We report measurements of the thermal conductivity of high-quality crystals of the cubic $\mathrm{I}\mathrm{\text{−}}\mathrm{V}\mathrm{\text{−}}{\mathrm{VI}}_2$ semiconductors ${\mathrm{AgSbTe}}_2$ and ${\mathrm{AgBiSe}}_2$. The thermal conductivity is temperature independent from 80 to 300 K at a value of approximately $0.70\mathrm{W}/\mathrm{mK}$. Heat conduction is dominated by the lattice term, which we show is limited by umklapp and normal phonon-phonon scattering processes to a value that corresponds to the minimum possible, where the phonon mean free path equals the interatomic distance. Minimum thermal conductivity in cubic $\mathrm{I}\mathrm{\text{−}}\mathrm{V}\mathrm{\text{−}}{\mathrm{VI}}_2$ semiconductors is due to an extreme anharmonicity of the lattice vibrational spectrum that gives rise to a high Grüneisen parameter and strong phonon-phonon interactions. Members of this family of compounds are therefore most promising for thermoelectric applications, particularly as $p$-type materials.

• Received 5 March 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.035901