Partitioning the vibrational spectrum: Fingerprinting defects in solids

Abstract

Vibrational spectroscopy techniques are some of the most-used tools for materials characterization. Their simulation is therefore of significant interest, but commonly performed using low cost approximate computational methods, such as force-fields. Highly accurate quantum-mechanical methods, on the other hand are generally only used in the context of molecules or small unit cell solids. For extended solid systems, such as defects, the computational cost of plane wave based quantum mechanical simulations remains prohibitive for routine calculations. In this work, we present a computational scheme for isolating the vibrational spectrum of a defect in a solid. By quantifying the defect character of the atom-projected vibrational spectra, the contributing atoms are identified and the strength of their contribution determined. This method could be used to systematically improve phonon fragment calculations. More interestingly, using the atom-projected vibrational spectra of the defect atoms directly, it is possible to obtain a well-converged defect spectrum at lower computational cost, which also incorporates the host-lattice interactions. Using diamond as the host material, four point-defect test cases, each presenting a distinctly different vibrational behaviour, are considered: a heavy substitutional dopant (Eu), two intrinsic point-defects (neutral vacancy and split interstitial), and the negatively charged N-vacancy center. The heavy dopant and split interstitial present localized modes at low and high frequencies, respectively, showing little overlap with the host spectrum. In contrast, the neutral vacancy and the N-vacancy center show a broad contribution to the upper spectral range of the host spectrum, making them challenging to extract. Independent of the vibrational behaviour, the main atoms contributing to the defect spectrum can be clearly identified. Recombination of their atom-projected spectra results in the isolated spectrum of the point-defect.