DTIC ADA593442: The Mechanical Robustness of Atomic-Layer- and Molecular-Layer-Deposited Coatings on Polymer Substrates

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JOURNALOFAPPLIEDPHYSICS105,093527(cid:1)2009(cid:2)
The mechanical robustness of atomic-layer- and molecular-layer-deposited
coatings on polymer substrates
David C. Miller,1,2,a(cid:1) Ross R. Foster,1,2 Yadong Zhang,1,2 Shih-Hui Jen,2,3
Jacob A. Bertrand,2,3 Zhixing Lu,1,2 Dragos Seghete,2,3 Jennifer L. O’Patchen,2,3
Ronggui Yang,1,2 Yung-Cheng Lee,1,2 Steven M. George,2,3 and Martin L. Dunn1,2
1DepartmentofMechanicalEngineering,UniversityofColorado,Boulder,Colorado80309,USA
2DARPACenterforIntegratedMicro/Nano-ElectromechanicalTransducers(iMINT),UniversityofColorado,
Boulder,Colorado80309,USA
3DepartmentofChemistryandBiochemistry,UniversityofColorado,Boulder,Colorado80309,USA
(cid:1)Received 26 January 2009; accepted 26 March 2009; published online 12 May 2009(cid:2)
The mechanical robustness of atomic layer deposited alumina and recently developed molecular
layer deposited aluminum alkoxide (cid:1)“alucone”(cid:2) films, as well as laminated composite films
composedofbothmaterials,wascharacterizedusingmechanicaltensiletestsalongwitharecently
developed fluorescent tag to visualize channel cracks in the transparent films. All coatings were
deposited on polyethylene naphthalate substrates and demonstrated a similar evolution of damage
morphologyaccordingtoappliedstrain,includingchannelcrackinitiation,crackpropagationatthe
critical strain, crack densification up to saturation, and transverse crack formation associated with
buckling and delamination. From measurements of crack density versus applied tensile strain
coupled with a fracture mechanics model, the mode I fracture toughness of alumina and alucone
films was determined to be K =1.89(cid:1)0.10 and 0.17(cid:1)0.02 MPam0.5, respectively. From
IC
measurementsofthesaturatedcrackdensity,thecriticalinterfacialshearstresswasestimatedtobe
(cid:2)=39.5(cid:1)8.3 and 66.6(cid:1)6.1 MPa, respectively. The toughness of nanometer-scale alumina was
c
comparable to that of alumina thin films grown using other techniques, whereas alucone was quite
brittle. The use of alucone as a spacer layer between alumina films was not found to increase the
criticalstrainatfractureforthecompositefilms.Thisperformanceisattributedtothelowtoughness
of alucone. The experimental results were supported by companion simulations using fracture
mechanics formalism for multilayer films. To aid future development, the modeling method was
usedtostudytheincreaseinthetoughnessandelasticmodulusofthespacerlayerrequiredtorender
improved critical strain at fracture. These results may be applied to a broad variety of multilayer
materialsystemscomposedofceramicandspacerlayerstoyieldrobustcoatingsforuseinchemical
barrier and other applications. © 2009 American Institute of Physics. (cid:3)DOI:10.1063/1.3124642(cid:4)
I. INTRODUCTION The mechanical properties of alumina16,17 and alucone18
films (cid:1)including modulus and coefficient of thermal expan-
Nanometer-scale thick films grown using the atomic sion(cid:2)havebeenexaminedrecently,whereasthepermeability
layer deposition (cid:1)ALD(cid:2) technique1–4 have found application ofaluminafilmshasbeenexaminedseparately.8,9Fromthese
as high (cid:3)dielectrics within the field of integrated circuit studies,ALD and/or MLD permeation barriers are expected
technology.5 The recently developed technique known as to benefit from the characteristics unique to the deposition
molecular layer deposition (cid:1)MLD(cid:2)6,7 may be used to create techniques, i.e., the resulting films are continuous, confor-
organic-based,polymerlikefilms.ALDand/orMLDcoatings mal, pin-hole free, and may be grown with subnanometer
havebeenproposedforabroadrangeofapplications,includ- thickness control. In particular, alumina should be less per-
ingthesurfacemodificationofcompliantsubstrates,8,9nano- meable based on its amorphous microstructure,4 i.e., it lacks
particles or nanotubes,10,11 porous films/membranes,11,12 and grain boundaries. Alternately, the covalent bonding present
microsystems.13 Such coatings may be used to tailor charac- between alumina and alucone6 is expected to result in im-
teristics including chemical permeation, charge dissipation, provedinterfacialadhesion,essentialtoapermeationbarrier.
surfaceadhesion,chemicalabsorption,ortribological(cid:1)wear- The mechanical robustness of alumina and alucone coatings
resistance(cid:2).Ofthese,achemicalbarriercoatingcouldconsist specific to the chemical barrier application has not been pre-
of a single layer, such as ALD alumina. Alternately, MLD viously examined.
aluminum alkoxide (cid:1)“alucone”(cid:2)6 may be interposed between Failure modes for a film on a substrate include delami-
ceramiclayers,8,9mechanicallydecouplingthelayersthereby nation, channel cracking, spalling of the film/substrate sys-
increasing the critical strain associated with film cracking,14 tem, simultaneous wrinkling of the film and substrate, and
while also creating a more tortuous path that limits the per- buckling combined with delamination.19–23 Additional
meation of chemical species.15 microstructure-specific mechanisms that may relieve stress
within a film, such as dislocation propagation and stacking
a(cid:2)Electronicmail:[email protected]. fault activity,24 are not applicable to alumina coatings, be-
0021-8979/2009/105(cid:2)9(cid:1)/093527/12/$25.00 105,093527-1 ©2009AmericanInstituteofPhysics
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
The mechanical robustness of atomic-layer- and
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molecular-layer-deposited coatings on polymer substrates
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University of Colorado,Department of Chemistry and REPORT NUMBER
Biochemistry,Boulder,CO,80309
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093527-2 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
causeoftheiramorphousnature.Theaforementionedfailure saturation, where the crack density is no longer increased
modes are known to depend upon the elastic mismatch be- withstrain,ashear-lagmodelmaybeusedtorelatebetween
tween the film and substrate, i.e., the Dunder’s parameters, the maximum shear across the load transfer region and the
Eqs. (cid:1)1(cid:2) and (cid:1)2(cid:2).20 applied load,31–34 Eq. (cid:1)6(cid:2).
