Surface growth in a model of molecular-beam epitaxy with correlated noise

Publisher Website
Google Scholar
Abstract
We study the effect of correlated noise on a model of molecular-beam epitaxy (MBE), in which desorption and formation of defects can be neglected. The MBE growth model is described by a random deposition process in which the deposited particles can relax to kink sites maximizing the number of saturated bonds. With only Gaussian white noise, the growth exponent β, defining the interface width W∼tβ at intermediate time t, is known to be β=38. We have solved exactly a continuum model and have determined the surface growth exponents α and β, in the presence of spatially and temporally correlated noise of the form 〈η(x,t)η(x′,t)〉∼|x-x′|2ρ-d′|t-t′|2θ-1, where d′ is the interface dimension and ρ and θ are the noise correlation parameters. Direct simulation of this noise spectrum in a (1+1)-dimensional model confirms our theoretical predictions. Agreement between theory and simulation in this more general case of correlated noise lends further support to the correspondence between the continuum model on which the theory is based and the discrete lattice models that are closer to experimental situations.