We have developed a Green's function (GF) based multiscale modeling of defects in a semi-infinite Si-substrate. Point defects and substrate surface (i.e., extended defect) at two different scales are modeled in a unified manner. Behaviors of the point defects are solved within the theory of lattice statics. The technique is based on the Dyson's equation that relates a defect GF to a reference GF and on the asymptotic relationship of the reference lattice-statics GF (LSGF) to continuum GF (CGF) of the semi-infinite substrate. The reference LSGF is obtained approximately by solving the boundary-value problem of a super cell of lattice subject to a unit force and under a boundary condition given by the reference CGF. The Tersoff potential of Si, Ge and their compound is used to derive the lattice-Ievel force system and force constants and further to derive the continuum-Ievel elastic constants (needed in the reference CGF). The atomic potential is the only required experimental input in the formulation. We have numerically verified the asymptotic approach of the reference LSGF to reference CGF in the semi-infinite Si-crystal. Upon the verification of the scale-bridging technique, we have applied it to investigate the lattice distortion of a single vacancy and a single Ge-substitution. We have examined the interaction of these point defects with the substrate (free) surface and the interaction of a single vacancy with a relatively large Ge-cluster in the presence of substrate surface. The point defects are both attracted to the substrate surface in the first case. The vacancy is attracted to both the Ge-cluster and the substrate surface in the second case.
Citation: Intl. J. Solids Structures
Pub Type: Journals
continuum Green's function, Ge cluster in Si, lattice Green's function, multiscale model for Si, point defects in Si