D1= Ef−Es. (cid:1)1(cid:2) c1(cid:3)D1(cid:4)(cid:7)hf (cid:11)(cid:2)(cid:11) 2c1(cid:3)D1(cid:4)(cid:7)hf. (cid:1)6(cid:2)
Ef+Es (cid:9)min c (cid:9)min
1E (cid:1)1+(cid:4)(cid:2)(cid:1)1−2(cid:4)(cid:2)−E (cid:1)1+(cid:4)(cid:2)(cid:1)1−2(cid:4)(cid:2) New parameters in the equation include the coefficient
D2= 2 Ef (cid:1)1+s(cid:4)(cid:2)(cid:1)1−(cid:4)s(cid:2)+Es(cid:1)1+(cid:4)f(cid:2)(cid:1)1−(cid:4)(cid:2)f . (cid:1)2(cid:2) c1 (cid:1)unitless(cid:2), (cid:7)as the net stress present in the far field (cid:1)Pa(cid:2),
f s s s f f (cid:2) as the critical interfacial shear between the film and sub-
c
The effective modulus of the film or substrate may be strate (cid:1)Pa(cid:2), and (cid:9) as the minimum crack spacing (cid:1)m(cid:2).Ap-
min
understood according to the condition of plane strain typi- plying to the case of a stiff film on a compliant substrate, c
1
cally present, Eq. (cid:1)3(cid:2). may be obtained from Fig. 9 in Beuth and Klingbeil34 to
account for more complex slip/crack interaction associated
E
E = i . (cid:1)3(cid:2) with plastic deformation of the substrate, which is not con-
i (cid:1)1−(cid:4)2(cid:2)
i sideredinthelinearstress/sliplengthprofileusedinthestan-
The energy release rate associated with the applied- and dard shear-lag representation.32,34
residual-mechanical conditions is represented in Eq. (cid:1)4(cid:2).19 Inadditiontochannelcracking,thePoisson’seffectdic-
(cid:5) (cid:6)
tatesthatthefilmwillbeaffectedinthedirectionorthogonal
G= (cid:5)hf Ef(cid:6)o +(cid:7) 2g(cid:3)D ,D (cid:4). (cid:1)4(cid:2) totheapplieddeformation.26,35Inthecaseofpoorinterfacial
2Ef 1−(cid:4)2f r 1 2 adhesion, the film may immediately delaminate in conjunc-
tionwithbucklingand/orcracking.20,36Inthecaseofacom-
In comparison, the energy release rate required to frac-
ture the strained film is given in Eq. (cid:1)5(cid:2). pliant substrate, the film and substrate may instead remain
adhered after mechanically buckling.23,37,38 In this
K2 “wrinkled” configuration, the film may fracture at the peri-
(cid:8)= IC. (cid:1)5(cid:2)
E odic wave peaks.Therefore, whether or not the film remains
f
adhered to the substrate, a series of transverse cracks may
In the equations, here for the international system of
come to exist in the direction parallel to the applied defor-
units, D represents the Dunder’s parameters (cid:1)unitless(cid:2), E is
mation. For an elastic film and substrate, the strain required
theelasticmodulus(cid:1)Pa(cid:2),(cid:4)isthePoisson’sratio(cid:1)unitless(cid:2),G to initiate buckling (cid:6) may be estimated from Eq. (cid:1)7(cid:2).23,37,38
istheenergyreleaserate(cid:1)Pam(cid:2),(cid:5)isthemathematicalcon- (cid:5) (cid:6) b
sistatnhte,hreissitdhueatlhsictrkensesssw(cid:1)imth(cid:2)in,(cid:6)tohiesfithlemap(cid:1)Ppali(cid:2)e,dthsteracione(cid:1)fmfic/mie(cid:2)n,t(cid:7)gr (cid:6)b= 14 3EEs 2/3 (cid:1)7(cid:2)
accounts for elastic misfit between the film and substrate f
(cid:1)unitless(cid:2),19 (cid:8) is the critical energy release rate (cid:1)Pam(cid:2), and In the case of a film on a very compliant substrate, i.e.,
K the mode I fracture toughness of the film (cid:1)Pam0.5(cid:2). The D →1,certaincharacteristicsofmechanicalfailuremaybe-
IC 1
subscripts f, s, and i refer to the film, substrate, or arbitrary come accentuated. For channel cracks as well as delamina-
layers, respectively. When residual stress is absent, the ap- tion, g (cid:3)Eq. (cid:1)4(cid:2)(cid:4) may be increased by more than an order of
plied strain (cid:6) in Eq. (cid:1)4(cid:2) equals the critical strain (cid:6) . magnitude, thereby increasing the energy release rate and
o c
The minimally sufficient condition required for cata- decreasing (cid:6) .39,40 Also, the crack length required to reach
c
strophicfailureisrealizedwhenEqs.(cid:1)4(cid:2)and(cid:1)5(cid:2)firstbecome the condition of steady state propagation, ordinarily
equal, where an isolated channel crack will propagate spon- (cid:7)4h ,29,41 is greatly increased for a stiff film on a compliant
f
taneously across the width of the film, in the direction per- substrate.Hence,thelengthofinterior-locatedcracksmaybe
pendicular to the applied strain. With increasing tensile increased by an order of magnitude before escaping arrest,
strain, a series of parallel channel cracks will form. For low whereas edge-located cracks may lengthen by two orders of
crack densities, the elastic fields surrounding the cracks will magnitude before achieving steady state propagation. Fur-
not interact and the process of crack densification may be thermore, the region of influence surrounding an isolated
analyzed according to a Weibull statistical crack will be increased as will the distance associated with
representation.25,26Cracksmaybeconsideredisolatediftheir interfacial shear, Eq. (cid:1)6(cid:2). Unlike for D (cid:12)0, the condition of
1
spacing, (cid:9) exceeds (cid:1)3(cid:5)h /2(cid:2)g(cid:3)D ,D (cid:4), i.e., (cid:9)(cid:10)8 to a stiff film additionally increases the likelihood that cracks
f 1 2
25h .21,27–29 At high crack densities, the elastic fields sur- will extend through the thickness of the film up to the inter-
f
rounding the cracks may interact and the crack spacing may face with the substrate.19 In addition to the aforementioned
be related to the applied deformation according to concerted solutions, e.g.,19–22 a unique solution specific to the case of
or sequential crack formation representations.21,22,27–30 For veryhighD valueshasbeenrecentlydeveloped.30Thechar-
1
extensive strain, the minimum spacing between cracks be- acteristics associated with D →1, including reduced (cid:6) , in-
1 c
comeslimitedbythetransferofloadalongitsinterfacewith creased length prior to spontaneous crack propagation and
the substrate such that the stress within the interior of the increased interaction zone between cracks will be further
film equals the stress present according to the applied load- compounded by inelastic behavior within the substrate,
ing conditions, i.e., (cid:7)=E (cid:6) +(cid:7). At the condition of crack which makes the characteristics more pronounced.30,34,39,40
f o r
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
093527-3 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
FIG.2. (cid:1)Coloronline(cid:2)Achemicaltagwasusedforthepostexaminationof
tensilespecimens.Alipophillicendgroupenablesthetagtoadherespecifi-
FIG.1. (cid:1)Coloronline(cid:2)Schematicshowingthesubreactionsequenceresult- cally to the hydrophobic surface of the PEN substrate; a fluorescent end
groupenablesdamagevisualizationviaexternalillumination.
inginthegrowthofALDorMLDcoatings.Filmsaregrowninmonolayer
incrementsbyalternatingbetweentwoseparatehalfreactions,i.e.,“A”and
“B”surfacespecies.
