8.13 NanoindentationMethodsinInterfacial FractureTestingvolinsky/CSI_8_13.pdf · 2015. 10. 19. · 8.13.5.1.3 Tungsten 478 8.13.5.2 Ductile Metal Films 479 8.13.5.2.1 Copper ﬁlms

8.13NanoindentationMethodsin InterfacialFractureTestingA.A. VOLINSKYMotorola Corporation, Mesa, AZ, USA

D.F. BAHRWashington State University, Pullman, USA

M.D. KRIESEOsmic, AuburnHills, MI, USA

N.R. MOODYSandia NationalLaboratories, Livermore, CA, USA

and

W. GERBERICHUniversity of Minnesota, Minneapolis, USA

8.13.1 INTRODUCTION 454

8.13.2 ADHESION 456

8.13.2.1 Thermodynamic Work of Adhesion 4568.13.2.2 Practical Work of Adhesion 457

8.13.3 INTERFACIAL FRACTURE TEST TECHNIQUES 459

8.13.3.1 Sandwich Specimen Tests 4598.13.3.2 Bulge and Blister Tests 4618.13.3.3 Superlayer Test 4628.13.3.4 Indentation Tests 4638.13.3.5 Superlayer Indentation Test 4658.13.3.6 Scratch Tests 465

8.13.4 NANOINDENTATION—MECHANICAL PROPERTIES 467

8.13.4.1 Elastic Properties 4678.13.4.1.1 Load vs. displacement curves 4678.13.4.1.2 Continuous stiffness 4688.13.4.1.3 Thin film—substrate effects 468

8.13.4.2 Plastic Properties 4698.13.4.2.1 Yield strength 4698.13.4.2.2 Bulk materials 470

453

8.13.4.2.3 Indentation size effects 4718.13.4.2.4 Thin films 472

8.13.5 THIN FILM FRACTURE 473

8.13.5.1 Ceramic and Refractory Metal Films 4738.13.5.1.1 Tantalum nitride 4738.13.5.1.2 Silicon nitride 4788.13.5.1.3 Tungsten 478

8.13.5.2 Ductile Metal Films 4798.13.5.2.1 Copper films 4798.13.5.2.2 Gold films 4838.13.5.2.3 Aluminum films 487

8.13.6 SUMMARY 488

8.13.7 REFERENCES 489

8.13.1 INTRODUCTION

Thin films are used in many applicationswhere properties such as resistance to abrasion,corrosion, permeation, and oxidation, or spe-cial magnetic and dielectric properties, areneeded to meet specialized functional require-

ments (Mittal, 1976). They are becoming veryimportant in optimizing performance of smallvolume systems inherent in microelectro-mechanical systems (MEMSs) and nanoelec-tromechanical systems (NEMSs) (Volinskyet al., 2002; Maboudian and Howe, 1997).They have also seen a dramatic increase in use

NOMENCLATURE

a interfacial crack length, delaminationradius

A fracture surface area, indenter contactarea, proportionality constant, initialfilm stress term

b Burgers vector, blister half-width, linewidth, contact radius, disk thickness

B unit width, specimen thickness, pro-portionality constant

c dislocation-free zoneC plastic zone size, complianceC or cr denotes criticald grain size, diameter of residual Brinel

indentationD diffusion coefficient, diameter of Bri-

nel indenter, dampening coefficientE Young’s modulusE0 plane-strain Young’s modulus

(E/(1�v2))f filmfric frictionalG strain energy release rateh thin-film thicknessH thin-film hardness, half the specimen

heightI or ind denotes indentationIT transformed moment of inertiaJ fluxk Hall-Petch constant, curvatureK stress intensity at a crack tip (KI,II,III

are used for modes I, II, and III)KC critical stress intensity of a materialm massM bending moment

P loadr contact radius, bulge radiusR, R residual, resistance to crack propaga-

tions substrateS stiffnesst timeT temperatureu0 max film deflectionU energyVI indentation volumeW half-width of wedge indentationWA thermodynamic work of adhesionWA,P practical work of adhesionY dimensionless geometric factora buckling constant, Dundurs parameterb angle between wedge or cone face and

sample surface, Dundurs parameterg surface energyGi interface fracture toughnessd displacement, buckle or bulge heighte strain, positive taken as compressivef phase angle between force and dis-

placement signalsy equilibrium contact angle, compres-

sion anglem shear modulus, buckling constantn Poisson’s ratios stress (sI,B,R are indentation, buckling

and residual stresses, respectively)sys thin-film yield strengtht shear stressC mode mixity (phase) angleo frequency of oscillationO activation volume

454 Nanoindentation Methods in Interfacial Fracture Testing

with the emergence of copper as the nextgeneration interconnect metallization materialfor ultralarge-scale integration (USLI) fabrica-tion for semiconductor applications (Krieseet al., 1998b). In all of these applications,performance, reliability, and durability are tieddirectly to interface structure and composition(Mittal, 1976; Evans and Ruhle, 1990; Trumbleand Ruhle, 1990). See also Chapter 8.08.

These interfaces are created by deposition ofdissimilar materials. This dissimilar naturecreates significant challenges concerning ther-momechanical integrity and reliability espe-cially when one of the constituents is brittle(Evans and Hutchinson, 1995). The challengesarise from changes in residual stress, structure,and composition. Mismatch in thermal coeffi-cients and high-energy deposition can createfilms with high residual stress levels capable ofdriving fracture along well-bonded film inter-faces. Differences in structure and compositioncan markedly alter interface adhesion andstrength. In brittle films, friction along con-tacting crack faces can increase performancewhile in ductile films, plastic deformation canmarkedly increase fracture energy (Evans andHutchinson, 1995; Evans, et al., 1999). Frac-ture processes can also have a strong effect ondevice performance. In brittle film systems,debonding can occur by rupture of bondsalong the interface plane at relatively lowfracture energies (Evans and Hutchinson,1995; Cannon et al., 1991). When brittleinterphases or reaction products form, fracturecan occur also within these phases andproducts at relatively low fracture energies. Incontrast, hole nucleation, growth, and coales-cence can markedly increase fracture energiesin ductile film systems (Evans and Hutchinson,1995; Evans and Dalgliesh, 1992).

Qualitative tests such as the scotch tape testor the pull-off test are often used to monitoradhesion, since they are quick and easy toperform (Steinmann and Hintermann, 1989;Ohring, 1992). While still useful for routinequality control, these tests do not measure theinterface fracture toughness, since the strainenergy release rate usually cannot be deconvo-luted from the work of the external load(Evans and Hutchinson, 1995; Hutchinsonand Suo, 1992; Wei and Hutchinson, 1997).Difficulties are further complicated by thevariety of film systems (metal–metal, metal–ceramic, polymer–metal, polymer–ceramic,etc.) found in even a single industry such asmicroelectronics. Thus, a number of research-ers have utilized linear elastic fracture me-chanics to develop test and analysis methodsthat are truly quantitative, allowing directassessment of the critical energies of interfacial

adhesion (Cao and Evans, 1989; Charalam-bides et al., 1989; Suo and Hutchinson, 1989,1990; Hutchinson and Suo, 1992; Rice, 1988;Evans et al., 1988, 1990).

When interfaces can be made by bondingprocedures at relatively high homologoustemperatures (such as diffusion bonding orbrazing), many different configurations areavailable for testing, based on those developedfor homogeneous systems (Evans and Dalgle-ish, 1992; He et al., 1995; Turner et al., 1995).Studies have shown that the physics andmechanics of bimaterial interface adhesionare comparable to that for cohesion in homo-geneous, isotropic solids (Rice, 1988; Evansand Dalgleish, 1992, 1993; He et al., 1995;Hutchinson and Suo, 1992; Jensen and Thou-less, 1993; Wei and Hutchinson, 1997). Thisenables established results to be applied tointerfaces (Tvergaard and Hutchinson, 1992;Evans et al., 1999; Suo et al., 1993). As a result,the values defining fracture energy can bedirectly related to energy-dissipative mechan-isms both at the interface and within near-interface regions of the film and substrate.However, bonding processes at relatively hightemperatures often create films with structuresand properties vastly different than thosecreated by evaporation or sputter depositionat relatively low homologous temperatures.

A number of thin-film adhesion assessmentmethods have been developed to measurefracture properties in the as-processed condi-tion. While many require difficult samplepreparation methods, as exemplified by theblister (Allen and Senturia, 1988, 1989; Jensen,1991; Jensen and Thouless, 1993; Jensen et al.,1990) and edge-delamination tests (Wan andMai, 1995; Akisanya and Fleck, 1994), somemethods such those using micromechanicalprobes require limited, if any, preparation toinduce and quantify interfacial failure (Marshalland Evans, 1984; Hutchinson and Suo, 1992).Microprobe techniques commonly utilize inden-tation or scratching with a diamond indenter, inconjunction with equipment that continuouslymeasure forces and displacements (Wu, 1991;Venkataraman et al., 1993a, 1993b, 1993c; deBoer and Gerberich, 1996a, 1996b, Kriese et al.,1998a; Moody et al., 1998). In these methods,the indenter both initiates and propagates adelamination. Analysis of the load–displace-ment curves and fractographic measurement ofthe delaminations yield the parameters for use inmodels giving fracture energy. Indentationmethods are generally preferred, because dela-mination is typically more stable with a regulargeometry indenter, allowing more rigorousmechanics of the strain energies which driveinterfacial failure (Marshall and Evans, 1984;

Introduction 455

Chiang et al., 1981; Rosenfeld et al., 1990; Bahrand Gerberich, 1996a; Bahr et al., 1997; Moodyet al., 1998). However, such tests are oftenimpractical for ductile or strongly adheringfilms, due to the difficulty of initiating adelamination. Ductile and strongly adheringfilms tend to simply deform plastically prior tothe development of sufficient elastic strainenergy for delamination (Turner and Evans,1996; Kriese et al., 1998b). In order to reducethis limitation, previous researchers have usedsuperlayers deposited over the film of interest(Bagchi et al., 1994; Bagchi and Evans, 1996).The superlayer, typically a refractory metalvapor-deposited at a low temperature that doesnot significantly alter the underlying film, isoften deposited with a high residual stress whichprovides additional driving force for delamina-tion. The combination of indentation and highlystressed superlayers provides a test approachthat has been used successfully to study inter-facial fracture in well-adhered ceramic films andhighly deformable ductile metal films.

In this chapter, we review nanoindentationmethods used to study interfacial fracture anddetermine interfacial fracture energies of tech-nologically significant thin films. The focus ison as-deposited ceramic and metallic filmsystems, emphasizing ductile metal films usedthroughout the microelectronics community. Itcomplements reviews by Nix (1989) on thin-film properties, Doerner and Nix (1988) ondevelopment of residual stresses in thin films,Evans et al. (1999) on the role of plasticity andsegregation on film adhesion, and the works ofEvans and Hutchinson (1995) and Hutchinsonand Evans (2000) on mechanisms of damageand fracture processes in thin films and multi-layers. The models employed were originallydeveloped and discussed in detail in the worksby Marshall and Evans (1984), Evans andHutchinson (1984), and Hutchinson and Suo(1992).

The review begins with a brief discussion ofthe true and practical works of adhesion. Thisis followed by a brief discussion of linear elasticfracture mechanics techniques used to measureinterfacial fracture energies and an in-depthpresentation of nanoindentation and stressedoverlayer (superlayer) test techniques. Thetechniques employed to measure thin-filmmechanical properties are presented as theseproperties are required for model inputs. Theyalso form the basis for comparing results. Themajor portion of the chapter is then devoted topresentation and discussion of how these testtechniques have been used to experimentallycharacterize thin film fracture for a number oftechnologically relevant applications and theirresults. Although the emphasis is predomi-

nantly on as-deposited films, data from ther-mally treated and diffusion bonded samples areincluded for comparison.

8.13.2 ADHESION

Adhesion can be quantitatively understoodin terms of two energy terms, the thermody-namic work of adhesion between the materialsof an interface, and the inelastic contributionsoccurring at and near the interface during theseparation process (Evans et al., 1990; Evansand Dalgleish, 1992, 1993; Hong et al., 1995;Hutchinson and Suo, 1992). The thermody-namic work of adhesion is a function ofthe surface energies of the materials and theinterface, the nonequilibrium state of theinterface, and the concentration of impuritysegregants at or near the interface. Theinelastic contributions include such terms asligament bridging, plasticity within a processzone near the delamination boundary, andfrictional dissipation of nonplanar surfacesbehind the delamination boundary. Theseterms have been empirically shown to havefunctional dependence on the state of stress atthe delamination boundary, i.e., the mixity ofshear and opening stresses. Moreover, the totalcontribution of such inelastic mechanisms hasbeen shown to scale with the thermodynamicwork of adhesion, such that the total energyrequired to produce delamination, G, can besimply expressed as

G ¼ Wad þ WpðWadÞ ð1Þ

where Wad is the thermodynamic work ofadhesion and Wp is the sum of the contribu-tions from inelastic dissipation mechanisms.The primary effects of both annealing andinterlayers can be easily rationalized in termsof their impact on Equation (1), in particularon the Wad term. Annealing influences thediffusion of segregants and changes the non-equilibrium nature of the interface from the as-deposited state; to a lesser extent it wouldaffect the degree of plasticity in a process zoneby changing the yield properties of the film.Interlayers introduce new interfaces, withdifferent values of Wad. In addition, the workof Russell et al. (1995) has shown that in thecase of Cr and Ti interposed between Cu/SiO2

interfaces, internal oxidation and intermetallicinterphase formation are empirical character-istics of enhanced adhesion.

8.13.2.1 Thermodynamic Work of Adhesion

From a thermodynamic standpoint, the truework of adhesion of the interface is the amount


of energy required to create free surfaces fromthe bonded materials:

WA ¼ gf þ gs � gfs ð2Þ

where gf and gs are the specific surface energiesof the film and the substrate, respectively, andgfs is the energy of the interface (Figure 1). Thetrue work of adhesion is an intrinsic-dependentproperty of the film/substrate pair; it dependson the type of bonding between the film andthe substrate and the level of initial surfacecontamination.

The true work of adhesion can be measuredby the contact angle technique (Lipkin et al.,1998; Furuya et al., 1995). If the tested materialparticle is in thermal equilibrium on a sub-strate, then,

gfs ¼ gs � gf cos Y ð3Þ

where Y is the contact angle between theparticle-free surface and the substrate (Figure1). The work of adhesion now can be expressedwith the Young–Dupre equation (1805)

WA ¼ gf þ gs � gfs ¼ gfð1þ cos YÞ ð4Þ

Particles in thermodynamic equilibrium canbe obtained by the sessile drop method (Leeand Lin, 1994) or by annealing (Lipkin et al.,1998; Furuya et al., 1995). In the case of theeasily oxidized particles such as Cu, annealingmust be performed in vacuum. When thesurface energy of the film gf is known at agiven temperature T0, at any temperature T, itwould be

gfðTÞEgfðT0Þ þ ðT � T0Þ@gf@T

� �T¼T0

ð5Þ

Solving Equations (4) and (5) for elevatedtemperature gives the value of the true (ther-modynamic) adhesive energy (Furuya et al.,1995). If crystallographic faceting occurs uponcooling, a different technique is used to assessthe work of adhesion, based on the aspect ratiomeasurements of the equilibrated crystals(Pilliar and Nutting, 1967). Usually, bothresults from contact angle and aspect ratiomeasurements agree well for metallic films(Lipkin et al., 1998). Contact angle distribution

can be obtained from SEM or AFM imageanalysis (Lipkin et al., 1998).

