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Pt multilayers by in-situ substrate curvature measurement
Materials Science and Engineering A319– 321 (2001) 887– 892 www.elsevier.com/locate/msea
Observation of the strengthening of Pt layers in Ni/Pt and Pd/Pt multilayers by in-situ substrate curvature measurement V. Ramaswamy *, M.A. Phillips, W.D. Nix, B.M. Clemens Department of Materials Science and Engineering, Stanford Uni6ersity, Stanford, CA 94305 -2205, USA
Abstract The high strength of metal multilayers may be due to small layer thicknesses and grain sizes, elastic modulus differences between components of the multilayered structure and high dislocation densities, possibly due to a large lattice mismatch between the layers. This high strength is reflected in the large stresses often observed in the individual layers of metal multilayer structures. In this study, a detailed comparison of the stress behaviors of Pt in Ni/Pt and Pd/Pt multilayers is presented. Stress is measured by monitoring the curvature of the substrate continuously during film deposition. Pt is observed to be in compression in both systems with contributions from coherency and atomic peening due to bombardment by energetic particles during the sputtering process. Pt is able to withstand a higher stress level when grown on Ni than when grown on Pd, implying that the Pt layers are stronger in the Ni/Pt multilayer. Likely causes for the observed increase in strength are the higher shear stiffness of Ni compared to Pt and the large lattice mismatch between Ni and Pt. Cross-section TEM micrographs show structural differences between Ni/Pt and Pd/Pt multilayers. The stress evolution in the Pt layers is compared to model predictions based on the Matthews– Blakeslee critical stress theory. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Ni/Pt and Pd/Pt multilayers; Lattice mismatch; Disslocation
1. Introduction Metal thin films are known to be stronger than their bulk counterparts. The reason for this increased strength is due, in part, to increased resistance to dislocation motion because of the small thickness, and in the case of polycrystalline films, due to the fine grain structure [1,2]. Multilayered films with individual layers only several atomic layers thick are strengthened not only by their small layer thickness, but also by the elastic modulus mismatch between the components, high dislocation densities, formation of an interfacial alloy, and differences in the crystal structure of adjacent layers [3–5]. In most experimental measurements of film strength, the film or the film-substrate composite are loaded externally. Thermal cycling, bulge testing, nanoindentation and micro-tensile testing are examples of such experiments. These techniques are not always practical * Corresponding author. Tel.: + 1-650-7233463; fax: +1-6507254034. E-mail address: [email protected] (V. Ramaswamy).
for studying the mechanical behavior of ultrathin films. It is well known that stress generated during film growth can be significant, and in some cases cause the film to yield. By measuring these stresses in-situ, and observing their evolution with thickness, it is possible to study the mechanical behavior of very thin films and multilayers non-invasively. These measurements provide useful insights into the average stress of the multilayer structure, as well as an understanding of stress in the individual layers. In the following sections, the behavior of Ni/Pt and Pd/Pt multilayers are compared and the mechanical behavior of Pt grown on Ni and Pd is discussed in detail.
2. Details of experiments Ni/Pt and Pd/Pt multilayers, with 26 and 60 A, bilayer periods (\) respectively, and with individual layers of equal thickness, were deposited on 110 mm thick glass substrates, following the deposition of a 300 A, Pt seed layer. The samples were grown in an Ar pressure of 3 mtorr, in a UHV chamber with a base
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pressure of 4×10 − 9 torr, equipped with three independently-shuttered D.C. magnetron sources. The substrates were at ambient temperature, and deposition rates were maintained at approximately 1 A, s − 1. The strong (111) texture of the Pt seed layer provides a template for (111)-oriented multilayer growth. In-plane grain orientation is random. Stress behavior during multilayer growth was monitored by means of a sub-monolayer-sensitive in-situ substrate curvature measurement technique described elsewhere [6–8]. The force in the film per unit width, F/w, is calculated from the measured curvature change, Ds·, using the Stoney equation, F/w= |ftf =
Mst 2s Ds , 6
(1)
where |f, tf, Ms, and ts are the film biaxial stress, film thickness, substrate biaxial modulus, and substrate thickness, respectively. In a plot of F/w as a function of film thickness, the incremental (or local) film stress, given by ((F/w)/(tf is tensile if the slope is positive and compressive if the slope is negative. The average slope of the F/w curve is a measure of the average stress in the film or multilayer. As the film is deposited, if the microstructure remains in the as-deposited state, the stress in an incrementally thick layer will be equal to the instantaneous stress, ((F/w)/(tf. Generally, in such cases, stress gradients will be present in the film. How-
ever, if the film were to relax continuously as it grows, the stress in the film might be constant through its thickness. Depending on the kinetics of processes occuring during film growth, the actual film stress and microstructure will lie in between these two extreme situations. Substrate curvature measurements alone are insufficient to distinguish between the two, and knowledge of growth processes and microstructural information is required to make the distinction. High Resolution TEM (HRTEM) images of the cross-section of Ni/Pt (\=50 A, ) and Pd/Pt (\=40 A, ) multilayers were obtained using a JEOL 3000 (300 keV) electron microscope.
