Three-phonon scattering processes and thermal conductivity in IV-chalocogenides

We present a systematic study of allowed three-phonon scattering processes, involving acoustic and optical branches, and their relative roles in explaining the low thermal conductivity κ of IV-chalcogenide thermoelectric materials PbTe, PbSe, PbS, and SnTe. Using numerical results for κ, computed by employing the isotropic continuum scheme, we have examined the extent of the additional contribution the Callaway theory and the Allen theory provide over the single-mode relaxation time theory. Within the Callaway theory, for all these materials the acoustic (TA, LA) and transverse optical (TO) phonons contribute between 10-25% towards κ at and above room temperature, with κ(TO) > κ(TA) > κ(LA). The longitudinal optical (LO) phonons contribute negligibly (<5%) in Pb-chalogenides, but their contribution is larger (22%) than that of TO phonons (18%) in SnTe. Due to the presence of high defect concentration in these materials, the high temperature conductivity varies less strongly than T(-1). In confirmation with experimental measurements, our study finds that below the Debye temperature the resistivity of SnTe varies as the square-root of the point defect concentration.