Impedance spectra of doped bismuth silicate Bi$_{12}$SiO$_{20}$:Ge crystals

The specific features of the behavior of the impedance spectra of germanium-doped Bi$_{12}$SiO$_{20}$ single crystals with the sillenite structure have been studied. It has been found that the obtained dependences exhibit a dispersion corresponding to the distribution of the relaxation times. An analysis of the experimental data performed by the graphical-analytic method has made it possible to separate the contributions to the conductivity due to the crystal bulk and the sample-electrode interface. The role played by the impurity factor and lone electron pairs of trivalent bismuth ions in the formation of the defect structure of the crystal has been demonstrated.