3. Results and discussion
3.1. In-situ stress measurement The results from curvature measurement experiments during growth of Ni/Pt (\= 26 A, ) and Pd/Pt (\=60 A, ) multilayers are shown in Fig. 1. In both cases, the stress behavior is reproduced from bilayer to bilayer, and is not affected by an increase in total thickness, or any cumulative structural change. Pt is in compression in both multilayers as seen from the negative slopes of the F/w plots during Pt growth. Ni is in tension while the Pd layers exhibit only a very small tensile response and are virtually stress-free. The observed behavior is consistent with coherency stress, as the lattice parameter of Pt is larger than that of Pd and Ni. The average stress | in the individual layers is estimated from the average slope, and using Hooke’s Law, the average strain is given by m=
| , M(111)
(2)
where, M(111) is the biaxial modulus of the (111)-oriented film. The magnitudes of the layer strains thus calculated for the Pd/Pt and Ni/Pt multilayer are given in Table 1, along with the magnitudes of the misfit strains for Pt on Ni and Pd. The misfit strain is defined as mmisfit = Fig. 1. In-situ stress measurements during growth of Pd/Pt (\= 60 A, ) and Ni/Pt (\= 26 A, ) multilayers. Table 1 Magnitudes of the layer strains in the Ni/Pt and Pd/Pt multilayers calculated from Fig. 1, and the magnitudes of the total misfit strains A/B
mA (%)
mB (%)
mmisfit (%)
Pd/Pt Ni/Pt
0 0.37
0.8 1.94
0.84 10.2
aA − aPt , aPt
(3)
where aPt is the bulk lattice parameter of Pt and aA represents the bulk lattice parameter of Ni or Pd. The negligible stress in the Pd layer implies that Pd is growing on Pt that is compressively strained to match the Pd underneath, and the layers are fully coherent. The sum of the magnitudes of the strain in the Ni and Pt layers of the Ni/Pt multilayer is only a fraction of the total misfit, implying that a sigificant portion of the misfit is accommodated by misfit dislocations. In both multilayers, the magnitude of strain in Pt is larger than
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surface and interface stresses, in addition to throughthickness film stress [13]. Surface stress contributions are strongest at small layer thickness and rapidly diminish with increasing thickness. However, other stress generating mechanisms (eg. coherency, atomic peening) may also be active in the small thickness regime, in which case the measured curvature change will be the net result of surface and layer stresses. In a separate study of the stress behavior of Pd/Pt multilayers [12], the effect on F/w of replacing a Pd surface with a Pt surface was determined to be a function of the form D(F/w)surface = A{1− exp(−Bt)},
Fig. 2. Superposition of the F/w behavior of Pt grown on a 100 A, thick Pd layer and a 30 A, thick Ni layer. The dashed curve is the Pt on Pd data, from which the effects of surface stress have been removed.
that in the other components, and as a result, the average stress in the multilayers is compressive (Fig. 1). This average compressive stress, ranging from 1.5 to 2 GPa is high enough to cause the film to debond from the substrate in samples made up of a large number of bilayers [9]. The Pt compressive stress is not solely due to coherency. Bombardment of the film surface by reflected neutral atoms, also known as atomic peening gives rise to compressive stress [10,11], possibly due to formation of point defects within the film. High atomic mass, low mobility metals like Pt are especially susceptible to this effect and the compressive stress in Pt has been observed to decrease considerably when the Ar pressure is increased [12]. Peening is also observed in Ni and Pd, but the effect is not as pronounced as in Pt. In the next section, the stress behavior of Pt grown to larger thickness on Ni and Pd will be discussed.
3.2. Pt stress beha6ior In Fig. 2, the stress evolution of Pt grown on 30 A, of Ni and 100 A, of Pd is superimposed. These layers were grown under the same conditions as the multilayers in Fig. 1. The initial stress behaviors of the Pt layers grown on Ni and Pd are exactly the same as those of the Pt layers in the corresponding multilayers. However, in this experiment, the Pt layers are grown to thicknesses of about 70 A, in order to obtain a more complete understanding of their mechanical behavior. The initial compressive stress in Pt grown on Pd is small, but soon increases, as seen from the increasing slope of the F/w plot in Fig. 2. This early trend is believed to be due to the surface stress difference between Pd and Pt. Substrate curvature can be caused by
(4)
where A and B are constants, and t is the layer thickness. As t increases, D(F/w)surface approaches A, which is the difference in surface stress of Pt and Pd and is determined to be about 2 N m − 1. Essentially, Eq. (4) describes the evolution of the coverage of the Pd underlayer as the Pt layer thickness increases; F/w reaches a constant value when the Pd is completely covered by Pt. The stress evolution of Pt on Pd after subtraction of surface effects is also shown in Fig. 2. In this plot, F/w changes almost linearly during the first 15 A, , after which the layer relaxes. Note that after the first few monolayers, the corrected F/w follows the same trend as the uncorrected data. In the Pt layer grown on Ni, a large change in F/w is observed during the first monolayer or so, after which a decrease in the slope is observed. This behavior is consistent with a high coherency stress, albeit not large enough to result in a fully coherent interface, as seen from Table 1. It is unlikely that the initial change in F/w is caused by a surface stress effect, since the surface energies of Pt and Ni are similar [14,15]. As in the Pt on Pd case, the stress in the Pt layer on Ni relaxes with increasing thickness. From the F/w plots its is clear that the Pt layer grown on Ni has a higher average stress compared to the Pt layer grown on Pd. In Fig. 3, the average stress in the Pt layers grown on Pd and Ni are plotted as a function of thickness and the stress relaxation of Pt on Pd and Ni is seen clearly. At very small thicknesses, compressive stress in Pt grown on Pd increases with thickness. This is probably due to fractional Pt coverage at small thicknesses. The maximum stress in Pt on Pd is around 5 GPa, and this stress level is maintained to a thickness of 14 A, before relaxation. The initial average stress in Pt on Ni is very high and relaxes rapidly to about 8 GPa at 8 A, , after which the relaxation rate drops. The difference in the initial stress levels is due to the higher lattice mismatch in the Ni/Pt case. The stress contribution from atomic peening, however, is likely to be similar in both cases. At 70 A, , Pt on Ni has an average stress of 3.4 GPa and Pt on Pd has an average stress of 2 GPa.
