Ballistic deposition on surfaces

We consider several aspects of the irreversible deposition of particles on surfaces. We show by direct numerical simulation that the well-known ``tangent rule'' for the orientation of the columnar microstructure is only qualitatively correct. We demonstrate that the interface width of the deposit for normal incidence scales according to the hypothesis of Family and Vicsek. This means that the width scales as h${\ifmmode\bar\else\textasciimacron\fi{}}^{\ensuremath{\nu}}$ for short times and ${l}^{\ensuremath{\alpha}}$ for the steady state where h\ifmmode\bar\else\textasciimacron\fi{} is the mean height and l the width. We find by simulation \ensuremath{\nu}\ensuremath{\simeq}(1/3),\ensuremath{\alpha}\ensuremath{\simeq}(1/2) in two dimensions (2D) and \ensuremath{\nu}\ensuremath{\simeq}(1/4),\ensuremath{\alpha}\ensuremath{\simeq}(1/3) in 3D. We give an analytic treatment which maps the problem onto a spin model. We find \ensuremath{\nu}=(1/3),\ensuremath{\alpha}=(1/2) for 2D in agreement with our simulations but \ensuremath{\nu}=0,\ensuremath{\alpha}=0 for 3D.