Separation of film thickness and grain boundary strengthening effects in Al thin films on Si

We have measured stress variations with temperature as a function of film thickness and a given grain size in pure Al and Al–0.5% Cu films on Si substrates. The variation in thickness for a given grain size is brought about by using the same film and the repeated controlled growth and dissolution of a barrier anodic oxide which can be grown uniformly on the film. Stress measurements were made as a function of temperature by measuring wafer curvature after successively removing each 0.1 μm of Al film. The components of strengthening due to the film thickness and the presence of grain boundaries were separated by assuming that the flow stress of the film is simply the sum of these two components. It is found that strengthening due to film thickness varies inversely with the thickness, which is consistent with results obtained by us using laser-reflowed films in an earlier work. The Hall–Petch coefficients calculated from the strengthening due to the grain boundaries are slightly higher than those reported for bulk Al. However, it is also recognized that the variation of the flow stress as g⁻¹, where g is the grain size, is more plausible than that predicted by the Hall–Petch relation (i.e., as g^−1/2). The variations of these two components with temperature, and under tension and compression, are discussed.