Development of the Microplasticity Theory of Internal Friction and its Application to the Evaluation of Thin-Film Mechanical Properties

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Internal friction in aluminum, copper and gold thin films on silicon substrates has been measured as a function of strain amplitude at various temperatures by means of a free-decay method of flexural vibration. According to the constitutive equation, the internal friction in the film can be evaluated separately from the measured damping of the composite system. The amplitude dependence for the aluminum and copper films is found in the strain range one or two orders of magnitude higher than that for the bulk. On the basis of the microplasticity theory, the amplitude-dependent internal friction can be converted into the plastic strain as a function of effective stress on dislocation motion. The stress-strain responses thus obtained for the aluminum and copper films show that the plastic strain of the order of 10^<-9> increases nonlinearly with increasing stress. The curves tend to shift to a higher stress with decreasing film thickness and also with decreasing temperature, both of which means a suppression of the microplastic deformation. The microflow stress at a constant level of the plastic strain varies inversely with the film thickness at all temperatures examined. The film thickness effect for the aluminum and copper films can be explained on the basis of a dislocation-bowing model. In contrast, the microflow stress for the gold films decreases with decreasing film thickness when the film thickness is less than 0.5 μm, which could be due to the stress relaxation caused by surface-grain boundary diffusion. It is found that, for the gold films covered by titanium films, the microflow stress varies inversely with the film thickness although the stress level is lower than that for the aluminum films.