Lipkin et al. (1998) measured a value for thethermodynamic work of adhesion of gold onsapphire of 0.9 Jm–2. Furuya and co-workers(1995) calculated adhesive energies of Cu/SiO2,Cu/TiN, and Cu/TiW interfaces using thecontact angle technique with the two lattervalues being more than double the Cu/SiO2

value of 0.8 Jm�2. The true work of adhesion isa constant for a given film/substrate pair, andfor metals on ceramic is typically of the orderof 1–2 Jm–2.

For the idealized case of Griffith (1920)fracture, the fracture resistance, Gi, is assumedto be equal to the thermodynamic work ofadhesion, WA: Gi¼WA. In practice, evenbrittle fracture is accompanied by some sortof energy dissipation, either through plasticdeformation at the crack tip or friction. In thisregard, relatively thin films of the order of100 nm thick can exhibit plasticity duringinterfacial fracture resulting in an elevatedwork of fracture.

8.13.2.2 Practical Work of Adhesion

Most test methods measure adhesion bydelaminating thin films from the substrate.While debonding from the substrate, the filmand/or the substrate usually experiences plasticdeformation making it difficult to extract thetrue adhesive energy from the total energymeasured. What is measured is the practicalwork of adhesion, or interfacial toughness,

WA;P ¼ WA þ Uf þ Us þ Ufric ð6Þ

where Uf and Us are the energies spent in plasticdeformation of the film and the substrate,respectively, and Ufric are the energy lossesdue to friction. Although the last three termsappear to be simply additive, it should be notedthat both Uf (WA) and Us(WA) are functions ofthe true work of adhesion (Jokl et al., 1980) andin many cases Ufric(WA) will be as well.Fracture mechanics uses the strain energyrelease rate, G, or the crack driving force, as ameasure of the practical work of adhesion:

GZR ð7Þ

where R is the resistance to crack propagation.We will discuss tests for measuring G, and laterconsider various resistance terms and severalpossible ways to interpret that resistance,e.g., phase angle, friction, and plastic energydissipation.

The amount of energy dissipation dependson the mode mixity (phase angle), a relative

Figure 1 Schematic of contact angle measurement(source Volinsky et al., 2002).

Adhesion 457

measure of the amount of shear, and normalstress components at the crack tip (c¼ tan�1(t/s)¼ tan�1(KII/KI)). The effect of mode mixity onfracture energy is presented in Figure 2, wherethe amount of energy dissipation is muchhigher in the pure shear compared to the pureopening fracture mode. Both experimental andtheoretical results show this behavior (Hutch-inson and Suo, 1992; Liechti and Chai, 1992;Cao and Evans, 1989; Wang and Suo, 1990;Jensen and Thouless, 1993). The most realisticphenomenological descriptions of the func-tional dependence of the interfacial toughnesson the mode mixity are given by Hutchinsonand Suo (1992):

GðcÞ ¼ G0 1þ tan2fcð1� lÞg� �

ð8Þ

GðcÞ ¼ G0 1þ ð1� lÞtan2c� �

ð9Þ

where G0 is the mode I interfacial toughness forc¼ 0 and l is an adjustable material parameter(Figure 3). Note that there is no mode mixitydependence for the ideally brittle material(l¼ 0), and both solutions reduce to one forl¼ 0 and l¼ 1. Strictly speaking, there isalways a mode-mixity effect in the case of acrack propagating along the interface betweentwo dissimilar materials just due to a mismatchin their elastic properties (Dundurs, 1969).Interfacial fracture mechanics is used todescribe crack growth along an interfacebetween two dissimilar isotropic materials.See also Chapters 8.03 and 8.08. The complexstress intensity factor for bimaterials is thenexpressed as (Hutchinson and Suo, 1992)

K ¼ ðK1 þ iK2Þ ¼Pffiffiffih

p � iM

h3=2

� �pffiffiffi2

p hieeio ð10Þ

where h is the film thickness, M is the bendingmoment due to load P, o is a real angularfunction, p ¼ ½ð1� aÞ=ð1� b2Þ�1=2; and e is abimaterial real constant:

e ¼ ð1=2pÞln½ð1� bÞ=ð1þ bÞ� ð11Þ

The Dundurs parameters a and b for planestrain are

a ¼ðm1=m2Þð1� n1Þ � ð1� n2Þðm1=m2Þð1� n2Þ þ ð1� n1Þ

b ¼ 1ðm1=m2Þð1� 2n2Þ � ð1� 2n1Þ2ðm1=m2Þð1� n1Þ þ ð1� n2Þ

ð12Þ

For bimaterials the phase angle c is

c ¼ tan�1 Ph sin o� 2ffiffiffi3

pM cos o

Ph cos oþ 2ffiffiffi3

pM sin o

" #ð13Þ

In the case of a weakly bonded film on thesubstrate the interface will be the most likelycrack path, although there are cases when thecrack can kink either into the substrate or intothe film itself (Hutchinson and Suo, 1992). Thecrack path depends on the phase angle, residualstress, and the modulus mismatch between thefilm and the substrate. When testing thin filmadhesion, knowledge of the fracture interfaceand the phase angle is necessary in order tointerpret the results correctly.

There is also a link between the thermo-dynamic work of adhesion (WA) and theinterfacial toughness (Gi). For example, whenthe thin film yield stress is low and WA is high,ductile fracture is the most likely mechanism.Conversely, brittle fracture occurs when thefilm yield stress is high and the true adhesion islow (Lipkin et al., 1996, 1998). In the case of ametal film on a brittle substrate, one mayimprove the interfacial toughness by decreasingthe film yield stress (annealing), or by using

Figure 2 Interfacial fracture toughness as a func-tion of the mode-mixity angle (source Volinsky et al.,2002).

Figure 3 Phenomenological functions for G(c)(source Volinsky et al., 2002).


underlayers that increase the adhesion. Wenow discuss different techniques for measuringthe interfacial fracture toughness of thin films.

8.13.3 INTERFACIAL FRACTURE TESTTECHNIQUES

There are more than one hundred differentmethods for measuring thin film adhesion thatemploy different sample geometries. Some testsuse continuous films, some require patterning,but all tests use some driving force or storedenergy to achieve thin film delamination. Theenergy may come from the external mechanicalforce imposed on the film, or it can be stored inthe film itself (through the internal film stress).These tests generally measure critical values ofapplied stress intensity, Ki, or strain energyrelease rate, Gi where i can be mode I, II, or IIIor of mixed-mode character.

Unfortunately, measurement techniques thatcan quantify the energy of adhesion for films inthe as-deposited or as-processed state arelimited. While such techniques exist, a combi-nation of difficult specimen preparation andtesting techniques along with the complexity ofdeconvolution have historically led to a relianceon simpler and quicker semi-quantitative andqualitative techniques such as tape and scratchtesting. Returning again to the work of Russellet al. (1995) as exemplary, a combination oftape testing and scratch testing is used. Thetape test is qualitative and often an all-or-nothing test, useful only for testing weaklyadhering films. It precludes observation ofincremental improvements from processingoptimization. The scratch test is semi-quantita-tive, in that the normal load at which apredefined failure event or morphology occursis defined as a measure of adhesion. Similarwork by LaFontaine et al. (1990) uses ameasure of the depth-dependent nanoindenta-tion hardness as a measure of the adhesion inCu/Cr, and Ti/SiO2 film structures. While thesesemi-quantitative tests are simple and informa-tive, they are incapable of incorporating all therelevant parameters. With regard to the scratchtest, the authors rely on the fact that all filmsare of approximately the same thickness, hard-ness, and residual stress, the substrates are ofnearly identical thickness, and the same scratchstylus is used for all tests. Nevertheless, a morequantitative testing procedure is needed.

8.13.3.1 Sandwich Specimen Tests

For the sandwich type of test, a macroscopicfracture mechanics sample is made with a thinfilm incorporated into the test structure. This is

typically done through diffusion bonding,which can alter both the film microstructureand the interfacial adhesion, since the bondingcan take several hours and occurs at hightemperatures close to the melting point.Usually it acts as an annealing step duringthe sample preparation, which may not happenin the actual film processing. So, typically thesetypes of measurements do not apply to thefilms in the as-deposited state. These tests aremodifications of classical fracture mechanicstests, for which mechanics has been developed.For an isotropic material the crack tends togrow in the opening mode I, but in the case ofan interface the crack tends to grow along theinterface. For this reason it is important toquantify interfacial fracture toughness as afunction of mode mixity.

Many sample geometries are possible, soonly the most common ones will be considered.The simplest example is the modified KIC

specimen (Suo and Hutchinson, 1989; Mennin-gen and Weiss, 1995), where a thin film isbonded between the two pieces of a compacttension sample (ASTM Standard E399-90)(Figure 4(a)). Another version of this test isthe double cantilever test, where a thin film isbonded between two rigid elastic plates. Forthe KIC test the interfacial fracture toughnesscan be expressed in the form

K ¼ PQ

BffiffiffiffiffiffiW

p f ða=W Þ ð14Þ

where PQ is the load determined from theload–displacement curve, B is the specimenthickness, W is the specimen width as definedin Figure 4(a), f (a/W) is a function of a and Wwhich is defined in the standard for the homo-geneous material (ASTM Standard E399-90).McNaney et al. (1995, 1997) provide theelastic compliance solution for the modifiedcompact tension as well as the four-point bendspecimens.

In the case of the double cantilever test, thestrain energy release rate can be expressed as inCao and Evans (1989) and Kanninen (1973):

G ¼ 12P2a0

EB2H31þ AH

a0

� �þ B

H

a0

� �2" #

ð15Þ

where P is the fracture load, a0 is the precracklength, and H is half the specimen height. Aand B are the proportionality coefficients(AE1.3 and BE0.5).

It turns out that the presence of a thinmiddle layer does not shift the phase anglemuch as compared to the homogeneous case aslong as the middle layer is thin compared tothe total sample thickness 2H (Suo and

Interfacial Fracture Test Techniques 459

Hutchinson, 1989). The importance of bothtests is that they provide the interfacial tough-ness at almost zero mode-mixity angle.

Another test which uses a sandwich structureis the Brazil disk test. The Brazil disk test isschematically shown in Figure 4(b). In thissample, a thin film is bonded between twopieces of a disk of radius R. The crack of thelength 2a is present in the interface. A load P isapplied at a certain compression angle Y to thecrack axis and mode mixity is varied bychanging Y. Pure mode I conditions areachieved when Y¼ 01 and pure mode II whenYD251 (O’Dowd et al., 1992).

Atkinson et al. (1982) presented explicitformulas for KI and KII valid for any crackorientation in the homogeneous Brazil disk:

KI ¼PNI

RB

ffiffiffia

p

r; KII ¼

PNII

RB

ffiffiffia

p

rð16Þ

where a is half the crack length, b is the diskthickness, and NI and NII are nondimensionalfunctions of the relative crack size (a/R).

O’Dowd et al. (1992) provided a stressintensity solution for a bimaterial Brazil diskas follows:

K ¼ YP

2R

ffiffiffiffiffi2a

p2að Þ�ieeic ð17Þ

where Y is a dimensionless geometric factor, eis the bimaterial real constant as in Equation(11). The dependence of c and Y on thecompression angle Y is not known. Since the

crack has two tips, stress intensity factors ateach tip will also be different, so c and Y mustbe provided for each crack tip. Brazil diskmechanics for orthotropic materials, as well asan FEM model, are discussed by Huang et al.(1996). Mechanics for a Brazil-nut-sandwichspecimen (Figure 4(b)) and different types offailure are discussed by Wang and Suo (1990).The advantage of the test is the ability tochange the phase angle by rotating the samplerelative to the axis of the applied load.

The last type of the sandwich samplesconsidered here is the four-point bent test(Figure 4(c)). This has been the most popularadhesion test for the microelectronics industry.Two elastic substrates with thin films on themare bonded together with another material(typically Cu or epoxy). The upper substratehas a notch in it, and a crack propagatesthrough the substrate and kinks into theinterface of interest upon loading. At thispoint the strain energy release rate reachessteady state, which corresponds to the loadplateau in the load–displacement curve. Thestrain energy release rate can be calculatedfrom the steady-state fracture plateau load P(Charalambides et al., 1989):

G ¼21 1� n2� �

P2L2

16Eb2h3ð18Þ

where the geometrical parameters L, b, and hare shown in Figure 4(c). After passing thelower support line, the crack does not grow

Figure 4 Sandwich specimen tests schematics: (a) modified KIc sample; (b) Brazil-nut sample; and (c) four-point bend (UCSB) sample (source Volinsky et al., 2002).


stably anymore, and numerical analysis isrequired to assess G (Hofinger et al., 1998).The phase angle for the test at steady-statecrack growth is B431 (Dauskardt et al., 1998).Limitations of the test in terms of the K-dominant region are discussed in work byBecker et al. (1997).

Note that sandwich specimen test analysesdo not account for the residual stress in thinfilms. The ideal test should simulate thepractical situation as closely as possible, whilealso being able to extract the value of practicaladhesion. The method must explicitly accountfor the contribution of the residual stress to thedecohesion process. If the test structure hasexperienced only low temperatures duringfabrication, using high homologous tempera-ture (T/Tm) processing steps in specimenpreparation, such as diffusion bonding, is notdesirable, since it can markedly alter interfaceadhesion properties.

8.13.3.2 Bulge and Blister Tests

The bulge test is analogous to uniaxialtension for bulk materials and has beendeveloped for measuring mechanical propertiesof thin films. In the bulge test, a freestandingthin film ‘‘window’’ is pressurized on one side,causing it to deflect (Figure 5). A stress–straincurve can then be constructed from measuredpressure, P, and film deflection d.

The pressure–deflection curve is a functionof sample geometry, the film’s mechanicalproperties, and residual stress. A sphericalcap model was initially used for stress andstrain determination in the bulge test (Vlassakand Nix, 1992):

s ¼ Pr2

4dhand e ¼ 1

3r2d2þ A ð19Þ

where d is the total bulge height, h is thefilm thickness, r is the bulge radius, and A isthe term which accounts for initial stress in thefilm. For slack films, A¼ 2d0/3r2 with d0the height due to the slack in the film. Fortaut films, A¼ s0/E0 with s0 the initial tensilestress in the film and E0 the biaxial modulus ofthe tested film.

The relation between pressure P and deflec-tion d may be expressed, based on the capmodel, as

P ¼ c1s0h

ar2þ c1Eh

r4 1� nð Þ d3 ð20Þ

where c1 and c2 are geometric parameters ofthe bulge form. Vlassak, and Nix (1992)showed the validity of Equation (20) for squareand rectangular membranes using an energyminimization technique.

