Microstructure and surface scaling in ballistic deposition at oblique incidence

Scaling properties of two-dimensional ballistic deposits grown at near-grazing angles of incidence are investigated analytically and numerically. We map the problem onto a system of coalescing Brownian particles and derive exact values for the static and dynamic surface exponents, ζ=1 and z=2, and for the exponents characterizing the self-affine columnar microstructure, τ=(4/3, ν=(2/3, and ${\nu }_{\perp }$=(1/3. This implies that the average column width increases as the square root of the deposit thickness. The distribution of surface step heights and the angular variation of the deposit density are also obtained analytically. The predictions are confirmed by large-scale computer simulations. Qualitative arguments are given to explain the slow crossover behavior at intermediate angles of incidence, which leads to apparently continuously varying scaling exponents. The substructure exponents for deposits grown at normal incidence are derived from a general scaling relation. We find τ=(7/5, νd∥=(3/5, and ν⊥=(2/5, in agreement with previous numerical work.