Continuum strain of point defects

Abstract

We propose a new Regularized Green's Function Method (RGFM) derived from electron densities and captures the disturbance due to point defects, successfully extending the elastic strain determination to the lattice scales. The RGFM circumvents the use of concentrated point forces, which results in unrealistic singular fields. The objective is to determine the force variations at the atomic scales from Ab-initio calculations as Quantum Mechanical Force Density (QMFD). QMFD encodes the information regarding the electronic structure of the defect since it is related to the gradients of electron wavefunctions generated from the Density Functional Theory (DFT) calculations. Once the QMFD is calculated, RGFM solves the force equilibrium equation via Fourier transforms to compute elastic fields. Therefore, the present treatment reflects the electronic structure of the atomic positions, hence the complex elastic deformations and interactions at short range, which represents a significant advancement compared to previous studies. The RGFM can also capture the long-range fields since it calculates the decay of the force fields away from the nuclei. Previous theories, such as the elastic dipole method, face two main shortcomings: they can only handle the long-range elastic fields, and contain an unphysical singularity at the center of the point defect. Our novel derivation of distributed forces addresses both challenges, i.e., it renders non-singular displacement and strain fields at the nuclei, and can also describe the elastic response accurately far from the nuclei center. The application of the method to the NV (nitrogen-vacancy) center in SiC is demonstrated in comparison with the elastic dipole theory, showing the advantages of the present methodology.