The spherical cap model assumes an equi-biaxial state of stress and strain in the bulgedfilm, which is an approximation since the filmis clamped and there is no circumferentialstrain at the edge. There is also an uncertaintyin measuring the initial bulge height at the startof pressurization. Finite element analysis hasbeen conducted to overcome such problems(Vlassak and Nix, 1992; Small et al., 1992;Small and Nix, 1992; Paviot et al., 1995) formeasurement of biaxial modulus and Poisson’sratio. Mechanics for the blister test is alsogiven in Hutchinson and Suo (1992). Adisadvantage of this method lay in its difficultspecimen preparation. If the film is too thin(o2 mm), it may wrinkle due to the residualstress relief when made freestanding (Small andNix, 1992).

The blister test is similar to the bulge testwith the only difference being that the pressureis increased until the film starts to debond fromthe substrate, forming a blister. The crackextension force (strain energy release rate) forthe blister test is (Hohlfelder et al., 1997)

G ¼ Pdkv

p4þ 5f4þ 4f

� �ð21Þ

where the coefficient kv accounts for the shapeof the blister and f¼ [(c2Ef

0)/(c1s0)](d/r)2. The

constant kv is E1.62 for a circular window and1.94 for a square window.

Blister tests are often invalid in the case ofthin ductile films due to film yielding beforedecohesion. In order to prevent film yielding, ahard elastic superlayer may be deposited ontop of the film of interest, similar to thesuperlayer indentation technique. The super-layer can be deposited directly on the free-standing film without causing it to wrinkle.Another problem with the blister test is that acrack often does not propagate uniformlyalong the perimeter of the blister, making itdifficult to interpret the results. A transitionbetween blister bending and stretching isdiscussed by Wan and Lim (1998). For ahomogeneous system the phase angle of load-ing in the blister test ranges from �401 to �901.

Figure 5 Schematic of the bulge test (sourceVolinsky et al., 2002).


A comprehensive analysis of mode mixity inthe blister test is presented by Jensen (1998).

8.13.3.3 Superlayer Test

A test based upon internally developedstresses was proposed by Bagchi et al. (1994).Here, residual tensile stresses in a thin film linedrive its delamination from a thick substrate.The nondimensional steady-state strain energyrelease rate, GSS, for a narrow line after crackinitiation is

GssEf

s2f hf¼ 1

2ð22Þ

where Ef is the Young modulus of the film, hf isthe film thickness, and sf is the residual stressin the film. The corresponding phase angle inthis case is B521 (Bagchi et al., 1994). For thewide line (line width is greater than itsthickness), the residual stress is biaxial andthe strain energy release rate is

GssEf

s2f hf¼ 1� nf ð23Þ

where nf is Poisson’s ratio of the film. For atypical film thickness of 1 mm and a residualstress of 100MPa, the stress-induced energyrelease rate is of the order of 0.1 Jm�2. As mostinterfaces in microelectronic devices have high-er debond energies, decohesion is difficult if notimpossible under these conditions. GSS needs tobe increased without substantially changing thephase angle. One of the ways is to increasestrain energy by depositing a thick overlayer(superlayer) on top of the tested structure. ForCu interconnects, Cr was found to be theoptimal superlayer (Bagchi et al., 1994; Bagchiand Evans, 1996). The superlayer increases thefilm total thickness and elevates the totalresidual stress without changing the testedinterface. It is deposited at ambient tempera-tures (by electron beam evaporation) and doesnot react with the tested Cu film. Moreimportantly, it has high residual tensile stressesupon deposition. Figure 6 illustrates the testschematically. In the first step, a thin carbonrelease layer is thermally evaporated and

patterned using the bilayer photolithographytechnique. This layer acts like a precrack forthe test structure. Its width is at least twice theCu film thickness to avoid edge effects on theenergy release rate. In the second step, the filmof interest (Cu) and the superlayer (Cr) aredeposited and patterned to form strips perpen-dicular to the carbon lines. In order to producea range of strain energy release rates, thesuperlayer thickness is varied. The metalbilayer structure is cut by wet-etching or ionmilling during the third step. If the strainenergy release rate exceeds the adhesionenergy, the strips decohere. If the films stayattached, the adhesion energy was not ex-ceeded and a thicker superlayer should be used.

The debond energy G is determined by thecritical superlayer thickness (Bagchi et al.,1994):

G ¼X

i

s2khi

E0i

�X

i

1

E0i

P2

hi

þ 12M2i

h3i

�

P ¼ kE01h31 þ E0

2h326 h1 þ h2ð Þ

�

k ¼ 6 h1 þ h2ð Þ e1 � e2ð Þh21 þ E0

2h32=E01h3

1 þ E01h31=E0

2h32 þ h22 þ 3 h1 þ h2ð Þ2

Mi ¼E0i k ð24Þ

where i¼ 1, 2 refers to the two materials in thebilayer, h1 and h2, Ei

0 are the biaxial elasticmoduli, Ei

0 ¼Ei/(1�ni), the load P is associatedwith the residual tension stress, si, in eachlayer, k is the curvature of the debonded layer,ei are misfit strains: ei¼ si /Ei

0, and Mi are thebending moments along the centerline of eachlayer due to the load P (Figure 7).

When stressed superlayers are applied over alarge surface area of a film, they will oftentrigger uniform width, telephone cord, andcircular blisters. The blisters provide the datafrom which interfacial fracture energies can beobtained using solutions for film systems whereresidual stresses dominate fracture behavior.These solutions were originally derived forsingle-layer film-on-substrate systems (Mar-shall and Evans, 1984; Evans and Hutchinson,

Figure 6 Schematic of the superlayer tests (sourceVolinsky et al., 2002).

Figure 7 Film decohesion in the superlayer test(source Volinsky et al., 2002).


1984; Hutchinson and Suo, 1992). The work ofBagchi et al. (1994) and Bagchi and Evans(1996) and by Kriese et al. (1999a) extendedthese solutions to multilayer systems by treat-ing the multilayer film as a single-layer film ofthe same total thickness with a transformedmoment of inertia, IT.

The uniform width blister is modeled as awide, clamped Euler column of width 2b for ablister to form between the multilayer film andsubstrate under these conditions; the compres-sive residual stress, sr, must exceed the stress forinterfacial delamination, sb, as follows (Krieseet al., 1999a; Hutchinson and Suo, 1992):

sb ¼ pBhb2

Efilm

1� n2film� �" #

ITð Þ ð25Þ

In this expression, nfilm is Poisson’s ratio of thefilm, b is the blister half-width, h is the total filmand superlayer thickness, and B is the unitwidth, which cancels when multiplied by thetransformed moment of inertia (Kriese et al.,1999a). The residual stress can then be deter-mined from the blister height and the stress fordelamination as follows (Hutchinson and Suo,1992):

sr ¼ sb3d2

4h2þ 1

� �ð26Þ

where d is the buckle height and sr is given byKriese et al. (1999a, 1999b)

sr ¼ srfilmhfilm

h

� �þ srsuperlayer

hsuperlayer

h

� �ð27Þ

The residual stress and stress for delamina-tion are then used to determine the strain energyrelease rate for interfacial fracture along thestraight side wall portions of the blisters from

G cð Þ ¼1� n2� �

h

2 %E

� sr � sbð Þ sr þ 3sbð Þ ð28Þ

where E and n are the thickness-weighted elasticmodulus and Poisson’s ratio values for themultilayer films, respectively. Under steady-state conditions, the width of the blister remainsfixed creating the straight-sided blister config-uration with growth occurring along the moreor less circular end of the blister. Under theseconditions, the steady-state fracture energy isgiven by (Hutchinson and Suo, 1992)

GSS ¼1� n2� �

hs2r2 %E

� 1� sb

sr

� �2

ð29Þ

Figure 8 shows typical G(c) and Gss fracturelocations.

8.13.3.4 Indentation Tests

Nanoindentation is normally used for mea-suring thin film mechanical properties such asthe elastic modulus and hardness (described inSection 8.13.4 in detail) and used for modelingfilm fracture behavior. In the case of a brittle,weakly bonded film, indentation tests can beused to delaminate the film from the substrate.From the delamination, interfacial fracturestrengths can be determined (Marshall andEvans, 1984; Rosenfeld et al., 1990; de Boerand Gerberich, 1996a; Vlassak et al., 1997;Drory and Hutchinson, 1996). Basically, thecone (plane stress) and the wedge (plane strain)are the two most popular indenter geometriesfor measuring brittle thin film adhesion byindentation. Marshall and Evans (1984) pro-vide the analysis for the conical indentation-induced thin film delamination. The strainenergy release rate is

GEf

1� nfð Þ ¼1

2hs2I 1þ nfð Þ þ ð1� aÞhs2r

� ð1� aÞhðsI � sbÞ2 ð30Þ

where Ef and nf are thin film’s Young’smodulus and Poisson’s ratio, respectively, h isthe total film thickness, and sr is the residualstress in the film. Here, a sharp diamond tip isindented into the tested thin film, and deformsa volume of 2VI (Figure 9(a)). Indentationcauses nucleation and propagation of aninterfacial crack. If the indenter is driven deepenough, so that the crack reaches its criticalbuckling length, the film double buckles(Figure 9(b)) during indentation. If the cracklength did not reach its critical buckling lengthon each side of the indenter, single bucklingmight occur upon tip removal (Figure 9(c)).When the tip is removed, the film underindenter is no longer under constraint, so itmay form a single buckle even in the initialdouble-buckling case.

Figure 8 Typical locations where G(c) and Gss aremeasured on telephone cord blisters.


The indentation stress, sI can be calculatedby using the indenter tip geometry:

sI ¼EfVI

2pa2h 1� nfð Þ ð31Þ

The indentation volume, VI can be calculatedfrom the plastic indentation depth using the tipgeometry, and the crack length, a, can directlybe measured by using microscopy or profilo-metry techniques. If the crack is driven farenough by the indenter (Figure 9(b) or (c)), thefilm can buckle, giving rise to the last term inEquation (30) through the Euler bucklingstress:

sb ¼ m2h2Ef

12a2 1� nfð Þ ð32Þ

In this equation, m is a constant that dependson the boundary condition (m2¼ 14.68 forsingle buckling, and m2¼ 42.67 for annulardouble buckling). The term a is equal to 1 if thefilm is not buckled, otherwise it represents theslope of the buckling load vs. the edgedisplacement on buckling as follows:

a ¼ 1� 1

1þ 0:902 1� nfð Þ ð33Þ

Note that in the case of nonbuckling fracture(a¼ 1), delamination is only driven by theindentation stress, and the residual stress doesnot come into play.

A microwedge indentation test (MWIT) hasbeen proposed by de Boer and Gerberich(1996a) for thin metal lines. Here, a diamondwedge is indented perpendicular to the line tocause its debonding. An approach, similar to

Marshall and Evans (1984), is employed, wherethe plastic volume is assumed to transform intothe film elastic displacement at the crack tip:

G ¼ E0fV

20

2b2ha2ð34Þ

where V0 is the half of the total indentationvolume, a is the crack length, b is the linewidth, and Ef

0 is the plane-strain elasticmodulus of the film: Ef

0 ¼ Ef/(1�nf2). The test

accounts for the line buckling, and appropriatesolutions are given by de Boer and Gerberich(1996a).

A similar wedge indentation test has beenapplied by Vlassak et al. (1997) to measureadhesion of hard films on ductile substrates. Itis based on the model for the plane-strainwedge indentation into a brittle continuousfilm on a ductile substrate:

G ¼1� n2f� �

sxxh

2Efð35Þ

where sxx is the stress in the film, perpendicularto the wedge line:

sxx ¼ sr � nfEf

1� n2f

� �W 2 tan b

pa2ð36Þ

Here, sr is the residual stress in the film, W isthe half-width of the wedge indentation, b isthe inclination of the face of the wedge to thesurface of the film, and a is the crack length.

The advantage of the wedge indenter geo-metry is the weaker 1/a2 dependence inEquations (34) and (36) compared to 1/a4 forthe axisymmetric case (Rosenfeld et al., 1990)which leads to less experimental scatter. Theproblem with the wedge indentation is thealignment. Usually, wedges are not perfectlysymmetric, and it is also extremely difficult toalign the wedge perpendicular to the plane ofthe thin film. Misalignment causes asymmetriccrack growth on both sides of the wedge. Thiseffect has been observed on both the micro-and macroscales (de Boer and Gerberich,1996a; Volinsky et al., 1999). A new revisionof the wedge indentation test is provided byBegley et al. (2000).

A relatively new idea of a cross-sectionalindentation for thin film delamination has beenproposed by Sanchez et al. (1999). An indenta-tion is made into the substrate cross-section,close to the film interface, which causes the filmto debond. The energy release rate can becalculated by knowing the maximum filmdeflection, u0:

G ¼ Eh3u20

12ða � bÞ21� lð Þ4 2F þ lF 0ð Þ ð37Þ

Figure 9 (a) No buckling during indentation; (b)double buckling during indentation; and (c) singlebuckling after indenter tip removal (source Volinskyet al., 2002).


where a and b are the delamination and contactradii, respectively, l¼ a/b, and F is defined as

FðlÞ ¼ 2 ln lþ ½ð1þ lÞ=ð1� lÞ� ln2lð1þ lÞ ln lþ 2 1� lð Þ½ �2

ð38Þ

and F 0 ¼ dF/dl. This test is particularly useful,since the film is not indented directly, and thecrack initiates in the brittle substrate, whichlimits the amount of plastic deformation.

Unfortunately, indentation tests on thinfilms of interest cannot often be used directlyin the case of ductile films on brittle substrates.A ductile strongly adhered film would form aplastic pileup around the indenter rather thandelaminate from the substrate. Even if the filmdebonds from the substrate, delaminations arenot reproducible, and plastic pileup has to betaken into account. Such problems have beensolved with the introduction of the superlayerindentation technique.

8.13.3.5 Superlayer Indentation Test

Kriese et al. (1999a, 1999b) have combinedthe idea of the superlayer test with theindentation test. Deposition of a hard film,capable of storing significant amounts ofelastic energy over the film of interest, canresult in multilayer debonding (Bagchi andEvans, 1996) producing large delaminationradii (Figure 7). It also acts like a cappinglayer, preventing plastic flow of the underlyingfilm in the vertical direction, and addingnormal stresses at the interfacial crack tip (Heet al., 1996). Presence of the superlayerprovides an additional driving force for de-adhesion as shown in Figure 7. For thesuperlayer indentation test, a sharp indenteralso provides additional stress for crack initia-tion/propagation at the interface.

A modified Marshall and Evans (1984)analysis is used, and the laminate theory isemployed in order to calculate the necessaryterms in Equation (30) for the bilayer (Krieseet al., 1999a, 1999b). In the case of a highlycompressed superlayer, the indentation stress isbeing added to the residual stress, so multiplesuperlayer depositions are avoided. Blanketfilms can be tested in the as-deposited, as-processed conditions; no pattern transfer isnecessary. When an indenter penetratesthrough a bilayer, it causes film debondingand blister formation, which can be seenafterwards in an optical microscope withNomarski contrast (Figure 10).

