Using ab initio total energy calculations we have studied the relation between the step atomic configuration and its properties (step energy, donor/acceptor behavior, and step interaction) on a ${\beta }_2(2\times 4)$ reconstructed GaAs (001) surface. The results have been tested against the widely used elastic dipole model for the step energy and step interaction considered valid for stress-free surfaces. We have found that acceptor-behaving steps have an attractive interaction and donor-behaving steps have a repulsive interaction in contrast with the elastic dipole model which predicts always a repulsive interaction between like-oriented steps. To account for the attractive interaction we consider the electrostatic dipole interaction having the $L^{-2}$ scaling with the step distance $L$ and therefore compatible with the standard elastic model. Using a model charge distribution with localized point charges at the step based on the electron counting model we show that the electrostatic step interaction can indeed be generally attractive and of the same order of magnitude of the negative elastic dipole interaction. Our results show however that the usually employed dipole model is unable to account for the repulsive/attractive step interaction between donorlike/acceptorlike steps. Therefore, the ab initio results suggest an important electronic contribution to the step interaction, at least at the short step distances accessible to the first-principles study. Our results explain qualitatively many experimental observations and provide an explanation to the step bunching phenomenon on GaAs(001) induced by doping or by critical growth conditions as due to the stabilization of attractively interacting step structures. These ideas would lead to the development of a bottom-up surface step engineering.

• Received 19 February 2014
• Revised 22 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.115314