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3.3. TEM results Cross-section TEM images of Pd/Pt and Ni/Pt multilayers are shown in Fig. 4 and Fig. 5, respectively. In the lower magnification images the Pt appears darker than either the Ni or Pd due to electron density contrast and reveals the multilayer structure. Due to the negative enthalpy of mixing of both Ni/Pt and Pd/Pt systems, intermixing at the interfaces is likely [16]. As a result the boundaries between layers are somewhat diffuse. Higher magnification insets show that in the Pd/Pt sample there are no obvious dislocations, consistent with coherent interfaces, whereas in the Ni/Pt sample, several dislocations (highlighted on the image) are present. A simple calculation shows that an average misfit dislocation spacing of 35 A, in the Ni/Pt multiFig. 5. Cross-section TEM image of Ni/Pt multilayer (\= 40 A, ).
layer will accommodate the portion of the misfit not accommodated by elastic strain.
3.4. Strengthening mechanisms
Fig. 3. The average stress in the Pt layers in Ni/Pt and Pd/Pt multilayers plotted as a function of layer thickness. The solid curves are the Matthews – Blakeslee critical stress for Pt on Pd (A) and Pt on Ni (B). The dashed curve (C) is the critical stress for Pt on an elastically-matched substrate (the reference critical stress).
Fig. 4. Cross-section TEM image of Pd/Pt multilayer (\= 50 A, ).
Small film thickness itself is a barrier to dislocation motion, enabling very thin films to sustain high stresses. Other effects commonly observed are grain boundary strengthening, much like the Hall-Petch effect found in bulk polycrystalline materials (in polycrystalline films, grain sizes are on the order of the film thickness), elastic modulus mismatch between the film and substrate or film and passivation, causing dislocations to be repelled from the stiffer layers, thus inhibiting plasticity in the more compliant layers, and high dislocation densities resulting in stronger films due to dislocation interactions. The high stresses sustained by the Pt layers in both Ni/Pt and Pd/Pt multilayers are a measure of the high strengths of these layers. Pt grown on Ni is able to sustain a much larger stress than when grown on Pd, and is therefore stronger. The difference in strength cannot be ascribed to grain boundary strengthening, since the two structures have very similar grain size. The striking differences between the two pairs are lattice mismatch and elastic modulus mismatch. Lattice mismatch, which is very small between Pd and Pt and much larger between Ni and Pt, suggests that the higher density of misfit dislocations present in the Ni/Pt sample may result in dislocation strengthening of the Pt layer grown on Ni. TEM micrographs are consistent with this reasoning. Alternately, the differences in strength of the Pt layers may be due to the mismatch in elastic modulii between the layers. The shear modulus of Pt (61 GPa) is higher than that of Pd (44 GPa) and lower than that of Ni (76 GPa). Dislocations in the Pt layer will therefore be repelled from the Ni layer, and
V. Ramaswamy et al. / Materials Science and Engineering A319–321 (2001) 887–892
attracted to the Pd layer. Also, the energy cost of a dislocation near an interface, which depends on the modulii of both layers, is higher near a Ni/Pt interface. It was shown by Matthews et al. [17] that a film under a given strain must reach a critical thickness before a dislocation can spontaneously thread through the film, partially relieving the strain. This result has become known as the Matthews– Blakeslee critical thickness condition. Following a rigorous treatment of the stability of a threading dislocation by Freund [18], Nix [19] gives an expression for the critical stress |c, as a function of film thickness, at which a dislocation spontaneously threads through the film, |c = −
!