Properties of the films, such as elasticmodulus, Poisson’s ratio, as well as thetip angle and radius, are needed for anadhesion assessment. Generally speaking,

there are two measurements that are necessaryfor strain energy release rate calculations.From the standpoint of blister formation,both blister diameter and indentation depthare required. Blister diameter is measured inthe optical microscope with Nomarski con-trast. Using the Oliver–Pharr (1992) method,inelastic indentation depth, dpl, is calculatedfrom

P ¼ A d� dpl� �m ð39Þ

where P and d are the load and displacementfrom the 65% of the unloading slope ofthe load–displacement curve, respectively, Aand m are fitting parameters. The indenta-tion volume, VI, is calculated from theinelastic depth by using the tip geometry.The indentation stress can be calculated fromEquation (31), assuming the conservation ofvolume.

The solution for the buckling stress inthe bilayer is also provided by Kriese et al.(1999a, 1999b). The advantage of the super-layer indentation test is that it providesinterfacial toughness measurements over awide range of phase angles. Prior to bucklingthe phase angle is equal to the real angularfunction, o, and at the onset of buckling arapid decrease occurs.

8.13.3.6 Scratch Tests

In a typical scratch test, a stylus or adiamond tip is drawn across the film surface.The test could be treated as a combination oftwo operations: normal indentation and hor-izontal tip motion. A vertical increasing load isapplied to the tip during scratching until thecoating detaches from the substrate. Theminimum critical load Pcr at which delamina-tion occurs is used as a measure of the practicalwork of adhesion (Benjamin and Weaver,

Figure 10 Optical micrographs of indentationinduced blisters with (right) and without (left) atungsten overlayer (source Volinsky et al., 2002).


1960; Burnett and Rickersby, 1987):

Pcr ¼pr2

2

2EWA;P

h

� �2

ð40Þ

where r is the contact radius and h is the filmthickness. This analysis is applicable only whenthe tensile stress normal to the film surfacedrives delamination.

Venkataraman et al. (1992, 1993c) developeda model for estimating the energy per unit areaG0 stored in the film from the scratch elasticstress distribution, which was modified later toaccount for residual stresses in the film (Moodyet al., 1998):

G0 ¼1� n2� �

s2rh

2EþX 1� n2

� �%t2ijh

2mþ

1� n2� �

%s2ijh

2E

!

ð41Þ

where the first term comes from the contribu-tion of the residual stress sr, %tij ; and %sij are theaverage elastic shear and normal stresses in thedelaminated film, h is the film thickness, m isthe film shear modulus. %tij and %sij can bedetermined from the scratch trace geometryobserved in SEM.

For a symmetric scratch trace, the strainenergy release rate can be found using acircular blister analysis (Moody et al., 1998):

G0 ¼1� nð Þhs2

E1� að Þ 1� sb

s

�ð42Þ

where sb is the Euler buckling stress, defined byEquation (32) for a circular blister with m¼ pand a is defined by Equation (33) (Hutchinsonand Suo, 1992).

de Boer and Gerberich (1996b) and de Boeret al. (1997) adjusted the original scratch testfor fine line structures. A schematic of the newtest, the precracked line scratch test (PLST), isshown in Figure 11. A thin metal line on asubstrate is pushed with the asymmetricdiamond wedge from one end. The thin linehas a processed precrack in the form of acarbon layer, which makes it a real fracture

mechanics specimen. It is similar to the super-layer test of Bagchi and co-workers (Bagchiet al., 1994; Bagchi and Evans, 1996). Theprecrack portion of the line is deformedelastically in the beginning of the test untilthe crack propagates. When the crack reachesits critical buckling length at a certain criticalload, Pcr, the film buckles. At the point ofbuckling, the strain energy release rate can becalculated as

G ¼ s2h

2E0f

¼ Pcr � Pfricð Þ2

2b2hE0f

ð43Þ

Here s is the stress in the cracked portion ofthe line, b is the line width, Pcr and Pfric are thecritical buckling load and the friction load,respectively, which are measured experimen-tally.

The test is applicable to the hard lines,capable of bearing a load to the crack tipwithout plastically deforming; it was originallycarried out on W thin lines on oxidized siliconwafers. The phase angle just prior to bucklingis 52.71, and decreases rapidly after bucklingdue to the increased normal stress component.Post-buckling solutions for the strain energyrelease rate are provided in de Boer andGerberich (1996a) and Volinsky et al. (1999).

The mechanics for the PLST has beenmodeled using the macroscopic setup of apolycarbonate line bonded to steel with cya-noacrylate (Volinsky et al., 1999). This alloweda construction of the strain energy releasecurve throughout the whole test, before andafter line buckling (Figure 12). Prior to linebuckling, an R-curve behavior is observed, asthe strain energy release rate increases with thecrack length. At the point of buckling, there isunstable crack growth, as the strain energyrelease rate, G, exceeds interfacial fracturetoughness, G(c) (Figure 13). This situationis analogous to circular blister buckling(Hutchinson and Suo, 1992). At a certain level

Figure 11 Schematic of the PSLT (source Volinskyet al., 2002).

Figure 12 Strain energy release rate for the PLST(source Volinsky et al., 2002).


of stress, sbuckle, and a certain crack length, a1,the line starts to buckle, at which point theinterfacial fracture toughness drops under theinfluence of a decreasing phase angle ofloading. The crack arrests at a2 when theinterfacial fracture toughness exceeds the strainenergy release rate. At this point, fracture isdominated by the mode I stress component,and continues to grow stably until the total linedecoheres (Volinsky et al., 1999).

The PLST allows measuring the interfacialfracture toughness over a wide range of phaseangles of loading. For this test to work, thematerial must transfer the stress down to thecrack tip without plastically deforming. As aconsequence, this test may not work withductile metals such as Cu, Al, and Au. Theproblem may be solved by using a stiff hardsuperlayer on top of the film of interest, justlike in the superlayer indentation test.

8.13.4 NANOINDENTATION—MECHANICAL PROPERTIES

For analysis of most adhesion test data, theknowledge of the thin film mechanical proper-ties is required. In the previous section, almostevery expression for the strain energy releaserate has the thin film elastic modulus. Themodulus can be measured by the microbeamcantilever deflection technique (Weihs et al.,1988; Baker and Nix, 1994), but the easiest wayis by means of nanoindentation (Oliver andPharr, 1992), since no special sample prepara-tion is required and the same technique can beused for measuring film adhesion.

8.13.4.1 Elastic Properties

8.13.4.1.1 Load vs. displacement curves

To begin with, the elastic modulus of amaterial can be determined using nanoindenta-

tion. The method first developed by Loubetet al. (1984) and refined by other researchers(Doerner and Nix, 1986; Oliver and Pharr,1992) uses the geometry shown in Figure 14. Inthis test, a diamond indenter is driven into asample while continuously measuring the loadand displacement. From analysis of the un-loading data, stiffness and elastic modulus canbe determined. The ‘‘unloading’’ slope analysisassumes that upon the initial unloading, thesample behaves in an elastic manner similar toa flat punch of the same contact radius incontact with the sample. This allows the use ofthe Sneddon (1965) models of flat punches incontact with surfaces under elastic loading. Inthis case, the remote load–displacement rela-tionship can be used to relate the stiffness, S,from the unloading curve to the area ofcontact, A, and the reduced elastic modulus,E*:

E� ¼ S

ffiffiffip

p

2

1ffiffiffiffiA

p ð44Þ

where

1

E� ¼1� n21

E1þ 1� n22

E2ð45Þ

In these equations, E1 and n1 are the modulusand Poisson’s ratio of the sample and E2 and n2are the modulus and Poisson’s ratio of theindenter.

The important parameter in Equation (44) isthe stiffness and therefore it’s inverse, i.e.,compliance. Compliance is the result of manycontributing factors. The sample contributes acompliance as does the loading system. Assum-ing compliance of the sample-tip interaction isa function of the area of contact whilecompliance from the test frame is constant, itis possible to relate the measured compliance tothe contact area of the indenter with the sampleas follows:

C ¼ Cframe þffiffiffip

p

2E

1ffiffiffiffiA

p ð46Þ

In this equation, the slope of the linecorrelates directly to the reduced elastic mod-ulus and the offset to the frame compliance.Indentations into standard samples withknown elastic constants can allow one toempirically determine the relationship betweenthe area of the tip and the penetration depth.

Several assumptions are implied in thismodel. First, the sample must not ‘‘pile up’’around the indenter tip. Many metallic materi-als (particularly with low work-hardeningcoefficients) do indeed pile up around indentertips during a test (Samuels and Mulhearn,

Figure 13 Schematic of unstable crack growthduring buckling for PLST (source Volinsky et al.,2002).

Nanoindentation—Mechanical Properties 467

1957; Bahr and Gerberich, 1996b), resulting inpossible inaccuracies in the determination ofdepth of contact. Second, the tip itself musthave a large included angle. Sharper angles willcause larger out-of-plane deformations, andthis will impact the analysis (Pharr, 1998).

8.13.4.1.2 Continuous stiffness

A newer, powerful technique for nanoinden-tation, coined ‘‘continuous stiffness,’’ allowsthe contact stiffness to be measured continu-ously during the course of a test enabling themodulus and hardness to be calculated as afunction of depth. The technique imposes asinusoidal forcing function (see Figure 15) atB45Hz, and uses this signal to calculate thecontact stiffness from

POS

hðoÞ

�� ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifðS�1 þ CfÞ�1 þ KS � mo2g2 þ o2D2

qð47Þ

or by using the phase difference between thedisplacement and force signals from:

tanðfÞ ¼ oD

ðS�1 þ CfÞ�1 þ KS � mo2ð48Þ

where Cf is the compliance of the load frame,KS is the stiffness of the column supportsprings, D is the damping coefficient, POS isthe magnitude of the force oscillation, h(o) isthe magnitude of the resulting displacementoscillation, o is the frequency of oscillation, fis the phase angle between the force anddisplacement signals, and m is the mass of thetip (Oliver and Pharr, 1992). Material proper-ties can then be calculated at each of these‘‘initial’’ unloading sequences. A dynamicmodel for this continuous stiffness setup isshown in Figure 16. Continuous stiffness isparticularly useful for indentation of thin filmstructures, since material properties can bedetermined for both the film and substrate inone easy test (see Figure 17 for an example ofthe hardness measured for a 200 nm thick Aufilm on sapphire and a 200 nm Au film on 6 nmof Cu on sapphire, fromWoodcock, 2002). Thefilm thickness can also be determined by

careful analysis of the changes in the modulusand hardness curves as a function of depth.

8.13.4.1.3 Thin film—substrate effects

King developed a model (King, 1987) whichrelates the measured stiffness to the expectedstiffness of the substrate to determine the filmproperties. Based on the measured or calculated

Figure 14 Indentation schematic before, during, and after test illustrating the different depths involved. Notethat hplastic corresponds to the contact depth referred to above (adapted from Oliver and Pharr, 1992).

Figure 15 Graphical representation of a load–displacement record using the continuous stiffnesstechnique.

Figure 16 A simplified dynamic model of ananoindentation system with continuous stiffnesscapability (adapted from Oliver and Pharr, 1992).


areas, the substrate stiffness, S0, is determined.The modulus of the film is then given by

Ef ¼ ð1� n2f Þ

� 1� e�ct=a

ð1=ERÞðS0=SÞð Þ � ðð1� n2s Þ=EsÞ e�ct=a� �

� ð1� n2i Þ=Ei

� �ð49Þ

where the subscript f refers to film properties, tis the film thickness, a is the contact areaparameter given by OA;S is the samplestiffness from a given indentation (after correct-ing for the frame compliance by inverting themeasured stiffness, subtracting the frame com-pliance from the measured compliance, andinverting that result to obtain the stiffness), andc is an empirically determined parameterrelated to the ratio a/t and the geometry ofthe indenter tip. The parameter c was calculatedby King to be between 0.3 and 2. This is onlyone of many available substrate correctionspossible (see, e.g., Saha and Nix, 2001), butmost follow the basic assumption that thesubstrate can influence the elastic moduluswhich is calculated by nanoindentation.

8.13.4.2 Plastic Properties

While the elastic properties are needed forindentation-induced fracture testing, the plasticproperties of the films will also play asignificant role, as plasticity in the film willlimit the amount of stored elastic strain energywhich can be present to drive a fracture. Theoriginal method of hardness testing wasintended to measure plastic, not elastic, proper-ties. Traditional hardness tests have been usedfor decades to measure the resistance of amaterial to deformation. In the late eighteenth

and early nineteenth century, several attemptswere made to rank the deformation of materi-als by scratching one material with another. Ifthe scratching material marked the testedmaterial, the scratching material was consid-ered ‘‘harder’’ than the scratched material.While this was useful for comparative purposes(and is still referred to as the Mohs hardnessscale), there remained the problem of quantify-ing hardness. In the late nineteenth century,work by Hertz (1896) and Auerbach (1893)brought about early examples of static inden-tation testing. In these cases, the samples(either balls or flat plates) were probed with aball of a given material, and the deformationwas measured by considering the contact areabetween the ball and sample.

It was not until the early 1900s (Brinell,1901) that a standard method of evaluatinghardness was presented, based on applying afixed load to a hard spherical indenter tip intoa flat plate. After 15–30 s, the load wasremoved and the diameter of the impressionwas measured using optical microscopy. TheBrinell hardness number (BHN) is defined as

BHN ¼ 2P

pD2 1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� d=Dð Þ2

q� � ð50Þ

where P is the applied load, D the diameter ofthe indenter ball, and d is the chordal diameterof the residual impression. Note that thismethod evaluates the load applied to thesurface area of the residual impression. How-ever, the Brinell test has been shown to beaffected by both the applied load and diameterof the ball used for the indenter.

8.13.4.2.1 Yield strength

The idea that hardness should be a materialproperty, and not dependent on test method,led to the observations that the parameterwhich remains constant for large indentationsappears to be the mean pressure, defined as theload divided by the projected contact area ofthe surface. Meyer (cited by Hoyt, 1924)suggested that the hardness should thereforebe defined as

H ¼ 4P

pd2ð51Þ

This type of hardness measurement is alter-nately referred to as the mean pressure of anindentation, and noted as either p0 or H in theliterature. Depending on the shape ofthe indenter and the friction between theindenter and material, the relationship formean pressure and yield strength can vary.

Figure 17 Hardness extracted for Au and Au–Cufilms on sapphire substrates using the continuousstiffness method (source Woodcock, 2002).


However, the basic relationship proposed(Tabor, 1951) is

syD13

p0 ð52Þ

This has been shown experimentally by Taborand others to be an adequate relationship formaterials which are elastic–perfectly plastic.For materials which work-harden, the effectivestrain around the indenter should be consid-ered. As described by Meyers, and quantifiedby Tabor, the effective strain, e (in %), aroundan indenter tip is approximately

e ¼ d

D� 20 ð53Þ

For a spherical indenter, where d is thediameter of the impression and D the diameterof the ball making the indentation. Thedevelopment of the Vickers (or diamondpyramid hardness) indentation test followedthe basic method of the Brinell test, butreplaced the steel ball with a diamond pyramidground to an included angle between faces of1361. It is interesting to note that the anglechosen was based on the Brinell test. It hadbecome common to make indentations withthe Brinell method to residual indent diameterscorresponding to 0.25–0.5 of the ball diameter.The average of these are 0.375, and if apyramid is formed around a spherical cap suchthat the ratio of the chordal diameter to balldiameter is 0.375, the angle must be 1361. Afterapplying a load, the indent is imaged, and thediagonals of the indentation are measured. TheVickers hardness is then defined as

DPH ¼2P sin 136E=2

� �d2

ð54Þ

where DPH is the diamond pyramid hardnessnumber, P is the load applied in grams, andnow d is the length of the diagonals in mm(usually the average of the two diagonals). Thisis analogous to the Brinell test, in that the DPHis the ratio of the load to the surface area of theindentation. The main advantages of thismethod is that there is a continuous scalebetween very soft and very hard materials, andthat the DPH is constant over a wide range ofloads until very low loads (less than 50–100 g)are reached.

