First-principles description of anomalously low lattice thermal conductivity in thermoelectric Cu-Sb-Se ternary semiconductors

Experimental measurements have recently shown that Cu₃SbSe₃ exhibits anomalously low and nearly temperature-independent lattice thermal conductivity, whereas Cu₃SbSe₄ does not exhibit this anomalous behavior. To understand this strong distinction between these two seemingly similar compounds, we perform density functional theory calculations of the vibrational properties of these two semiconductors within the quasiharmonic approximation. We observe strikingly different behavior in the two compounds: almost all the acoustic-mode Gr\"uneisen parameters are negative in Cu₃SbSe₄, whereas almost all are positive in Cu₃SbSe₃ throughout their respective Brillouin zones. The average of the square of the Gr\"uneisen parameter for the acoustic mode in Cu₃SbSe₃ is larger than that of Cu₃SbSe₄, which theoretically confirms that Cu₃SbSe₃ has a stronger lattice anharmonicity than Cu₃SbSe₄. The soft frequency and high Gr\"uneisen parameters in Cu₃SbSe₃ arise from the electrostatic repulsion between the lone s² pair at Sb sites and the bonding charge in Sb-Se bonds. Using our first-principles-determined longitudinal and transverse acoustic-mode Gr\"uneisen parameters, zone-boundary frequencies, and phonon group velocities, we calculate the lattice thermal conductivity using the Debye-Callaway model. The theoretical thermal conductivity is in good agreement with the experimental measurements.