Kinetic Roughening in the Molecular Beam Epitaxy Growth in the Presence of Long-Range Temporal Correlations

Abstract

To study the effects of long-range temporal correlations on kinetic roughening of the molecular beam epitaxy (MBE) growth systems in both \((1+1)\)- and \((2+1)\)-dimensions, we adopt fast fractional Gaussian noise (FFGN) technique to generate temporally correlated noise to the continuum growth equations including Mullins–Herring (MH) and Villain–Lai–Das Sarma (VLDS), and the typical discrete growth models including Das Sarma–Tamborenea (DT) and Wolf–Villain (WV) with slight modifications. Extensive numerical simulations on these continuum and discrete growth systems are performed in the presence of long-range temporal correlations, and the scaling exponents are obtained correspondingly. We find that these correlated growth systems exhibit high dependence on the temporal correlation exponent within the large temporal correlated regimes, and there exist non-trivial scaling properties in the correlated DT and WV models. Our results also show that the scaling exponents in these linear and nonlinear MBE growth equations are in good agreement with the theoretical predictions. Furthermore, the saturated surface morphologies are compared qualitatively through simulating numerically these continuum and discrete growth systems in the presence of long-range temporal correlations. Generally, as the temporal correlation exponent increases, the surface heights of these correlated discrete and continuum growth systems exhibit evident increasing trends. Likewise, with the temporal correlation exponent increasing, the surface morphologies of the modified DT and WV models undergo a gradual transition from self-affine hills to sharp peaks, while the growing surfaces of the correlated MH and VLDS equations gradually become relatively smooth.