Using the same method by which the anglesfor the Vickers test were decided, it is possibleto come up with an effective strain around anindenter tip. For example, the ‘‘effective’’strain which a Vickers or Berkovich tipproduces is B8%. So for materials whichwork harden, the tip geometry can be used toprobe different effective strains, making it

possible to begin to extract ‘‘indentation stressstrain curves.’’

The nanoindentation method of extractinghardness is analogous to the Meyer hardness;by measuring the applied load and the pro-jected area of contact under load, a meanpressure very similar to the Meyer hardness isdetermined.

8.13.4.2.2 Bulk materials

The experiments of Atkins and Tabor (1965)demonstrated that the hardness as a functionof cone angle changes with the amount ofwork-hardening strain present in the sample.Materials, which were work hardened prior toindentation (i.e., have relatively elastic–per-fectly plastic stress strain behavior), exhibitedeither constant hardness or increases in hard-ness over the range of indenters used in thisstudy. Annealed materials tended to exhibit adecrease in hardness as the cone angle wasincreased. Increasingly, sharp indenter tips willlead to observed increase in hardness; this is ameasurement and not a materials effect.

As the field of nanoindentation continues togrow, the technique is being used for a widevariety of testing situations spanning multipledisciplines. One common trend, however, is thepush to smaller and sharper tips for samplingnear-surface properties and small volumes.Unfortunately, several problems can ariseusing these sharper tips. It has been shown(Hay and Pharr, 1998) that sharp tips aredifficult to calibrate correctly, especially at veryshallow depths. This problem manifests itselfas a disparity in the calculated hardness andmodulus due to length scale issues in the tipgeometry that are not accounted for in tradi-tional indentation mechanics.

One large-scale limitation of indentationtechniques is that primarily blunt angle tipsare used (such as the Berkovich or Vickersgeometry). This leads to problems in achievinglateral resolutions better than 50 nm, as a10 nm deep indentation has a contact radiusof B50 nm. For probing nanostructured fea-tures, it is also necessary to position the tip inrelationship to the surface using nonopticalimaging techniques. A common method in thiscase is to couple the indentation equipmentwith scanning probe microscopy (SPM), wherethe surface can be imaged prior to indentation.In SPM, tips, 601 or sharper, are used toimprove the lateral resolution of the image,and are commercially available. Many re-searchers now using SPM techniques to per-form nanoindentation are utilizing the same tipto both indent and image (Tian et al., 2000).


This creates a controversy between eitherusing a tip that is robust and developed forindentation and one that is fragile and deformswith an additional ‘‘cutting’’ mode rather thanthe traditional indentation deformation me-chanics. However, with the advent of nano-structured materials, researchers are beingforced to choose either high lateral resolutionor an indentation approach based on tradi-tional methodologies. With the use of sharptips at shallow depths, traditional measures ofhardness appear to be unable to fully define theplastic deformation around these small indents.If the measured hardness values cannot be fullytrusted, perhaps revisiting an early parameterc/a, where c is the radius of the plastic zone anda is the contact radius of the indentation, willbe more useful than continuing to use hardnesseven if the tip is well calibrated.

8.13.4.2.3 Indentation size effects

The ratio of the plastic zone size to thecontact radius, c/a, will measure the extent ofplastic deformation. According to Johnson’sconical spherical cavity model of an elastic–plastic material (Johnson, 1970), the plasticzone is determined by

c

a¼ E� tan b

6sy 1� nð Þ þ2

3

1� 2n1� n

� �� 1=3ð55Þ

where b is the angle between the face of thecone and the indented surface, 90–y, and E* isagain the reduced modulus of the indenter andsubstrate. When the ratio E*tan b/sy440,Johnson suggests that the analysis of elastic–plastic indentation is not valid, and that therigid-plastic case has been reached. Once thefully plastic state has been reached, the ratioc/a becomes B2.33 (Johnson, 1985).

Another model of the plastic zone size basedupon Johnson’s analysis has been developed(Kramer et al., 1999), whereupon the plasticzone boundary, c, is determined by

c ¼ffiffiffiffiffiffiffiffiffiffi3P

2psy

sð56Þ

where P is the load, and sy is the yield strengthof the material. Assuming the fully plasticstate, where p0E3sy, the ratio c/a can bedetermined by

sy ¼1

3p0 ¼

P

3pa2ð57Þ

Substituting Equation (57) into (56) gives

c

a¼ 3ffiffiffi

2p D2:12 ð58Þ

These measurements of plastic zone dia-meters can be made on the surface of thesample using scanning probe techniques, asshown in Figure 18. This phenomenon has beendemonstrated for several bulk materials (Bahrand Gerberich, 1996b) and does hold to verysmall depths and with sharper indenter tipangles (Kramer et al., 1999; Woodcock andBahr, 2000). Indentations into single crystals ofFe–3%Si generate significant pileup lobescorresponding to the crystallographic natureof the indentation. For the purposes of thisdiscussion only, the size of the lobes isconsidered for measurements of c. It is, there-fore, expected that the ratio c/a will be greaterthan in the bulk polycrystalline case where slipis fully developed to the shape of the indenterand a variety of slip systems are activated. Allthe indentations in this study were imaged toassure self-similarity, and therefore the effectiveincluded angle of the indenter is assumedconstant for all indentations in the followingdata. Obviously, the assumption that thedeformed region on the surface corresponds tothe deformed region underneath the indenter tipmust be made to utilize this analysis technique.

Indentations were made with three tips: astandard Berkovich geometry tip, a ‘‘cubecorner’’ tip which has a 901 angle between theedge and face of a three-sided pyramid, and a901 cone which has a 1 mm root radius. For theBerkovich tip, the indentations show anindentation size effect, the material appears tobe harder at smaller sampled volumes. How-ever, sharper tips show a slightly differentbehavior at the smallest depths sampled.

Figure 18 Contact AFM image of a 20mN conicalindent, 20� 20 mm image (source Woodcock, 2002).


A mechanistic solution to the problem of theindentation size effect lies in the formulation ofstrain gradient plasticity models (Fleck andHutchinson, 1993) for microindentations andfor nanoindentations (Nix and Gao, 1998). TheNix–Gao model depends on the idea ofgeometrically necessary dislocations, whichare formed to accommodate the permanentdeformation around the indenter. The hard-ness at any indentation depth could then becalculated by

H

H0¼

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ h�

h

rð59Þ

where H0 is the hardness at infinite indentationdepth, h* is a constant depending on materiallength scale and indenter geometry, and h is thecontact depth of the indentation test. Thisaccounts for hardness due to both geometri-cally necessary dislocations and statisticallystored dislocations, but also makes the as-sumption that the hardness is related to theyield strength by a factor of 3. A fit to the Nix–Gao model for the data using the Berkovich tipis shown in Figure 19. Using this method, thehardness at ‘‘infinite’’ depth is 1.6GPa, and ayield strength of 533MPa. However, forsharper tips the trends do not hold in the sameway, as shown in Figure 20 for a cube cornertip (source Woodcock and Bahr, 2000).

When Johnson’s cavity model (Equation(55)) is solved for yield strength, and formu-lated in a similar manner as a function ofcontact depth, a similar value of yield strengthat infinite depth can be reached. When thisratio is examined, as shown in Figure 21, bothtips exhibit an identical size effect behavior,and extracting the yield strength from Equa-

tion (55) gives a yield strength of either133MPa (Berkovich) or 600MPa (cube cor-ner), bracketing the value using the straingradient model of Nix and Gao (1998).

8.13.4.2.4 Thin films

Since there is a contribution of plastic energydissipation to the fracture process, the max-imum amount of this energy would be con-trolled by the film yield stress. In the case of athin film, the yield stress is typically muchhigher than for a bulk material (Kramer et al.,

Figure 19 Hardness as a function of contact depthdemonstrating an indentation size effect using aBerkovich indenter tip (source Woodcock, 2002).

Figure 20 Hardness vs. contact depth data for bothtip geometries. While both tips show an ISE, thesharper tips appear to harden at low loads (sourceWoodcock and Bahr, 2000).

Figure 21 Yield strength extracted from plasticzone size measurements for both cube corner andBerkovich tip geometries. The bulk values extra-polate to bracket the value given by the model ofNix and Gao (source Woodcock and Bahr, 2000).


1999). This is partly explained by the Hall–Petch-type relationship between the film yieldstress, sy, and its grain size, d:

sy ¼ si þ kd�n ð60Þ

where si is some intrinsic stress, independent ofthe grain size d, and n is typically between 0.5and 1. Since the grain size of a thin film scaleswith the film thickness, h, the latter can be usedinstead of the grain size as the scaling para-meter (Wei and Hutchinson, 1997):

sy ¼ sið1þ bIh�0:5Þ ð61Þ

where bI is a constant. For a metal film, theyield stress can be approximated as one-thirdof the hardness measured by indentation(Tabor, 1951). However, it has been foundthat for very thin films where penetrationdepths are small, the yield strength is oftenhigher than that given by Equation (61). Thishas been attributed to either a substrate orindentation size effect (Kramer et al., 1999). Toavoid this, a technique also used is todetermine the yield strength by back calculat-ing it from the observed elastic–plastic bound-ary described in Equation (56). Such yieldstress data for sputter deposited Cu films canbe found in Tymiak et al. (2000). While thealgorithm used by Wei and Hutchinson givesvalues B10% higher than ‘‘observed,’’ theuncertainty in the elastic–plastic boundary issuch that Equation (61) easily applies to bothsets of data. In a similar way, we haveextracted data from aluminum (Vinci et al.,1995) and gold (Venkataraman and Bravman,1992; Evans et al., 1999) films to arrive atsimilar values of the yield stress.

In all cases, having the ability to measure theproperties of the film of interest for interfacialfracture testing is a critical component ofaccurately determining the toughness of theinterface. Both elastic and plastic propertiescan be measured either prior to or post-adhesion testing in many cases. These measure-ments, and the ability to determine relativeeffects of parameters such as plastic flow andyielding, will greatly impact the separation ofthermodynamic work of adhesion and thepractical work of adhesion which includesother dissipative properties such as the motionof dislocations.

8.13.5 THIN FILM FRACTURE

In this section, property and fracture dataare gathered from a number of sources forfilms in surface, embedded and multilayer thinfilm systems. The data include as-deposited

and diffusion bonded films and were obtainedusing a variety of test techniques with theemphasis on data obtained using nanoindenta-tion test techniques. All of these data werecollected for films mostly below several micro-meters in thickness. The data are given in Table1 (Volinsky et al., 2002) and grouped intoceramic and metallic film systems with empha-sis on nitride films and copper, gold, andaluminum films due to their commercialsignificance. Presentation of the data for thesesystems includes a brief discussion of applica-tions that motivated studies to date and adetailed discussion of the techniques used todetermine fracture energies. Discussion of theresults is designed to show how nanomechani-cal testing fits into the scope of test techniquesavailable.

8.13.5.1 Ceramic and Refractory Metal Films

Ceramic and refractory films are used inmany applications where unique properties areneeded to ensure performance and reliability(Mittal, 1976). Of particular interest are thintantalum nitride films. They are used exten-sively as thin film resistors in microelectronicsapplications because of their excellent long-term stability and low-temperature coefficientsof expansion (Adams and Kramer, 1976; Auet al., 1990). However, they are sputterdeposited, which produces films with highstructural defect contents and high residualstresses that can alter both the physical andmechanical properties of the films (Klokholm,1971; Sun et al., 1975). Tantalum nitride filmshave also emerged as promising diffusionlayers for copper interconnects while providinggood adhesion between the copper lines andsilicon dioxide substrates (Lane et al., 2000). Inthis application, the adhesive strength mustwithstand the high residual stresses associatedwith thermal expansion mismatch and filmgrowth processes as well as the high backstresses developed during electromigrationprocesses in copper lines.

8.13.5.1.1 Tantalum nitride

The potential for high compressive residualstresses inherent in sputter deposited tantalumnitride films to trigger film failure motivated astudy of resistance to interfacial fracture forthis film system. This study employed nanoin-dentation (Doerner and Nix, 1986; Wu et al.,1988; Oliver and Pharr, 1992; Venkataramanet al., 1993a) and continuous nanoscratchtesting (Wu, 1991; Venkataraman et al., 1992,1993a, 1993b). Use of these test techniques

Thin Film Fracture 473

maintained the as-deposited free surface con-figuration of production monitors withoutadditional sample preparation. The indenta-tion fracture tests were easy to perform withstrain energy release rates determined frommechanics-based analyses (Marshall andEvans, 1984; Evans and Hutchinson, 1984;Hutchinson and Suo, 1992). However, theforce that can be applied was limited inmagnitude and extent. The continuous nano-scratch tests applied a much greater force overa larger area in comparison with indentationtests but lacked a rigorous derivation of stressdistributions and strain energy release rates(Wu, 1991; Venkataraman et al., 1992, 1993a,1993b). Nevertheless, good approximations forstrain energy release rates were obtained usingblister and buckling solutions for systemswhere residual stresses dominate fracturebehavior (Marshall and Evans, 1984; Evansand Hutchinson, 1984; Hutchinson and Suo,1992).

The indentation fracture tests were con-ducted using a conical diamond indenter witha nominal 1 mm tip radius and a 901 included

angle. The indenter was driven into the films ata loading rate of 500 mNs�1 until a portion ofthe film spalled from the substrate. Figure 22shows a load–displacement curve where thedisplacement excursion defines the onset offracture. In all cases, fracture occurred byreverse or double buckle formation duringindentation with the material under the in-denter pinned to the substrate. There were noobservations of buckling or fracture when testswere stopped prior to the displacement excur-sion. Furthermore, loading beyond the point ofrapid excursion did not lead to additionalcrack growth. These observations clearly showthat interfacial crack growth and film fractureoccurred rapidly after crack nucleation.

It could not be determined if crack advancewas driven to completion from the storedenergy at the onset of crack nucleation or ifadditional crack growth occurs as the indenterdrove into the film and substrate. Nevertheless,it was evident that not all displaced materialwas forced into the film contributing to filmstress. Since the tests were run at ever increas-ing maximum load, atomic force microscopy

Table 1 Mechanical properties and measured fracture energies of thin-film systems.