AlCH(cid:1)+C H (cid:1)OH(cid:2) →(cid:1)Al–OCH CH OH(cid:2)(cid:1)+CH .
3 2 4 2 2 2 4
The goal of this study is to examine the mechanical ro- (cid:1)9b(cid:2)
bustness of alumina and alucone coatings subject to pre-
For the 4.7 l chamber, the dose time of 1, 0.2, or 120 s
scribed uniaxial mechanical elongation. First, monolayer
were utilized for TMA, H O, or EG, respectively, at the in-
coatings will be used to determine the behavior of each ma- 2
jectionpressureof300mTorr.Dosingwasfollowedbypurg-
terial. Second, the two materials will be incorporated into a
ing with ultrahigh purity N at the injection pressure of 300
multilayerarchitecture,withthegoalofincreasingthemaxi- 2
mTorrfor75s.Thegrowthtemperatureof155 °Candbase-
mumcriticalstrainpriortofailure.Third,theperformanceof
line chamber pressure of 650 mTorr were utilized for all
themultilayercompositewillbecomparedtoarecentmodel
experiments. Direct deposition, with no substrate surface
based on a multilayer thin-film fracture mechanics analysis.
treatment, was performed after stabilizing the temperature
The model will be used to identify the characteristics of the
overnight.
ideal spacer layer material.While the study here examines a
Alumina, alucone, or alumina/alucone/alumina coatings
three-layer architecture consisting of specific materials, the
weregrownon75 (cid:13)mthickpolyethylenenaphthalate(cid:1)PEN(cid:2)
basic behavior is expected to apply broadly to more compli-
(cid:1)Dupont Teijin Inc.(cid:2) substrates. In particular, the optical
cated architectures composed of other materials.
grade “Teonex Q65” is commonly used in the organic light
emittingdiode(cid:1)OLED(cid:2)fieldbecauseitisbothheatstabilized
and coated with a scratch resistant layer on its top
II. EXPERIMENTAL surface.42,43Similartothestandardmethodfortensiletesting
of thin plastic materials,44 coated PEN sheets were cut into
Filmsweredepositedinaviscousflowreactorusingthe
strips (cid:1)50(cid:14)10 mm2 gage section(cid:2) using a paper cutter.
ALD1–4 or MLD6 techniques.The coating techniques do not
Other methods such as die stamping or laser cutting to the
requirelineofsightfordepositionandaredepositedinblan-
American Society for Testing and Materials (cid:1)ASTM(cid:2)
ket format. The deposition techniques are based on a se-
D638–03 (cid:1)type IV(cid:2) profile45 proved unsuccessful because of
quence of two self-limiting reactions between vapor-phase
the toughness of or damage to the PEN substrate.As in the
precursor molecules and a solid surface, as shown schemati-
method 45, each specimen strip was then tensioned in ambi-
cally in Fig. 1. For alumina, film growth proceeds according
to the two half reactions, Eqs. (cid:1)8a(cid:2) and (cid:1)8b(cid:2), where the as- ent (cid:1)25 °C(cid:2) to a prescribed strain (cid:6)o at the displacement
terisks designate the surface species.3,4 controlled strain rate of 0.015 s−1 using a mechanical load-
frame(cid:1)Insight2,MTSSystemsCorp.(cid:2)whilebeingmeasured
AlOH(cid:1)+Al(cid:1)CH3(cid:2)3→AlOAl(cid:1)CH3(cid:2)2(cid:1)+CH4, (cid:1)8a(cid:2) using a laser extensometer (cid:1)LE-05, Electronic Instrument
ResearchCorp.(cid:2).Topreventfracturerelatedtothesharpgrip
AlCH3(cid:1)+H2O→AlOH(cid:1)+CH4. (cid:1)8b(cid:2) teeth, polymer strips (cid:1)“Flex-o-Pane,” Warp Brothers, Inc.(cid:2)
The reactants, trimethyl aluminum (cid:3)TMA,Al(cid:1)CH (cid:2) (cid:4) were attached over the grip ends outside of the gage region
andwater(cid:1)H O(cid:2),arealternatelyinjectedvianitrogencar3rie3r of the specimens using epoxy (cid:1)E6000, Eclectic Products.
2 Inc.(cid:2).
gas. Using computer-controlled pneumatic valves, the sub-
strate surface is first exposed to reactantA, Fig. 1(cid:1)b(cid:2), which As the thickness of the film coatings renders them opti-
cally transparent, damage was inspected using a recently de-
reactswiththeactivesurfacesites.Then,afterpurgingtheby
velopedfluorescenttag.46Thetaghasaspecificallydesigned
products from reactionA, the surface is exposed to reactant
B, Fig. 1(cid:1)c(cid:2). This reaction regenerates the initial functional lipophilic moeity that facilitates selective binding to damage
sitesbasedonthesurfaceadhesioncharacteristicsofthema-
groups, preparing the surface for the next exposure to reac-
tantA, Fig. 1(cid:1)e(cid:2). The film is grown to the desired thickness terial system. As illustrated in Fig. 2, the tag binds to the
PEN substrate, not alumina or alucone, based on its greater
byrepeatingtheABsequence.Foralucone,filmgrowthpro-
ceedssimilarlyaccordingtothetwohalfreactions,Eqs.(cid:1)9a(cid:2) hydrophobicity. The tag molecules also bear a fluorescent
and (cid:1)9b(cid:2), where the initial reactant species are TMA and moiety, with primary emission at the optical wavelength of
ethylene glycol (cid:3)EG,C H (cid:1)OH(cid:2) (cid:4).6,7 515 nm. In addition, the tag has a small molecule size, i.e.,
2 4 2 molecular weight of (cid:7)300, allowing molecules to enter eas-
AlOH(cid:1)+Al(cid:1)CH3(cid:2)3→AlOAl(cid:1)CH3(cid:2)2(cid:1)+CH4, (cid:1)9a(cid:2) ily into nanometer-scale damage sites. To verify its validity,
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
093527-4 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
the fluorescent tag method was compared with the optical
visualization method described by others,47–49 which incor-
porates an oxygen plasma etch to undercut the substrate at
damagesites.Inthatmethod,oxygenionspassthroughdam-
aged regions of the film and consume the substrate, render-
ing the damage visible in an optical microscope.After com-
paring instances of the same damaged region, the tag was
chosen over the plasma etching method based on its ability
to obviate finer features as well as the greater contrast ren-
dered by the tag.46
The procedure for damage inspection is as follows. The
top surface of coated specimens, previously tensioned to (cid:6) ,
o
was soaked in a 2.9% volume (cid:1)tag:ethanol(cid:2) solution for 5
min. A 70:30 vol% (cid:1)ethanol:de-ionized water(cid:2) solvent so-
lution was then used to wash away the excess tag. The
sample was then dried using clean dry air and maintained in FIG.3. (cid:1)Coloronline(cid:2)Tensiletestdata(cid:1)engineeringstress/strain(cid:2)fora5nm
an ultraviolet-safe environment. Fluorescent emission was thickAlO layerdepositedona75 (cid:13)mthickPENsubstrate.
