Cu interface stress

NanoStmcturcd Materials. Vol. 6, pp. 201-204, 1995 Copyright © 1995 Elsevier Sci¢=aeeLtd Printed in the: USA. All fights rcs~eed 0965-9773D5 $9.50 + .00

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THE Ag/Cu INTERFACE STRESS S. Berger* and F. Spaepen Division of Applied Sciences, H,'u'v,'u'd University, Cambridge MA, 02138 USA,

ABSTRACT The interface stress iu Ag/Cu muitilayered thin films of various repeat lengths on Si(100) substrates was determined from the difference between the average bulk stress in the fihn and tile substrate curvature stress. The interface stress me~,~ured for repeat lengths between 5.3 and 11.4nm is equal to -3.19_0.43J/m2; it is tensile: elastic expansion of tile interface lowers its energy. Its effect on the substrate curvature stress increases line,'u'ly with decreasing bilayer repeat length. The average film stress detennined from the lattice strains is tensile, and increases by about one order of magnitude with decreasing bilayer repeat length over the range studied. Both the Ag and Cu layers have a [111] texture, which becomes gradually less pronounced as tile bilayer repeat length increases from 5.3nm to 12.6nm. The interface stress found in this system has the same sign aud a magnitude simil~ to that found by the same method in e,'u'iier work on the Ag/Ni interface. INTRODUCTION The interface stress is a tensor that represents the work required to deform elastically by a unit strain a unit area of interface[l-4]. If the interface has threefold or higher rotational symmetry and tile elastic strain.~ in the two phases are the stone, the interface stress can be represented by a single scalar,f. The interface stress, like the surface stress, plays an important role in tile thermodyn,-unics and mechanical behavior of small p,'uticles. It represents the mechanical action of the interface on the adjacent particles or layers. When the interface density is sufficiently l,'u'ge, the strains induced by the interface stress may be l,'uge enough to cause measurable non-linear el~L,;tic effects. Direct measurements of the interface stress ,are scarce: Ruud el al.[5] have measured it to be -2.27J/m 2 fi~r (111) Ag/Ni interfaces, and Scanhm et al.[6] have measured a value of -l.SJ/m 2 in (100) Ag/Fe interfaces. A negative interface stress is a tensile one, i.e., one that does positive work when the interface is stretched. Both of these represent systems with minimal mutual solubility and no compound formation in the solid state. Bain et al.[7] have investigated Mo/Ni interfaces, and measured an interface stress close to zero. Their results may have been influenced by possible thin compound formation at the interfaces in this system. C,'unm,'u'ata and Eby have determined values for the interface stress in a number of polymeric systems[8]. We have applied the method developed for the measurements of Ag/Ni to Ag/Cu. These ,are also two f.c.c, metals with a l,'uge mismatch in atomic size, which do not form

201

202

S BERGERAND F SPAEPEN

comlm)unds, but which have a slightly greater mutual solubility. As discussed in the earlier paper[5], the interface stress can be found by performing two sets of measurements on a series of artificial multilayers with different repeat length, )~, deposited on a substrate. The thickness of the individual layers in each multilayer ~ue the s,'une. The stress in each multilayer, Gsc, is determined from the substrate curvature, 1/R.

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2f

%c

< a>

:

T

where <~> is the average of the stresses in the two components determined from the X-ray measurements.

EXPERIMENTS Ag/Cu multilayers were deposited on a single cryslalline (100)Si substrate. The deposition was carried out at room temperature by Ar ion sputtering of pure Ag and Cu targets attached to a computer-controlled-rotaling holder[9]. Six fihns with different bilayer repeat length(3.0nm, 5.4nm, 7.4ran, 9.4urn, 11.4urn and 12.6nm) were deposited each to a total thickness of 21J.m on the Si substrate(the first layer deposited on the Si substrate was Ag). The thicknesses of the individual layers in each fihn were made as closely as possible. The deposition was done at a base pressure of about 8x 10-5 Iorr. In addition, pure Ag and Cu fihns were deposited, under the same conditions, each to a thick'~less of 2t.tm, on the Si substrate. The transmission X-ray diffraction measure|nents were made with MoKct radiation in 0-20 scans. The curvature of the substrates coated with the mullilayered fihns was measured with a custommade He-Ne laser reflection system[ 10].