Work of adhesion

Systemsys

(MPa)E

(GPa)h

(nm)G0

(J/m2) Wdtheor

T(1C)

G cb

(Jm�2)

Taa/Al/C/Al2O3 298 70 500 0.33 20 1.05Wa/Al–Cu/C/SiO2/Si 298–203 70 500–3,200 0.25 20 0.2–0.65Wa/Al– 700–203 70 40–3,200 0.41 20 0.3–27Cu/Cu/SiO2/SiTa2N

a/Al/Al2O3 190 70 178 20 7.0SiO2/TiN/Al– 430–196 70 150–400 5.0 20 4.9–13Cu/SiO2/SiSiO2/Al/TiN/Ti/SiO2 70 250 20 1.9Taa/Al–Cu/Al2O3 298 70 500 20 5.6Wa/Al–Cu/SiO2/Si 329–252 70 340–1,000 4.3 20 7.7–8.2Au/C/Al2O3 338 80.8 15,000 0.317 0.3 20 1.7Au/Al2O3 338 80.8 15,000 1.27 0.6,0.5 20 80,230TaNa/Au/Al2O3 517 80.8 200 0.63 0.6,0.5 20 1.4TaNa/Au/Cr/Al2O3 517 80.8 200 1.35 20 2.9Wa/Cu/SiO2/Si 974–466 120 40–3,000 0.90 0.8 20 0.6–100Wa/Cu/Ti/SiO2/Si 974–466 120 40–3,000 3.63 2.2c 20 4–110SiO2/Cu/TaN/Ta/SiO2/Si 1,060–435 120 30–10,500 5.0 1.8c 20 4.5–80W/Cu/Cr/SiO2/Si 630–509 120 440–1,100 5.3 20 7–15Wa/Cu/SiO2Si 806–540 120 80 0.90 0.8 20–130 1–4.1Wa/Cu/SiO2/Si 560–300 120 500 0.90 0.8 20–130 14–215Cra/Cu/SiO2 913–528 120 50–800 0.5 0.8 20 0.5–1.0Nb/Al2O3 2,000d 103 105 0.95 0.8 0.95Nb/Ag/Al2O3 2,000d 103 105 0.78 0.5 0.78W/SiO2/Si 1,220–1,088 360 530–760 1.73 20 5.5–9.0Ta2N/Al2O3 100–600 0.5 20 0.5–0.5SixNy/SiO2/Si 171 1,000 20 1.5NbN/304SS 468 2,800 400

Source: Volinsky et al. (2002).aUsed as a superlayer on top of the film of interest. bRange refers to the variation with either thickness or temperature. cActually TiWand TiN as opposed to Ti and TaN used at the interface as a thin adhesive layer. dYield estimated from nanohardness of 6GPa by H/3.


was used to characterize the evolution of theindentation process and showed that two-fifthsof the displaced material was thrust up aroundthe indenter prior to film failure (Moody et al.,1998; Venkataraman et al., 1994). Assumingthat 60% of the displaced material wascompressed into the film, the average strainenergy release rate ranged from 9.8 Jm�2 at thefirst indication of fracture to 13.2 Jm�2 at theend of the fracture. A phase angle of loadingequal to �56.51 for the upper limit wasobtained by back-calculating an effective load-ing parameter, (sc/sr)

* from the measuredfracture energy, G, and using solutions forunpinned circular blisters (Marshall andEvans, 1984; Hutchinson and Suo, 1992). scis the delamination stress for a circular blister.This gave an average mode I value of 7.2 Jm�2.

The nanoscratch tests were conducted usinga conical diamond indenter with a nominal1 mm tip radius and a 901 included angle thatwas simultaneously driven into the films at aloading rate of 500 mNs�1 and across the films

at a rate of 0.5 mms�1 to force film failure.Failure in the as-deposited films occurred bythe formation of large spalls as shown inFigure 23(a). The fractures occurred consis-tently at loads near 100mN and were accom-panied by a sharp increase in indenter depthand tangential load as shown in Figure 23(b).The normal loads were much lower thanrequired for indentation fracture. The frac-tured substrate surfaces were distinctly inter-facial in character with no evidence oftantalum nitride within the limits of energydispersive spectroscopy. Circular blister solu-tions gave an average strain energy release rateof 15.5 Jm�2, a phase angle of loading equal to�60.11, and a corresponding mode I value of8.2 Jm�2.

In two tests the initial spalls triggereduniform width buckles that ran back alongmuch of the scratch track lengths as shown inFigure 24. These uniform-width buckles pro-vided a third approach to determine strainenergy release rates for interfacial fracture of

Figure 22 (a) Indentation fracture of as-deposited film occurred consistently at loads between 250mN and300mN producing (b) large circular spalls. In all fracture tests, the center point was constrained giving rise toa reverse or double buckle configuration (source Moody et al., 1998).

Figure 23 (a) Scratch test fractures in the as-deposited film occurred consistently near 100mN and werecharacterized by an abrupt increase in tangential load. (b) The fractures propagated along the film–substrateinterfaces producing well-defined spalls ahead of the indenter (source Moody et al., 1998).


these films. Using uniform blister width solu-tions gave an average interfacial fractureenergy of 17.5 Jm�2, a phase angle of loadingof �53.21, and a mode I fracture energy of9.9 Jm�2. The values from each of the threetests are in very good agreement. In all cases,the values are significantly higher than van derWaals forces and forces for chemical bonding.However, they are consistent with fracture ofan amorphous oxide that forms on the surface

of alumina substrates during backsputtercleaning procedures (Moody et al., 1998).

When an interlayer of aluminum was addedto the system, three types of failure wereinitiated (Bahr et al., 1997). Figure 25 showsthree load–depth curves into 500 nm of Ta2Non 28 nm of Al on a sapphire substrate. Anoptical micrograph taken after the sample wasremoved from the indenter is shown in Figure26. While delamination and spalling occurredfor indents A and B, indent C exhibited adelaminated region with no evidence of spal-ling. Acoustic emission (AE) was used to moni-tor elastic waves which propagated from thefilm delamination event (Bahr and Gerberich,

Figure 24 Two scratches triggered uniform width buckles that propagated back along much of the scratchtrack length (source Moody et al., 1998).

Figure 25 Different types of indentation-inducedfailures in 500 nm thick Ta2N on sapphire with a154 nm Al interlayer. Curve A shows delaminationand spalling during loading, curve B shows delami-nation and spalling during unloading, and curve Cshows evidence of a stable delamination on unload-ing (source Bahr and Gerberich, 1998).

Figure 26 Optical micrograph of delaminationsand spalling events from indentations shown inFigure 25. Note that indent C has only delaminated,and the crack has arrested without spalling (sourceBahr and Gerberich, 1998).


1998). The AE voltage signals from curves A,B, and C are shown in Figure 27. Forcomparative purposes, the signal from curveC has been multiplied by a factor of 10. It isclear that a failure did occur during unloadingon curve C. The delamination alone gave anAE signal that was significantly smaller thanthe spalling events. This is due to the fact thatwhen a film buckles, a fraction of stored strainenergy is released, which is the driving force forcrack advance. However, a buckled film stillcontains a significant amount of strain energy.When a film spalls, all of the energy which wasstored in the film prior to buckling is released.This leads to the larger AE signals observed forthe delaminations that spalled. In addition tothe buckle driven indentations, nanoscratcheswere made on the Al interlayer samples. Thesescratches generated one-dimensional (1D) blis-ters. Strain energy release rates were calculatedfor all three tests with the results given in Table2. The similarity between values for all threetests suggests the following: the calculationmethods are self-consistent and the amount ofaluminum at the interface does not impact thetoughness in this case.

The interface that failed was identified usingatomic force microscopy and Auger electronspectroscopy to be the aluminum–sapphireinterface. As shown in Figure 28, a profile ofthe edge of a spalled double buckle regionshows that the crack propagated along oneplane, kinked up through B150 nm of materi-al, continued to propagate for a distance ofB1 mm, and then kinked up through theremaining 0.5 mm of material. This strongly

Figure 27 AE signal from curves A, B, and Cshown in Figure 25. Signals A and B achieved highervoltages than the range set on the oscilloscope;therefore, only a limited voltage range from thesewas recorded. Signals are offset for clarity (sourceBahr and Gerberich, 1998).

Table 2 Fracture energy of the interface of 0.5 mm Ta2N on sapphire with different thickness Al interlayers(Al—sapphire interface failure).

SystemGI Single buckling

(Jm�2)Gi Double buckling

(Jm�2)Gi Scratch initiated buckle

(Jm�2)

500 nm Ta2N/28 nm Al/Al2O3 8.1 7.870.14 8.9

500 nm Ta2N/154 nm Al/Al2O3 8.0 7.570.24 8

Figure 28 AFM image and section analysis of edgeof spalled region. The fracture path was along thealuminum–sapphire interface. The crack proceededto kink into the aluminum, travel along thealuminum–Ta2N interface for 1 mm, and then kinkthrough the nitride film (source Bahr and Gerberich,1998).


suggests that the crack propagated along thealuminum–sapphire interface, and only kinkedinto the aluminum for a short distance. Itshould be noted that much of the delaminationedge did not show any evidence of aluminum,and only in the largest spallations were therefailures such as the one shown here. The lowvalues for interfacial toughness of aluminum-on-sapphire in this case were likely due tocarbon contamination of the aluminum–sapphire interface.

8.13.5.1.2 Silicon nitride

Silicon nitride on silicon oxide is anotherhard film on brittle substrate system used inmicroelectronics where adhesion of the inter-face controls reliability. Work by Sanchez et al.(1999) has developed and applied cross-sec-tional nanoindentation in the study of inter-facial fracture in this system. It is a quick testcapable of producing controlled thin filmdelaminations and it provides direct observa-tion of the interfacial crack path in cross-section. The film system they studied wasfabricated by chemical vapor depositing a1 mm thick layer silicon oxide onto a siliconsubstrate followed by chemical vapor deposi-tion of a 1 mm thick layer silicon nitride.Indentations are then made normal to thewafer cross-section using a diamond three-sided Berkovich indenter with one indenter sideparallel to the interface of interest as shown inFigure 29. Delamination produced an excur-sion in the load–displacement curve clearlydemarcating conditions for fracture. The testsgave fracture energies that ranged from1.2 Jm�2 to 1.8 Jm�2. The same film structuretested using the four-point bend techniquegave a value of 1.65 Jm�2 in good agreementwith cross-sectional indentation.

8.13.5.1.3 Tungsten

Sputtered tungsten is a hard film on rigidsubstrate also used in the microelectronicsindustry as a popular alternative to aluminummetallization (de Boer et al., 1997). However, itcan exhibit poor adhesion especially whensubjected to high tensile stresses from chemicalvapor deposition which limits its use. Severalindentation-based tests have been developed tomeasure interfacial fracture energies of tung-sten films.

The microwedge indentation technique wasdeveloped by de Boer and Gerberich (1996a,1996b) to determine the fracture energy oftungsten thin film fine lines on oxidized siliconsubstrates. Because tungsten is classically iso-tropic, Young’s modulus is independent ofgrain texture. The thermally grown amorphoussilicon oxide on the silicon substrate is elasti-cally isotropic as well. The tests are easilyconducted on a nanoindenter and the analysisis based on linear elastic fracture mechanics.The test samples were fabricated by RFsputtering 800 nm of tungsten onto thermallyoxidized silicon wafers coated in photoresist tocreate 5 mm, 10 mm, and 15 mm wide lines. Asharp 20 mm wide diamond microwedge withan included angle of 901 was used to indent thelines perpendicular to the line direction andtrigger double-buckling and crack extensionalong the length of the lines. Using onlyunspalled buckles, the interfacial fracture en-ergies were shown to range from 16 Jm�2 to20 Jm�2. This is somewhat higher than thefracture toughness the authors estimated forthe tungsten–silicon oxide interface of 5 Jm�2

and can be attributed to cracking of thesubstrate during indentation testing.

To overcome these test method difficulties,de Boer and Gerberich (1996a, 1996b) devel-oped a fracture-mechanics-based ‘‘precracked

Figure 29 Schematic of the cross-sectional indentation test showing: (a) indenter orientation and (b) interfacefracture (source Sun et al., 2001).


line scratch test.’’ It differs from conventionalscratch tests, because the crack tip is wellremoved from the indenter tip. In addition, thetangential load is measured directly, thenormal to tangential load ratio is near unity,and substrate cracking does not occur underthe indenter. Tungsten line samples, 10 mm and15 mm wide and 500 nm and 1,500 nm thick,were fabricated as in earlier work but with athin carbon film over a portion of the substrateto act as a precrack. In these tests, a 20 mmwide diamond microwedge with an includedangle of 301 was used to push against the‘‘precracked’’ ends of the fine lines with adisplacement-controlled IBM microindenteruntil the films buckled. When the precrackswere short and the lines long, the cracks kinkedinto the interface. When the precracks werelong, the cracks grew along the interface untilthey kinked into the film and the film spalled.These conditions provided lower and upperbounding interfacial fracture energies between3.5 Jm�2 and 16 Jm�2. When the precrack andline lengths were short, the cracks remainedalong the interface giving an interfacial frac-ture energy of 7 Jm�2.

Kriese et al. (1999b) used indentationfracture techniques to study interfacial fractureof thin tungsten films on silicon oxide sub-strates. The films were sputter deposited to athickness of 530 nm. Wafer curvature showedthat the films were deposited with tensileresidual stresses ranging from 510MPa to615MPa. Onto these films, superlayers oftungsten or chromium were sputter depositedgiving residual stresses that ranged from a1.3GPa residual tensile stress for a 500 nmthick chromium overlayer to a �1.1GParesidual compressive stress for a 355 nm thicktungsten superlayer. Nanoindentation with a1 mm root radius conical diamond tip was usedto nucleate fracture. In all cases fracture

occurred along the tungsten–silicon oxideinterface with blisters forming a circularmorphology. These are shown in Figure 30.The film with the compressive overlayerexhibited a smooth blister profile with noevidence of radial cracking. The films withtensile overlayers exhibited radial cracking thatincreased in severity with increasing tensilestress. Interfacial fracture energies were thendetermined using solutions for pinned circularblisters. The highest value was 15 Jm�2 for thesample with the compressive overlayer. Thevalues decreased to 4.0 Jm�2 as the severity ofradial cracking increased. These values are invery good agreement with values of 5–15 Jm�2

from previous work using different measure-ment techniques.

8.13.5.2 Ductile Metal Films

8.13.5.2.1 Copper films

Semiconductor applications have seen adramatic increase in importance with theemergence of copper as the next generationinterconnect metallization material for USLIfabrication. As a result, Cu/dielectric adhesionis one of the main reliability issues. Unfortu-nately, copper exhibits poor adhesion to mostdielectric substrates (Russell et al., 1995;Bagchi and Evans, 1996; Kriese et al., 1997;Chang, 1989; Chae et al., 1994; LaFontaineet al., 1990). Several methods have beendeveloped to address this problem with anneal-ing, alloying, and the interposing of a metallicinterlayer to act as an adhesion promoter(Russell et al., 1995). In particular, muchattention has focused on the use of titaniumand chromium as interlayers or alloying addi-tions (Russell et al., 1995; LaFontaine et al.,1990). While the exact mechanisms by whichthese metals increase adhesion have yet to be

Figure 30 Indentation-induced delaminations imaged with optical interference contrast: (a) sample II-AW/W multiplayer with no radial cracking; (b) sample II-B W/W multilayer with minor radial cracking; and(C) sample II-C Cr/W multilayer with pronounced radial cracking (source Kriese et al., 1999b).


fully explored, the empirical characteristicshave been addressed in these studies. Thefollowing discussion shows how nanomechani-cal testing is being used to measure copper filmadhesion, first in assessing adhesion of copperon SiO2/Si and then with the use of titaniumand chromium adhesion layers.

