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Grain growth and the puzzle of its stagnation in thin films: The curious tale of a tail and an ear

: Barmak, Katayun; Eggeling, Eva; Kinderlehrer, David; Sharp, Richard; Ta'asan, S.; Rollett, Anthony D.; Coffey, Kevin


Progress in Materials Science 58 (2013), No.7, pp.987-1055
ISSN: 0048-5500
ISSN: 0079-6425
Journal Article
Fraunhofer Austria ()
simulation and modeling; materials research; mathematics

The underlying cause of stagnation of grain growth in thin metallic films remains a puzzle. Here it is re-visited by means of detailed comparison of experiments and simulations, using a broad range of metrics that, in addition to grain size, includes the number of sides and the average side class of nearest neighbors. The experimental grain size data reported is large and comprises nearly 35,000 grains from 27 thin film samples of Al and Cu with thicknesses in the range of 25-158 nm. The size distributions for the Al and Cu films are remarkably similar to each other despite the many and significant differences in experimental conditions, which include sputtering target purity, substrate type, film thickness, deposition temperature, actual as well as homologous annealing temperatures, annealing time, absolute grain size, and the twin density within the grains. This similarity argues for a universal experimental grain size distribution, which for grain diameters is lognormal as found previously for thin films at stagnation. Comparison of the experimental grain size distribution with that for two dimensional grain growth simulations with isotropic boundary energy shows the distributions to differ in two regions, termed the "ear" and the "tail". It is shown that the excess small grains in the region of the "ear" are primarily the 3 and 4-sided grains, whereas the excess of large grains in the "tail" region are grains with more than nine sides. The excesses in the ear and tail regions of the experimental distributions are necessarily balanced by a deficiency in the mid-sized grains with 6-8 sides. Five causes are examined to identify the puzzling difference between simulations with isotropic boundary energy and experiments. These are (i) driving forces other than grain boundary energy reduction, (ii) anisotropy of grain boundary energy, (iii) grain boundary grooving, (iv) solute drag and (v) triple junction drag. No single cause is seen to provide an explanation for the observed experimental behavior. However, it is speculated that a combination of causes that include the anisotropy of grain boundary energy will be needed to explain the experimental behavior.