RESULTS

AND

DISCUSSION

The transmissiou X-ray diffraction spectra of tile Ag/Cu lnullilayers ,are shown in Fig. 1.a. The precise posilions of the Cu(220) and Ag(220) peaks were determined by fitting the peak shapes, and tile con'esponding d-spacings were calculated from the Bragg equalion. The results for Cu ,are shown in Fig. l.b). The in-plane strains in each of the layers were determined by comparing these d-spacings with their respective strain-free values (d220(Cu) = 1.2781,A: d220(Ag) = 1.~n,.'!.7A). The results me shown in Figure 2.a). Note that the strains in the Cu and Ag layers become, respectively, more tensile and compressive with decreasing multilayer repeat

THE Ag/Cu INTERFACESTRESS

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length, as would be expected from an increasing degree of coherence between the layers. The corresponding stresses were calculated using the second[11] and third order[12,13] biaxial moduli for the [111] orientation, since that is the dominant texture of the multilayers. The results ,'ue shown in Fig.2.b). The stress calculated from the substrate curvature according to Eq. (1) for each of the |nultilayers is shown in Fig.3.a). The difference between this stress and the average stress <~> of Fig. 2.b) is plotted as a function of 1/~. in Fig.3.b). According to Eq.(2), the points in Fig.3.b) should lie in a straight line through the origin. For four of the points this is the case. Tile slope of tile fit through these points con'esponds, using Eq.(2), It an interface stress of -3.19+0.43 J/m 2. The deviation of the point at the highest repeat lengths may be due to a deterioration of the texture of the multilayers[14]. The deviation of the point at lowest repeat lengths may reflect the higher degree of coherence and the corresi'xmding change in the interfacial diskxzation su'ucture. CONCLUSIONS The interface stress in Ag/Cu is of the same magnitude and has the same sign(tensile)as that in Ag/Ni and Ag/Fe. This reinforces an interesting conflict with the reported theoretical results, all of which have opposite sign[5]. This may be resolved if tile substantial tensile contribution from the interaction between interfacial dislocations is properly taken into account[15].

ACKNOWLEDGMENTS This work has been supported by the Office of Naval Research under Contract No. N00014-91J-1281. S. Berger acknowledges partial support by the Rothschild Fellowship.

REFERENCES *- Permanent address-Faculty of Materials Engineering, Technion, Haila, Israel. 1. J.W. Cahn, in Segregation to Interfaces ASM Seminar, 3-23 (1978). 2. W.W. Mullins, in Metal Surtaces, Aanerican Society for Metals, 17-66 (1962). 3. H. Brooks, in Metal Interfaces(American Society of Metals, Metals Pm'k,OH) p.20 (1956). 4. R.C. Cmmmata, Prog. Surf. Sci. 46, I (1994). 5. J.A. Ruud, A. Witvrouw and F. Spaepen, J. Appl. Phys. 74, 2517 (1993). 6. M.R. Scanlon, R.C. Cmnm,'uata, D.J. Keavney, J.W. Freeland, J.C. Walker and C. Hayzelden, to be published. 7. J.A. Bain, L.J. Chuug, S. Benman and B.M. Clemens, Phys. Rev. B44, 1184 (1991). 8. R.C. C~unmarata and R.K. Eby, J. Mater. Res. 6, 888 (1991). 9. F. Spaepen, A.L. Greer, F. Kelton, and J.L. Bell, Rev. Sci. Instrum., 1340 (1985). 10. P.A. Flinn, in Thin Fihns:Stresses and Meclmnical Properties, edited by J.C. Bravman, W.D. Nix, D.M. Bmnett, and D.A. Smith(Mater. Res. Soc. Syrup. Proc.130 Pittsburgh, PA), 41 (1989). 11. J.P. Hirth and J. Lothe. Theory of Dislocations, (McGraw-Hill, New York,), p.762, 1968. 12. D.C. Wallace, Phys. Rev. 162, 776 (1967). 13. R. Behmann, R.F.S. Hemmon and S.K. Kurtz, Landoit-B~Srnstein Numerical Data and Functional Relationships in Science and Technology: Group III, Volume 2,(SpringerVerlag, B erl in) pp. 112-116 ( 1969 ). 14. S. Berger and F. Spaepen, to be published. 15. F. Spaepen and J.P. Hirth to be published.