Phonon-generated microfields and temperature dependence of the absorption edge in II-VI compounds

The strong temperature dependence of the exponential absorption edges in three structures of ZnS has been measured between 10 and 300 °K. The Dow-Redfield theory of phonon-generated microfields and their influence on the absorption edge through a Franz-Keldysh mechanism are used to explain the results. Below 50 °K only a very slight change in the edge energy $E_g$ was observed. Between 55 and 100 °K the energy of the edge could be described by $E_g\mathrm{}\left(T\right)=E_{g1}\mathrm{}\left(0\right)-S_1[1-tanh(\frac{\hslash {\omega }_{\mathrm{LA}}}{2k T}\left)\right]$ and between 100 and 300 °K the edge changed as $E_g\mathrm{}\left(T\right)=E_{g2}\mathrm{}\left(0\right)-S_2[1-tanh(\frac{\hslash {\omega }_{\mathrm{LO}}}{2k T}\left)\right]$, where $\hslash {\omega }_{\mathrm{LA}}=13.6\mathrm{}$ meV, $\hslash {\omega }_{\mathrm{LO}}=43.5\mathrm{}$ meV, and $E_{g1}\mathrm{}\left(0\right)\mathrm{}$, $E_{g2}\mathrm{}\left(0\right)\mathrm{}$, $S_1$ and $S_2$ are specific constants of each ZnS structure. The experimental values of the LO-phonon-generated rms field ${\left(〈F_{\mathrm{LO}}^2〉\right)}^{\frac{1}{2}}$ at room temperature were found (in units of ${10}^5$ V/cm) to be 3.90 in the cubic case, 4.77 ($\overrightarrow{\mathrm{E}}\perp \overrightarrow{\mathrm{C}}$) and 5.20 ($\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{C}}$) in the $4H$ polytype, and 6.34 ($\overrightarrow{\mathrm{E}}\perp \overrightarrow{\mathrm{C}}$) and 7.62 ($\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{C}}$) in the hexagonal structure of ZnS. The applicability of the postulated model of the temperature shift of the absorption edge was checked also on known data pertaining to hexagonal CdS. The experimental values of the ${\left(〈F_{\mathrm{LO}}^2〉\right)}^{\frac{1}{2}}$ (in units of ${10}^5$ V/cm) were found to be 3.97 ($\overrightarrow{\mathrm{E}}\perp \overrightarrow{\mathrm{C}}$) and 5.90 ($\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{C}}$).