Using a pseudopotential approach to density functional theory in ABINIT plane wave code [1] we performed a simulation of the antiphase boundaries (APB's) formation between islands on the clean Ge(100)2×1 and Si(100)2×1 surfaces. The calculations were carried out using LDA Troullier-Martins pseudopotentials for Si, Ge and H terminators, 1×2×1 k-point grid and 13 Ry cutoff energy. The unit cell used was 7 layers deep with the bottom layer terminated with hydrogen. The length of the cell was 2 dimer wide and from 2 to 8 dimer long to control the supercell size effects. The energy of the APB's formation is restricted to 0.15/0.2 eV depending on the length of the unit cell. For Ge(100)2×1 it is about 0.05 eV higher than for Si(100)2×1 surface. The APB's formation energy is shown to be strongly dependent on the orientation of the outermost dimers at the boundaries of the supercell. When the supercell has the even periodicity 2×2, 2×4, 2×6 and so on the outermost dimers at the boundaries of the supercell are oriented at the same manner: parallel or antiparallel. According to our calcutations the energy of APB's formation for supercell with antiparallel boundary dimers is higher by about 0.1 eV than that with parallel boundary dimers. Consequently the energy of the APB's formation for supercell of the odd periodicity is higher because the boundary dimers are oriented in the different manner: one pair is parallel when another one is antiparallel. The calculation of the electronic structure and born effective charges also agree with this results. Therefore the formation of the supercell of the even periodicity with parallel dimers at the boundaries is more preferable.
[1] First principles computation of material properties: the ABINIT software project, X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuch, G.-M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Joller et. al., Comput. Mater. Sci. 25, 478 (2002); www.abinit.org |