Be and Be-related impurities in diamond: density functional theory study

TL;DR

This study uses first-principles density functional theory to dissect Be incorporation in diamond, comparing interstitial Be$_i$, substitutional Be$_s$, and Be–N co-doped complexes. It shows Be$_s$ is energetically preferred over Be$_i$, but all Be-related defects face sizable formation energies; nitrogen co-doping dramatically stabilizes Be-containing complexes, with Be$_s$–N$_3$ and Be$_s$–N$_4$ forming shallow donors near the conduction band, suggesting a viable path toward $n$-type diamond. The work also characterizes interstitial Be reorientation barriers and Be$_s$’s acceptor behavior, and provides comprehensive hyperfine tensors to guide experimental identification. Overall, Be–N co-doping emerges as a promising strategy to tailor diamond’s electronic properties, potentially enabling practical $n$-type diamond devices.

Abstract

First-principles density functional simulations were employed to investigate the geometries, electrical properties, and hyperfine structures of various beryllium-doped diamond configurations, including interstitial (Be$_i$), substitutional (Be$_s$), and beryllium-nitrogen (Be-N) complexes. The incorporation of Be into the diamond lattice is more favorable as a substitutional dopant than as an interstitial dopant, although both processes are endothermic. Interstitial Be could potentially exhibit motional averaging from planar to axial symmetry with an activation energy of 0.1 eV. The most stable Be$_s$ configuration has $T_{d}$ symmetry with a spin state of $S=1$. Co-doping with nitrogen reduces the formation energy of Be$_s$-N$_{n}$ $(n=1-4)$ complexes, which further decreases as the number of nitrogen atoms increases. This is attributed to the smaller covalent radius of nitrogen compared to carbon, resulting in reduced lattice distortion. Be$_s$-N$_3$ and Be$_s$-N$_4$ co-doping introduces shallow donors, while Be$_s$ exhibits $n$-type semiconductivity, but the deep donor level renders it impractical for room-temperature applications. These findings provide valuable insights into the behavior of beryllium as a dopant in diamond and highlight the potential of beryllium-nitrogen co-doping for achieving $n$-type diamond semiconductors.

Figures (6)

• Figure 1: (Colour online) Schematic structures of the substitutional Be configurations. Grey and red spheres represent C and Be, respectively (a) off-axis C$_{s}$, (b) off-axis C$_{2}$, (c) C$_{2v}$, (d) BC-$D_{3d}$, (e) H-$D_{3d}$ and (f) T$_d$. Transparent sticks indicate broken bonds.
• Figure 2: (Colour online) The Kohn-Sham band structure in the vicinity of the band gap for Be$_i$ 64 supercell. Filled and empty circles show filled and empty bands, respectively, with the bands from the defect-free cell superimposed in full lines for comparison. The energy scale is defined by the valence band top at zero energy ($E_v = 0 \hbox{,eV}$).
• Figure 3: (Colour online) Geometry structures of the interstitial Be defects. (a) and (b) describes the bond centered configuration Be$_{i,oa1}$ with different orientation.
• Figure 4: (Colour online) (a) Schematics for Be$_s$ ($T_d$). Grey and red spheres represent C and Be, respectively. (b) Band structure for Be$_s$ configuration. Filled and empty circles show filled and empty bands, respectively. The energy scale is defined by the valence band top at zero energy.
• Figure 5: (Colour online) Unpaired electron Kohn-Sham functions for Be-N$_3$ complex.