Substitutional nitrogen in diamond: A quantum mechanical investigation of the electronic and spectroscopic properties

Abstract

This paper reports the fully-relaxed lattice and electronic structures, vibrational spectra, and hyperfine coupling constants of the substitutional Ns defect in diamond, derived from B3LYP calculations constructed from all-electron Gaussian basis sets and based on periodic supercells. Mulliken analyses of the charge and spin distributions indicate that the defect comprises a single unpaired electron distributed very largely over both the negatively-charged substituted site and one of the four nearest-neighbour carbon sites, which relaxes away from the impurity. This leads to a local C3v symmetry, with the nitrogen ‘lone pair’ lying along the C3 axis and pointed towards the ‘dangling’ bond of the shifted carbon neighbour. The calculated band gap is 5.85 eV, within which a singly-occupied, majority spin donor band is found ∼2.9 eV above the valence band, and an unoccupied, minority spin acceptor band ∼0.9 eV below the conduction band. Atom-projected densities of states of the donor and acceptor levels show that, contrary to a widespread description, ∼30% only of the donor band derives from nitrogen states per se, with the majority weight corresponding to states associated with the shifted carbon atom. The defect formation energy is estimated to be ∼3.6 eV. The calculated IR spectrum of the impurity centre shows several features between 800 and 1400 cm−1, all of which are absent in the perfect crystal, for symmetry reasons. These show substantial agreement with recent experimental observations. The calculated hyperfine constants related to the coupling of the unpaired electron spin to the N and C nuclei, for which the Fermi contact terms vary from over 200 MHz to less than 3 MHz, are generally in good agreement with the largest experimental values, both in terms of absolute magnitudes and site assignments. The agreement is less good for the smallest two values, for which the experimental assignments are less certain. The results lend support to previous suggestions that some of the weaker lines in the observed spectra, notably those below ∼7 MHz, which are difficult to assign unambiguously, might result from the overlap of lines from different sites.