Anharmonic vibrational effects of thermoelectric Cu-Sb-Se ternary semiconductors: Density-functional theory studies

Strong anharmonicity can lead to intrinsically minimal thermal conductivity even in defect-free single crystals. In an effort to understand this behavior, we have investigated two Cu-Sb-Se ternary semiconductors, Cu$_3$SbSe$_4$ and Cu$_3$SbSe$_3$, by both experimental measurements and density functional theory (DFT) calculations. The experimental lattice thermal conductivity measurements show that while Cu$_3$SbSe$_4$ exhibits classical behavior, the lattice thermal conductivity in Cu$_3$SbSe$_3$ is anomalously low and nearly temperature independent. The vibrational properties of these two semiconductors are calculated by DFT phonon calculations within the quasi-harmonic approximation. The average of the Gr\"{u}neisen parameters of 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$_4$. Using our DFT-determined longitudinal and transverse Gr\"{u}neisen parameters, Debye temperatures, and phonon velocities, we calculate the lattice the lattice thermal conductivity using the Debye-Callaway model (without the use of any adjustable parameters). The calculated thermal conductivity is in good agreement with the experimental measurements.