2 3
measured using a confocal microscope (cid:1)LSM 510, Carl
Zeiss, Inc.(cid:2) equipped with an argon/2 laser (cid:1)(cid:9)=488 nm(cid:2). IV. RESULTSAND DISCUSSION
The average crack spacing was determined from the number A.Alumina monolayer deposited on PEN
ofcrackswithinaknownsamplesizeregion,wherethefinal
value(cid:9) wastheaverageofsixmeasurements(cid:1)top,middle, Figure 3 shows the tensile results for a set of separate
avg
and bottom of two separate images(cid:2). strips of alumina deposited on PEN, identifying the stress/
strainrelationshipasthespecimensweretensionedto(cid:6) and
o
then more rapidly unloaded to 0% strain. Figure 3 identifies
III. MODELING theinitial(cid:6) valuesusedtoevaluateallcoatings,whereupon
o
In addition to the aforementioned analytical models, the subsequent iterative tests were always used to identify the
failure of thin film(cid:1)s(cid:2) may be understood according to a re- onsetofdamagetowithin1/8%strain.Becausehs isatleast
cently developed fracture mechanics based formalism.14 As three orders of magnitude greater than hf, the mechanical
in the analytic representation, Eq. (cid:1)4(cid:2), and other equivalent response in Fig. 3 applies to the PEN substrate. Therefore,
models,20–22 the (cid:6) required to propagate a crack may be fromthestandardtestprotocol,45theelasticmodulusofPEN
determined from tohe associated change in energy. In the is 8.4(cid:1)1.5 GPa and the flow stress at the applied strain of
method here, the energy associated with fracture may be de- 8% is 141(cid:1)8 MPa. Instrumented indentation was per-
terminedfromcombinationofthestresspresentintheregion formed according to the procedure in Ref. 17 to further ex-
ahead of the crack tip and the displacement present in the amine the properties of the substrate material. Using a nu-
wake remaining far behind a propagated crack, Eq. (cid:1)10(cid:2). merical postprocessing algorithm,50 the hardness of
(cid:8) 0.45(cid:1)0.03 GPa, yield strength of 207(cid:1)0.03 MPa, and
U= 1 (cid:7)(cid:3)y(cid:4)(cid:15)(cid:3)y(cid:4)(cid:3)y. (cid:1)10(cid:2) yield strain of 4.6% were identified for PEN. Because of the
2 viscoelasticnatureofpolymericmaterials,thecharacteristics
of PEN depend upon the loading rate and temperature used
The total energy will scale according to the number of
during testing.
layerspresent,Eq.(cid:1)11(cid:2),whichmayberelatedtotheapplied-
and residual-mechanical conditions, Eq. (cid:1)12(cid:2).
U=nh (cid:8) +nh (cid:8) , (cid:1)11(cid:2)
i c c j p p
(cid:5) (cid:6) (cid:9) (cid:10)
(cid:7) h E
U=(cid:1)E (cid:6) +(cid:7)(cid:2) (cid:6) + r h2f p, p . (cid:1)12(cid:2)
f o r o E f h E
f f f
NewparametersintroducedintheequationsincludeUas
the energy (cid:1)J(cid:2), (cid:15)as the displacement in profile along the
crack face (cid:1)m(cid:2), y as the through-thickness axis location (cid:1)m(cid:2),
n as the number of material layers (cid:1)unitless(cid:2), and f as a
dimensionless function specific to the geometry and materi-
als. Additional notation includes the indices i and j as well
thesubscriptscandp,whichrepresenttheceramicandpoly-
merlike spacer layers, respectively. The numerical analysis
(cid:1)ABAQUS, Dassault Systèmes Inc.(cid:2) was conducted using an
automated routine (cid:1)PYTHON, Python Software Foundation(cid:2).
FIG. 4. (cid:1)Color online(cid:2) Measured crack density for a single AlO layer
Analysis here was solely limited to the linear elastic regime (cid:1)deposited on a 75 (cid:13)m thick PEN substrate(cid:2), following tensile2tes3ting to
for all materials considered. prescribedstrains.
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093527-5 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
FIG.5. (cid:1)Coloronline(cid:2)Evolutionofthedamagemorphologyforasingle125nmthickAlO layerdepositedonPEN.Thesetofimagesincludesseparate
2 3
specimenstensionedtothe(cid:6) of(cid:1)a(cid:2)0%,(cid:1)b(cid:2)0.9%,(cid:1)c(cid:2)1.5%,(cid:1)d(cid:2)7.5%,and(cid:1)e(cid:2)25%.
o
Themodulusvaluesof195.3and36.8GPaforalumina17 surface, whereas image (cid:1)d(cid:2) identifies the localized three-
andalucone,18determinedseparatelyusingindentation,com- dimensional (cid:1)buckled(cid:2) geometry motivating transverse crack
bined with that of the substrate dictates the D values (cid:3)Eq. formation.Images(cid:1)a(cid:2)and(cid:1)b(cid:2)wererenderedusinganoxygen
1
(cid:1)1(cid:2)(cid:4) of 0.91 and 0.62, respectively. The resulting configura- plasma etching method,47–49 while images (cid:1)c(cid:2)–(cid:1)e(cid:2) were ren-
tionforamonolayerALDorMLDcoatingonPENisthere- dered using the chemical tag method, Fig. 2.
fore that of a stiff material on a very compliant substrate. The results for alumina are further summarized in Table
Second,themacroscopicresponseforthestripsisdominated I,whichidentifies(cid:6) ,thecriticalstrainforsteadystatechan-
c
by the inelastic behavior of PEN. In particular, the inelastic nel crack propagation, R , the equivalent critical bending ra-
c
behavior is dominant above the (cid:6) of 4.6%, where the final dius for h =75 (cid:13)m, (cid:15), the predicted crack opening dis-
o s c
strain becomes greatly increased with applied strain for (cid:6) placement at (cid:6) , (cid:8), the critical energy release rate, K , the
o c IC
(cid:10)4%. mode I fracture toughness for alumina, (cid:6), the critical strain
t
Tensionedspecimenswerethenexaminedusingthefluo- for transverse cracking, (cid:9) , the saturated crack spacing, and,
s
rescent tag and the channel crack density (cid:1)1/(cid:9) (cid:2) was mea- (cid:2), the critical interfacial shear between alumina and PEN.
avg c
sured according to (cid:6) , as shown in Fig. 4. Three different R , an engineering quantity often specified for design and
o c
coating thicknesses (cid:1)h =5, 25, and 125 nm(cid:2) were studied. safe application, was determined from Eq. (cid:1)13(cid:2).
