Abstract
We have developed a theory of the alternating-current (ac) relaxation-type conductivity due to small bipolaron (SB) hopping in amorphous semiconductors and insulators that possess deep centers of the dangling-bond type (D centers) with a negative two-electron correlation energy ${\mathit{U}}_{\mathrm{eff}}$. Unlike small po- larons, SB's were treated as essentially three-level systems in the framework of a two-site approximation. To calculate, both numerically and analytically, the real part ${\mathrm{\ensuremath{\sigma}}}_{1}$\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{\mathit{s}}$${\mathit{T}}^{\mathit{n}}$ of the ac hopping conductivity for different temperatures T in a wide range of audio and low radio frequencies \ensuremath{\omega}, the dynamic polariz- ability, and the SB hopping rates for dangling bond pairs have been determined. When the electron tunneling integral corresponding to the smallest intersite separations is greater than the doubled polaron shift, both the polarizability and the hopping rate strongly depend upon the shape and parameters of the ground-state adiabatic potential of a small-size pair of strongly interacting D centers. This intimate pair can be viewed as a stretched or weakened bond. A classification of possible regimes of relaxation-type SB hopping (adiabatic and nonadiabatic, as well as tunnel and activation) has been proposed. Each of these corresponds to a specific temperature dependence of the exponents s and n. A comparison to experimental data on ac losses in chalcogenide glasses and a-${\mathrm{SiO}}_{2}$ has been made.
Published Version
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