Scaling properties of the shadowing model for sputter deposition

Abstract

We analyze a deterministic, one-dimensional solid-on-solid model for sputter deposition where the local growth rate is a function V(θ) of the exposure angle θ. For long times an algebraic height distribution N(h)∼${\mathit{h}}^{\mathrm{-}(1+\mathit{p})}$ develops, where the exponent p depends on the behavior of V(θ) close to θ=π and the extremal statistics of the substrate roughness. Analytic predictions for p, based on scaling arguments, are verified by large-scale simulations using a hierarchical algorithm.