atomic force microscopy study of the morphological shape of thin film buckling

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Thin Solid Films 406 (2002) 190–194

0040-6090/02/$ - see front matter ᮊ 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 040- 6090 Ž0 1 .0 1 7 7 2 - 2

Atomic force microscopy study of the morphological shape of thin filmbuckling

C. Coupeau *

Laboratoire de Metallurgie-Physique, Universite de Poitiers, UFR Sciences-Bat. SP2MI yTeleport 2, Bd Pierre et Marie Curie, BP 30179,

86962 Futuroscope Cedex, France

Received 24 April 2001; received in revised form 10 December 2001; accepted 11 December 2001

Abstract

Thin films elaborated by sputtering methods often develop very high internal compressive stresses and are then susceptible todelamination and buckling. The various buckling patterns have been investigated by atomic force microscopy and are reviewedand discussed in the frame of elastic theory. ᮊ 2002 Elsevier Science B.V. All rights reserved.

Keywords: Thin films; Buckling patterns; Atomic force microscopy

Thin films and coatings elaborated by sputteringmethods improve the mechanical properties of bulk materials but often develop high residual compressivestresses during the deposition process w1,2x. Such large

residual stresses may cause the nucleation and thegrowth of individual blisters over initially debondedpatch, resulting in interesting topographical structures,such as typical circular blisters, worm-like structures orstraight-sided wrinkles w3–12x. Spontaneous bucklingpatterns observed just after the deposition process areof various dimensions and structures, depending on theinternal stresses and film thickness w10x. Buckling net-works can be homogeneously generated at the compositesurface (Fig. 1a), leading sometimes to the full delam-ination of the film (Fig. 1b).

Amazing structures of buckling are also observed by

atomic force microscopy w13x. As an example is shownin Fig. 2a, a buckling pattern in nickel 240 nm thick film on polycarbonate substrate explained by high localheterogeneous stresses. Taking advantage of its highspatial resolution, atomic force microscopy (AFM) isparticularly suited to characterizing the mechanicalbehavior of thin films on substrates and to analyzingthe fine structure of buckling, which are difficult to

*Tel. q 33 05 4949 6652; fax: q 33 05 4949 6692. E-mail address: [email protected]

(C. Coupeau).

investigate by conventional techniques. Dendrite andbrain-like structures around and above blisters has, thus,been underscored by atomic force microscopy (Fig.2b,c).

The delamination of compressed thin films from solidsubstrates has been extensively studied with continuumelasticity theory w9,14–17x. It is now well-establishedthat buckling of a film above a circular separation atthe filmysubstrate interface, and subject to equibiaxialcompression stresses, occurs at a critical stress givenby:

2B EB E E h f Cs sK (1)C FC F xx 2D 1yy GD b G f

where b is the interface separation, h the film thickness, E and the Young modulus and Poisson ratio of they

f f film, and K is a constant depending on the buckled

shape ( for a straight-sided wrinkle w9,14x and2p

K s1 D12

for a circular blister w11x).K s1.222 D

The buckled solution determined from the resolutionof the Foppl– von Karman equations (equilibrium of ¨

thin plates under compressive stresses) w18x is in goodagreement with AFM cross sections of buckling patternsover a large range of dimensions, from micrometer tonanometer scale, as shown in Fig. 3.



191C. Coupeau / Thin Solid Films 406 (2002) 190–194

Fig. 1. Optical micrographs of buckling patterns (a) nickel 350 nm thick on polycarbonate substrate, (b) molybdenum 300 nm thick on siliciumsubstrate (Courtesy of V. Branger and P. Goudeau).

Fig. 2. Fine structures of buckling patterns observed by atomic forcemicrocopy in nickel thin films on polycarbonate (a) atoll-like, (b)dendrite-like, (c) brain-like structures.

In many cases, the delaminated part of the film adoptsa sinusoidal shape behind a propagation tip, and lookslike telephone cords observed in a vast variety of filmy

substrate systems w6,8,12,19–21x. Anisotropy was at onepoint thought to be essential for the phenomenon w22x.However, it has been experimentally established thatundulated blisters propagate in films under isotropicstress w23x and confirmed numerically by simulationsperformed on a lattice model with microscopic debond-ing w24,25x. Instabilities resulting from the mixed-modenature of the interfacial crack are established at thecrack tip w12x and are then responsible for such charac-teristic delamination patterns frequently observed.

Occasionnaly, however, delaminations occurs in theform of straight-sided wrinkles. The factors that deter-

mine whether a telephone cord or straight-sided blisterdevelop are not well-known. Straight delaminationappeared first to have a sharp crease at the ridge of theblister corresponding to a crack in the film w5x. In thecase of film completely cracked through its thickness atthe midpoint of the delaminated region, the critical stressrequired for buckling is reduced by a factor of four w26x

and is associated with a change of curvature of thebuckling pattern. An example is presented in Fig. 4, thedelamination structure of a molybdenum 300 nm thick film on a silicon wafer. A crack of only a few nano-meters depth is clearly distinguishable at the top of thedelaminated area (Fig. 4b) and results in the falling-

down of buckling. Areas labeled a in Fig. 4a, whereone side of the film slides under the other (like platetectonics) are also visible.

