Valence-band parameters andgfactors of cubic zinc selenide derived from free-exciton magnetoreflectance

Reflectance spectra were measured on cubic ZnSe crystals in magnetic fields up to 18 T and transverse energies of the $1s$-exciton states derived by a line-shape fit. The results are analyzed combining the existing low-field theory of ${\Gamma }_6-{\Gamma }_8$ exciton states with the results of variational calculations for excitons in polar materials without valence-band degeneracy. The observed linear Zeeman splitting yields a conduction-band electron $g$ factor $g_c=1.37\mathrm{}\pm 0.25$, an effective hole $g$ factor $\tilde{\kappa }=-0.21\mathrm{}\pm 0.06$, corresponding to $\kappa =-0.28\mathrm{}\pm 0.08$, and an upper limit for the short-range electron-hole spin exchange $2{\Delta }_1\lesssim 0.1$ meV. From the $1s-2s$ exciton-state energy separation we derive the exciton Rydberg $R_0^{*}=16.8\mathrm{}\pm 0.4$ meV and obtain $E_{1s}=17.4\mathrm{}\pm 0.4$ meV exciton binding energy. The observed diamagnetic-shift rates yield an exciton reduced mass $\frac{{\mu }_0^{*}}{m_0}=0.095\mathrm{}\pm 0.003$ corresponding to ${\gamma }_1^{*}=4.3\mathrm{}\pm 0.5$ for $\frac{m_e^{*}}{m_0}=0.16\mathrm{}$. We further determine ${\gamma }_2^{*}=0.59\mathrm{}\pm 0.07$ and ${\gamma }_3^{*}=1.34\mathrm{}\pm 0.30$. The bare valence-band parameters ${\gamma }_i$ derived from the renormalized parameters ${\gamma }_i^{*}$ are ${\gamma }_1=4.8\mathrm{}\pm 0.6$, ${\gamma }_2=0.67\mathrm{}\pm 0.08$, and ${\gamma }_3=1.53\mathrm{}\pm 0.35$. With the parameters derived, energy shifts and splittings of exciton states not used for the evaluation of the parameters are calculated in good agreement with the experimental results. The exciton reduced mass derived from diamagnetic-shift rates yields an exciton Rydberg in good agreement with the Rydberg obtained from the $1s-2s$ exciton-state energy separation. Finally, the energy separations of $2p$-exciton states calculated from our parameters are in close agreement with two-photon absorption measurements. This is taken as a justification for the theoretical model applied and suggests the derivation of fundamental parameters of related compounds such as CdTe or ZnTe along similar lines.