Surface morphology of GaAs during molecular beam epitaxy growth: Comparison of experimental data with simulations based on continuum growth equations

Abstract

Using atomic force microscopy and in situ elastic light scattering we show that the surface of molecular beam epitaxy ~MBE! grown GaAs tends towards an equilibrium roughness independent of the initial condition, as predicted by kinetic roughening theory. Two separate continuum growth equations are consistent with the observed equilibrium roughness, namely, the Kardar-Parisi-Zhang ~KPZ! equation ]h/]t5n„ 2 h1(l/2) 3(„h) 2 1h, where h is the surface height and h represents nonconservative noise, and the MBE equation ]h/]t52k„ 4 h2(L/2)„ 2 („h) 2 1h c , where h c represents conservative noise. These equations represent different physical smoothing mechanisms, so to distinguish between them we have numerically solved both equations. A novel geometric implementation of the nonlinear terms avoids instabilities associated with stiffness of the equations. We find that the time and length scale dependence of the smoothing of initially rough substrates is consistent with the KPZ equation but not the MBE equation. As the growth temperature is increased the coefficient n increases relative to l, but the KPZ description remains valid over the entire measured temperature range of 550‐600 °C. Reducing the As overpressure increases the anisotropy of the surface morphology. We provide a physical interpretation of the KPZ equation in which the incorporation rate of mobile adatoms on the surface is governed by evaporation/condensation type dynamics. These results provide important insight into the MBE growth mechanism of GaAs.