintymer et al [34℄ on hromium

GLADlmsinmi ro-andma rotribologi altests,respe tively,theinitial olumnarstru tureisnotdamaged

after sliding using amulti-asperity nanotribometer (Fig. 10). So, theadhesion and the ohesion of these

lmsarestrongenoughto sustainthe onta tsoli itations-150MPa-whateverthe oating onditions.

Fig. 11 shows the evolutionof the average dynami fri tion oe ient (

µ

d

) vs. the in iden e angle

α

for thedierent argonsputteringpressures. Forthe lowestpressure(0.11Pa),

µ

d

abruptly in reaseswhen the in iden eangle ishigher than50°. In onstrastfor thehighestargon pressure(0.53Pa),

µ

d

displaysa minimum for in iden e anglesin-between 20and 40° revealing a bowl shapearound these values. Forthe

mediumsputteringpressure(0.40Pa),

µ

d

showstwomaxima(about0.32)for20°and55°respe tively,whi h reveal some kind of lo al ee ts probably indu ed by ne variations of the stru ture. As an unexpe ted

Figure11:Variationsoftheaveragedynami fri tion oe ientvs. in iden eangle

α

forthethreeargonsputteringpressures

result, no dieren e is observed in the tribologi al behaviours arried out in the dire tion parallel and

perpendi ular totheorientation ofthe olumnsasreportedby[23, 61℄. However,theseauthors useda17

µm radius diamondindenter tip asa slider - ommonly used in nanoindentation test - whi h is probably

more sensitivebut also more destru tive than ours (2 mm radius

Si

3

N

4

ball). In the sameway, there is no real dieren e between tribologi al tests arried out with and against the tilt axis of the olumns.

This isprobablydue tothesize ofthe onta tarea,whi h ismu h moreimportantthanboththe olumns

size and the distan e between the olumns. Hen e, the onta t in multi-asperity nanotribology appears

quiteinsensitivetotheindividual orientationofthe olumns. Indeed,asreportedbymanyauthorsworking

on GLADmethod [62, 63, 64℄, obtainingsurfa etopographieswithoutsto hasti and non-separatesurfa e

features isthe main hallengeof thiste hnique. However,arouteto bypassthisissue ouldbeto reatea

seeded layerof known density and heightprior to the GLADdeposition [27℄. So, in our ase, the olumn

orientation

β

doesnotappearas thedriving for e that ontrols the hange in thefri tion behaviour. But, referringtomanyauthors[eg. 7℄,thelms'density-andmoreparti ularlythelms'porosity-areprobably

themainones.

Whentheerrorbarsappearto belowenough-asobservedin Fig. 11-apseudo3D-map-asshownin

Fig. 12-willbeusedinsteadofthe lassi al2Dviewinorderto onsiderboththesputteringpressureand

thein iden eangle

α

(Fig. 12a)orthe olumnangle

β

(Fig. 12b). Thusthe omparisionofFig. 12andFig. 4revealsthat thein rease of

µ

d

startingfrom 45° and55° (for0.11Paand 0.53Pa,respe tively) strongly orrespondsto thedropof thelms' density down to 93%. Inthe sametime, theminimunof

µ

d

observed in-between20° and50° (Fig. 11at 0.53Pa) greatly orrespondsto the zonewhere the lm'sdensitystays

onstant(Fig. 4). Thus,

µ

d

appearsasaparameterthatisverysensitivetoany hangeinthelms'density asabulkparameter.

However,inmi ro-grippingthestati fri tion oe ientandmoreparti ularlythetransitionbetweenthe

stati anddynami fri tion oe ienthasprobablyagreaterimportan ethanthedynami oneonly.

3.2.2. Evolutionof theaverage stati fri tion oe ientwiththe sputteringparameters

Fig. 13showsthepseudo3D-maps oftheaveragestati fri tion oe ient

µ

s

omputedfromthewhole of y les (10 y les ba k and forward). Overall,

µ

s

has the same global behaviour than

µ

d

with respe t to the operating parameters. Neverthelessit denitely appears moresensitive than thelatter to anylo al

Figure12:Pseudo3D-mapsdisplayingtheevolutionoftheaveragedynami fri tion oe ient

µ

d

asafun tionofthesputtering argonpressureand(a)thein iden eangle

α

and(b)the olumnangle

β

tribologi alvariationslinkedto lowvariationsin thesputteringparameters. Thus,

ˆ forthelowestpressure(0.11Pa),

µ

s

is rather onstantuntil

α = 50

°and stronglyin reaseswhenthe lm'sdensitydropsasreportedfor

µ

d

;

ˆ whentheargonsputteringpressurein reasesfrom0.11to0.53Pa,thereare olumnangles

β

(Fig. 13b) where

µ

s

displays amaximum(

µ

s

≃

0.5 at0.40 Pa) oraminimum (

µ

s

≃

0.17 at 0.53Pa). Besides, aroundthese latter,

µ

s

an bestrongly modied- i.e multiplied ordividedbyafa tor 2-when

β

is shiftedto

±

5

°( orrespondingtoashiftof

α

around

10

°asshownin Fig. 13a).

