Dispersion of acoustic phonons in quasiperiodic superlattices

Abstract

The aim of this work is to present an up-to-date study of acoustic phonon excitations that can propagate in multilayered structure with constituents arranged in quasiperiodic fashion. In this paper, the dispersion relation of acoustic phonons for the quasiperiodic superlattice using different semiconducting materials, with the help of transfer matrix method, is derived at normal angle of incidence. Calculation is presented for (a) Ge/Si and (b) Nb/Cu semiconductor superlattices from 5th to 9th generations and dispersion diagrams are plotted using the famous Kronning-Penny model obtained from the transfer matrix of the structure. The concept of allowed and forbidden bands with the help of these dispersion curves in various generations of Fibonacci superlattices and the relation between imaginary value of propagation vector and the existence of forbidden bands is demonstrated. © World Scientific Publishing Company.