DOI: 10.1007/s00339-007-4303-3 Appl. Phys. A 90, 457–463 (2008)
Materials Science & Processing
Applied Physics A
tong hong wang1,2 te-hua fang3 yu-cheng lin1,u
Finite-element analysis of the mechanical
behavior of Au
/Cu and Cu/Au multilayers
on silicon substrate under nanoindentation
1Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan, R.O.C. 2Thermal Laboratory, Advanced Semiconductor Engineering, Inc., Kaohsiung 811, Taiwan, R.O.C. 3Institute of Mechanical & Electromechanical Engineering, National Formosa University, Yunlin 632,
Taiwan, R.O.C.
Received: 2 July 2007/Accepted: 21 September 2007 Published online: 30 October 2007 • © Springer-Verlag 2007
ABSTRACTFinite-element analysis of the nanoindentation into Au/Cu and Cu/Au multilayers was performed to deduce their mechanical characteristics from nanoindentation response. Dif-ferent bilayer thicknesses, numbers, and sequences were studied using the load–displacement curve, hardness, indentation, and the residual surface profile as well as the von Mises equiva-lent stress. The characteristics of the multilayers were found to be dispersed between the Au and Cu. Nevertheless, if the in-dentation depth is smaller than the uppermost individual layer thickness of the multilayers, the intrinsic properties can be obtained. Using the von Mises equivalent stress as a failure cri-terion, the results showed that thinner multilayers would induce a greater potential of shear banding deformation.
PACS61.43.Bn; 62.20.-x; 68.03.Hj; 68.05.Cf; 68.08.De
1 Introduction
Recently, multilayered thin films have created much interest due to their enhancing mechanical proper-ties [1–5]. These multilayered thin films may be potential candidates for protecting, isolating, or other applications. Multilayered thin films prepared by the sputtering process can be a combination of metal, semiconductor, alloy, and other materials. For ease of fabrication, most multilayered studies only focus on bilayer or trilayer repeats. There are a number of low mutual solubility multilayered thin films like Cu/Ni, Ag/Ni, Au/Cu, and others, which produce sharp interfaces and do not form intermetallic compounds [1]. This is prefer-able for a basic study since intermetallic compounds may bring unknown mechanical properties.
Ruud et al. [1] measured the hardness and the elastic mod-ulus of the Ag/Ni multilayered thin films, whose properties lie between those of homogeneous Ag and Ni thin films. They found a decrease in modulus at the smallest repeated length. Barshilia and Rajam [2] discovered that the hardness of the Cu/Ni multilayered thin films, with a total film thickness ranging between 68 and 90 Å, was enhanced by a factor of 2.5 times the rule of mixture. This enhancement in hardness is at-u Fax: +886-6-276-2329, E-mail: yat-uclin@mail.nckat-u.edat-u.tw
tributed to the arrest of the propagation of dislocations along the interfaces and a large number of interfaces in the mul-tilayered coatings. Nevertheless, the hardness and effective Young’s modulus of TiN/(Ti,Al)N multilayers [3] exhibited slightly higher values than monolithic TiN. This is thought to be due to either the higher covalence of the bonds in the (Ti,Al)N layer or a hardening effect related to the large num-ber of interfaces which are present in the coating. Zhang et al. [4] demonstrated that the plastic deformation instability in Au/Cu multilayers becomes prevalent when the length scales of grains and the individual layer thickness of the multilay-ered composite approach the nanometer regime. However, the indentation depth of more than the total thickness of the multilayers must induce a large boundary effect from the sub-strate, bringing the intrinsic combined mechanical behaviors of Au/Cu multilayers in doubt.
Numerous compositions of layers have been studied for their mechanical behaviors. However, the study of the ef-fects of different multilayer thicknesses, repeated numbers, and repeated sequences are insufficient, not to mention studies on the plastic-induced residual surface profile after indenta-tion. This lack of research is mainly due to the high cost of both time and fabrication for such a large number of different combinations of multilayered thin films. To estimate the me-chanical behavior of this particular structure, finite-element analysis (FEA) remains the preferred tool for the direct and economic way it provides to predict the mechanical response from the pre-set load. In the present study, we investigate nanoindentation on Au/Cu multilayers on silicon substrates of different bilayer thicknesses, numbers, and sequences by means of FEA. These low, mutually soluble multilayers were chosen because of the sharp interfaces, which can be ana-lyzed numerically. The load–displacement curve, hardness, indentation, and residual surface profile, as well as von Mises equivalent stress are examined and compared in the present paper.
