Performance and stability of optical and electron devices are sensitive to material issues such as the presence of various defects in the solid. Lattice defects induce strain fields in the lattice, which affects the mechanical stability and therefore the materials reliability of the solid. The strain field also affects the electronic reliability and device performance by distorting the electronic wave functions. Moreover, aggregation and the concentration profile of neutral as well as charged defects in solids are partly determined by the long-range strain-field interaction between defects and by the interaction of defects with the free surfaces and interfaces in solids. A precise knowledge of the strain field due to defects is required for defect engineering of semiconductors that involves control and manipulation of defects for design of novel devices. This explains the renewed topical interest in modeling of vacancy and associated lattice defects in semiconductors such as nano and bulk diamonds, used in quantum computers and other devices. Defect systems of special interest are pairs of lattice defects such as V-V (vacancy-vacancy), Si-V (silicon-vacancy) and N-V (nitrogen-vacancy) in diamond.
Modeling of defect pairs in a lattice is essentially a multiscale problem because of the long range nature of their strain field. The model must account for the disctrete atomistic structure of the lattice near the defect, along with the extended structure of the surfaces/interfaces. Standard density functional theory can be very reliable for solid state simulations because, in principle, it does not depend upon phenomenological parameters. However, it is computationally limited to small crystallites containing a few hundred atoms, which may introduce spurious size effects in strain calculations.
In our calculations, we use our multiscale lattice statics Green’s function method for modeling of defects. This method is computationally very efficient and can simulate several million atoms on an ordinary desktop computer. One advantage of the Green’s function method is that it can be formulated in ‘modules’ of increasing complexity. We first consider a single mono-vacancy, and then a single di-vacancy in diamond. In the final stage, we introduce an interstitial defect such as silicon or nitrogen and an extended defect such as a free surface. The vacancies are assumed to be neutral. We calculate the elastic strain field due to isolated defects and the strain field interaction between the defect and a free surface. In the presentation, we will describe the multiscale Green’s function method along with its limitations, and its application to modeling of lattice defects with actual numerical results for diamond.