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

利用弯曲振动的自由衰减方法，测量了硅衬底上铝、铜和金薄膜的内摩擦在不同温度下作为应变幅值的函数。根据本构方程，膜内的内摩擦可以从复合材料系统的测量阻尼中分离出来。在应变范围内，铝和铜薄膜的振幅依赖性比块体的要高一到两个数量级。根据微塑性理论，可以将随幅值变化的内摩擦转化为有效应力对位错运动的函数。铝膜和铜膜的应力应变响应表明，随着应力的增加，10^<-9>数量级的塑性应变呈非线性增加。随着膜厚的减小和温度的降低，应力曲线趋向于向高应力方向移动，这意味着微塑性变形受到抑制。在所有测试温度下，恒定塑性应变水平下的微流应力与薄膜厚度成反比。铝和铜薄膜的厚度效应可以用位错弯曲模型来解释。当膜厚小于0.5 μm时，金膜的微流应力随膜厚的减小而减小，这可能是由于表面晶界扩散引起的应力松弛所致。结果表明，对于钛膜覆盖的金膜，微流应力随膜厚呈反比变化，但其应力水平低于铝膜。

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.