Fractal analysis of inorganic thin solid films with network structures

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I.Experimental procedure-Formation of Al/Ti Multilayr-The fractal island or network structure was deposited by dc magnetron sputtering. The cathodes used in the experiment were two 75mm diameter magnetrons equipped in an ultra high vacuum chamber pumped by a turbo molecular pump. Target materials were Al (99.99%) and Ti (99.98%). Substrates used were aluminobolosilicate glass. The discharge gas was Ar (99.9999%). Subatrate temperature was varied from 200C to 600C.In order to accelerate the formation of island structure of Al thin films, a Ti underlayr was deposited first on to the substrate, and then an Al layr was deposited sequentially on the Ti layr without breaking the vacuum. (The oxidation of the Ti surface deteriorated the formation of isolated Al island structures.) The thickness of the Ti underlayr was 500nm throughout all of the deposition, and that of the Al layr was changed from 10nm to 80nm.The surface morphology of the deposited films was analyzed by atomic force scanning … More probe microscope (AFM,Topo-Metrix : Type TMX-2000). The scan renge was 10mum squared with 300x300 digits. Fractal dimension of island or network dimension was obtained by a lake filling method from the digitized AFM data. Surface roughness, bearing ratio, average diameter of islands, and surface coverage were also obtained from the digitized AFM data.II.Experimental results-Surface morphology and Fractal dimension-It was found by AFM that isolated island structures with island's diameters ranging from about 0.5 to about 1mum were obtained for Al average thickness values of 20 to 40nm deposited at 550C.The large diameters of each island were the feature of the Al/Ti bilayr island stucture. For a further increase in the substrate temperature, the island shape form convex in the its center, then formed a network-like structure. The determination of fractal dimensions were tried for both island and network structure. The fractal dimension was well obtained for an island stucture, while it was not for a network shape by applying the lake filling method because of the complexity of the network shape.For the island structures, fractal dimensions of about 2.0 to 2.2 were obtained. The fractal dimensions of about 2.0 point that the island-structure-like film growth for these Al thickness values was two-dimensional growth where the fractal dimension was almost equal to the Euclidean dimension of 2 and where the geometrical similarity was kept. In addition the analysis showed that the distribution of the diameters of the islands was narrow in this region. As Al average thickness increased more, islands were connecting together, increasing a fraction of area covered by Al islands. In this Al thickness region, fractal dimensions were more than 2.5 and an Euclidean dimension did not define the stucture. In this region the geometrical similarity of the structure was not found, though the structure kept the statistical similarity.Although the fractal dimension was well determined for the network structure, the network structure was thought to be fractal because the structure was obtained by growing the island structure further at a higher temperature keeping the perimeter shapes of asch islands.III.ConclusionsThe Al/Ti bilayr films were deposited by dc magnetron sputtering.At a Al thickness of 20 to 50nm, Al islands structure obtained were fractal. By increasing the substrate temperature further, the network-like structure was obtained. The network-like structure was thought to be fractal although the fractal dimensions were well defined for the network-like structure because of its complexity that caused the difficulty to apply a lake filling method to obtain the dimension. Less