Fractal Aggregates in Sputter-Deposited NbGe2Films

Abstract

Fractal-like structures have been observed in sputter-deposited thin films of NbGe2. These structures exhibit a striking resemblance to those produced by computer simulations of diffusionlimited aggregation using the Witten-Sander model. An effective fractal dimensionality of about 1.9 has been determined from digitized photomicrographs. Our results indicate a two-stage growth process in which an initial structure with a fractal dimensionality of about 1.7 is thickened by a subsequent growth process.PACS numbers: 06.30.Bp, 61.10.Fr, 81.15.Cd Sputter deposition has come into use over the past twenty years as a major technique for preparing thin films for a variety of applications. Many materials and metastable phases not otherwise obtainable as thin films have been produced by this process. One of the major concerns with all thin films is the morphology of the surface, since it often strongly influences the electrical characteristics of devices made with such films.Recently considerable interest has also developed in a wide variety of growth and aggregation models. This work was stimulated by the discovery by Witten and Sander 1 that a simple diffusion-limited aggregation model in which particles are added, one at a time, to a growing cluster of particles via random-walk trajectories leads to scale-invariant structures with a fractal dimensionality 2 (D) which is considerably smaller than the Euclidean dimensionality of the space in which the growth process is occurring. Two-dimensional simulations lead to structures with a fractal dimensionality of about 1.7. 2 ' 3 This paper reports the existence of fractal-like structures on the surface of sputterdeposited NbGe 2 films and correlates their fractal dimensionality with the results of simulations to provide hypotheses for the growth mechanisms.In 1978, a unique sputter-deposition process was developed at the Naval Research Laboratory to produce films of Nb 3 Ge. This process initially produced films of NbGe 2 with a previously unobserved surface structure. Complex clusters were visible on the surface under an optical microscope at magnifications of a few hundred. Figure 1 shows a digitally reproduced image of a photomicrograph from one of these films. Changing the sputtering conditions to produce the desired material eliminated the surface features, and study of this phenomenon languished. Our interest in these systems was recently revived by the striking visual similarity between the surface structure found in the Nb-Ge thin films and pictures of twodimensional simulations of diffusion-limited aggrega-tion. 1,3 ' 4 This led to the hope that information concerning the mechanisms which yielded the structures might be obtained from a more quantitative analysis.The films were prepared by rf reactive sputtering of a niobium target in a mixture of argon and germane gases at pressures less than 100 mT. The quartz substrates were heated to 840 °C during deposition by a carbon-fiber-heated Mo table. The temperature was measured with an infrared pyrometer focused on th...

Microstructural evolution of oxides and semiconductor thin films

“…This model neither correlates the fractal patterns with the microstructure in detail nor systematically considers the dependence of the fat fractal patterns on the annealing temperature and time or the film thickness ratio, and nor systematically considers the dependence of fractal growth on the nanocrystals formation. In previous studies [55,148,238,244,246,[267][268][269][270][271][272][273][274][275][276][277][278][279][280][281][282][283], we found that the mechanism of the fractal formation in metal/semiconductor bilayer films is completely different from DLA mechanism. Fox example, Hou and Wu [244,273] suggested that the appearance of fractal-like patterns in Si-ion-implanted amorphous Ge/ Au (abbreviated as a-Ge/Au) bilayer films after annealing was due to the Random-Successive Nucleation (RSN) of polycrystalline Ge grains, while they deposited Au at first and then Ge without breaking the vacuum, and the thickness of polycrystalline Au and amorphous Ge films was about 25 and 30 nm, respectively, (the total thickness of the bilayer films was about 55 nm).…”

“…Moreover, the sample annealed at 70 min with the lower fractal dimension value has higher number of fine branches and larger fractal size. Such behavior is not completely consistent with the theories based on diffusion-limited aggregation and previous experimental observations [245,[267][268][269]. In DLA model, Witten et al found that the DLA is an idealization of the process by which matter irreversibly combines to form dust, soot, dendrites, and other random objects in the case where the rate-limiting step is diffusion of matter to the aggregate.…”

“…57a and b show TEM bright-field images of Au/a-Ge bilayer film annealing at 100°C for 60 and 70 min, respectively. It is clear that the films present the fat fractal patterns comparing with the fractal patterns from DLA [245,267,268]. The fractal pattern average sizes are about 0.43 lm (see Fig.…”

“…Witten et al demonstrated in their classic work that a fractal pattern can be formed when random walkers join a seed by the hit-and-stick model without any relaxation [245]. Since then, much effort has been devoted to study the fractal growth by diffusion-limited aggregation (DLA) model [236,239,[267][268][269][270][271][272]. To date, little effort has been devoted to understand the precise formation mechanism for fat fractal patterns in metal/semiconductor bilayer films after annealing.…”

Control over the wettability of amorphous carbon films in a large range from hydrophilicity to super-hydrophobicity

“…Sputtering is a simple and useful technique for preparing thin films with expected structure and properties, and recently, the growth of some interesting fractal aggregates on solid surface were also studied by this process [16,17]. In the present work, a-C films were prepared by magnetron sputtering on substrates as Si (1 0 0) and glass, without any special pretreatment.…”