Periodic arrays of large hexagonal tiles (up to 170 Å in size) are observed on $\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{e}(111)$ surfaces. First-principles total energy calculations combined with scanning tunneling microscopy reveal a (5-7-5)-ringed structure for the trenches that separate the tiles. We find that trenches form via an exothermic process. The calculated equilibrium trench spacing of $\sim 104\AA$ agrees with experiment. Comparison between first-principles calculations and continuum elasticity theory suggests that the observed mesoscopic reconstruction is driven entirely by long-range surface strain relaxation.

• Received 4 February 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.076103