Density-functional-theory-based calculations of formation energy and concentration of the silicon monovacancy

By using first-principles calculations, we study the formation energy and concentration of the silicon monovacancy. We use large-scale supercells containing up to 1728 atomic sites and confirm the convergence of calculational results with respect to the cell size. The formation energy is calculated to be 3.46 eV, and the vacancy concentration at the silicon melting point is estimated to be 7.4 × 1016cm-3. These values are consistent with experimental results. We find that the vibrational effect significantly increases the vacancy concentration about 104 times.