Phonons in Si-Ge systems: An ab initio interatomic-force-constant approach

The vibrational properties of Si-Ge systems are studied theoretically with ab initio techniques. Full dispersion relations for pure silicon and germanium crystals under several (homogeneous and epitaxial) strain conditions are obtained from interatomic force constants (IFC's). High-symmetry vibrations for a few short-period ordered superlattices (SL's) are studied from first principles as well. In order to study conveniently more complicated systems, such as partially disordered SL's or homogeneous SixGe1-x alloys, higher-order IFC's have been obtained that account for the first-order change in the IFC's of a reference system because of chemical disorder and lattice relaxation. With our scheme we can easily handle quite large supercells while keeping the same accuracy as a complete first-principles calculation, which we demonstrate for the homogeneous alloy.