Infrared and Raman spectroscopic features of the self-interstitial defect in diamond from exact-exchange hybrid DFT calculations

Abstract

Quantum-mechanical calculations are performed to investigate structural, electronic, and Infrared (IR) and Raman spectroscopic features of one of the most common radiation-induced defects in diamond: the "dumb-bell" 100 split self-interstitial. A periodic super-cell approach is used in combination with all-electron basis sets and hybrid functionals of the density-functional-theory (DFT), which include a fraction of exact non-local exchange and are known to provide a correct description of the electronic spin localization at the defect, at variance with simpler formulations of the DFT. The effects of both defect concentration and spin state are explicitly addressed. Geometrical constraints are found to prevent the formation of a double bond between the two three-fold coordinated carbon atoms. On the contrary, two unpaired electrons are fully localized on each of the carbon atoms involved in the defect. The open-shell singlet state is slightly more stable than the triplet (the energy difference being just 30 meV, as the unpaired electrons occupy orthogonal orbitals) while the closed-shell solution is less stable by about 1.55 eV. The formation energy of the defect from pristine diamond is about 12 eV. The Raman spectrum presents only two peaks of low intensity at wave-numbers higher than the pristine diamond peak (characterized by normal modes extremely localized on the defect), whose positions strongly depend on defect concentration as they blue shift up to 1550 and 1927 cm −1 at infinite defect dilution. The first of these peaks, also IR active, is characterized by a very high IR intensity, and might then be related to the strong experimental feature of the IR spectrum occurring at 1570 cm −1 . A second very intense IR peak appears at about 500 cm −1 , which, despite being originated from a "wagging" motion of the self-interstitial defect, exhibits a more collective, less localized character.

Comparison between cluster and supercell approaches: the case of defects in diamond

“…The corresponding cluster has been denominated specifying that one C atom is missing or has been added: then, for instance, C 35−1 H 36 and C 35+1 H 36 indicate, respectively, a cluster with a vacancy or an interstitial defect. Cluster properties have been compared with those of supercells (S 128 ) containing, before the defect creation, 128 carbon atoms [39][40][41].…”

“…This combination has shown to provide accurate description of the properties of both regular and defective diamond. [39][40][41] In the cluster calculations, terminal hydrogen atoms have been described at the STO-3G [48] level. To increase the variational freedom in the vacancy region, the same C basis set has been placed at the vacancy site (see the GHOSTS option in the CRYSTAL manual [44] Fig.…”

“…Cluster SCF equations have been solved at the Γ point of the reciprocal lattice while 4 k-points in the irreducible part of the Brillouin zone (corresponding to a "shrinking factor" of 4) had been selected for the reference S 128 supercell calculations, see Refs. [39][40][41] for details. In geometry optimization two different procedure have been followed: in the former only the H atoms have been kept fixed at their initial positions and all C atoms have been fully relaxed (we refer to these clusters as FULL); in the latter approach only C atoms in the internal shells of the clusters have been relaxed, that means all C atoms not linked to H but also not at the border of the cluster (we refer to these clusters as FRAGMENT).…”

“…Pure diamond is characterized by a single Raman peak at 1332 cm −1 ; the same peak, computed within the periodic approach is at 1318 cm −1 , see Refs. [39][40][41] for a detailed discussion. However, when a cluster approach is adopted, spurious peaks due to border effects are expected.…”

“…Defect formation energies, atomic relaxations, band structure of the defect, relative energies of different spin states and Raman spectra are investigated as a function of the cluster size, and are compared directly with the results of wellconverged supercells calculations. [39][40][41]. This latter method involves a periodic array of unit cells of the host crystal containing the defect at the centre.…”