Three-dimensional ballistic deposition at oblique incidence

A simple lattice model has been used to investigate (2+1)-dimensional ballistic deposition for angles of incidence θ in the range 0°≤θ<90°. In the oblique-incidence limit (θ→90°) a pattern of overlapping scales inclined at an angle of about 37.5° is formed. The individual scales can be characterized in terms of their characteristic length, width, and thickness which grow algebraically with increasing scale size. All of the scaling exponents characterizing the growing surface can be obtained from exponents ${\mathrm{\sigma }}_{\mathit{x}}$=1/3 and ${\mathrm{\sigma }}_{\mathit{y}}$=2/3 that describe the growth of the correlation lengths ${\xi }_{\mathit{x}}$ and ${\xi }_{\mathit{y}}$ parallel and perpendicular to the plane of incidence. The scaling properties of the columnar patterns can be understood in terms of the (1+1)-dimensional dynamics of the leading edges of the advancing scales. An anisotropic generalization of the finite-size scaling form of Family and Vicsek [J. Phys. A 18, L75 (1985)] is proposed and its validity is demonstrated for ballistic deposition at near-grazing incidence.