Lower limit to the lattice thermal conductivity of nanostructured Bi ₂ Te₃ -based materials

We investigate the lower limit to the lattice thermal conductivity of Bi₂ Te₃ and related materials using thin films synthesized by the method of elemental reactants. The thermal conductivities of single layer films of (Bi_0.5 Sb_0.5)₂ Te₃ and multilayer films of (Bi₂ Te₃) _m (TiTe ₂) _n and [(Bi_x Sb_1-x) ₂ Te₃] _m (TiTe₂) _n are measured by time-domain thermoreflectance; the thermal conductivity data are compared to our prior work on nanocrystalline Bi₂ Te₃ and a Debye-Callaway model of heat transport by acoustic phonons. The homogeneous nanocrystalline films have average grain sizes 30<d<100 nm as measured by the width of the (003) x-ray diffraction peak. Multilayer films incorporating turbostratic TiTe₂ enable studies of the effective thermal conductivity of Bi₂ Te₃ layers as thin as 2 nm. In the limit of small grain size or layer thickness, the thermal conductivity of Bi₂ Te₃ approaches the predicted minimum thermal conductivity of 0.31 W/m K. The dependence of the thermal conductivity on grain size is in good agreement with our Debye-Callaway model. The use of alloy (Bi,Sb) ₂ Te₃ layers further reduces the thermal conductivity of the nanoscale layers to as low as 0.20 W/m K.