Influence of temperature and pressure on the electronic transitions in SnS and SnSe semiconductors

Optical-absorption measurements in the near infrared have enabled us to determine the direct and indirect band gaps of SnS and SnSe layered compounds, in the a and b polarizations, at temperatures ranging from 7 to 295 K (at P=0 kbar) and pressures up to 40 kbar (at T=295 K). At T=295 K and P=0 kbar, we obtain, for SnS, ${\mathit{E}}_{\mathrm{ind}}$ ${\mathrm{i}}_{\mathrm{a}}$ a=1.076 eV, ${\mathit{E}}_{\mathrm{ind}\mathbf{b}}$=1.049 eV, and ${\mathit{E}}_{\mathrm{dir}}$ b=1.296 eV; and for SnSe, ${\mathit{E}}_{\mathrm{ind}\mathbf{a}}$=0.898 eV, ${\mathit{E}}_{\mathrm{ind}\mathbf{b}}$=0.903 eV, ${\mathit{E}}_{\mathrm{dir}\mathbf{a}}$=1.238 eV, and ${\mathit{E}}_{\mathrm{dir}\mathbf{b}}$=1.047 eV. For both crystals, an additional structure, associated with an impurity level, is observed in the a polarization. Its shape reveals the three-dimensional nature of the electronic properties in these compounds. The measured pressure coefficients for the transitions ${\mathit{E}}_{\mathrm{inda}}$, ${\mathit{E}}_{\mathrm{ind}\mathbf{b}}$, ${\mathit{E}}_{\mathrm{dir}\mathbf{a}}$, and ${\mathit{E}}_{\mathrm{dir}\mathbf{b}}$ are, for SnS, -5.6, -6.0, -8.3, and -7.3 meV/kbar, respectively; and for SnSe, -5.2, -8.9, -3.6, and -11.2 meV/kbar, respectively. The corresponding temperature coefficients are, for SnS, -0.24, -0.36, . . . (undetermined), and -0.563 meV/K; and for SnSe, -0.32, -0.29, -0.43, and -0.43 meV/K. The behavior of the transition energies with temperature is explained by a self-energy correction attributed to the interaction between electrons and nonpolar phonons. Concerning this temperature dependence, we find that the effect of volume dilatation is opposite in sign to that of the electron-phonon interactions. The latter effect dominates.