Spatial distribution of hillocks in AlTa and AlCu alloy films

The differences in spatial distributions of thermally induced hillocks between AlTa and AlCu alloy films were studied in relation to microstructural features and stress relief mechanisms. The minimal spanning tree method was applied to quantitatively characterize the disordered spatial distributions. Two parameters, the average edge length m and the standard deviation σ, were derived to correlate the geometry of hillocks with their underlying formation mechanisms. While the average nearest-neighbor spacing between hillocks differed significantly, measuring 63.9 μm for the Al-2at.%Ta film and 2.5 μm for the Al-2at.%Cu film, the (m, σ)-diagram revealed that the geometry of hillocks was fundamentally similar and highly randomized. The grain sizes, measuring approximately 0.1 μm, were smaller than the average spacing between hillocks by one to three orders of magnitude. From a microstructural perspective, the observed hillock density was significantly lower than the frequency of potential hillock formation sites. The contribution of hillock formation to macroscopic stress relief accounted for approximately two-thirds of the total relaxed stress at 573 K in both alloy films. In addition, the area influenced by individual hillocks extended across the range represented by the spacing between hillocks. The spatial distributions with low hillock density in the AlTa films were attributed to higher thermal stresses at the onset of hillock formation. It is presumed that the high stress induced a sufficient stress gradient for long-range lateral diffusion beyond nearby potential hillock formation sites, resulting in the observed spatial distribution. • A novel minimal spanning tree approach for hillock study is presented. • Hillock geometry in Al alloy films exhibited similar distribution patterns. • Microstructural factors had no direct effect on selecting hillock nucleation sites. • A model linking stress relaxation to hillock density is demonstrated. • Dominant factors determining spatial distribution of hillocks are proposed.