Intrinsic stresses in compositionally modulated Au-Ni thin films and the supermodulus effect
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The stresses that arise in compositionally modulated Au-Ni thin films as a result of the constraint of the substrate were determined from the curvatures of micrometer-scale bilayer cantilever beams consisting of a silicon dioxide layer upon which the metal film had been deposited. These substrate interaction stresses were found to vary strongly with the wavelength of the composition modulation. Simulations of the bulge test show that such stresses can account for the major features of the "supermodulus effect" as artifacts of the analysis method. I. INTRODUCTION
Extremely large (>100%) enhancements from ruleof-mixtures (ROM) values in the elastic stiffness of certain thin metal compositionally modulated thin films (CMF's) have been reported.1"6 These enhancements have been dubbed the "supermodulus effect" and exhibit the following characteristics: (i) elastic moduli that approach ROM values as the wavelength of the composition modulation, A, becomes large, with increases of 100% or more occurring as either single or bimodal peaks at composition wavelengths near 2 nm1'3"6; (ii) nonlinear "elastic" behavior in the enhanced modulus regime1'3'4; and (iii) elimination of the stiffness enhancement by annealing.1"6 In particular, in some cases the magnitude of the enhancement was observed to vary with the square of the composition amplitude.1-3'4'6 The elastic properties of a material are determined by the type and density of atomic bonds within the material and are therefore generally insensitive to changes in microstructure at constant composition. Furthermore, while it is possible to reduce stiffness (e.g., by incorporating extremely high defect densities), significant increases in stiffness were previously neither predicted nor observed. Thus, these reports of the "supermodulus effect" stimulated a great deal of theoretical and experimental work. As reported elsewhere,7 we observe three general types of results in the reported experimental work: (i) "supermodulus" results—all obtained by mechanical deflection methods, (ii) a single small (on the order of 10%) minimum in stiffness at A = 2 nm—until recently7 detected only by phonon velocity measurements, and (iii) no variations with A—the most common result, obtained by both mechanical deflection and phonon velocity techniques. We focus here on the results in the first category. These include bulge tests
a)Present
address: Max-Planck-Institut fur Metallforschung, Institut fiir Werkstoffwissenschaft, SeestraBe 92, 70174 Stuttgart, Germany. J. Mater. Res., Vol. 9, No. 12, Dec 1994 http://journals.cambridge.org
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of Au-Ni and Cu-Pd,1 Ag-Pd 3 and Cu-Ni, 4 vibrating reed,2-5 and torsional pendulum5 tests of Cu-Ni, as well as tension tests of Cu-Ni 5 and Cu-NiFe.6 We have also studied Au-Ni CMF's using two mechanical deflection techniques: nanoindentation and cantilever beam deflection.7 We detected no "supermodulus effect." In fact, we obtained results of type (ii), a "small" minimum in stiffness at A ~ 1.6 nm, by both methods. We did, however, ob
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