Coupled theoretical interpretation and experimental investigation of the lattice thermal conductivity of Bi2Te3 single crystal

An essential challenge in thermoelectric material research is the selection of materials having potentially a high figure-of-merit and their improvement by the reduction of their lattice thermal conductivity. In the present article the Debye model is modified for the calculation of the lattice thermal conductivity and used to gain insight into the anisotropy of single crystalline bismuth telluride (Bi2Te3). In this article the minimum wavelength of phonons that moved, which is closely related to the concept of cutoff frequency, is not taken twice the atoms separation. The Debye temperature is in fact not used to estimate the cutoff frequencies of the phonons that carry heat. The cutoff frequencies are defined in this work by setting an upper limit to the energy of acoustic phonons using the complete dispersion relations. Our work indicates that the cutoff frequencies of acoustic phonons are anisotropic in Bi2Te3. The anisotropy of the thermal conductivity is surprisingly found to be unrelated to the anisotropy of the sound velocities that are calculated as a function of the tensor of the elastic constants. The sound velocity is in fact almost isotropic when the longitudinal and two transversal waves are added together. In addition it is suggested that the relaxation time is also a function of the cutoff frequencies and that this may counterbalance the anisotropy arising from the variation of the number of acoustic phonons traveling in various directions. Finally, the anisotropy of the thermal conductivity of Bi2Te3 single crystal is found to be mostly related to the Gruneisen's constant if the main scattering mechanism is a phonon-phonon interaction.