The growth of hillocks and voids in metal films was studied. The applicability of a model involving fractals and kinetic equations was examined on the basis of whether there is independent justification for using scaling arguments in the model and whether there is reason to connect the evolution of hillocks with that of voids. Hillocks and voids were found to be self-similar across about three orders of magnitude of variation in spatial scale with the same fractal dimension. Voids and hillocks were found to have the same fractal dimension whether studied using atomic force microscopy (AFM) or scanning electron microscopy (SEM). The parameters obtained from these fractal analyses demonstrate quantitative internal consistency with an earlier time dependent study of thermal annealing effects on hillock distributions. Remarkably, area-perimeter data obtained from either a long-time study of a single void or a spatial average of a large number of different voids both yield quantitatively identical results.
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Chaiken, J., Goodisman, J., Villarica, R.M. et al. AFM/SEM Study of Thermally Induced Hillock Coalescence. MRS Online Proceedings Library 356, 489–494 (1994). https://doi.org/10.1557/PROC-356-489