Peculiar Electronic Structure of Decavacancy V₁₀ in Si Crystal

The electronic structure created by an atomic vacancy, called V₁₀, in silicon crystals is investigated by first-principles calculations based on the density-functional theory. The remixing of dangling bonds of silicon atoms adjacent to the vacant sites creates four deep levels in the band gap, and an unexpected result was obtained for these dangling-bond states: wave functions with nodes have lower energy than wave functions without nodes. This completely contradicts the textbook statement that "wave functions with more nodes have higher energy than wave functions with fewer nodes by the amount of kinetic energy." Detailed analysis reveals that this peculiar electronic structure is generated by the interaction between the rebond states buried in the valence and conduction bands and the dangling-bond states in the band gap. We argue that the Jahn-Teller instability of the atomic structure of this system reflects this seemingly strange electronic structure. We also argue that large-scale ab initio calculations with 2000 Si atoms were essential for this discovery.