v it [b 21 +b 22 +(1 −6)b 23]ln 4ytb1(1− 6) b
"
1 − (b 21 +b 22) , 2
(5)
where b1, b2, and b3 are the components of the burgers vector, t is the film thickness, v and w are the film shear modulus and poisson’s ratio, respectively and i is a numerical constant of order one. For the present case of (111) oriented, FCC films with a {111} slip plane and a 110 Burger’s vector, the critical stress becomes [19] |c =
n
3vb it 3 (4 −6)ln − . 8y(1− 6)t b 2
(6)
In order to account for the different elastic modulii of the film (Pt) and substrate (Ni or Pd), v=2vf vs/vf + vs is used, where vf and vs are the shear modulii of the film and substrate respectively [2]. |c as a function of thickness is also shown for Pt on Pd, and Pt on Ni in Fig. 3, along with the measured average stress. The best match to the Pt stress data was obtained with i = 0.75 for the Pt on Pd case, and i =0.9 for the Pt on Ni case. The tensile stress predicted at low thickit nesses is unphysical, and is due to the ln term, as t b approaches the core cut-off radius. At thickness greater than 20 A, , there is very good agreement between the average stress obtained from curvature measurements and the critical stress model. The critical stress calculated using the modulus of pure Pt lies between that predicted for Pt on Ni and Pt on Pd, and is also shown in Fig. 3, as a reference critical stress. In Pd/Pt multilayers, even if all the misfit were accommodated by misfit dislocations, their spacing would be roughly 300 A, , and dislocation interactions would have little effect on the yielding behavior of Pt on Pd. In the Ni/Pt case, even though misfit dislocations are more closely spaced, the higher strength of Pt can be accounted for simply by the higher modulus of the Ni underlayer, and ignoring dislocation interactions. The effect of a stiff underlayer can also be quantified using the image force method to calculate the equilibrium
891
distance of the misfit dislocation away from the interface [19]. From this analysis, the critical stress in a film with a very rigid substrate is found to increase by about 30% relative to the reference critical stress in the absence of elastic mismatch. The Matthews critical stress model discussed above, as well as the average stress data is consistent with such an increase in strength. From preliminary results of stress evolution in Cu/Pt multilayers (\= 40 A, ), Pt was observed to sustain compressive stress comparable to the stress of Pt on Ni. Cu and Pt have a high lattice mismatch (8%), but Cu has much lower shear modulus than Ni. For the case of Pt grown on Cu, the Matthews critical stress model used above would not predict high strength. It is speculated that the large stress sustained by Pt in this case is related to the large lattice mismatch resulting in a high misfit dislocation density. In calculating average stress from F/w, the Pt layer at all thicknesses is assumed to to be continuous, and uniformly thick. At very small thicknesses, neither of these assumptions is valid for the growth of a low mobility metal like Pt under the present growth conditions. Even after the Pt coverage is complete, it is likely that the layer is rough and the load-bearing thickness of Pt may be smaller than the average thickness used to calculate stress. Therefore, the stress sustained in the small thickness regime may be underestimated by the average stress plotted in Fig. 3.
4. Conclusions Significant compressive stresses are observed in Ni/Pt and Pd/Pt multilayers, with bilayer periods of a few tens of A, ngstroms. The overall compression is due to the large compressive stresses in the individual Pt layers. The Pt in the Ni/Pt case sustains significantly higher stress than in the Pd/Pt case. The large lattice mismatch between Ni and Pt will result in a high density of misfit dislocations. This is seen in the cross-section TEM image of the Ni/Pt multilayer. In contrast, the TEM results show that the Pd/Pt multilayer is almost dislocation free, consistent with the small lattice mismatch between Pd and Pt. The difference in dislocation densities suggests that the high stress in Pt on Ni, compared to Pt on Pd may be due strengthening as a result of dislocation interactions. The higher shear modulus of Ni relative to Pt increases the energy of a dislocation near the interface (or repels the dislocation), thus inhibiting plasticity in the Pt layer and increasing its strength. The lower shear modulus of Pd relative to Pt, on the other hand predicts weakening of the Pt layer. A simple Matthews critical stress model, in which dislocation interactions are not considered, but the shear modulii of the underlayers are taken into account, agrees remarkably well with the
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measured stress of Pt on both Ni and Pd. The difference in the stress and strengthening of Pt on Ni and Pd can therefore be fully explained by modulus strengthening due to the higher stiffness of the Ni underlayer, and dislocation strengthening appears to be negligible.
Acknowledgements The authors are grateful to Dr Harriet Kung of Los Alamos National Laboratory for the help and guidance provided during TEM sample preparation and imaging. Funding for this work, provided by the National Science Foundation through Grant No. DMR-9408552, is gratefully acknowledged.
References [1] E. Arzt, Acta Mater. 46 (1998) 5611. [2] W.D. Nix, Metall. Trans. A 20A (1989) 2217. [3] S.P. Baker, W.D. Nix, J. Mater. Res. 9 (1994) 3131.
[4] B.J. Daniels, W.D. Nix, B.M. Clemens, Mater. Res. Soc. Symp. Proc. 356 (1995) 373. [5] B.M. Clemens, S.A. Barnett, H. Kung, MRS Bulletin 24 (1999) 20. [6] J.A. Floro, E. Chason, S.R. Lee, Mater. Res. Soc. Symp. Proc. 406 (1996) 491. [7] V. Ramaswamy, W.D. Nix, B.M. Clemens, Mater. Res. Soc. Symp. Proc. 505 (1998) 589. [8] V. Ramaswamy, B.M. Clemens, W.D. Nix, Mater. Res. Soc. Symp. Proc. 528 (1998) 161. [9] B.J. Daniels, W.D. Nix, B.M. Clemens, Mater. Res. Soc. Symp. Proc. 382 (1995) 315. [10] J.A. Thornton, D.W. Hoffman, Thin Solid Films 171 (1989) 5. [11] C. Hudson, R.E. Somekh, Thin Solid Films 171 (1989) 5. [12] V. Ramaswamy, W.D. Nix, B.M. Clemens, Unpublished results (1999). [13] F. Spaepen, J. Mech. Phys. Solids 44 (1996) 675. [14] P. Gumbsch, M.S. Daw, Phys. Rev. B 44 (1991) 3934. [15] D. Udler, D.N. Seidman, Mater. Res. Soc. Symp. Proc. 356 (1995) 373. [16] J.A. Bain, B.M. Clemens, S. Brennan, Mater. Res. Soc. Symp. Proc. 187 (1990) 315. [17] J.W. Matthews, S. Mader, T.B. Light, J. Appl. Phys. 41 (1970) 3800. [18] L.B. Freund, Adv. Appl. Mech. 30 (1994) 1. [19] W.D. Nix, Scripta Materialia 39 (1998) 545.
