Lattice thermal conductivity reduction and phonon localizationlike behavior in superlattice structures

Abstract

A study of thermal conductivities perpendicular to the interfaces in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}{/\mathrm{S}\mathrm{b}}_{2}{\mathrm{Te}}_{3}$ superlattices is presented. The lattice thermal conductivities in these short-period superlattices are less than those in homogeneous solid-solution alloys and exhibit a minimum for a period of \ensuremath{\sim}50 \AA{}. For periods less than 50 \AA{}, the adjoining layers of the superlattice apparently become coupled and, in effect, make their thermal conductivities approach that of an alloy. Using the mean free path from kinetic theory, a diffusive transport analysis suggests a low-frequency cutoff $({\ensuremath{\omega}}_{\mathrm{cutoff}})$ in the spectrum of heat-conducting phonons. A physical model based on the coherent backscattering of phonon waves at the superlattice interfaces is outlined for the reduction of lattice thermal conductivity; this suggests conditions of localizationlike behavior for the low-frequency phonons. The ${\ensuremath{\omega}}_{\mathrm{cutoff}}$ from the diffusive transport model is comparable to that estimated from applying the Anderson criterion to the potential localization of phonon waves. The general behavior of localizationlike effects is not unique to ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}{/\mathrm{S}\mathrm{b}}_{2}{\mathrm{Te}}_{3}$ superlattices; it is also apparent in the thermal conductivities of Si/Ge superlattices. These superlattice structures offer a scope for studying the phonon localization phenomena while the lattice thermal conductivity reduction could lead to high-performance thermoelectric materials.