Scaling analysis of surface roughness in simple models for Molecular-Beam Epitaxy

There is currently interest in simple models for molecular-beam epitaxy (MBE) which mimic the effect of thermal mobility by allowing immediate incorporation of deposited atoms at kink sites within a distance l of the deposition site. Scaling of the interface width, W, with mean film height, [h], of the form W approximately [h]beta, is analysed. Studies for a solid-on-solid geometry in d = 1 + 1 dimensions revealed a sudden transition from the T = 0 K (l = 0) behavior of beta = 1/2 to a new universality class for l greater-than-or-equal-to 1 with beta = 3/8. We consider the effect of incorporating realistic adsorption-site geometries and deposition dynamics into these d = 1 + 1 MBE models. We find that beta is always less than 3/8 at T = 0 K (l = 0) due to lateral coupling, and that the effective beta increases smoothly with smaller l at least to 3/8. However, for larger l, the simple scaling of W described above breaks down in the physically relevant range of [h]