First-Principles Investigation of the Effect of M-Doped (M = Zr, Hf) TiCoSb Half-Heusler Thermoelectric Material

The M-doping (M = Zr, Hf) effects on the electronic structures and thermoelectric performance of TiCoSb were studied by first-principles calculations. The band structure analysis shows that substituting Ti with M does not change the band structures of these systems significantly. Most of the M-doped systems have a lower band gap value than that of TiCoSb; especially Ti0.5Zr0.5CoSb has the lowest energy band gap value of 0.971 eV. Besides, the amplitudes of the density of states in the region of the valence bands for M-doped systems show a similar but slightly higher value than TiCoSb. Those suggest that these compounds could have better thermoelectric performance than TiCoSb. The phonon dispersion relations show that the larger mass of Zr/Hf with respect to Ti lowers the optical modes and induces mixing with the acoustic branches. Our calculations offer a valuable insight on how to characterize complicated crystal structures of thermoelectric materials and optimize the material composition.