Effects of the ehrlich-schwoebel protential barrier on the wolf-villain model simulations for thin film growth

Abstract

Recently, there are many studies on kinetic surface roughening in Molecular Beam Epitaxy (MBE) growth. Wolf-Villian (WV) model is proposed as a simple limited mobility model to study ideal MBE growth. In this model, adatom is deposited at a randomly chosen site on a one dimensional substrate. The adatom then diffuses instantaneously within a finite diffusion length and it tries to maximize its coordination numbers or its bondings. We study statistical properties of the morphology and surface width (the root mean square height fluctuation) of thin films grown according to this model. The morphology is kinetically rough surface with no mound formation. The surface width gives a growth exponent β ≈ 0.37 and a roughness exponent α≈ 1.40. These exponents are used to identify the universality class of the WV model. In real MBE growth, there exists a potential barrier known as an Ehrlich-Schwoebel (ES) barrier. The ES barrier is a step-edge potential barrier for the adatom diffusing over a step edge from upper to lower terraces. We study the effect of the ES barrier on the WV model. It has been found that the morphology is rough with mound formation on the surface. The growth exponent in this situation increases with the value of β approaching 0.5. To confirm these results, the particle diffusion current and the correlation function are also studied. We find the uphill current and the oscillation of correlation function. These results confirm that the ES barrier is a cause of mound formation on the surface in our study.