Theory of phonon conductivity of semiconductor superlattices
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Theory of phonon conductivity of semiconductor superlattices
Gyaneshwar P. Srivastava1 , Steven P. Hepplestone2 1 School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK 2 Department of Physics, University of Surrey, Guildford GU2 7XH, UK
ABSTRACT We present a single-mode relaxation-time theory of phonon conductivity of semisonductor superlattices with nanoscale periodicities. Analytic expressions have been obtained for phonon-interface scattering and phonon-phonon scattering taking into consideration the effects of interfaces and the presence of two materials in superlattices. Numerical calculations have been performed by using phonon eigensolutions obtained from an enhanced adiabatic bond charge model and by carrying out Brillouin zone integration using the special q-points scheme. The experimental measured conductivity results for Si(19)/Ge(5) and Si(72)/Ge(30) superlattices have been successfully explained. INTRODUCTION It is well accepted that solid structures with reduced dimensions exhibit some physical properties that are unavailable in their three-dimensional form. A superlattice, made as a periodic array of two materials along an specific direction, provides an example of a lowdimensional structure. Over the past two decades, electronic properties of semiconductor superlattices have been successfully studied, both experimentally and theoretically. However, the same cannot be said of their thermal properties. One particularly unresolved issue is heat transport in superlattices with nanoscale periodicities. In semiconductor superlattices heat conduction is almost exclusively acomplished by phonons, the atomic vibrational energy quanta within the system. At low and intermediate temperatures the mean free path of phonons in a nanostructured A/B superlattice can be severely controlled by their scattering with chemical composition and atomic structure at the interface between the material constituents A and B. In addition, the presence of two material species and a larger periodicity than in bulk A or B results in an enhanced level of anharmonic phonon scatterings. These two issues have been recently discussed using an atomic-level theory [1]. In this work we present the essential features of our recent theory [1] of phonon-interface and phonon-phonon interactions. Within the concept of single-mode relaxation time, we obtain numerical results for the phonon conductivity of nanoscale Si/Ge superlattices, and attempt to explain the experimental measurements on such systems [2].
THEORY In bulk semiconductors the main contributions for the relaxation time τ come from the scattering of phonons from sample boundaries, isotopic and other point defects, and anharmonicity in crystal potential. Useful expression for phonon scattering rates from these mechanisms are available [4]. Three additional considerations must be made when making a complete assessment of τ in superlattices: presence of different material constituents, quality of interfaces between constituent layers, and the larger periodicty
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