Space groups and lattice dynamics of Ge/Si superlattices grown in the [001] direction

Abstract

Ge l Si n superlattices grown along [001] appear in four different space groups: T d 2( l= n=1), D 2h 5( l, neven), D 2d 9( l, nodd), and D 4h 19( l + nodd). They thus give rise to a rich variety of optical phonon symmetries at k = 0. We illustrate the properties of these phonons with lattice dynamical calculations based on Keating parameters. Because two of the types mentioned (D 2h 5, D 4h 19) are centrosymmetric, they generate mutually exclusive Raman and ir-active phonons. For the orthorhombic case (D 2h 5) the transverse optical phonons split even at k = 0.