Observation of the strengthening of Pt layers in Ni/Pt and Pd/Pt multilayers by in-situ substrate curvature measurement V. Ramaswamy *, M.A. Phillips, W.D. Nix, B.M. Clemens Department of Materials Science and Engineering, Stanford Uni6ersity, Stanford, CA 94305 -2205, USA
Abstract The high strength of metal multilayers may be due to small layer thicknesses and grain sizes, elastic modulus differences between components of the multilayered structure and high dislocation densities, possibly due to a large lattice mismatch between the layers. This high strength is reflected in the large stresses often observed in the individual layers of metal multilayer structures. In this study, a detailed comparison of the stress behaviors of Pt in Ni/Pt and Pd/Pt multilayers is presented. Stress is measured by monitoring the curvature of the substrate continuously during film deposition. Pt is observed to be in compression in both systems with contributions from coherency and atomic peening due to bombardment by energetic particles during the sputtering process. Pt is able to withstand a higher stress level when grown on Ni than when grown on Pd, implying that the Pt layers are stronger in the Ni/Pt multilayer. Likely causes for the observed increase in strength are the higher shear stiffness of Ni compared to Pt and the large lattice mismatch between Ni and Pt. Cross-section TEM micrographs show structural differences between Ni/Pt and Pd/Pt multilayers. The stress evolution in the Pt layers is compared to model predictions based on the Matthews– Blakeslee critical stress theory. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Ni/Pt and Pd/Pt multilayers; Lattice mismatch; Disslocation
1. Introduction Metal thin films are known to be stronger than their bulk counterparts. The reason for this increased strength is due, in part, to increased resistance to dislocation motion because of the small thickness, and in the case of polycrystalline films, due to the fine grain structure [1,2]. Multilayered films with individual layers only several atomic layers thick are strengthened not only by their small layer thickness, but also by the elastic modulus mismatch between the components, high dislocation densities, formation of an interfacial alloy, and differences in the crystal structure of adjacent layers [3–5]. In most experimental measurements of film strength, the film or the film-substrate composite are loaded externally. Thermal cycling, bulge testing, nanoindentation and micro-tensile testing are examples of such experiments. These techniques are not always practical * Corresponding author. Tel.: + 1-650-7233463; fax: +1-6507254034. E-mail address: [email protected] (V. Ramaswamy).
for studying the mechanical behavior of ultrathin films. It is well known that stress generated during film growth can be significant, and in some cases cause the film to yield. By measuring these stresses in-situ, and observing their evolution with thickness, it is possible to study the mechanical behavior of very thin films and multilayers non-invasively. These measurements provide useful insights into the average stress of the multilayer structure, as well as an understanding of stress in the individual layers. In the following sections, the behavior of Ni/Pt and Pd/Pt multilayers are compared and the mechanical behavior of Pt grown on Ni and Pd is discussed in detail.
2. Details of experiments Ni/Pt and Pd/Pt multilayers, with 26 and 60 A, bilayer periods (\) respectively, and with individual layers of equal thickness, were deposited on 110 mm thick glass substrates, following the deposition of a 300 A, Pt seed layer. The samples were grown in an Ar pressure of 3 mtorr, in a UHV chamber with a base
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 0 0 6 - 1
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pressure of 4×10 − 9 torr, equipped with three independently-shuttered D.C. magnetron sources. The substrates were at ambient temperature, and deposition rates were maintained at approximately 1 A, s − 1. The strong (111) texture of the Pt seed layer provides a template for (111)-oriented multilayer growth. In-plane grain orientation is random. Stress behavior during multilayer growth was monitored by means of a sub-monolayer-sensitive in-situ substrate curvature measurement technique described elsewhere [6–8]. The force in the film per unit width, F/w, is calculated from the measured curvature change, Ds·, using the Stoney equation, F/w= |ftf =
Mst 2s Ds , 6
(1)
where |f, tf, Ms, and ts are the film biaxial stress, film thickness, substrate biaxial modulus, and substrate thickness, respectively. In a plot of F/w as a function of film thickness, the incremental (or local) film stress, given by ((F/w)/(tf is tensile if the slope is positive and compressive if the slope is negative. The average slope of the F/w curve is a measure of the average stress in the film or multilayer. As the film is deposited, if the microstructure remains in the as-deposited state, the stress in an incrementally thick layer will be equal to the instantaneous stress, ((F/w)/(tf. Generally, in such cases, stress gradients will be present in the film. How-
ever, if the film were to relax continuously as it grows, the stress in the film might be constant through its thickness. Depending on the kinetics of processes occuring during film growth, the actual film stress and microstructure will lie in between these two extreme situations. Substrate curvature measurements alone are insufficient to distinguish between the two, and knowledge of growth processes and microstructural information is required to make the distinction. High Resolution TEM (HRTEM) images of the cross-section of Ni/Pt (\=50 A, ) and Pd/Pt (\=40 A, ) multilayers were obtained using a JEOL 3000 (300 keV) electron microscope.
