Phonon band gaps in the IV-VI monochalcogenides

The origin of the phonon band gap and its controlling factors in low-symmetry crystals are studied in the monochalcogenide family of semiconductors through a combination of first-principles calculations and the introduction of quantitative measures of bond distortion in phonon modes. The phonon spectra were calculated for the recently discovered low-symmetry 64-atom cubic $\ensuremath{\pi}$-phase of the monochalcogenides in four materials: SnS, SnSe, GeS, and GeSe. The phonon spectra of all these systems exhibit phonon band gaps in the optical phonon spectrum with widths of 0.7--2 THz. Raman measurements were performed that support the existence and magnitude of the calculated phonon band gaps in $\ensuremath{\pi}$-SnS and $\ensuremath{\pi}$-SnSe. The origin of the phonon band gaps was examined through the contributions of the bond strengths and of the mass differences to the phonon spectrum in several monochalcogenide phases. An analysis of the normal modes found more rigid bond motion below the phonon gap and less rigid bond motion above the gaps as well as differences in the relative motion of the two types of atoms. These differences are identified as originating from the acoustic and optical modes of the symmetric parent rocksalt structure. The effect of the phonon band gap on the thermodynamic properties is discussed.