Theory of boron aggregates in diamond: First-principles calculations

It is well known that nitrogen forms aggregates in diamond. However, little is known regarding aggregation of boron, an impurity that can be incorporated in very high concentrations. In this paper we present the results of first-principles calculations regarding the structure and properties of boron-aggregates, and simple complexes with native defects. We find that certain complexes are shallower acceptors than ${\mathrm{B}}_s$, and that pairs of boron interstitials, suggested as having a role in the recently observed low-temperature superconduction in B-doped diamond, are unstable and do not provide the shallow acceptor states required.

Figure 1

Diffusion of ${\mathrm{B}}_s$. (b) and (c) show ${\mathrm{B}}_s$ and saddle point structures, with (a) being a defect free section of diamond for comparison. Black and white circles represent C and B atoms, respectively.

Figure 2

Structures of ${\mathrm{B}}_s\text{−}{\mathrm{B}}_s$ for the first six shells of neighbors. Black and white circles represent C and B atoms, respectively. There are $n_m$=4, 12, 12, 6, 12, and 24 equivalent versions of (1)–(6), respectively.

Figure 3

Calculated ${\mathrm{B}}_s\text{−}{\mathrm{B}}_s$ acceptor levels for various separations $\left[R\right({\mathrm{B}}_s\text{−}{\mathrm{B}}_s\left)\right]$, relative to the computed level of ${\mathrm{B}}_s$. The inset shows a schematic one-electron picture for the combination of ${\mathrm{B}}_s$ acceptor states, with $\Delta$ showing the increase in the acceptor level due to the interaction.

Figure 4

Schematic structures for ${\mathrm{B}}_{n}V$, $n=1,2,3$ and 4 in diamond, (b)–(e). Black and white circles represent C and B, respectively, and the dashed lines are the cubic axes. (a) shows a section of defect-free diamond for comparison.

Figure 5

Kohn-Sham eigenvalues for ${\mathrm{B}}_{n}V$, $n=1,2,3$, and 4 in diamond. Arrows and circles represent filled and empty levels, respectively, and the shaded areas represent the valence and conduction bands of pure diamond.

Figure 6

Schematic of ${\mathrm{B}}_{1}V$ migration. Black gray and white circles represent B, C and vacant sites in a hexagonal ring.

Figure 7

Schematic of ${\mathrm{B}}_s\text{−}{\mathrm{B}}_i$ pairs in diamond. (b) $C_{2v}$, [110]-oriented split-interstitial, (c) $D_{2d}$, [001]-oriented split-interstitial, and (d) a planar ${\mathrm{B}}_s\text{−}{\mathrm{B}}_i$ complex. (a) shows the comparable section of defect free material. Colors and axes are as in Fig. 4.

Figure 8

Schematic of ${\mathrm{B}}_i\text{−}{\mathrm{B}}_i$ pairs in diamond. (b) $C_{2h}$ (R1), (c) $C_{2v}$ (3H), (d) $C_{2h}$ ($\pi$-bonded) and (e) $C_2$ structure obtained from relaxing two T-site ${\mathrm{B}}_i$ defects. (a) shows the comparable section of defect free material. Colors and axes are as in Fig. 4.