Kriese et al. (1998b) looked at the use ofstressed overlayers (superlayers) in measuringadhesion of thin copper films on oxidesubstrates. The films were sputter depositedonto silicon oxide substrates and divided intotwo groups. One group was left in the as-deposited condition while a tungsten overlayerwas deposited on the other. Nanoindentationwas then conducted on both groups of samplesusing a 901 conical indenter with a sphericaltip radius of 1 mm, driven at a rate of600mN s�1.

The as-deposited copper films and thecopper films with stressed overlayers delami-nated forming large circular blisters duringindentation testing, as shown in Figure 31.However, there were differences. All indenta-tion tests on copper with stressed overlayersproduced a delamination while more than one-third of the copper-only tests formed the‘‘ring’’ morphology, shown in the bottom rowof Figure 31(a), due to film pileup. Thedelaminations in the copper with stressedoverlayer films were also significantly largerthan in the copper only films.

Indentation load–displacement curves typi-cally contained significant slope changes orexcursions indicative of delamination andfracture (Figure 32). These changes are much

more pronounced for the copper with stressedoverlayer films, as the tungsten exhibits pro-minent through-film cracking. Solutions forpinned circular blisters were then used todetermine interfacial fracture energies. Theseenergies were independent of film system andfell predominately within the same range ofadhesion energies, namely 0.2–2 Jm–2. Thecopper with stressed overlayers did have lessvariation and an upper limit of 1 Jm–2. Thiscompares favorably with measurements byBagchi et al. (1994) and Bagchi and Evans(1996) of 0.4–0.8 Jm–2 for vacuum evaporatedcopper films and with measurements by Ohet al. (1988), who report a range of 1–10 Jm–2

for a copper/glass system using a doublecantilever beam macroscopic specimen (Char-alambides et al., 1989).

Kriese et al. (1998b) note that an especiallyencouraging aspect of their work is that the useof a stressed overlayer promotes delaminationwith indentation, allowing calculation of adhe-sion energy. With regard to the copper films,the result was dramatic, in that occurrence ofdelamination was far more consistent with astressed overlayer. In addition, use of stressedoverlayers decreased experimental error andappeared to give a more reliable estimate of theadhesion energy. What is especially interestingis that the films exhibit the same range ofinterfacial toughness if one ignores the highercopper-only values where film thicknessleads to significant crack-tip plasticity. Thisthen supports the idea that the tungstenoverlayer does not fundamentally change themechanisms associated with the delamination

Figure 31 Indentation-induced copper and tungsten–copper delamination. Tests correspond to 100mN (toprows), 250mN (middle rows) and 400mN (bottom rows). Photos are collages; original indents were 100–300mm apart. Nomarski optical contrast was used to make delamination identifiable: (a) pure Cu. The ringdelamination at 400mN may be double buckling: (b) W/Cu bilayers (source Kriese et al., 1998a).


of as-sputtered copper films, and further thatthese mechanisms are independent of filmthickness.

(i) Annealing effects

Annealing is commonly used to promoteadhesion and performance of thin films with itseffects often ascribed to its influence on thediffusion of segregants and changes in thenature of the interface. It also affects plasticityin the process zone by changing yield proper-ties. Kriese et al. (1998b) studied the effects ofannealing on copper film adhesion usingsputter deposited films that ranged in thicknessfrom 200 nm to 1,000 nm. The films weredivided into two groups with one group leftin the as-deposited condition while the othergroup was annealed at 6001C for 2 h in anargon atmosphere. A stressed overlayer wasthen deposited on all samples and followedby nanoindentation using a conical indenterwith a spherical tip to trigger delamination.The results are shown in Figure 33 as afunction of film thickness and annealedstate. The trend lines are smooth fits to thedata, and do not represent any specific model-ing prediction. While in several cases there isoverlap, it is clear that both thickness andannealing increase adhesion with the effect ofannealing being more pronounced at greaterthickness.

(ii) Interlayer effects

Kriese et al. (1998b) then addressed theeffects of metallic interlayers on copper filmadhesion. They deposited three sets of copper

films to thicknesses of 420–450nm and 1,100–1,170 nm. The as-deposited residual tensilestress in all films ranged from 195MPa to275MPa. The magnitude and sign of stress iscomparable to the thermal mismatch stressinduced as the wafer cools from deposition toroom temperature. Films of each thicknesswere deposited onto bare SiO2/Si wafers whiletwo other sets of films were deposited with 7–10 nm of titanium and chromium interlayers,respectively, prior to deposition of the copper.All copper films were then deposited simulta-neously on the substrates followed by deposi-tion of a 590–680nm thick tungsten superlayer.The residual stresses in the tungsten superlayerswere compressive, and ranged from 95MPa to345MPa, with no clear trends of any sort.

Figure 34 clearly shows a strong effect of theinterlayer on load–displacement curves for

Figure 33 Indentation fracture measurements onthin copper films show that film thickness andannealing increase measured fracture energies(source Kriese et al., 1998a).

Figure 32 Characteristic indentation data of Cu and W/Cu. Each sample was loaded to 100mN, 250mN,and 400mN. (a) The copper-only film has deviations in loading behavior representing delamination anddeformation constraint. (b) The companion copper/tungsten bilayer has abrupt transitions and greaterpenetration depths (source Kriese et al., 1998a).


95mN load indents into 1,100 nm thick films.This effect is indicative of the effect interlayers,and more specifically increases in adhesion,have on film properties. The correspondingfracture energies are shown in Figure 35 as afunction of interlayer composition and filmthickness. There appears to be no appreciableeffect of thickness in the absence of aninterlayer. However, the two sets of films hadbeen prepared at different operating parametersof the sputtering chamber, and are expected tohave different microstructures and hence dif-ferent adhesion. The notable result in Figure 35is the strong increase in adhesion energy forfilms with Ti and Cr interlayers. The presenceof an interlayer increases adhesion energy from1.3 to 7.5 times depending on the compositionof the interlayer and thickness of copper film.Moreover, the effect of the interlayer becomesmore pronounced at greater thickness. Thesequantitative trends corroborate the semi-quan-titative results previously reported (Russellet al., 1995; LaFontaine et al., 1990). Theincrease in adhesion with increasing thicknesshas been reported by Evans and Dalgleish(1992) and Venkataraman et al. (1996).

(iii) Film thickness effects

The work by Volinsky et al. (2000) system-atically studied the effect of film thickness overtwo orders of magnitude on a single Cu/SiO2

system. Copper films of eight thicknessesbetween 40 nm and 3 mm were sputter depos-ited on top of oxidized Si wafers with andwithout a 10 nm thick Ti adhesion-promotinglayer. All films were passivated with a 1 mmthick layer of W for adhesion measurements.Nanoindentation using a 1 mm radius conical

diamond intenter was used to nucleate frac-ture. This study showed that a 40–3,000 nmvariation in thickness increased measuredfracture energies from approximately 0.6 Jm–2

to 100 Jm–2 (Figure 36). Also shown is anupper bound from a previous study (Volinskyet al., 1999) and a dislocation-free zone model(Zielinski et al., 1992; Volinsky et al., 2003).Fracture energies for films less than 100 nmthick exhibited a nearly uniform lower limitingvalue of 0.8 Jm–2. The value corresponds to thethermodynamic work of adhesion of Cu toSiO2 measured by the contact angle technique(Furuya et al., 1995). This means that for filmsless than 100 nm thick, there is almost noplastic deformation at the crack tip (Volinskyet al., 1999; Tymiak et al., 2000). For thickerfilms there is a definite contribution of crack-tip plastic deformation (Uf) to the practical

Figure 35 Measured adhesion energies of copperthin films (source Kriese et al., 1998b).

Figure 36 Film thickness effects on fracture ofcopper on oxidized silicon substrates with andwithout a titanium interlayer (sources Tymiaket al., 2000; Gerberich et al., 2000; Volinsky et al.,1999, 2002).

Figure 34 Effect of interlayers on indentationbehavior of B1,100 nm Cu films with B650 nm Wsuperlayers (source Kriese et al., 1998b).


work of adhesion (Wp), which scales with thefilm thickness. In that same series of studies,the interfacial fracture energies could beincreased by about a factor of 3 using a10 nm thick innerlayer of titanium (Tymiaket al., 2000; Gerberich et al., 2000; Volinskyet al., 1999). However, in these films fractureoccurred along the Ti/Cu interface with frac-ture energies substantially greater than for thecopper only film fractures. In a similar type ofstudy using four-point bend tests, Lane et al.(2000) also demonstrated an increase in tough-ness as thickness increased from 30 nm to1.05� 104 nm. Here a thin innerlayer of TaN/Ta was utilized to improve adhesion, so thatthe lower limit for the thinner films gave valuesof B5 Jm–2.

(iv) Temperature effects

The effect of test temperature on fractureenergy was addressed by Volinsky et al. (2000)in a study of copper films. Copper films weresputter deposited onto oxidized silicon sub-strates to thicknesses of 80 nm and 500 nm. Atungsten overlayer was then deposited touniformly stress the films. A range of testtemperatures from 801C to 1301C was utilizedto evaluate temperature effects on fractureenergy. For this purpose, a resistance heatingstage from Digital Instruments (Volinsky,2000; Gerberich et al., 2000) was used inconjunction with the Nano Indenter IITM.With a sample glued to a puck using thermo-epoxy, this assembly was then clamped ontothe top of the microheater with the thermo-couple sample clamp. The heating element isthermally isolated from the surrounding atmo-sphere as the sample is the only surface thatconducts heat into the atmosphere. Since theloads used were relatively high (up to 600mN),operation of the Nano Indenter IITM was notdisturbed with the presence of a heater.Indentation testing with a 1 mm radius conicaldiamond indenter was used to nucleate fracturein all samples as a function of test temperature.Tests were also run at room temperature priorto and after conducting temperature indenta-tion experiments to ensure that there were noannealing effects on sample behavior. In thecase of the dense tungsten superlayer, passi-vated copper did not form an oxide duringelevated temperature testing. As is shown inFigure 37, fracture resistance increased by afactor of 4 for the thinner film, whereas for thethicker film it increased by more than an orderof magnitude. This brittle-to-ductile transitionin a normally low adhesion interface of Cu/SiO2 with the same Cu thickness and the same

bond strength eliminated variables other thanthe yield strength as possible sources ofincreased toughening.

8.13.5.2.2 Gold films

Adhesion is a critical factor in controllingthe performance and reliability of gold–chro-mium hybrid microcircuits (Mattox, 1973;Mittal, 1976). Though superceded by otherdesigns and materials, there are circuits of thistype still in use. These circuits consist of analumina substrate, a thin chromium layer foradherence, and a gold layer for conductance toconnect components on the microcircuit (Rair-den et al., 1971; Thomas and Haas, 1972;Munitz and Komem, 1976). A gold-coatedcopper lead is thermomechanically bondedonto a gold pad layer to complete the connec-tion. During post-deposition annealing, lead-frame bonding, and service at elevated tem-perature, diffusion and segregation of chro-mium and copper changes the composition andstructure of the films and interfaces (Rairdenet al., 1971; Thomas and Haas, 1972; Munitzand Komem, 1976, 1980; George et al., 1990).Although chromium and copper diffusion andsegregation are critical issues in long-termdurability of devices with these films, theeffects of these processes on film adhesion arenot well defined (Moody et al., 1998; Krieseet al., 1998b, 1999a).

Until recently, gold films have been almostexclusively studied as diffusion bonded sand-wich layers between sapphire slabs (Jensenet al., 1990; Reimanis et al., 1990, 1991; Evansand Dalgleish, 1992; Mao and Evans, 1997).Lipkin et al. (1998) and Turner and Evans

Figure 37 Test temperature effects on the fractureenergies of 80 nm and 500 nm thick copper films onoxidized silicon substrates (source Volinsky et al.,2002).


(1996) used double-cleavage-drilled compres-sion test samples similar to the Brazil disk testloaded along the crack line. While tests did notaddress fracture and adhesion with a methodi-cal study of thickness variations, data show atwo order of magnitude decrease in toughness(1.4–150 Jm–2) over a two order of magnitudedecrease in thickness.

The work has begun addressing adhesion ofsub-mm thick gold films (Moody et al., 2000).These films were sputter deposited ontosapphire substrates at thicknesses down to10 nm.The weak gold to substrate bonds andsoft films necessitated testing these films in as-deposited configurations using stressed over-layers which apply a uniform stress to theductile films while constraining out-of-planeplasticity (Bagchi et al., 1994; Bagchi andEvans, 1996; He et al., 1996). The depositionof these overlayers triggered formation ofclassic telephone cord blisters in all sputterdeposited gold films as shown in Figure 38.There is a point between each turn in the blisterwhere the blister becomes uniform in shape.The morphology or the blister at this pointprovides the data from which interfacialfracture energies were obtained using solutionsfor film systems where residual stresses dom-inate fracture behavior.

Fracture energies were determined usingmechanics-based models (Hutchinson andSuo, 1992; Marshall and Evans, 1984; Evansand Hutchinson, 1984) modified for bilayerfilms (Bagchi et al., 1994; Bagchi and Evans,1996; Kriese et al., 1999a, 1999b). Correspond-ing mode I contributions were then determinedusing empirical relationships based on calcu-lated phase angles of loading (Hutchinson andSuo, 1992; Thouless et al., 1992). Figure 39shows that the measured values decreased to alower limiting value at thicknesses less than100 nm with corresponding mode I values of0.5 Jm–2. These values are similar to the true

works of adhesion for gold on aluminum oxide(Reimanis et al., 1990). The full range ofmeasured values from all studies are given inFigure 40 and clearly show the marked effectfilm thickness has on interfacial fractureenergies.

(i) Gold–chromium bilayer films

Poor adhesion of gold to all oxide substrateshas led to the use of adhesion layers. One of thefirst metals used for this purpose was chro-mium. However, chromium diffusion anddepletion raised significant concerns for long-term performance of gold film devices. This hasbeen addressed in studies of chromium diffu-sion effects on adhesion for hybrid microcircuitapplications (Moody et al., 2000, 2003). Thesamples were prepared by sputter deposition ofa 6 nm thick chromium adhesion layer onto

Figure 38 Telephone cord blisters triggered by sputter deposition of tungsten overlayers in: (a) 10 nm and (b)200 nm thick gold films on sapphire substrates (source Moody et al., 2003).

