Separation of film thickness and grain boundary strengthening effects in Al thin films on Si
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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 ^am 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~l, where g is the grain size, is more plausible than that predicted by the Hall-Petch relation (i.e., as g~m). The variations of these two components with temperature, and under tension and compression, are discussed.
I. INTRODUCTION Due to the effect of the rigid substrate to which it is bonded, the small grain size, and other thin film effects, the mechanical behavior of aluminum thin films is very different from that of bulk samples. The variation of stress with thermal cycling in such films and their isothermal stress relaxation characteristics have been well documented.1"10 It is expected to be greatly influenced by the thickness of the film, its grain size, and the presence of alloying elements. When a thin film of aluminum is thermally cycled on a rigid substrate such as silicon, the imposed thermal strain is accommodated as elastic and plastic strains in the film. By measuring stress as a function of temperature, with a wafer curvature technique one may obtain, at a given temperature, the flow stress of a thin film, which is the stress at which the film would deform plastically at that temperature. However, it is important to understand the conditions under which the flow stress can be obtained from the stress-temperature curves. At all temperatures, the strain relationship = 0
(1)
-AadT.
(2)
^thermal "•" ^elastic ~f~ -plastic
and thus de,elastic
de,plastic =
In a curve of stress versus temperature, provided there are no volume changes, the slope can never exceed the 2040 http://journals.cambridge.org
J. Mater. Res., Vol. 7, No. 8, Aug 1992 Downloaded: 26 Jan 2015
value [ £ / ( l — v)]Aa, where Ej{\ — v) is the biaxial modulus of the film, and A a is the difference in thermal expansion coefficients between the substrate and film. Only when the slope of the stress-temperature curve is significantly smaller than this elastic slope may the measured stress be called the flow stress. This is an inherent limitation in
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