Raman Study of Pure and Semiconducting CdF2. The Polaron Problem

The technique of Raman spectroscopy is employed to investigate pure and semiconducting Cd${\mathrm{F}}_2$. The results in the pure material are used together with previously reported optical data to calculate, within the framework of the rigid-ion model, the phonon dispersion relations and density of states of pure Cd${\mathrm{F}}_2$. The dispersion relations cannot be obtained experimentally because of the large neutron-capture cross section of cadmium. In semiconducting Cd${\mathrm{F}}_2$, two new Raman peaks are observed. One of them is interpreted, through a Green's-function calculation, as being due to a local vibrational mode associated with the presence of the semiconducting electron. The accompanying lattice distortion is related via a small polaron model to the polaron mass; we obtain a value of 18 for the ratio of polaron mass to band mass. Ultraviolet reflection data on pure Cd${\mathrm{F}}_2$ are presented and interpreted in terms of a hydrogenic exciton model which predicts a band mass of $0.8m_e$. These results, taken together with the measured cyclotron mass $11m_e$, suggest that neither large- nor small-polaron models are appropriate to describe the Cd${\mathrm{F}}_2$ polaron, but that an intermediate-polaron model is necessary.