Interstitial nitrogen and its complexes in diamond

Nitrogen, a common impurity in diamond, can be displaced into an interstitial location by irradiation. The resultant interstitial defects are believed to be responsible for a range of infrared and electronic transitions that vary in thermal stability, and on the type of diamond. Of particular prominence, and the only center for which an atomistic model has been suggested, is the $H1a$ infrared band, which has previously been correlated with the vibration of isolated, bond-centered interstitial $\mathrm{N}$. We present the results of a local-density-functional investigation of interstitial $\mathrm{N}$ and a range of complexes made up from $\mathrm{N}$ and self-interstitials. We disagree with the previous assignment of $H1a$ to bond-centered interstitial $\mathrm{N}$ as we find it is not the ground state structure and it is mobile at temperatures at which $H1a$ is stable. Instead we assign $H1a$ to a complex of two $\mathrm{N}$ atoms sharing a single site in a [001]-split configuration, which is both more stable than isolated interstitial $\mathrm{N}$ and can simultaneously explain the infrared absorption and dependence on the aggregation stage of $\mathrm{N}$ in the irradiated material. We also make tentative assignments for other optical systems thought to involve interstitial $\mathrm{N}$, and suggest schemes for hierarchical formation of complexes for Ia and Ib material.

Figure 1

The (b) [001]-oriented split-interstitial and (c) bond-centered configurations of ${\mathrm{N}}_i$. Black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$, respectively. (a) shows the corresponding section of defect-free diamond for comparison, and the dashed lines indicate the cubic axes.

Figure 2

Schematic representation of ${\mathrm{N}}_s$ and $I$ in (a) nearest-neighbor, (b) next-nearest-neighbor, and (c) and (d) third-neighbor sites with different orientations. Circle shading as in Fig. 1, with the addition of white circles highlighting the $\mathrm{C}$ atoms in the split interstitial in each case. Threefold coordinated $\mathrm{C}$ atoms are indicated with the heavy black circles. The vertical and horizontal axes are approximately [001] and [110], respectively.

Figure 3

Kohn-Sham eigenvalues in the vicinity of the band gap for ${\mathrm{N}}_i$-related defects. (a) ${\mathrm{N}}_s^{+}$, (b) ${\mathrm{N}}_s^0$, (c) $I$, (d) $I^{\text{–}}$, (e) [001]-oriented ${\mathrm{N}}_i$, (f) ${\mathrm{N}}_s$ neighboring $I$, (g) ${\mathrm{N}}_s$ and $I$ second neighbors, and (h) ${\mathrm{N}}_s$ and $I$ third neighbors. The valence-band top is at 0 eV, and the gray-shaded areas represent bulk bands. Arrows indicate occupied levels and their spin and white circles indicate empty levels. The calculated band gap of 4.2 eV is typical of the method.

Figure 4

(a) suggested trajectory for ${\mathrm{N}}_i$ in diamond. Black and white circles represent $\mathrm{C}$ and $\mathrm{N}$, respectively. (b) is the saddle point structure.

Figure 5

Barrier to convert Fig. 1b into Fig. 1c. The $x$ axis is the constraint as discussed in the text. The computed data are indicated by black circles. The line joining the data is to guide the eye.

Figure 6

An illustration of the LVM’s of ${\mathrm{N}}_{i,\left[001\right]}$. Black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$, respectively, the arrows the direction of displacement for the core atoms in each mode, and the dashed lines the cubic axes.

Figure 7

Schematics of ${\mathrm{N}}_i\text{−}{\mathrm{N}}_s$ complexes. (a) [001]-oriented split-interstitial, (b) and (c) nearest-neighbor ${\mathrm{N}}_i\text{−}{\mathrm{N}}_s$, (d) second-neighbor pair, (e) and (f) third-neighbor pairs. Shading and orientation are as defined in Fig. 2.

Figure 8

A possible scheme for the migration of ${\mathrm{N}}_i\text{−}{\mathrm{N}}_s$. Black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$, respectively. All atoms plotted are within a single $(1\overline{1}0)$ plane.

Figure 9

Schematics of the low-energy forms of ${\mathrm{N}}_i\text{−}I$ found in this study. (b), (c) and (d) are analogous to the $R1$, Humble, and $\pi$-bonded di-interstitial structures, respectively. Black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$ atoms. (a) shows a section of defect free diamond for comparison.

Figure 10

A possible scheme for the migration of ${\mathrm{N}}_i\text{−}I$. Black and white circles represent $\mathrm{C}$ and $\mathrm{N}$, respectively. All atoms plotted are within a single $(1\overline{1}0)$ plane, except in the case of the second step where the right-hand split-interstitial (indicated by the gray atoms) is aligned approximately along [010].

Figure 11

Kohn-Sham levels in the band gap for ${\mathrm{N}}_i\text{−}I$ in various charge states. (a)–(c): Humble, +1, 0, and –1; (d) and (e): $\pi$ bonded, +1, and 0; (f)–(h): $R1$, +1, 0, –1; (i) partially dissociated ${\mathrm{N}}_i\text{−}I$ pair, made up from ${\mathrm{N}}_{i,\left[001\right]}$ and $I$ similarly oriented and separated by two host sites. Notation as Fig. 3.

Figure 12

Schematics of the low energy forms of ${\mathrm{N}}_i\text{−}{\mathrm{N}}_i$ found in this study. (b), (c), and (d) are analogous to the $R1$, Humble, and $\pi$-bonded di-interstitial structures, respectively. Black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$ atoms, respectively. (a) shows a section of defect-free diamond for comparison.

Figure 13

A possible scheme for the migration of ${\mathrm{N}}_i\text{−}{\mathrm{N}}_i$. Black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$, respectively. All atoms plotted are within a single $(1\overline{1}0)$ plane.

Figure 14

Schematic representation of (b) ${\mathrm{N}}_i\text{−}{\mathrm{N}}_i\text{−}I$ and (c) ${\mathrm{N}}_i\text{−}{\mathrm{N}}_i\text{−}I2$. The black and gray circles represent $\mathrm{C}$ and $\mathrm{N}$ respectively. (a) shows the corresponding section of defect free diamond for comparison, and the dashed lines indicate the cubic axes.