Using a dynamical scaling form for the surface fractal dimension as well as efficient algorithms for the simulation and analysis of the surface in three-dimensional ballistic deposition, we show that while the top of the surface is self-affine, the complete surface including overhangs has fractal dimension $D_f\simeq 3.$ The existence of such a fractal surface is a consequence of the difficulty of closing off voids in three and higher dimensions. By studying a modified ballistic deposition model in which sticking is allowed with a given probability p, we show that the surface undergoes a phase transition from fractal to compact at a finite value of p. Our results also have implications for understanding the surface morphology in sedimentary rocks and low-temperature thin films.

• Received 10 October 2001

DOI:https://doi.org/10.1103/PhysRevE.65.060601