The surface morphology of ${\mathrm{Cl}}_2$-etched GaAs(001) is measured as a function of etch time by atomic force microscopy and elastic light scattering. A flat surface is found to become rougher during the etch whereas a textured substrate becomes smoother. We have numerically simulated this behavior. It is found that the evolution of surface roughness at length scales between 50 nm and $5\hspace{0.5em}\mu \mathrm{m}$ can be described with excellent accuracy by a continuum equation for the surface height $h(\overrightarrow{x},t),$ which is given by $dh/dt=\nu {\nabla }^{2}h-\lambda /2(\nabla {h)}^2-K{\nabla }^{4}h+\eta ,$ where $\eta$ is a random noise input.

• Received 29 September 2001

DOI:https://doi.org/10.1103/PhysRevB.65.155315