We developed a rigorous and exhaustive method for calculating the 0 K surface phase diagram of Bi/GaAs(001) by using density functional theory in conjunction with the cluster expansion formalism. In a search for ground-state alloy configurations of low energy surface structure prototypes, we found that the $(2\times 1)$, $\alpha 2(2\times 4)$, and $\beta 2(2\times 4)$ structures possess only a few stable configurations, though each is stable over a wide range of chemical potential. In contrast, the $c(4\times 4)$ and $(4\times 3)$ structures exhibit many stable configurations, suggesting their tendency towards configurational disorder at finite temperature. Monte Carlo simulations confirm a continuous disordering of the $(4\times 3)$ reconstruction with increasing temperature that comes to completion well below typical MBE growth conditions, in contrast to the $(2\times 1)$ structure, which remains ordered at high temperature. The calculated zero Kelvin phase diagram and finite temperature Monte Carlo results are in excellent agreement with STM in this work and experimental observations seen elsewhere. Furthermore, these results provide important insights into challenges posed by growth of GaAsBi alloys, namely Bi incorporation, CuPt${}_B$ ordering, and Bi clustering.

• Received 16 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.035313