Through numerical calculations and Monte Carlo simulations, we examine the roughening behavior of a shadowing model, with lateral growth, for $\mathrm{}(2+1)\mathrm{}$-dimensional systems. The results show that the roughening growth exponent $\beta =1\mathrm{}$ for growth and $\beta =0\mathrm{}$ for etching. For the Monte Carlo simulation of the growth model, tall columns are formed, and the correlation length obeys $\xi \propto (t-t_0{)}^{1/z},$ with $1/z=0.93\pm \mathrm{0.1.}$ For the Monte Carlo simulation of the etching model, we obtain $1/z=0,$ and the height-height correlation function $H\left(r\right)\mathrm{}$ is proportional to $\log \mathrm{}\left(r\right)\mathrm{}$ for $r\ll \xi .$ The results are compared to previous computational studies of shadowing and to experimental studies of sputter deposition.

• Received 18 October 1999

DOI:https://doi.org/10.1103/PhysRevB.62.2118