Thus, for thelowest sputtering pressure, the behaviour of the stati fri tion oe ient is the sameas the

dynami one-i.e ontrolled bythelms'sdensityasabulkproperty. But, foragivensputteringpressure

higherthan0.11Pa- orrespondingtoa hangeinthesputteringme hanismfromapureballisti toamore

randomisedone( f. Ÿ3.1)-thestati fri tion oe ient ana uratelybe ontrolledbyadjustementofthe

in iden eangle

α

. Sin ethedynami fri tion oe ientislesssensitivethanthestati one,itisalsopossible to adjust theratio

µ

s

µ

d

bytuning

µ

s

that allowsto a urately ontrol thetransition fromsti king tosliding byavoidingthesti k-slip o urren e[65℄and its onsequen es onthefri tion[66℄ andwearbehaviours[67℄.

Forexample, Fig. 14 showstwo dierent aseswhere the sti k-slip o uren e is ompletely avoided when

µ

s

= µ

d

(at0.40Paand

α = 5

°or

α = 35

°)orwhenthesti kingisfavouredovertheslippingwhen

µ

s

≫

µ

d

(e.g.

µ

s

> 2.µ

d

at 0.40Paand

α = 45

° or

α = 75

°). Hen e,tuneabletribologi alproperties aneasilybe obtainedinmi ro-grippingbyusing suitablesputteringoperatingparameters.

However,in onstrasttowhat isobservedfor

µ

d

(Fig. 4and 12),theevolutionof

µ

s

withtheoperating parameters an not be dire tly explained by onsidering the lms' density only. Indeed, Fig. 13a is not

dire tly omparablewithFig. 4asreportedfor

µ

d

. So,it isne essaryto remindthephysi aloriginsofthe stati oe ienta ordingtotheliterature:

µ

s

originatesfromthestati real onta tarea ontrolledbythe physi o- hemi alpropertiesof thesurfa es, in ontrastto

µ

d

, whi h is mainly governedby theme hani al propertiesat thes aleofthemi ro-asperitiesin ludingelasti ity,stinessandinertiaofthe onta t[18℄. In

orderto understandtherelationshipbetweenthestati oe ientbehaviourandtheoperatingparameters,

thephysi o- hemi alandme hani alpropertiesofGLADlmswillbestudiedsu essivelyusing(i)wettability

[15,18, 38℄andfra taldimension assessment[36,37,45,47,48,68,69,70℄ontheonehand,and (ii)lateral

onta tstiness measurementontheotherhand[56℄.

3.3. Wettability - Evolutionof the onta tangle of awaterdrop withthe sputteringparameters

Fig. 15 showsthevariationsof the onta tangle

θ

ofawaterdropasafun tion ofthein iden e angle

Figure13: Pseudo3D-mapsdisplayingtheevolutionoftheaveragestati fri tion oe ient

µ

s

asafun tionofthesputtering argonpressureand(a)thein iden eangle

α

and(b)the olumnangle

β

Figure14: 3D-mapdisplayingtheevolutionoftheratio

µ

s

µ

d

asafun tionofthesputteringargonpressureandthein iden eangle

α

. Thismapisveryusefultopredi ttheoperatingparameters(i)toavoidanysti k-slipphenomenon-e.g. when

µ

s

= µ

d

for 0.40Pa,

α

= 35

°-oronthe ontrary,(ii)tofavoursti kingoverslippingwhen

µ

s

≫

µ

d

(e.g.0.40Pa,

α

= 75

°when

µ

s

>

2.µ

d

)

Figure15: Variationofthe onta tangle

θ

ofawaterdropvs. in iden eangle

α

forthethreesputteringpressures

(

θ > 90

°

)

in ontrasttotheinitial hromiumtarget,whi hishydrophili (

θ = 49.1

°

±

0.6

). Thus,the onta t angle

θ

ofawaterdrop-and onsequentlytheunderlyingadhesive ontributionoffri tionduetothe apillary ee ts -seemsto be ontrolled bythenanostru turationofthesurfa es[7,71,72℄. Inour ase,the onta t

angleofthewaterdrop learlydependsonthesputteringpressure:

