After deposition of rare-earth elements (Dy, Tb) on Si(111) at elevated temperatures, a formerly unknown $\left(2\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }$ reconstruction is observed by low-energy electron diffraction, while scanning tunneling microscopy measurements exhibit a $\left(\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }$ reconstruction. On the basis of density-functional theory calculations, the structure of the larger unit cell is explained by periodically arranged subsurface Si vacancies. The vacancy network in the first subsurface layer has a $\left(\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }$ periodicity, while strain is released by a $\left(2\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }$ Si vacancy network in the second subsurface layer. In addition, this vacancy network forms quasi-one-dimensional structures (striped domains) separated by periodically arranged antiphase domain boundaries. The diffraction spot profiles are explained in detail by kinematic diffraction theory calculations, and average domain widths are deduced.

• Received 14 July 2016
• Revised 1 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.205431