Stable thin clathrate layers

We explore elemental Si, Ge and Sn free-standing slabs in diamond, clathrate and other competing structures and evaluate their stability by comparing Kohn-Sham total energies at the same atom/area coverage ρ. We find that within a 3-6 ML range (in units of diamond monolayers), the surface energy stabilizes clathrate thin films compared to the diamond slabs or other competitors, lowering the internal energy per atom, for all three elements. At 1.3-1.6 ML coverages, stable Si and Ge layers constitute adatomic decorations on the puckered honeycomb lattice, forming a dumbbell-decorated pattern with a rectangular unit cell. The analogous Sn layer transforms to a web-like net of interconnected Sn₉ clusters. The zoo of stable thin-layer non-diamond structures is completed by a metallic Sn bilayer at 2.3 ML coverage.