ˆ forthehighestpressures(0.53Pa)the onta tangleisrather onstant(about117°);

ˆ in ontrastforthelowestpressure(0.11Pa),the onta tangle ontinuouslyin reasesfromahydrophili

behaviour to ahydrophobi one. A lineartrend is evennoti ed with agood orrelation oe ient (r

=0.99)revealinganenhan ementofthehydrophobi behaviourwiththein iden eangle

α

. However, the onta t angle does not evolve anymore for the highest in iden e angles. This result is in good

agreementwiththetheoriesproposedsu essivelybyWenzel(1936)andCassie-Baxter(1944)in order

to explain thewettabilityof heterogeneous surfa es [7, 9,10, 71, 72℄. This saturation value(around

125°)isprobablyduetotheshadowingee t attheatomi s aleasmentionedinŸ2.2.1.

As reported in Fig. 16, the evolution of the water drop onta t angle

θ

as a fun tion of the operating parametersrevealsthatthewettabilityvariesaswellasthelms'density(Fig. 4)leadingto the on lusion

thatthevariationsofthe onta tangle

θ

isdire tly ontrolledbythelms'porosity-des ribedasairpo kets, whi hareableto ontrolthewaterdropletspreadingout[7℄.

However,thesize ofthewaterdropbeinggreatlylargerthanthestati real onta tarea,thevariations

of the onta tangle

θ

asa fun tion of thelm's density arenot really a urateenough to explainthat of

µ

s

. Hen e,ana urateexperimental assessementofthe oatings'densityisneeded. Thefra tal dimension isoneofthembe auseitprovidesa urateinformationsaboutthedegreeoffragmentationofthesurfa es.

3.4. Evolution ofthe fra taldimension with the sputteringparameters

For thin oatings, the fragmentation of the surfa es is strongly onne ted to the degree of porosity of

these ones: themore thesurfa e is fragmented, the higheris the fra tal dimension (

D

f

in-between2 and 3). Thus,aswettability,fra taldimension shouldberepresentativeofthelm'sporositybutwithagreater

sharpness due to thetopographi assessment te hnique -i.e AFM and interferometri prolometry -more

Figure16: Pseudo3D-mapsdisplayingtheevolutionoftheaverage onta tangle

θ

ofawaterdrop(in°)asafun tionofthe sputteringargonpressureand(a)thein iden eangle

α

and(b)the olumnangle

β

Figure17: Pseudo3D-mapsdisplayingtheevolutionoftheaveragefra taldimension

D

f

asafun tionofthesputteringargon pressureand(a)thein iden eangle

α

and(b)the olumnangle

β

Figure18: a)Pseudo3D-map displayingthe evolution ofthe average lateral onta t stiness (

N m

−1

)

as a fun tion ofthe sputteringargonpressureandforvarious olumnangles

β

andb)X-raydira tionpatternsof hromiumthinlmsdeposited at0.40Paandforvariousin iden eangles

α

(thesharp entralpeakisthe hromiumone orrespondingtotheinitialtarget)

As expe ted, in rst approximation and in great agreement with the literature [68, 69, 70℄, Fig. 17

revealsthat

D

f

varies asthewettabilityresults. Inthe sameway, there isno obvious orrelation between

µ

d

(Fig. 12)and

D

f

in agreementwithGantietal [47℄. However,asanunexpe tedresult, itappearsthat

D

f

has the same variations as

µ

s

(Fig. 13): espe ially the positions of their maximum (at 0.40 Pa and

α = 20

°)andminimum(at0.53Paand

α = 20

°)arequitesimilar. Thus,thevariationsof

µ

s

seemstrongly orrelatedwiththatof

D

f

,whi happearsasthelo al variationsofthelms'porosity-shownasairpo kets. Besides,thefra taldimension'smap(Fig. 17)givesmorea urateinformationsaboutthesurfa ethanthose

omputedfromatheoreti almodel(Fig. 4),whi h annottakeinto a ountthelo al variationsofthereal

nanostru tures. It iswellknown[71℄, that thelatter-bymeansofse ondarygraingrowthforinstan e- is

ableto reatesomekindofinstabilitiesatthes aleofthemi ro-nano onta tdueto apillaryee ts. Thus,

thelo al variationsof

µ

s

ouldbeexplainedby onsideringthelo al variationsofthelms'porosity-i.e at thes aleofthe olumns-revealedbythelo al variationsofthefra taldimension

D

f

. However,theseones ould alsolo ally hange theme hani alpropertiesof thesurfa es and onsequently thefri tionbehaviour

too. Theseevolutions anbeassessedbymeansofthelateral onta tstiness (

k

L

)