f
Specifically labeled in the figure for 5 nm alumina, cracks
b(cid:9)es.giTnhteorreesaudlitlsyopfroapatgreantedlaitn(cid:6)ec,fiatnadrethepirrodveidnesdityinsaFtuigra.te4staot Rc= (cid:1)hf2+(cid:6)hs(cid:2). (cid:1)13(cid:2)
guide the eye, but do not imply a specific relationship. c
Lastly,theresultsofnumericalanalysis,usingtheaverageof Thepredictedcrackopeningdisplacementwasestimated
the measured K values for alumina (cid:1)below(cid:2), are indicated analyticallyaccordingtothepreviouslydevelopedmethod.19
IC
in the figure with a hourglass. Specifically, the (cid:6) of 0.97%, (cid:8) was determined at (cid:6) , i.e., when Eq. (cid:1)4(cid:2) becomes equal to
c c
2.17%, and 4.85% are identified for 5, 25, and 125 nm thick Eq. (cid:1)5(cid:2). K follows from (cid:8) according to Eq. (cid:1)5(cid:2). (cid:6) was
IC t
Al O , respectively. determinedtowithinafewpercentstrainrelativetotheonset
2 3
Using the 125 nm thick alumina coating as an example, of cracking, e.g., Fig. 5(cid:1)e(cid:2). If the three different coatings are
the evolution of the damage morphology is shown in Fig. 5. consideredcollectively,then(cid:8)=18.6(cid:1)1.9,K =1.89(cid:1)0.10,
IC
The set of images includes separate specimens tensioned to and (cid:2)=39.5(cid:1)8.3 for alumina.
c
the(cid:6) of0%inFig.5(cid:1)a(cid:2),wherethesurfaceroughnessofthe For alumina, (cid:6) is observed to increase as h is de-
o c f
PENaswellascontaminationarerenderedapparent,0.9%in creased, as suggested in Eq. (cid:1)4(cid:2). Specifically, the critical
Fig. 5(cid:1)b(cid:2), where the first channel cracks have already propa- strain of 5% for h =5 nm is notably greater than the (cid:6) of
f c
gated and others are initiating, 1.5% in Fig. 5(cid:1)c(cid:2), showing 0.5%–2% commonly observed in the literature for conven-
continuedcrackdensification,7.5%inFig.5(cid:1)d(cid:2),wheretrans- tional (cid:1)micrometer scale(cid:2) thin film materials51 including
verse cracks have formed, and 25% in Fig. 5(cid:1)e(cid:2), where a SiO ,26 Si N ,49 indium tin oxide,51,52 and amorphous Si.53
2 3 4
dense network of both channel and transverse cracks is evi- Thegreater(cid:6) forthe5nmthickaluminafilmisattributedto
c
dent. The details of crack propagation about defects at the its nanometer-scale thickness, allowed by the ALD tech-
surfaceortransversecrackformationareshownseparatelyin nique. In contrast, K for bulk crystalline Al O typically
IC 2 3
the insets of Fig. 5(cid:1)b(cid:2) or Fig. 5(cid:1)d(cid:2), respectively. Image (cid:1)b(cid:2) ranges from 4–6 MPam0.5,54 however K of 1.7 and
IC
identifies crack nucleation (cid:1)but not propagation(cid:2) and is spe- 1.4 MPam0.5 was measured for amorphous thin films cre-
cific to defects, contamination, or antiblock particles at the atedviathephysicalvapordepositionandthermaldecompo-
TABLEI. SummaryofresultsforasingleAlO layer(cid:1)depositedonPEN(cid:2),tensionedtoprescribedstrains.
2 3
h (cid:6) R (cid:15) (cid:8) K (cid:6) (cid:9) (cid:2)
f c c c IC t s c
(cid:1)nm(cid:2) (cid:1)%(cid:2) (cid:1)mm(cid:2) (cid:1)nm(cid:2) (cid:1)J/m2(cid:2) (cid:1)MPam0.5(cid:2) (cid:1)%(cid:2) (cid:1)(cid:13)m(cid:2) (cid:1)MPa(cid:2)
5 5.08(cid:1)0.08 0.64 6.8 25.3(cid:1)0.8 2.22(cid:1)0.04 12.5(cid:1)2.5 2.8(cid:1)0.1 25.0(cid:1)1.8
25 1.56(cid:1)0.06 2.40 10.4 11.9(cid:1)1.0 1.53(cid:1)0.06 6.25(cid:1)1.25 3.2(cid:1)0.2 32.3(cid:1)4.3
125 0.88(cid:1)0.06 4.30 29.2 18.7(cid:1)1.9 1.91(cid:1)0.10 6.25(cid:1)1.25 5.0(cid:1)0.2 61.1(cid:1)8.3
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093527-6 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
sition techniques, respectively.55,56 K as reported inTable I
IC
for alumina is thought to be typical of amorphous Al O ,
2 3
however, toughness does not limit mechanical performance
heremoresignificantlythanh .Thedifferencein(cid:6) for5and
f c
125 nm thick alumina films would be significant in applica-
tions, as this difference results in a 6.7 times decrease in the
allowable radius of curvature, permitting much greater fold-
ing of the chemical barrier. (cid:6) is of primary importance here
c
because a fully propagated crack would catastrophically
compromiseachemicalpermeationbarrier;57crackinitiation
at specific defect sites as in Fig. 5(cid:1)c(cid:2), which may occur for
(cid:6) (cid:12)(cid:6) , may also be unacceptable in certain applications.
o c
The(cid:2) foralumina/PENisgreaterthantherangeof1–11
c
MPa mentioned for thin films,27,31 but is comparable with
values observed for the biopolymer/ceramic system present
in nacre (cid:1)37–46 MPa(cid:2)58 or in synthetic fiber/composite sys-
FIG.6. (cid:1)Coloronline(cid:2)Measuredcrackdensityfora100nmthickalucone
tems (cid:1)often 5–50 MPa(cid:2).59 A robust alumina/PEN interface layer,tensionedtoprescribedstrains.Theinsetsshow(cid:1)a(cid:2)aschematicrep-
was anticipated as the vapor phase precursors used to grow resentingthespecimensincrosssectionand(cid:1)b(cid:2)themorphologyofthetop
alumina were determined to permeate into the subsurface of surface(cid:1)orientationisindicatedwithrespectto(cid:6)o(cid:2)ofaspecimentensioned
PEN during deposition,6 allowing alumina to form in the to(cid:6)o=25%.
porous regions between polymer chains, greatly improving
159.5(cid:1)35.9 (cid:13)m, while the edge-specific crack density in
interfacial adhesion.