2 Finite-element modeling
The simulated sample in this study consisted of Au/Cu multilayers lying on a cylindrical silicon substrate. The diameter and the thickness of the silicon substrate are 7µm and 10 µm, respectively. The Au/Cu multilayers have an identical individual layer thickness. A 1.5-µm-height
462 Applied Physics A – Materials Science & Processing
monly used to investigate the possibility and the location of mechanical failures. Among them, the von Mises equivalent stress,σeqv, is defined by
σeqv= 1 2 (σ1− σ2)2+ (σ2− σ3)2+ (σ3− σ1)2 , (5)
where σ1, σ2, and σ3 are the 1st, 2nd, and 3rd principal
stresses, respectively. Yielding occurs when the equivalent stress exceeds the yield stress of the material, i.e.σeqv> σy.
Figure 8 shows the contour plots of σeqv on the
multi-layers after unloading of the test structures a and d with
n(Cu/Au)/Si and n(Au/Cu)/Si, respectively. For n(Cu/Au)/ Si with the test structures a and d, Fig. 8a, the maximumσeqv
occurs around the bottom surface of the uppermost Cu layer right beneath the indenter at both test structures. This is ac-ceptable because of the smaller yield stress of Cu compared to that of Au. Thus, Cu will show a larger plastic deforma-tion at an earlier stage. Compared to all these, the test structure
ewith 50-nm-thickλ and 20n has the highest σeqv, while the
test structure a with 1000-nm-thickλ and 1n is the lowest. This implies that a smallerλ induces a greater σeqvand causes
earlier failure and possibly the initiation of shear banding de-formation at the surface. Moreover, there is a significant band of σeqv discontinuity among the multilayers at the location
we circled in Fig. 8. This discontinuity, however, could be re-alized in that the layers cannot easily move or slide in the in-plane direction owing to the limitation of different neigh-boring layers. In the meantime, in-plane plastic instability de-formation is suppressed. Nevertheless, the slanted band tends the out-of-plane deformation, known as shear banding [19], has the potential of occurring. These trends are similar to the experimental observations of Zhang et al. [4] in that the shear banding becomes more prevalent with the decrease in individ-ual layer thickness.
For n(Au/Cu)/Si with test structures a and d, Fig. 8b, the maximumσeqvoccurs at the indented edge of the Au layer and
around the bottom surface of the Cu layer at the second upper-most layer, respectively. Here, the test structure a is different from that of n(Cu/Au)/Si since, at such shallow (100-nm) indentation, the plastic deformation remains within the 500-nm-thick upper Au layer. For λ decreasing to 50-nm-thick individual layers of the test structure d, the softer second Cu layer beneath the uppermost Au layer suffers the maximum
σeqv. Again, a significantσeqv discontinuity among
multilay-ers occurs.
The corresponding maximumσeqvafter unloading for
dif-ferent test structures are summarized in Fig. 9. By comparing the maximumσeqvon multilayers among the test structures, it
is evident that the maximumσeqvof bulk Au and bulk Cu are
the smallest compared to the others and the maximumσeqvof
bulk Cu is smaller than that of bulk Au. Nevertheless, all of the maximumσeqvwere greater than their yield stress, i.e.
yield-ing developed. There is an obvious trend for the maximum
σeqv to increase whenλ decreases, which indicates that the
thinner multilayers possess a greater potential for shear band-ing. Moreover, when comparing sequences with identical λ and n, the von Mises stresses of n(Au/Cu)/Si’s are generally smaller than those of n(Cu/Au)/Si’s. However, the difference
FIGURE 9 Maximumσeqvon multilayers after unloading for different test structures, bulk Au and bulk Cu
is quite small whenλ is sufficiently thin, say 50-nm λ in the present study.
4 Conclusion
In this work, we investigated the mechanical char-acteristics of Au/Cu and Cu/Au multilayers. These multi-layers had an identical total multilayer thickness of 1µm with bilayers of different thicknesses, different numbers of bilayers, and different sequences on a silicon substrate by means of FEA. One-tenth of the total multilayer thickness, 100 nm, was chosen as the nanoindentation depth in order to prevent the substrate effect. Load–displacement curves, hardness, indentation, and residual surface profiles of Au and Cu multilayers were generally scattered between those of bulk Au and bulk Cu. For the two different bilayer se-quences, the intrinsic behavior on the uppermost layer of the multilayers was similar to its bulk material for indentation depths that were smaller than its thickness. Furthermore, it was found that thinner multilayers will induce a greater von Mises stress and a significant band of stress discontinuity, in-dicating there is a greater potential for shear banding to take place.
ACKNOWLEDGEMENTS The authors would like to thank the National Science Council of Taiwan for the partial financial support under Grant Nos. NSC95-2221-E150-033 and NSC95-2221-E150-066.
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