Geometric construction of large dynamical matrices: Applications to reconstructed surfaces, superlattices and mixed crystals

Abstract

We present a very straightforward procedure to calculate the dynamical matrix of an extended-cell system, on the grounds of the force constants pertaining to a smaller unit cell. This method, outlined here for the first time, allows for a computer-operated construction of the dynamical matrix and has been applied to reconstructed surfaces [ Si(111) 2 × 1], superlattices [(100)( GaAs) 3/( AlAs) 3] and mixed crystals [ Al xGa 1−xAs ]. In the present work we briefly review the results that we have obtained and discuss to which extent the experimental features can be reproduced by a geometric folding of the original dynamics into the new Brillouin zone.