the direction of the applied strain was 0.11(cid:1)0.031/(cid:13)m for
Regarding the data in Fig. 4, the results are similar to
previous studies,26,27,31,60,57 which likewise demonstrate the all (cid:6)o. No overt trend for Le or crack density was observed
with (cid:6) for h =5 nm (cid:1)or qualitatively for h =25 and 125
asymptotic densification of channel cracks up to a saturation o f f
nm(cid:2)andthelongestedge-locatedcracksextendedto(cid:11)4%of
value. For alumina, the saturation spacing is significantly
the 10 mm sample width. The influence of sample prepara-
greater than the film thickness, so the shape of the crack
tion,particularlyinthemiddleofthesampleswherechannel
density should vary with strain according to the distribution
crack density was determined, is therefore not significant.
ofdefectsinthefilm,25,26ratherthanaccordingtointeraction
Thelackofvariationwith(cid:6) fortheedgecracksisconsistent
betweencloselyseparatedcracks.(cid:6) ,however,dependsonly o
c with Refs. 29 and 39, where propagation is expected to be
on the intrinsic properties of the material system and not the
hindered for film and substrate systems bearing a large D
distribution of flaws. There is quite reasonable agreement 1
value.
between the measured and numerically calculated (cid:6) (cid:1)dia-
c
monds(cid:2), considering that the influence of residual stress and
B.Alucone monolayer deposited on PEN
substrate yielding were not included in the analysis. For ex-
ample, intrinsic stress as great as 474 MPa has been mea- Like the alumina coatings, tensioned alucone specimens
suredforaluminafilms16,17andthemeasuredstrainatyield- were examined using the fluorescent tag. The results of this
ing for PEN is (cid:7)4%. examination are shown in Fig. 6, which identifies the crack
The measured (cid:6) is similar between the coatings of dif- density versus (cid:6) . Both the (cid:6) and (cid:9) are identified (cid:1)labeled(cid:2)
t o c s
ferent thicknesses. Equation (cid:1)7(cid:2), in conjunction with the inthefigure.AsinFig.4,atrendlinefitisprovidedinFig.6
Poisson’s effect, identifies (cid:6) to be 15.3%.As the PEN sub- to guide the eye. Similar to Table I, key results for alucone
t
strate yields at (cid:7)4%, variation from the elastic-regime is on PEN are summarized in Table II. Unlike alumina, no
expected, e.g., (cid:4)→0.5, and Eq. (cid:1)7(cid:2) becomes qualitative. transverse cracking was observed for alucone, even at (cid:6)
s o
Also, (cid:6) here applies to the localized condition, where =25%, Fig. 6(cid:1)b(cid:2).
t
defects/contamination may promote buckling, facilitate For alucone, cracks were not as distinctly rendered by
delamination, or raise stress prior to the condition of global the fluorescent tag as they were for alumina. At greater (cid:6) ,
o
damage. the crack density was verified using electron microscopy,
ThedamageoccurringwhenthecoatedPENsheetswere e.g., Fig. 6(cid:1)b(cid:2). In contrast, initial attempts to inspect alucone
cutintospecimenstripswasexplicitlyexaminedforalumina, deposited on polyimide (cid:1)Kapton HN, DuPont, Inc.(cid:2) proved
h =5 nm.L ,themaximumlengthofcracks,measuredfrom unsuccessful.Thetagwaspreviouslyknowntonotadhereto
f e
the cut edge to the interior-located tip, was polyimide.46 This failed imaging scheme (cid:1)tagging the film
TABLEII. Summaryofresultsfora100nmthickaluconelayer(cid:1)depositedonPEN(cid:2),tensionedtoprescribed
strains.
(cid:6) R (cid:15) (cid:8) K (cid:9) (cid:2)
c c c IC s c
(cid:1)%(cid:2) (cid:1)mm(cid:2) (cid:1)nm(cid:2) (cid:1)J/m2(cid:2) (cid:1)MPam0.5(cid:2) (cid:1)(cid:13)m(cid:2) (cid:1)MPa(cid:2)
0.69(cid:1)0.06 5.46 7.7 0.8(cid:1)0.1 0.17(cid:1)0.02 1.23(cid:1)0.80 66.6(cid:1)6.1
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093527-7 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
andnotthesubstrate(cid:2),oppositeofthatusedinFig.5(cid:1)tagging
thesubstrateandnotthefilm(cid:2),indicatesthatthetagdoesnot
adhere to alucone.
Most interesting among the results for alucone is the
brittle failure (cid:1)channel cracking(cid:2) observed at a modest (cid:6)
o
=0.69%, corresponding to R =5.46 mm. For alucone, made
c
according to the recently developed MLD technique, K is
IC
estimated to be notably less than that of many polymeric
materials.54 From the observed damage morphology and es-
timated K , alucone is expected to exhibit the stress/strain
IC
profile typical of a brittle material, i.e., sudden catastrophic
FIG.7. CrosssectionofmultilayercoatingonPEN(cid:1)micrographisoriented
failure, rather than that of a tough plastic material such as obliquelytothespecimen(cid:2).
PEN (cid:1)Fig. 3(cid:2), i.e., significant inelastic deformation may oc-
curpriortofailure.Notethat(cid:8)andK applytothedirection
IC might be explained by the permeation of tag molecules into
orthogonal to the direction of film growth. Anisotropy in
porous materials. For alumina, the tag became absorbed
properties,includingE andK ,mayexistforaluconebased
f IC within the regions of the PEN substrate adjacent to damage
onitsmechanismofgrowth.Toexplain,aluconeisexpected
sites, thereby exaggerating the feature size. Alternately, the
toformchainsand/orlayersthatarecovalentlybondedinthe
tag may diffuse into both the alucone film and PEN sub-
direction of growth, whereas alucone is held together by
strate, rendering the materials less distinct. Disparity be-
weak hydrogen bonds in the in-plane direction.
tween observed and physical size also results in part from
In contrast with channel cracking, the lack of transverse
instrument related image diffraction.
