Multiscale modeling of point defects in Si-Ge(001) quantum wells

A computationally efficient hybrid Green's function (GF) technique is developed for multiscale modeling of point defects in a trilayer lattice system that links seamlessly the length scales from lattice (subnanometers) to continuum (bulk). The model accounts for the discrete structure of the lattice including nonlinear effects at the atomistic level and full elastic anisotropy at the continuum level. The model is applied to calculate the discrete core structure of point defects (vacancies and substitutional impurities) in Si-Ge(001) quantum wells (QWs) that are of contemporary technological interest. Numerical results are presented for the short range and long range lattice distortions and strains in the lattice caused by the defects and their formation energy and Kanzaki forces that are basic characteristics of the defects. The continuum and the lattice GFs of the material system are used to link the different length scales, which enables us to model the point defects and extended defects such as the quantum well in a unified formalism. Nonlinear effects in the core of the point defects are taken into account by using an iterative scheme. The Tersoff potential is used to set up the lattice structure, compute the unrelaxed forces and force constants in the lattice, and derive the elastic constants required for the continuum GF. It is found that the overall elastic properties of the material and the properties of defects vary considerably when the material is strained from the bulk to the QW state. This change in the defect properties is very significant and can provide a characteristic signature of the defect. For example, in the case of a single vacancy in Ge, the strain reverses the sign of the relaxation volume. It is also found that the defect properties, such as the defect core structures, change abruptly across a Ge/Si interface. The transition occurs over a region extending from two to four lattice constants, depending upon the defect species.