Polaron Effects in Semiconducting CdF2: Cyclotron Resonance and Far-Infrared Properties

The results of cyclotron-resonance and far-infrared investigations on rare-earth-doped semiconducting Cd${\mathrm{F}}_2$(SC Cd${\mathrm{F}}_2$) which were briefly reported previously are presented in greater detail. A tight-binding model is presented for the polaron trapped near the trivalent rare-earth ion. The optical properties of this trap, as determined from the calculated wave functions and energies of the trapped polaron, are related to the absorptions observed in the near and far infrared. In addition, the parameters evaluated from fitting the model calculation to the observed spectra are used to calculate a polaron mass. This is found to agree remarkably well with the mass of 11±1 determined from the cyclotron-resonance measurements. A limited comparison is made between the results obtained here and existing polaron theories. The appropriateness of the various polaron models for SC Cd${\mathrm{F}}_2$ is discussed in light of the apparent polaron size and the possible importance of other than LO modes.