This kind of consideration (shape of buckling with orwithout nano-cracking) is of great interest to determinethe mechanical properties of thin films. Indeed, althoughthe buckling phenomenon is undesirable for future tech-nological applications, one may take benefit of it: thebuckling analysis allows the determination of reducedYoung’s modulus E y1yn of the film, from the knowl-2

f f

edge of the in-plane residual stresses w27x. This method

to extract elastic properties of the film is only workingin the case of well-defined buckling patterns and showsthe necessity of AFM analysis of fine buckling structure.

Straight-sided wrinkles without cracking at the topare now, however, observed under specific conditions.It has, thus, been experimentally shown that straighttunnels are induced in thin films during uni-axial com-pression of substrates w28x. Regular straight-sided wrin-kles arise and have a progress direction perpendicularlyto the compression axis, from the edges to the centralpart of the specimen (Fig. 5). The amount of stress Dsinduced in the nickel thin film by the axial compression



192 C. Coupeau / Thin Solid Films 406 (2002) 190–194

Fig. 3. 3D AFM images and related cross sections of circular blisters (a) gold (630 nm)ysilicium, (b) nickel (200 nm)ypolycarbonate.

along the x axis is determined by the followingrelationship:

E 1yy y f s f Ds s Ø s xx S2

E 1yys f

(2) E y yy f f s

Ds s Ø s yy S2 E 1yys f

where E and are the elastic parameters of substrate,ys s

and s is the stress-induced in the substrate during theS

experiment. The total stress s in the film is the sum of the internal stress s and the stress Ds generated duringi

the compression experiment; the stress along the x axisis, thus, sufficient to induce development of straighttunnels. It is worth noting that the experimental criticalstress for buckling is greater than defined in Eq.Cs xx

(1). This discrepancy is attributed to the necessaryenergy to create a debonding area in well-adherent thinfilms w29x, i.e. with no specific defects at filmysubstrateinterface, which is considered in buckling models.

The formation of these straight-sided wrinkles exper-imentally-induced is in contrast with the very rareobservations of such buckling structures just after thedeposition process in the vacuum chamber. Recently,the stability of straight delamination blisters has beeninvestigated in the frame of Foppl–von Karman theory¨

of thin plates. It is demonstrated that undulations in thedelamination patterns permit an optimal release of theelastic energy stored in the film w30x. The worm-like

structures can thus only be explained by a morphologicalinstability from straight-sided to telephone cords. Thistransition has been found to be energetically favorablefor longitudinal (along the tunnel axis) critical stressess of a few GPa w31x. A transition to varicose pattern yy

(line of circular blisters) is also predicted at low Poissonratios w30x.

The internal stresses of thin films elaborated bysputtering processes can be determined both by X-raydiffraction (sin c method) and curvature (Stoney meth-2

od) w32,33x measurements and are found to be also of



193C. Coupeau / Thin Solid Films 406 (2002) 190–194

Fig. 4. AFM analysis of buckling pattern of molybdenum 300 nm thick film on silicium (a) signal error mode AFM images, (b) topographicalmode 3D AFM image, (c) related cross section of wrinkles.

Fig. 5. Straight-sided wrinkles generated perpendicular to the com-pression axis s (a) optical micrograph, (b) 3D AFM image of ones

buckling pattern.

Fig. 6. Transition from straight-sided wrinkles to (a) telephone cordsstructures observed in stainless steel 58 nm thick film on polycarbon-ate substrate, (b) varicose structures observed in nickel 240 nm thick film on polycarbonate substrate.

the order of a few GPa in compression. The instabilityfrom straight-sided to telephone cords is, thus, energet-ically favorable for these as-deposited thin films andmay be a relevant explanation for the high frequentobservations of telephone cord structures compared tostraight tunnels.

Such instabilities from straight-sided to both telephonecords or varicose structures have been already observed

by atomic force microscopy in thin films on polycar-bonate substrates (Fig. 6) w31,34x.

The stability of the straight-sided wrinkles generatedduring the uni-axial compression of substrates isaccounted for in this case by the Poisson ratio values.Since n -n , Ds -0 wEq. (2)x; when the substrate is f s yy

under compression (maximum load), the longitudinalstress along the y axis is relaxed (sys ) allowing thei yy

straight tunnel to develop. The release of external

stresses (Ds sDs s0) induces the increase of s yy xx yy

up to s and the subsequent transition of straight-sidedi

to telephone cords or varicose.The reason that determines whether one or the other

structure appears is currently unknown but it is worthemphasizing that the second possible transition may leadto well-defined periodic structures (Fig. 7).

In conclusion, atomic force microscopy has proved to

be particularly suitable to investigate the fine structureof delamination and buckling. It is also shown that mostof buckling patterns can be simply understood in the



194 C. Coupeau / Thin Solid Films 406 (2002) 190–194

Fig. 7. Periodic structures of circular blisters observed by atomic forcemicroscopy in a nickel 240 nm thick film on polycarbonate substrate.

frame of elastic theory, as an optimum release of energyin the film.

Acknowledgments

The author would like to thank P. Goudeau, J. Colinand J. Grilhe for fruitful discussions and useful´

suggestions.

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atomic force microscopy study of the morphological shape of thin film buckling

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