Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors: ZnO

Abstract

The temperature dependence of the $A$, $B$, and $C$ excitons of ZnO, observed in modulated reflectivity spectra of $^{68}\mathrm{Zn}^{18}\mathrm{O}$ and $^{\mathit{nat}}\mathrm{Zn}^{\mathit{nat}}\mathrm{O}$ in the range $10--400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, reveal the superposition of band-gap renormalization originating in electron-phonon interaction and volume changes associated with thermal expansion and (or) isotopic composition in combination with anharmonicity. At low temperatures, the $A$, $B$, and $C$ excitons in natural ZnO reach limiting values depressed from their values for the infinitely massive isotopes (the latter are free from electron-phonon interaction and anharmonicity). The C excitons of $^{68}\mathrm{Zn}^{18}\mathrm{O}$ and $^{\mathit{nat}}\mathrm{Zn}^{\mathit{nat}}\mathrm{O}$ converge with increasing temperature, demonstrating the independence of the band gap from isotopic mass at high temperatures.