Theoretical determination of stable fourfold coordinated vacancy clusters in silicon

We have identified stable fourfold coordinated vacancy clusters (V(n)3 <= n <= 18) in Si using a combination of metropolis Monte Carlo, tight-binding molecular-dynamics, and density-functional theory calculations. Our calculations show that the small vacancy defects exclusively favor fourfold coordination thermodynamically rather than hexagonal ringlike structure formation, which has widely been adapted to explain the behavior and properties of vacancy defects. Among those examined, the fourfold V-12 cluster with S-22 symmetry is identified to be the most stable, yielding a formation energy of 1.16 eV per vacancy. The fourfold V-12 structure is about 4 eV more favorable than the conventional hexagonal ring structure. We also discuss how the relative stability between the fourfold and hexagonal ring configurations will change as the cluster size increases to greater than a few tens of vacancies.