Electron paramagnetic resonance of sulfur at a split-vacancy site in diamond

In natural diamonds a sulfur-related paramagnetic center labeled W31 has been previously tentatively assigned to an interstitial sulfur species in a positive charge state. However, we show by combining an assessment of available experimental data and density-functional simulations that the hyperfine tensors can be attributed to a defect made up from sulfur at the center of a divacancy, the so-called split vacancy, in the negative charge state. These acceptors are highly likely to be formed in S-implanted material and are a likely cause for high resistivity in material implanted with sulfur in the attempt to produce $n$-type conduction.

Figure 1

(Color online) Road map (angular variation of spectral line positions) for $\left(01\overline{1}\right)$ from [100] through [111] to [011]. All four $C_{3v}$ sites (threefold axes along [111], $\left[1\overline{1}\overline{1}\right]$, $\left[\overline{1}\overline{1}\text{l}\right]$, and $\left[\overline{1}1\overline{1}\right]$: EPR is not sensitive to inversion) have three off-axis neighbors with $C_{1h}$ symmetry relative to a {110} plane. One of these symmetry planes for each $C_{3v}$ site contains [100]. Their road maps correspond to the thick lines. The others are shown by thin lines. The $C_{3v}$ sites are indicated by (red) continuous lines for [111], (green) dashed lines for $\left[1\overline{1}\overline{1}\right]$, and (blue) dot-dash-dot lines for both $\left[\overline{1}1\overline{1}\right]$ and $\left[\overline{1}\overline{1}1\right]$ which are superimposed. The number of superimposed lines is shown adjacent to the lines and crossing points. The thick (red) continuous, (blue) dot-dash-dot, and (green) dashed lines at the center show the angular variation because of the anisotropy of $B\left(\alpha \right)$ for the central lines due to sites without any ${}^{13}\text{C}$ neighbor. Although this road map was generated using the ${}^{13}\text{C}$ hyperfine parameters given by Ref. 36 for three off-axis nearest neighbors in $C_{3v}$ sites, the road map would be identical for the six nearest-neighbor sites in $V\text{S}V$ (with $D_{3d}$ symmetry) with the same hyperfine parameters, as these neighbors are related in pairs by inversion symmetry in the S atom site.

Figure 2

Schematic structures of (a) ${\text{S}}_s^{+}$, (b) ${\text{S}}_i$, (c) ${\text{S}}_s\text{−}I$, and (d) $V\text{S}V$. Dark and light atoms are C and S, respectively, and the cubes indicate the underlying cubic lattice of diamond.

Figure 3

(Color online) Kohn-Sham bands in the vicinity of the band gap along high-symmetry directions of the first Brillouin zone of a 216-atom supercell containing (a) ${\text{S}}_s^{+}$ and (b) ${\left(V\text{S}V\right)}^{-}$. Filled (green) filled circles show occupied levels and empty (red) circles show empty bands. Black lines are defect-free bands. The zero of energy is defined as the valence-band top of diamond.

Figure 4

(Color online) Electron density for the unpaired electrons in (a) ${\text{S}}_s^{+}$ and (b) ${\left(V\text{S}V\right)}^{-}$. Dark and light atoms are C and S respectively.

Figure 5

(Color online) Schematics of (a) ${\text{S}}_s^{+}$ and (b) ${\left(V\text{S}V\right)}^{-}$ showing the ${}^{13}\text{C}$ sites and arrows showing the directions of the hyperfine tensor elements listed in Table in each case.