cracking, indicates that (cid:1)a(cid:2) film/substrate buckling (cid:1)“wrin-
kling”(cid:2) does not occur, as generally suggested by Eq. (cid:1)7(cid:2), or
D.Alumina and alucone composite coatings
(cid:1)b(cid:2) that the stress in such a configuration is insufficient to
deposited on PEN
motivate cracking. While Eq. (cid:1)7(cid:2) is limited by the inelastic
deformation of the PEN substrate for (cid:6) (cid:10)4%, the better Following the study of individual film layers, multilayer
o
match in modulus between the film and substrate would be coatings were examined using the same methodology. An
expected to increase (cid:6) . exampleofanalumina/alucone/aluminacoatingdepositedon
b
The asymptotic profile in Fig. 6 suggests a load transfer a PEN substrate is shown in Fig. 7, where the specimen was
limited (cid:1)shear-lag(cid:2) interfacial condition. Because (cid:9) (cid:16)h , in- milled using a focused ion beam (cid:1)FIB, Nova Nanolab, FEI
s f
teraction between cracks is not expected. The crack density Co.(cid:2). The material layers present are labeled according to
for alucone, which is greater than that for alumina, implies their electron contrast in the image. In Fig. 7, the measured
excellentinterfacialadhesionbetweenaluconeandPEN,Eq. thicknesses of 20, 29, and 24 nm for the ALD, MLD, and
(cid:1)6(cid:2).Aswithalumina,thegaseousprecursorspeciesmayper- ALD layers agree well with the nominal thickness values of
meate into the subsurface of the PEN, such that film growth 25, 15, and 25 nm. Regarding the thickness of the MLD
originates within the porous microstructure of polymeric layer, the growth rate for alucone varies significantly with
substrate. deposition temperature.6
Measured crack density versus (cid:6) for the alumina/
o
alucone/alumina coatings is shown in Fig. 8, where the data
C.Asessing the tag-based inspection method from profiles exhibit the same character as the single-layer coat-
the examination of monolayer films ings. The thickness of the alucone layer was varied over
The data profiles, Figs. 4 and 6, as well as the damage
morphology, Fig. 5, demonstrate the ability of the tag to
facilitatedamageinspection.Forexample,acrackaspectra-
tio (cid:1)h /(cid:15)(cid:2) ranging from 1.4 to 4.3 was readily examined for
f c
alumina, Table I. In contrast, the processing parameters for
the oxygen plasma etch technique47–49 must be tailored ac-
cording to the aspect ratio examined, which ranged from
0.1148 to 1049 in the literature. In our own studies, a
specimen-specific sequence of brief etches was required to
utilize plasma etching for damage inspection. The tag-based
examination also exceeded the ability of electron
microscopy-based inspection, where inelastic strain (cid:1)(cid:6)
o
(cid:10)4%(cid:2) was required open cracks beyond their initial (cid:15), en-
c
abling observation.
As in Ref. 46, however, the size (cid:1)width(cid:2) of the tag ren-
deredfeaturesalwaysexceededthephysicalsizeofthedam-
age, i.e., the estimated (cid:15)c. Further, the feature sharpness for FIG.8. (cid:1)Coloronline(cid:2)MeasuredcrackdensityforseparateALD/MLD/ALD
alucone was less than that of alumina. These observations coatings(cid:1)thicknessh /h /h(cid:2),tensionedtoprescribedstrains.
c p c
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093527-8 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
TABLEIII. SummaryofresultsformultilayerAlO /alucone/AlO coat-
2 3 2 3
ings,tensionedtoprescribedstrains.
(cid:6) R (cid:6) (cid:9)
c c t s
h /h /h (cid:1)ALD/MLD/ALD(cid:2) (cid:1)%(cid:2) (cid:1)mm(cid:2) (cid:1)%(cid:2) (cid:1)(cid:13)m(cid:2)
c p c
25/3/25 1.19(cid:1)0.06 3.16 4.5(cid:1)0.5 5.08(cid:1)0.12
25/15/25 1.31(cid:1)0.06 2.86 6.3(cid:1)1.3 4.63(cid:1)0.24
25/192/25 1.19(cid:1)0.06 3.17 6.3(cid:1)1.3 4.38(cid:1)0.18
10/3/10 1.69(cid:1)0.06 2.22 6.3(cid:1)1.3 2.76(cid:1)0.25
nearly three orders of magnitude (cid:1)3–112 nm(cid:2) to study its
influence; the thickness of the alumina layers was also inde-
pendently varied in order to ascertain its influence. Channel
cracks in the composite coatings were distinctly rendered by
the fluorescent tag.
Results for the composite coatings are further summa-
rized in Table III. Transverse cracking was observed for the
composite coatings, however (cid:6) was determined to within a
t
few percent strain. Edge-located channel cracks generated
duringsamplepreparationwereexaminedspecificallyforthe
25/15/25 nm thick coating, where no significant variation
wasobservedaccordingto(cid:6) ,andthevaluesof250.0(cid:1)48.1
o
and 14.9(cid:1)6.3 (cid:13)m were determined for L and (cid:9) , respec-
e s,e
tively.
Thedamagemorphologyforcompositecoatingsiscom-
paredtothatofanaluminafilminFig.9.Therepresentative
micrograph images for specimens were obtained using an
electron microscope. Similar to Fig. 9, a network of channel
andtransversecrackswasobservedat(cid:6) =25% forallofthe
o
ALD/MLD/ALD specimens examined in Fig. 8. The layers
FIG. 9. (cid:1)Color online(cid:2) Damage morphology for coatings tensioned to (cid:6)
underneath the alumina surface layer were frequently ob- c
=25%,including(cid:1)a(cid:2)25nmAlO ,aswellas(cid:1)b(cid:2)25/15/25nm,(cid:1)c(cid:2)25/192/
2 3
servedtobetornintheregiondirectlyadjacenttotransverse 25,and(cid:1)d(cid:2)10/3/10nmmultilayers.Tearing,concludedtooccurinthePEN
cracks. One such tear extends for several micrometers, Fig. substrate,isindicatedwithanarrowin(cid:1)a(cid:2),(cid:1)b(cid:2),and(cid:1)d(cid:2).Thedelaminationof
9(cid:1)d(cid:2). Separately, select regions of the topmost layer(cid:1)s(cid:2) were filmlayersisshownin(cid:1)c(cid:2).Thedirectionofthestrainappliedduringtesting
isshownin(cid:1)d(cid:2).
detached from the substrate, Fig. 9(cid:1)c(cid:2).
To begin discussion, the 25 nm thick alumina systems
(cid:1)Table III(cid:2) have a lower (cid:6) (cid:1)and corresponding greater R (cid:2) the composite coatings, Fig. 9(cid:1)b(cid:2), are observed adjacent to
c c
than the 25 nm thick alumina monolayer (cid:1)Table I(cid:2). The in- the transverse cracks in an alumina film, Fig. 9(cid:1)a(cid:2), corrobo-
corporation of the alucone spacer layer, which was meant to rating that tearing (cid:1)and through-thickness fracture(cid:2) is not
mechanically isolate two alumina layers and improve the unique to the composite coatings. In contrast, localized tear-
overall strength, instead reduced (cid:6) for the composite sys- ing was never observed for tensioned alucone monolayer
c
tem.Similarly,fora10nmthickaluminamonolayer,Eq.(cid:1)4(cid:2) films,thereforealuconeisnotexpectedtotearinacomposite
predicts that (cid:6) should exceed 3%. In contrast, (cid:6) for the 10 coating. Substrate tearing is consistent with the tough char-
c c
nm thick alumina composite system (cid:1)Table III(cid:2) was 0.6% acter of PEN (cid:1)Fig. 3 and Ref. 61(cid:2), which would be expected
greater than the 25 nm thick alumina composite systems to result in localized tearing rather than brittle fracture.