Figure 39 One dimensional, G(c), and steady-state,Gss, fracture energies from gold on sapphire showingthe independence of fracture energy on film thick-ness for very thin gold films. The correspondingmode I values are equal to the true works ofadhesion for gold on sapphire.


sapphire substrates followed by sputter deposi-tion of 200 nm of gold film. One group of filmswas left in the as-deposited condition. Asecond group was heated at 4001C for 2 h inair at which point chromium had begun tocome off the sapphire interface in manyregions. The third group was then heated at4001C for 8 h in air after which all thechromium had migrated off the interface.Stressed overlayers were then deposited touniformly stress the films. Unlike the gold onsapphire films, the stresses were not sufficientto trigger delamination and buckling whichnecessitated the use of nanoindentation totrigger film failure.

The mode I fracture energies are plotted inFigure 41 as a function of blister size. Thefracture energies for the gold–chromium films

on sapphire are two times greater than for puregold clearly demonstrating the better adhesionproperties of chromium interlayers. All ener-gies are significantly higher than for gold onsapphire. The fracture energies increase forsamples where the chromium interlayer isreduced in size but is consistent with the effectsof annealing on film adhesion observed inother systems. Complete depletion of thechromium adhesive layer led to a markedincrease in fracture energies. In addition, thefracture path changed from along the film–substrate interface to mixed mode of fracturealong the overlayer–gold film interface, in thegold film, and along the gold substrate inter-face. Diffusion has replaced the thin hardchromium adhesive layer with a solid solutionof gold and chromium in the lattice andenhanced concentrations of chromium alongthe gold grain boundaries.

Figure 42 presents the fracture energies as afunction of blister diameter normalized withrespect to indentation diameter at the pointof the last excursion. Plotting data in thismanner shows that the large increase infracture energy at the small blister sizes resultsfrom crack-tip plastic zone interactions withthe plastic zone created under the indenter(Volinsky et al., 1999, 2002). It also reveals twotrends in behavior that depend on the fracturepath. When fracture occurs cleanly along thesubstrate interface, there is much less interac-tion between crack tip and indenter plasticzones than when fracture occurs through thegold film and along the overlayer–gold filminterface. This parallels the relationship be-tween fracture energies and failure modes(Volinsky et al., 2003) observed in low-kdielectric films and supports the conclusionthat plastic zone interactions have a strong

Figure 40 Superposition of fracture energies ofgold on sapphire from a number of studies usingdifferent test techniques shows the strong effect filmthickness has on performance of these films.

Figure 41 (a) Mode I fracture energies for as-deposited and annealed gold on chromium samples as afunction of blister diameter. (b) An expanded view of the data shows that as-deposited and partially annealedfilm fracture energies are similar. The fracture energies increased when going from as-deposited to annealedsamples with very high values and significant scatter observed for samples where annealing depleted thechromium adhesive layer (source Moody et al., 2003).


effect on measured fracture energies even forrelatively large blisters. At very large blistersizes, the lower limit represents values wherecrack-tip–indenter interactions no longer havea significant effect on measured fractureenergies.

Table 3 shows that as-deposited film inden-tation fracture energies are slightly higher thanvalues obtained from telephone blisters on thesame film. This is consistent with the observa-tion that the portion of the as-deposited film,which did not exhibit telephone cord blistering,is more strongly adhered to the substrate.Fracture energies measured in the partiallyannealed film were similar, as expected for acontinuous chromium interlayer. When fullyannealed, the average fracture energy increaseddramatically. This increase can be attributed toa change in fracture path from along thesubstrate interface to a mixed mode offractures along the overlayer–gold interface,within the gold, and in isolated instances alongthe substrate interface.

Following indentation testing, nanoscratchtests were used to force fracture to occur alongthe substrate interface in the fully annealed

samples. Under these conditions, the fractureenergies in fully annealed samples equaledvalues measured in partially annealed films,even though the film systems had markedlydifferent compositions and structures. Thepartially annealed films had a continuouschromium adhesive layer between the goldand sapphire substrate, whereas diffusionhad reduced the fully annealed films to asolid solution of gold and chromium. Therewere no reactions between film and substrateat these temperatures or in samples heldat high temperatures for much longertimes (Moody et al., 2000, 2003; Zhao et al.,1986). As a result, the increase in fractureresistance following annealing appearsattributable to the effects of interfacial struc-ture on deformation and fracture. Theseresults clearly show that chromium in solutionis as effective in promoting adhesion ascontinuous chromium adhesive layers. Theimpact on hybrid microcircuits service life isdramatic as the film adhesion and deviceperformance do not degrade as long aschromium remains in solution along thesubstrate interface.

Figure 42 Fracture energies plotted as a function of normalized blister diameter indicates that the largeincrease in fracture energy at the small blister sizes results from crack-tip plastic zone interactions with theplastic zone created by the indenter (source Moody et al., 2003).

Table 3 Fracture energy results for as-deposited gold, gold–chromium, and annealed gold–chromium films.

FilmG(c)

(Jm�2) cGI

(Jm�2) Fracture path

SuperlayerAu–AD 1.3 �75 0.5 Au–Al2O3

Au–Cr–AD 2.9 �82 0.9 AuCr–Al2O3

NanoindentationAu–Cr–AD 2.6 �63 1.3 AuCr–Al2O3

4001C/2h 2.2 �60 1.2 AuCr–Al2O3

4001C/8h 13.2 �71 5.5 Ta2N–Al2O3,Au, AuCr–Al2O3

Nanoscratch4001C/8h 3.1 �71 1.3 AuCr–Al2O3


(ii) Gold–copper bilayer films

The effect of copper migration on filmdurability in hybrid microcircuits has beenstudied using laboratory samples and acceler-ated aging (Moody et al., 2002). Steady-statecopper migration was simulated using anAu2w/oCu target to sputter deposit a 200 nmthick gold alloy film. Long-term effects, wheresegregation leads to a continuous copper layerat the gold substrate interface, were simulatedby sputter depositing a 6 nm thick layer ofcopper onto a sapphire substrate followed by a200 nm thick layer of gold. An 840 nm thicktungsten overlayer was then sputter depositedonto these films. This layer triggered extensiveblistering in the Au–Cu film while additionalstresses from nanoindentation were required totrigger delamination and buckling in theAu2w/oCu film. In all cases, fracture occurredalong the film–substrate interfaces with noevidence of gold or copper left on the sapphiresubstrates. The blisters are shown in Figure 43.

The uniform width blister analysis was usedto determine fracture energies from the tele-phone cord blisters in the Au–Cu film and thecircular blister analysis was used to determinefracture energies from indentation-inducedblisters in the Au2w/oCu alloy. The measuredfracture energies are given in Table 4 alongwith material properties. The data in Table 4suggest that the higher fracture energy mea-

sured for the Au2w/oCu films on sapphire wasdue to solid solution hardening effects ondeformation. These results are consistent withthe conclusions of Volinsky et al. (1999) thatdeformation makes a significant contributionto measured fracture energies in 200 nm thickfilms.

8.13.5.2.3 Aluminum films

Most aluminum thin film adhesion data (Xuet al., 1999; Dauskardt et al., 1998; Schneideret al., 1998; Bahr et al., 1997; Gerberich et al.,2000) have been generated using either super-layer indentation (Kriese et al., 1999a, 1999b)or the four-point bend UCSB test (Charalam-bides et al., 1989; Hofinger et al. 1998;Dauskardt et al., 1998; Becker et al., 1997).In all cases, the substrates were either siliconwith SiO2 between the silicon and depositionlayer(s) or sapphire. For the superlayer in-dentation tests, either W or Ta2N superlayersB1 mm thick were used incorporating a resi-dual stress of the order of 1GPa compressionor 100MPa tension. Within the data scatter, asmall effect of residual stress was found on theresulting adhesion measurements. Three typesof interfaces were evaluated: a direct deposit ofaluminum, one with 40 nm of carbon as aninterlayer, and one with 40 nm of copper as aninterlayer (Gerberich et al., 2000). The lattertwo were known to provide lower adhesion.For 500 nm thick films, these provided fractureenergy values of 8.0 Jm–2, 0.65 Jm–2, and0.6 Jm–2. These results are consistent withvalues determined by Schneider et al. (1998)using the same type of test but with a Tasuperlayer and 500nm of aluminum on Al2O3.Here, with and without carbon as a contami-nant, the toughness was 5.6 Jm–2 and 1.05 J m–2.Another consistent result was found by

Figure 43 Deposition of a tungsten overlayer: (a) triggered extensive blistering in the Au–Cu film while (b)additional stresses from nanoindentation were required to trigger delamination and buckling (source Moodyet al., 2002).

Table 4 Fracture energy results for as-depositedgold, gold–copper, and gold-2w/o-copper films.

FilmH

(GPa)G(c)

(Jm�2) cGI

(Jm�2)

Au 1.8 2.0 �78 0.6Au–Cu 2.2 6.7 �79 2.2Au2Cu 3.0 7.2 �69 3.2

Source: Moody et al. (2002).


Dauskardt et al. (1998) on Al–Cu depositionswith a 120 nm thick TiN/Ti/TiN innerlayer.For a 500 nm film their interpolated valuewould be 8.5 Jm–2. In another study using athinner 70 nm TiN/Ti/TiN innerlayer, Xu et al.(1999) found the TiN/SiO2 interface failureenergy to be of the order of 1.9 Jm–2 in theabsence of humidity effects. Irrespective ofwhether the substrate is SiO2/Si or Al2O3, orthe presence of a strong interlayer, there is aconsistent increase in fracture resistance fromabout 4 Jm�2 to 12 Jm�2 with an order ofmagnitude increase in thickness from 200 nmto 2,000 nm. It appears then that for stronginterfaces, the measured strain energy releaserate is dominated by the aluminum thickness inAl/Xi/SiO2 or Al/Xi/Al2O3 systems as long asall Xi innerlayers are reasonably thin. Notethat this would apply equally to Al or Al–Cufilms.

8.13.6 SUMMARY

In general, it is clear that nanomechanicaltest techniques are useful for quantifying theadhesion of thin films. It is equally clear thateach technique requires further work, bothexperimentally and theoretically. The primarytechnique, nanoindentation, is the simplest toconduct and is quite robust, and the use of astiff superlayer appears especially promising.However, it does have experimental difficultiesassociated with assessment of indentation-induced stress and the occurrence of noninter-facial phenomena such as spallation and radialcracking. The scratch technique is also simpleto conduct, but lacks theoretical rigor. Finally,the line-scratch technique seems promising, butis more difficult in terms of sample prepara-tion, both to manufacture the lines and insert aprecrack.

Nanoindentation-based methods of filmadhesion suffer from many of the problemsof film adhesion measurements, namely thatseparating the thermodynamic work of adhe-sion from a practical work of adhesion (whichincludes additional effects such as plasticdeformation in films, postcracking interactionsbetween the film and substrate, and cracking ineither the film or substrate) is challenging.Several thin film or interfacial adhesion testshave been reviewed with emphasis towardductile, thin metallic films. In addition, singleand multilayer films on silicon or aluminasubstrates are reviewed to show how variationsin thickness, chemistry, and temperature affectadhesion. Major roles are shown for thickness,test temperature, and interface chemistry as tohow they affect yield strength and the thermo-dynamic work of adhesion. For copper, gold,

and aluminum, any one of these variables areshown to change the practical work of adhe-sion by an order of magnitude or more. Forthin films, fracture energies asymptoticallyapproach the thermodynamic work of adhe-sion with decreasing film thickness while forthick samples plastic energy dissipation con-trols fracture energy. It is shown that resis-tance-based models need yield strength, afailure criterion, and at least one length scalefor predictive quality.

Realistically, the implementation of thesenanoindentation-based adhesion tests is likelyto continue in the near future, given the relativesimplicity of performing the test. This is verysimilar to the developments in nanoindenta-tion, which has become a dominant method ofmeasuring the mechanical properties of thinfilms, in spite of the difficulties in analyzing thedeformation relationships between films andsubstrates. The ease of sample fabrication, theability to perform tests on films under the sameprocessing conditions as the actual devices (noadditional processing steps are needed), andthe well-documented testing methods makenanoindentation more common than methodssuch as micromachined tensile testing or bulgetesting. There are competing adhesion testingmethods, such as four-point bending, andcantilevered beams, but in most cases theseinvolve additional processing steps beyond thatof film deposition, and can be challenging totest unique substrates or small samples. It islikely, therefore, that continued research intothe mechanics of buckling and fracture in thinfilms induced by nanoindentation will berequired. In general, nanomechanical testtechniques are useful for quantifying theadhesion of thin films.

Clear trends of increasing practical worksof adhesion with increasing thickness, anneal-ing, and the presence of titanium and chro-mium interlayers were exhibited. Thiscorroborated previous semi-quantitative stu-dies of similar films. While non-negligiblevariance was exhibited in the calculated adhe-sions, the magnitudes and trends of themeasured adhesion energy are comparablebetween many studies. Further, by measuringthe adhesion in terms of the energy dissipationrequired for delamination, not only can theincremental effects of process optimization beassessed, but the relationships between filmmicrostructure and material micromechanismscan be investigated and modeled. Increases intesting temperature were demonstrated toincrease the practical work of adhesion ofmetal films. Even larger increases in fractureresistance may be obtained by increasingductile film thicknesses.


Several comments are in order regarding theeffects of residual stresses in these thin films.As pointed out at the end of the superlayer testdiscussion, the residual stress is taken intoaccount for buckled films. For the four-pointbend test, it is considered that the residualstress is a second-order effect on the drivingforce side of the equation. Such an effect mightbe a change in the local curvature and hencethe mode mixity. Alternatively, a residual stressclearly could change the yield criterion andplastic zone size at a crack tip affecting theresistance size of the equation.

Probably the most important issue to con-sider when utilizing nanoindentation-basedadhesion testing is that these tests are almostalways under a mixed-mode loading condition.The use of superlayers, which is required forsome films to delaminate, often adds to theshear components of loading. Therefore, plas-ticity in the films (related directly to thehardness of the films) will often be exaggeratedwhen the shear component of loading isincreased. Mismatches in the elastic moduli ofthe films will also impact this value. Thischange in phase angle will undoubtedly lead todifficulty, in some cases, for determining thework of adhesion for a true mode I condition.However, by judicious selection of combina-tions of the stresses and thicknesses of stressedsuperlayers, it should be possible to probe aselection of phase angles, which should aid indetermining the mode I fracture criteria. Ingeneral, minimizing the interactions betweenthe tip doing the indentation and the positionat which the interfacial crack arrests will leadto increasing accurate values of film adhesion.

In conclusion, nanoindentation testing todetermine the interfacial fracture toughness ofthin film–substrate systems has been shown tobe a valid testing method to relatively easilyprobe the effects of interfacial chemistry, filmthickness, yield strength, and testing tempera-ture on film adhesion. While work is stillneeded to fully develop the effects of mixed-mode loading and develop experimental meth-ods of accessing various loading conditions,indentation and scratching will continue toplay a very significant role in the assessmentand study of interfacial fracture.

ACKNOWLEDGMENTS

The authors gratefully acknowledge thetechnical assistance, review, and helpful com-ments of Megan Cordill, Washington StateUniversity. They also thank John Jungk andWilliam Mook, University of Minnesota, andJames Lucas, Michigan State University, for

their reviews and helpful comments. NRM andDFB also acknowledge the support of the USDOE through Contract DE-AC04-94AL85000.

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