Acoustic impedance and interface phonon scattering in Bi₂Te ₃ and other semiconducting materials

We present first-principles calculations of the phonon dispersions of Bi₂Te₃ along with calculations of the sound speed anisotropy for a number of materials, and we discuss these in relation to acoustic phonon interface scattering in ceramics. The Bi₂Te ₃ phonon dispersions show agreement with what is known from neutron scattering for the optic modes, while we find a difference between the generalized gradient approximation and local density results for the acoustic branches. This is a consequence of an artificial compression of the van der Waals bonded gaps in the Bi₂Te₃ structure when using the generalized gradient approximation. As a result, local density approximation calculations provide a better description of the phonon dispersions in Bi ₂Te₃. A key characteristic of the acoustic dispersions in several materials studied is the existence of a strong anisotropy in the velocities. Such an anisotropy may be a significant consideration in the reduction of lattice thermal conductivity by nanograin boundary scattering. This is a well-known technique commonly employed to improve thermoelectric performance. We develop a model to quantify the effect of this anisotropy for this interface scattering in ceramics, and we apply this to Bi ₂Te₃ and compare with PbTe and several other semiconductors.