(cid:1)TableIII(cid:2).Themarginalperformanceforthecompositesys- Lastly,theasymptoticcrackdensityprofilesforthecom-
tems will be shown to result from the toughness of alucone. posite coatings, Fig. 8, indicate good adhesion between the
The density characterization, Fig. 8, as well as the mor- material layers. The fractured coatings remain intact even at
phologicalexamination,Fig.9,identifiesthatchannelcracks (cid:6) =25%, well above the application limit of (cid:6) , but benefi-
o c
extend through the entire thickness of the composite coat- cial in minimizing damage associated with catastrophic im-
ings.Toexplain,thetagwaspreviouslyfoundtoadhereonly pact. Although separation between the layers for the 25/
to the PEN substrate and not the ALD or MLD coatings. 192/25 nm coating is observed, Fig. 9(cid:1)c(cid:2), such damage is
Therefore, the strong fluorescent signal enabling the visual- localized and not widespread. Lastly, for the 25 nm thick
ization of cracks in Fig. 8 can only be explained if the com- alumina systems, the measured (cid:9) (cid:1)Table III(cid:2) is similar to
s
posite coatings were fractured through their entire thickness, that observed for the 25 nm thick alumina films (cid:1)Table I(cid:2),
allowingthetagtoaccessthePENsubstrate.Thisconclusion suggesting that the adhesion between the bottommost alu-
implies that the tears observed in Fig. 9 occur within the minalayerandthePENsubstratehasnotbeencompromised
PEN substrate layer. Tear morphologies identical to those in by the incorporation of additional MLD and ALD layers.
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093527-9 Milleretal. J.Appl.Phys.105,093527(cid:2)2009(cid:1)
FIG. 11. (cid:1)Color online(cid:2) Results of numerical analysis for an alumina/
arbitrary polymer/alumina coating configuration on a PEN substrate. The
resultspredict(cid:6) accordingtothemodulusandcriticalenergyreleaserate
c
(cid:1)“toughness”(cid:2) of the spacer layer. The particular geometry considered is
shownininset.
thickness cracking(cid:2). For a tough polymer layer (cid:1)(cid:8) /(cid:8)
p c
FIG. 10. (cid:1)Color online(cid:2) Results of numerical analysis for anALD/MLD/ (cid:10)25(cid:2), the greatest (cid:6) possible (cid:1)labeled (cid:6) (cid:2) is realized for
c max
ALDcoatingonaPENsubstrate.ThecriticalstrainsmeasuredfromALD/
the MLD thickness of 8.5 nm. Here, simultaneous cracking
MLD/ALDspecimens,Fig.8,arealsoshowninthefigure.
is expected for h (cid:12)8.5 nm, while fracture specific to the
p
topmostceramiclayerispredictedforh (cid:10)8.5 nm.The(cid:6)
Good adhesion between the ALD and MLD layers was ex- p max
of 3.03% is roughly twice the (cid:6) of 1.56% measured for 25
pected based on the covalent bonding inherent to the depo- c
nmthickaluminafilms,TableI.As(cid:8) /(cid:8) isdecreasedto10,
sition process, Fig. 1. p c
through-thickness fracture corresponding to decreased (cid:6) is
c
predicted for h (cid:12)25 nm, whereas fracture specific to the
p
E.Analysis of the composite coatings with topmostlayercorrespondingtothemaximum(cid:6) of2.94%is
consideration for future design improvements c
expectedforh (cid:10)25 nm.Performanceislimitedforabrittle
p
To better understand the composite coatings, their per- polymerlayer(cid:1)(cid:8) /(cid:8) (cid:12)5(cid:2)andcracksareexpectedtoalways
p c
formance was analyzed according to a recently developed form through the entire thickness of the coating. Here, the
fracture mechanics based formalism.14 In practice, cracking maximum (cid:6) is greatly reduced and does not strongly vary
c
may occur: (cid:1)a(cid:2) through the thickness of all three layers, (cid:1)b(cid:2) with h .
p
exclusivelyinthetopceramiclayer,or(cid:1)c(cid:2)simultaneouslyin For the measured (cid:8), Tables I and II, the ratio (cid:8) /(cid:8) is
p c
both of the ceramic layers. The input parameters, here E determined to be (cid:7)0.05. For the composite coatings in Fig.
c
=195.3 GPa, (cid:4)=0.13, (cid:8) =18.6 J/m2, h =25 nm, E 8,theanalysisinFig.10thereforeaffirmsthemeasured(cid:6) as
c c c p c
=36.8 GPa, (cid:4)=0.33, E =8.4 GPa, (cid:4)=0.33, and h well as the assertion that fracture occurs through their entire
p s s s
=75 (cid:13)m, were used to generate (cid:6) versus h profiles for the thickness.Figure10predictsthespacerlayerwillbeineffec-
c p
three separate failure modes. The solution sets vary for the tive at increasing (cid:6) , analogous to the layer being absent.
c
composite architecture (cid:3)number of layers, Eq. (cid:1)11(cid:2)(cid:4) accord- Specifically, if the alumina was made twice as thick, cracks
ing to the mode-specific geometry, Eq. (cid:1)10(cid:2), and also the would occur across the entire thickness and (cid:6) would scale
(cid:11) c
independent parameters, (cid:8) and h . The solution set bearing byafactorof1/ 2,Eq.(cid:1)4(cid:2).Asinthecaseofasinglefilmon
p p
thelowest(cid:6) isthefailuremodeexpectedtoberealizedata a substrate,34 inelastic behavior in the substrate or spacer
c
particular h . layers can greatly influence the strain/thickness relationship,
p
The results of this analysis, along with the critical strain which may also vary with loading rate, temperature, and
measured from ALD/MLD/ALD specimens (cid:1)Table III(cid:2), are specimen history.
shown in Fig. 10. In the figure, which applies to linearly Inordertoidentifyhowthemechanicalrobustnessofthe
elastic materials, the conditions of crack formation specific three-layer composite system might be improved, the mod-
to the top ceramic layer as well as simultaneous crack for- eling was extended to examine a broad range of properties
mationinbothceramiclayersmaybedeterminedabsolutely. for the polymer layer, Fig. 11. Certain material properties
Theconditionofcrackingthroughtheentirethicknessofthe were fixed (cid:1)including E =195.3 GPa, (cid:4)=0.132, (cid:8)
c c c
compositecoating,however,dependsonthetoughnessofthe =18.6 J/m2, h =25 nm, (cid:4)=0.33, E =8.4 GPa, (cid:4)=0.33,
c p s s
polymer spacer layer, represented in Fig. 10 using a family and h =75 (cid:13)m(cid:2), while polymer specific properties (cid:1)E , (cid:8) ,
s p p
of profiles. and h (cid:2) were varied. The results, however, have been nor-
p
InFig.10,ifthethicknessandtoughnessofthepolymer malized so that they may be applied to a variety of similar
spacer layer are known, (cid:6) is predicted to occur at the mini- multilayerarchitectures.AsinFig.10,theregimesofsimul-
c
mal energy condition (cid:1)either top, simultaneous, or through- taneous versus top-specific, through-thickness versus top-
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