3. Results and discussion
3.1. In-situ stress measurement The results from curvature measurement experiments during growth of Ni/Pt (\= 26 A, ) and Pd/Pt (\=60 A, ) multilayers are shown in Fig. 1. In both cases, the stress behavior is reproduced from bilayer to bilayer, and is not affected by an increase in total thickness, or any cumulative structural change. Pt is in compression in both multilayers as seen from the negative slopes of the F/w plots during Pt growth. Ni is in tension while the Pd layers exhibit only a very small tensile response and are virtually stress-free. The observed behavior is consistent with coherency stress, as the lattice parameter of Pt is larger than that of Pd and Ni. The average stress | in the individual layers is estimated from the average slope, and using Hooke’s Law, the average strain is given by m=
| , M(111)
(2)
where, M(111) is the biaxial modulus of the (111)-oriented film. The magnitudes of the layer strains thus calculated for the Pd/Pt and Ni/Pt multilayer are given in Table 1, along with the magnitudes of the misfit strains for Pt on Ni and Pd. The misfit strain is defined as mmisfit = Fig. 1. In-situ stress measurements during growth of Pd/Pt (\= 60 A, ) and Ni/Pt (\= 26 A, ) multilayers. Table 1 Magnitudes of the layer strains in the Ni/Pt and Pd/Pt multilayers calculated from Fig. 1, and the magnitudes of the total misfit strains A/B
mA (%)
mB (%)
mmisfit (%)
Pd/Pt Ni/Pt
0 0.37
0.8 1.94
0.84 10.2
aA − aPt , aPt
(3)
where aPt is the bulk lattice parameter of Pt and aA represents the bulk lattice parameter of Ni or Pd. The negligible stress in the Pd layer implies that Pd is growing on Pt that is compressively strained to match the Pd underneath, and the layers are fully coherent. The sum of the magnitudes of the strain in the Ni and Pt layers of the Ni/Pt multilayer is only a fraction of the total misfit, implying that a sigificant portion of the misfit is accommodated by misfit dislocations. In both multilayers, the magnitude of strain in Pt is larger than
V. Ramaswamy et al. / Materials Science and Engineering A319–321 (2001) 887–892
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surface and interface stresses, in addition to throughthickness film stress [13]. Surface stress contributions are strongest at small layer thickness and rapidly diminish with increasing thickness. However, other stress generating mechanisms (eg. coherency, atomic peening) may also be active in the small thickness regime, in which case the measured curvature change will be the net result of surface and layer stresses. In a separate study of the stress behavior of Pd/Pt multilayers [12], the effect on F/w of replacing a Pd surface with a Pt surface was determined to be a function of the form D(F/w)surface = A{1− exp(−Bt)},
Fig. 2. Superposition of the F/w behavior of Pt grown on a 100 A, thick Pd layer and a 30 A, thick Ni layer. The dashed curve is the Pt on Pd data, from which the effects of surface stress have been removed.
that in the other components, and as a result, the average stress in the multilayers is compressive (Fig. 1). This average compressive stress, ranging from 1.5 to 2 GPa is high enough to cause the film to debond from the substrate in samples made up of a large number of bilayers [9]. The Pt compressive stress is not solely due to coherency. Bombardment of the film surface by reflected neutral atoms, also known as atomic peening gives rise to compressive stress [10,11], possibly due to formation of point defects within the film. High atomic mass, low mobility metals like Pt are especially susceptible to this effect and the compressive stress in Pt has been observed to decrease considerably when the Ar pressure is increased [12]. Peening is also observed in Ni and Pd, but the effect is not as pronounced as in Pt. In the next section, the stress behavior of Pt grown to larger thickness on Ni and Pd will be discussed.
3.2. Pt stress beha6ior In Fig. 2, the stress evolution of Pt grown on 30 A, of Ni and 100 A, of Pd is superimposed. These layers were grown under the same conditions as the multilayers in Fig. 1. The initial stress behaviors of the Pt layers grown on Ni and Pd are exactly the same as those of the Pt layers in the corresponding multilayers. However, in this experiment, the Pt layers are grown to thicknesses of about 70 A, in order to obtain a more complete understanding of their mechanical behavior. The initial compressive stress in Pt grown on Pd is small, but soon increases, as seen from the increasing slope of the F/w plot in Fig. 2. This early trend is believed to be due to the surface stress difference between Pd and Pt. Substrate curvature can be caused by
(4)
where A and B are constants, and t is the layer thickness. As t increases, D(F/w)surface approaches A, which is the difference in surface stress of Pt and Pd and is determined to be about 2 N m − 1. Essentially, Eq. (4) describes the evolution of the coverage of the Pd underlayer as the Pt layer thickness increases; F/w reaches a constant value when the Pd is completely covered by Pt. The stress evolution of Pt on Pd after subtraction of surface effects is also shown in Fig. 2. In this plot, F/w changes almost linearly during the first 15 A, , after which the layer relaxes. Note that after the first few monolayers, the corrected F/w follows the same trend as the uncorrected data. In the Pt layer grown on Ni, a large change in F/w is observed during the first monolayer or so, after which a decrease in the slope is observed. This behavior is consistent with a high coherency stress, albeit not large enough to result in a fully coherent interface, as seen from Table 1. It is unlikely that the initial change in F/w is caused by a surface stress effect, since the surface energies of Pt and Ni are similar [14,15]. As in the Pt on Pd case, the stress in the Pt layer on Ni relaxes with increasing thickness. From the F/w plots its is clear that the Pt layer grown on Ni has a higher average stress compared to the Pt layer grown on Pd. In Fig. 3, the average stress in the Pt layers grown on Pd and Ni are plotted as a function of thickness and the stress relaxation of Pt on Pd and Ni is seen clearly. At very small thicknesses, compressive stress in Pt grown on Pd increases with thickness. This is probably due to fractional Pt coverage at small thicknesses. The maximum stress in Pt on Pd is around 5 GPa, and this stress level is maintained to a thickness of 14 A, before relaxation. The initial average stress in Pt on Ni is very high and relaxes rapidly to about 8 GPa at 8 A, , after which the relaxation rate drops. The difference in the initial stress levels is due to the higher lattice mismatch in the Ni/Pt case. The stress contribution from atomic peening, however, is likely to be similar in both cases. At 70 A, , Pt on Ni has an average stress of 3.4 GPa and Pt on Pd has an average stress of 2 GPa.