. 3.5. Evolution ofthe lateral onta tstinesswith the sputteringparameters

Asmentionedbefore(Ÿ2.3),thelateral onta tstiness (

k

L

)istheslopefromthefri tionfor evs. lateral displa ementwhentheos illationamplitudeislowerthanthe onta tradius(±10µm) -i.e whenthethin

lm is submittedto analternativeshear testing whereno sliding o urs. Referringto Mindlin et al. [56℄,

thislateral onta tstiness

k

L

(N m

−1

)

is onne tedto theelasti propertiesofsamplesasfollow:

k

L

= 8a

1

2−ν

1

G

1

+

2−ν

2

G

2

(2)

where

a

isthe onta tradius(m),

G

i

and

ν

i

aretheshearmodulus(

N m

−2

)andthePoisson'ratioofea h

sample,respe tively.

Fig. 18arevealsthatthevariationsoftheaveragelateral onta tstiness

k

L

arequitelow(from95to109

N m

−1

)be ausethesurfa eisratherhomogeneousanddenseenoughinthethi knesstoinsuretheme hani al

ohesionofthelms(the averagevalueisabout103

N m

−1

). Theseresultsareingoodagreementwiththe

XRD ones, whi h reveal similar dira tion patterns with respe t to the operating parameters. Hen e,

k

L

- and onsequentlythe elasti properties of thelms - is notreally ontrolled by the sputteringoperating

parameters.

Howeversome variations of

k

L

- similar to that of

D

f

and

µ

s

- are lo ally observed: thus, as shown in Fig. 18a,the maximum of thelateral onta tstiness learly orresponds to the maximumof

µ

s

(Fig. 13b) butelsewherethevariationsof

k

L

annotbedire tly onne tedtothevariationsof

µ

s

. Theseresults are alsoin goodagreementwiththeXRD ones (Fig. 18b), whi hreveal bothawidening andashiftofthe

Figure19: Angulardistributionof hromiumsputtered parti lesobtainedfromSIMTRA[73℄foranin iden eangle

α

=80° andforanargonsputteringpressureofa)0.11Pa;b)0.40Pa; )0.53Pa.

some hanges ofthe rystallitessize or(ii) thepresen eof potentialtensionmi ro-stresseswithin thelms

fabri ated at 0.40Pawith these in iden eangles. Thus, the global variationsof the lms'porosity donot

really hangetheme hani alpropertiesofthelms: thelatterarequitehomogeneousand ontrolledbythe

densersubsurfa e. However,thelo al variationsofthelateral onta tstiness -whi harethesameasthose

of

D

f

and

µ

s

- ould be orrelated with either (i) thepresen e of internal stressesor(ii) some hanges of the rystallitessizeasreportedbeforebythese ondarygraingrowth. So,thereis learlyarelationbetween

growth,stru tureandtribologi alproperties.

3.6. Relationbetweengrowth,stru tureandtribologi al properties

Forthelowest sputteringpressure(0.11Pa), hromiumthin lms exhibitaregular olumnarstru ture.

As previously observedin Fig. 9,growingof the highest olumn angle

β

is produ ed fora systemati rise of the in iden e angle

α

. Inaddition, the olumnarstru ture is kept forhigh sputteringpressures but,

β

anglesaturates at35and 22°forthe orrespondingpressureof0.40and 0.53Pa,respe tively. Su hregular

olumnargrowthobservedat0.11Pais mainlyattributed to thedire tionalux ofthesputteredparti les,

whi hisespe iallyfavouredatlowsputteringpressure(Fig. 19).

Simulation of the parti les ux from SIMTRA software [73℄ allows thedetermination of the sputtered

parti les traje toriestaking intoa ountthe geometryof thesputtering hamberand operating onditions

(e.g. pressure, ion urrent density on the target, ...). It is worthof notingthat this spatial distribution

exhibit a strong dire tional ux at 0.11 Pa and for an in iden eangle

α

= 80°(Fig. 19a). An in reasing sputtering pressureup to 0.40 Paleads to a spreadingof the distribution (Fig. 19b), whi h is even more

emphasizedat0.53Pa(Fig. 19 ). Asaresult,su halossofthedire tionalparti lesuxwiththesputtering

pressurehasto be orrelatedwithsomefeatures ofthe olumnargrowthaswellassomesingularitiesofthe

stati fri tion oe ient,thefra taldimension andtosomeextentsthelateral onta tstiness.

