Phonons and fundamental gap in ZnSe: Effects of the isotopic composition

We have investigated the effects of isotopic composition on the phonon frequencies and linewidths as well as the fundamental gap of ZnSe on a series of samples made from the stable isotopes ${}^{64}\mathrm{Zn},$ ${}^{68}\mathrm{Zn},$ ${}^{76}\mathrm{Se},$ and ${}^{80}\mathrm{Se}.$ Besides four nearly isotopically pure samples, we have measured natural ZnSe, which is highly isotopically disordered. In addition, we have investigated samples with monoisotopic cation or anion sublattices for which the anion or cation sublattice, respectively, consists of an artificial mixture of isotopes. Using Raman spectroscopy, we find a $\mathrm{TO}\left(\Gamma \right)$ linewidth of $\sim 0.4$ ${\mathrm{cm}}^{-1}$ for nominally isotopically pure samples at low temperatures, as compared to $1.75\left(1\right)\mathrm{}$ ${\mathrm{cm}}^{-1}$ in natural ZnSe. In samples with only cation or anion disorder, the linewidths amount to 1.16(6) ${\mathrm{cm}}^{-1}$ ${(}^{\mathrm{dis}}{\mathrm{Zn}}^{80}\mathrm{Se})$ and 0.84(3) ${\mathrm{cm}}^{-1}$ ${(}^{68}{\mathrm{Zn}}^{\mathrm{dis}}\mathrm{Se}).\mathrm{}$ This strong isotope-disorder-induced broadening of the TO$\left(\Gamma \right)$ phonon can be attributed to a large one-phonon density of states in this energy range. With linear optical spectroscopy (luminescence), we find, also at low temperature, that the fundamental gap of ZnSe increases by $214\left(30\right)\mathrm{}\mu \mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ when increasing the Zn mass. It increases by $216\left(30\right)\mathrm{}\mu \mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ when increasing the Se mass. A two-harmonic-oscillator model for the temperature dependence of the gap yields values for its mass dependence that are in qualitative agreement with this observation.