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3.3. TEM results Cross-section TEM images of Pd/Pt and Ni/Pt multilayers are shown in Fig. 4 and Fig. 5, respectively. In the lower magnification images the Pt appears darker than either the Ni or Pd due to electron density contrast and reveals the multilayer structure. Due to the negative enthalpy of mixing of both Ni/Pt and Pd/Pt systems, intermixing at the interfaces is likely [16]. As a result the boundaries between layers are somewhat diffuse. Higher magnification insets show that in the Pd/Pt sample there are no obvious dislocations, consistent with coherent interfaces, whereas in the Ni/Pt sample, several dislocations (highlighted on the image) are present. A simple calculation shows that an average misfit dislocation spacing of 35 A, in the Ni/Pt multiFig. 5. Cross-section TEM image of Ni/Pt multilayer (\= 40 A, ).
layer will accommodate the portion of the misfit not accommodated by elastic strain.
3.4. Strengthening mechanisms
Fig. 3. The average stress in the Pt layers in Ni/Pt and Pd/Pt multilayers plotted as a function of layer thickness. The solid curves are the Matthews – Blakeslee critical stress for Pt on Pd (A) and Pt on Ni (B). The dashed curve (C) is the critical stress for Pt on an elastically-matched substrate (the reference critical stress).
Fig. 4. Cross-section TEM image of Pd/Pt multilayer (\= 50 A, ).
Small film thickness itself is a barrier to dislocation motion, enabling very thin films to sustain high stresses. Other effects commonly observed are grain boundary strengthening, much like the Hall-Petch effect found in bulk polycrystalline materials (in polycrystalline films, grain sizes are on the order of the film thickness), elastic modulus mismatch between the film and substrate or film and passivation, causing dislocations to be repelled from the stiffer layers, thus inhibiting plasticity in the more compliant layers, and high dislocation densities resulting in stronger films due to dislocation interactions. The high stresses sustained by the Pt layers in both Ni/Pt and Pd/Pt multilayers are a measure of the high strengths of these layers. Pt grown on Ni is able to sustain a much larger stress than when grown on Pd, and is therefore stronger. The difference in strength cannot be ascribed to grain boundary strengthening, since the two structures have very similar grain size. The striking differences between the two pairs are lattice mismatch and elastic modulus mismatch. Lattice mismatch, which is very small between Pd and Pt and much larger between Ni and Pt, suggests that the higher density of misfit dislocations present in the Ni/Pt sample may result in dislocation strengthening of the Pt layer grown on Ni. TEM micrographs are consistent with this reasoning. Alternately, the differences in strength of the Pt layers may be due to the mismatch in elastic modulii between the layers. The shear modulus of Pt (61 GPa) is higher than that of Pd (44 GPa) and lower than that of Ni (76 GPa). Dislocations in the Pt layer will therefore be repelled from the Ni layer, and
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attracted to the Pd layer. Also, the energy cost of a dislocation near an interface, which depends on the modulii of both layers, is higher near a Ni/Pt interface. It was shown by Matthews et al. [17] that a film under a given strain must reach a critical thickness before a dislocation can spontaneously thread through the film, partially relieving the strain. This result has become known as the Matthews– Blakeslee critical thickness condition. Following a rigorous treatment of the stability of a threading dislocation by Freund [18], Nix [19] gives an expression for the critical stress |c, as a function of film thickness, at which a dislocation spontaneously threads through the film, |c = −
!