ˆ On the one hand, for sputtering pressure of 0.11 Pa, the evolution of the olumnar orientation vs.

in iden eangle

α

issmooth. A regulargrowthisprodu eddue toanarrowspatialdistribution ofthe parti lesux(Fig. 19a). So,mostofthesputteredatomsimpingeonthegrowinglma ordingtothe

givenin iden eangle

α

. Thus,agradualvariationofthetribologi alproperties(Fig. 11), waterdrop onta tangle

θ

(Fig. 15),fra taldimension(Fig. 17)aremeasuredasafun tionofthein iden eangle

α

. Asaresult,variationsof

µ

s

arequitesimilartothe

µ

d

ones.

ˆ Ontheotherhand,anin reasingsputteringpressuredoesnotsolelyredu e themeanfreepathofthe

sputteredatomsand so,the s atteringofthe ux. It alsofavoursthese ondarygrain growthin thin

lms,asillustrated in Fig. 20for hromium thin lmsexhibiting aspiral olumnarstru ture. Thus,

amulti-dire tional hara teroftheparti les ux prevailsagainstasingleorienteduxfor the hosen

in iden e angle

α

= 80°. Thermalization ee t of the sputtered parti les o urs and gives rise to a morerandomizedgrowthofthe olumnarstru tureleadingtolo al variationsofsurfa espropertiesas

porosityasre entlyreported[31℄. Tribologi albehavioursof thelms preparedathigh pressure an

usinga onstantin iden eangle

α

=80°andasubstraterotation

φ

=0.5revolutionperhour. Ase ondarygraingrowth an be learlyobserved.

sputteredparti les. Typi allo al variationsofstati fri tion oe ient,thehighestfra taldimension

orthestrongest lateral onta tstiness aresystemati allyobservedforin iden eangles

α

=0to 30° ( orresponding

β

anglesare0to20°)andforpressuresin-between0.30to0.50Pa. Therefore,thisrange ofin iden eanglesandpressureswell orrelatewith hangesofthenanostru tureduetose ondarygrain

growth,andfri tionbehaviours. Hen e,thisrangeofsputteringpressuresenablestotailortribologi al

propertiesfavouringsti kingoversliding or,in ontrast,avoidinganysti k-slip o urren e.

4. Con lusion

Inthiswork, hromium thinlms weresputterdepositedimplementingtheGLan ingAngleDeposition

(GLAD)method(i.e thein identvapouruxstrikesontothesubstrateattiltedangles

α

)inorderto reate in linednanos ulpturedthinlmsfor ontrollingtribologi albehaviourinmi ro-grippingappli ations. Three

sputtering pressures0.11,0.40 and 0.53Pa were used and thein iden e angle

α

of thesputtered parti les wassystemati ally hangedfrom0to80°. Firstly,resultsrevealthattheme hani alpropertiesofthelms

-asabulkparameters-donotreally hangewiththesputteringparameters. Se ondly,tribologi albehaviour

- in luding surfa eproperties - is strongly orrelatedwith the growth me hanism andthe stru ture of the

lms,whi harebothlinkedwiththeoperatingsputteringparameters. Thus,

ˆ forthelowestsputteringpressures,aregulargrowthisprodu edduetoanarrowspatialdistributionof

theparti lesux. So, hromiumlmsexhibitaregular olumnarstru ture. Thevariationofthe olumn

orientationisverysmoothwiththein iden eangle

α

. Agradualvariationofthetribologi alproperties, andespe ially thewettabilityisnoti ed asafun tion of thein iden eangle

α

. In pra ti e,this level ofsputteringpressureisquiteinterestingfortailoringsurfa es displayingagradientofwettability;

ˆ in ontrast,when thesputteringpressuresare in reasedbeyondthepure balisti sputteringarea,the

meanfreepathofthesputteredatomsisstronglyredu ed,andsothes atteringoftheuxprevails. In

the olumnarstru ture. Lo al variationsofstati fri tion oe ient, wettability,surfa eporosityand

lateral onta tstinessaretypi allyobservedinthisrangeofsputteringpressures. Thislatterenables

totailorsuitablesurfa espropertiesbytuningthein iden eangle

α

favouringsti kingoverslidingor, in ontrast,avoidinganysti k-slip o urren e. Indeed,thestati fri tion- andmoreparti ularly the

ratio

µ

s

µ

d

- an easilybeadjusted to ontrolthetransitionfromsti kingtosliding inmi ro-gripping.

A knowledgments

TheauthorsaregratefultotheRégionFran heComté (Fran e)foritsnan ialsupportundertheawards

FIMICAP :Reliability ofmi ros ale assemblyanddesign of smartsensorsusingsurfa eengineering.

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