Theoretical study of isolated dangling bonds, dangling bond wires, and dangling bond clusters on a H:Si(001)-(2x1) surface

We theoretically study the electronic band structure of isolated unpaired and paired dangling bonds (DBs), DB wires, and DB clusters on H:Si(001)-(2x1) surface using extended Huckel theory and report their effect on the Si band gap. We show that an isolated unpaired DB introduces a near-midgap state, whereas a paired DB leads to pi and pi(*) states, similar to those introduced by an unpassivated asymmetric dimer (AD) Si(001)-(2x1) surface. On the other hand, the surface state induced due to an unpaired DB wire in the direction along the dimer row (referred to as [(1) over bar 10]) has a large dispersion due to the strong coupling between the adjacent DBs, being 3.84 A apart. However, in the direction perpendicular to the dimer row (referred to as [110]), the DBs are 7.68 A apart and there is a reduced coupling between them due to exponential dependence of the wave function, leading to a small dispersion. Moreover, a paired DB wire in the [(1) over bar 10] direction introduces pi and pi(*) states similar to those of an AD surface, but with a large dispersion, and a paired DB wire in the [110] direction exhibits surface states with a smaller dispersion, as expected. Besides this, we report the electronic structure of different DB clusters, which exhibit states inside the band gap that can be interpreted as superpositions of states due to unpaired and paired DBs.