v it [b 21 +b 22 +(1 −6)b 23]ln 4ytb1(1− 6) b
"
1 − (b 21 +b 22) , 2
(5)
where b1, b2, and b3 are the components of the burgers vector, t is the film thickness, v and w are the film shear modulus and poisson’s ratio, respectively and i is a numerical constant of order one. For the present case of (111) oriented, FCC films with a {111} slip plane and a 110 Burger’s vector, the critical stress becomes [19] |c =
n
3vb it 3 (4 −6)ln − . 8y(1− 6)t b 2
(6)
In order to account for the different elastic modulii of the film (Pt) and substrate (Ni or Pd), v=2vf vs/vf + vs is used, where vf and vs are the shear modulii of the film and substrate respectively [2]. |c as a function of thickness is also shown for Pt on Pd, and Pt on Ni in Fig. 3, along with the measured average stress. The best match to the Pt stress data was obtained with i = 0.75 for the Pt on Pd case, and i =0.9 for the Pt on Ni case. The tensile stress predicted at low thickit nesses is unphysical, and is due to the ln term, as t b approaches the core cut-off radius. At thickness greater than 20 A, , there is very good agreement between the average stress obtained from curvature measurements and the critical stress model. The critical stress calculated using the modulus of pure Pt lies between that predicted for Pt on Ni and Pt on Pd, and is also shown in Fig. 3, as a reference critical stress. In Pd/Pt multilayers, even if all the misfit were accommodated by misfit dislocations, their spacing would be roughly 300 A, , and dislocation interactions would have little effect on the yielding behavior of Pt on Pd. In the Ni/Pt case, even though misfit dislocations are more closely spaced, the higher strength of Pt can be accounted for simply by the higher modulus of the Ni underlayer, and ignoring dislocation interactions. The effect of a stiff underlayer can also be quantified using the image force method to calculate the equilibrium
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distance of the misfit dislocation away from the interface [19]. From this analysis, the critical stress in a film with a very rigid substrate is found to increase by about 30% relative to the reference critical stress in the absence of elastic mismatch. The Matthews critical stress model discussed above, as well as the average stress data is consistent with such an increase in strength. From preliminary results of stress evolution in Cu/Pt multilayers (\= 40 A, ), Pt was observed to sustain compressive stress comparable to the stress of Pt on Ni. Cu and Pt have a high lattice mismatch (8%), but Cu has much lower shear modulus than Ni. For the case of Pt grown on Cu, the Matthews critical stress model used above would not predict high strength. It is speculated that the large stress sustained by Pt in this case is related to the large lattice mismatch resulting in a high misfit dislocation density. In calculating average stress from F/w, the Pt layer at all thicknesses is assumed to to be continuous, and uniformly thick. At very small thicknesses, neither of these assumptions is valid for the growth of a low mobility metal like Pt under the present growth conditions. Even after the Pt coverage is complete, it is likely that the layer is rough and the load-bearing thickness of Pt may be smaller than the average thickness used to calculate stress. Therefore, the stress sustained in the small thickness regime may be underestimated by the average stress plotted in Fig. 3.
4. Conclusions Significant compressive stresses are observed in Ni/Pt and Pd/Pt multilayers, with bilayer periods of a few tens of A, ngstroms. The overall compression is due to the large compressive stresses in the individual Pt layers. The Pt in the Ni/Pt case sustains significantly higher stress than in the Pd/Pt case. The large lattice mismatch between Ni and Pt will result in a high density of misfit dislocations. This is seen in the cross-section TEM image of the Ni/Pt multilayer. In contrast, the TEM results show that the Pd/Pt multilayer is almost dislocation free, consistent with the small lattice mismatch between Pd and Pt. The difference in dislocation densities suggests that the high stress in Pt on Ni, compared to Pt on Pd may be due strengthening as a result of dislocation interactions. The higher shear modulus of Ni relative to Pt increases the energy of a dislocation near the interface (or repels the dislocation), thus inhibiting plasticity in the Pt layer and increasing its strength. The lower shear modulus of Pd relative to Pt, on the other hand predicts weakening of the Pt layer. A simple Matthews critical stress model, in which dislocation interactions are not considered, but the shear modulii of the underlayers are taken into account, agrees remarkably well with the
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measured stress of Pt on both Ni and Pd. The difference in the stress and strengthening of Pt on Ni and Pd can therefore be fully explained by modulus strengthening due to the higher stiffness of the Ni underlayer, and dislocation strengthening appears to be negligible.
Acknowledgements The authors are grateful to Dr Harriet Kung of Los Alamos National Laboratory for the help and guidance provided during TEM sample preparation and imaging. Funding for this work, provided by the National Science Foundation through Grant No. DMR-9408552, is gratefully acknowledged.
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[4] B.J. Daniels, W.D. Nix, B.M. Clemens, Mater. Res. Soc. Symp. Proc. 356 (1995) 373. [5] B.M. Clemens, S.A. Barnett, H. Kung, MRS Bulletin 24 (1999) 20. [6] J.A. Floro, E. Chason, S.R. Lee, Mater. Res. Soc. Symp. Proc. 406 (1996) 491. [7] V. Ramaswamy, W.D. Nix, B.M. Clemens, Mater. Res. Soc. Symp. Proc. 505 (1998) 589. [8] V. Ramaswamy, B.M. Clemens, W.D. Nix, Mater. Res. Soc. Symp. Proc. 528 (1998) 161. [9] B.J. Daniels, W.D. Nix, B.M. Clemens, Mater. Res. Soc. Symp. Proc. 382 (1995) 315. [10] J.A. Thornton, D.W. Hoffman, Thin Solid Films 171 (1989) 5. [11] C. Hudson, R.E. Somekh, Thin Solid Films 171 (1989) 5. [12] V. Ramaswamy, W.D. Nix, B.M. Clemens, Unpublished results (1999). [13] F. Spaepen, J. Mech. Phys. Solids 44 (1996) 675. [14] P. Gumbsch, M.S. Daw, Phys. Rev. B 44 (1991) 3934. [15] D. Udler, D.N. Seidman, Mater. Res. Soc. Symp. Proc. 356 (1995) 373. [16] J.A. Bain, B.M. Clemens, S. Brennan, Mater. Res. Soc. Symp. Proc. 187 (1990) 315. [17] J.W. Matthews, S. Mader, T.B. Light, J. Appl. Phys. 41 (1970) 3800. [18] L.B. Freund, Adv. Appl. Mech. 30 (1994) 1. [19] W.D. Nix, Scripta Materialia 39 (1998) 545.