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

Abstract

Experimental measurements have recently shown that Cu${}_{3}$SbSe${}_{3}$ exhibits anomalously low and nearly temperature-independent lattice thermal conductivity, whereas Cu${}_{3}$SbSe${}_{4}$ 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 Cu${}_{3}$SbSe${}_{4}$, whereas almost all are positive in Cu${}_{3}$SbSe${}_{3}$ throughout their respective Brillouin zones. The average of the square of the Gr\"uneisen parameter for the acoustic mode in Cu${}_{3}$SbSe${}_{3}$ is larger than that of Cu${}_{3}$SbSe${}_{4}$, which theoretically confirms that Cu${}_{3}$SbSe${}_{3}$ has a stronger lattice anharmonicity than Cu${}_{3}$SbSe${}_{4}$. The soft frequency and high Gr\"uneisen parameters in Cu${}_{3}$SbSe${}_{3}$ arise from the electrostatic repulsion between the lone ${s}^{2}$ 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.