Bipolaron ac conductivity in amorphous semiconductors and dielectrics

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 Ueff. 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 σ₁{∝}ωˢ{T}ⁿ$ of the ac hopping conductivity for different temperatures T in a wide range of audio and low radio frequencies {ω}, 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-SiO₂ has been made.It demonstrates that, in these materials, a tunneling adiabatic (TA) regime of SB hopping with s{}1 and n{}1 has been observed at low temperatures provided that there are (i) strong Coulombic correlations in the intersite occupations and (ii) strong scattering of one-electron energies. As the temperature is increased, the TA regime seems to be replaced by the activation adiabatic regime with s1 being a decreasing function and n>1 being an increasing function of T. It was found that in the negative-Ueff amorphous systems the stretched bonds of size of 3.5--4.5 {} can be responsible for ac losses within the wide frequency range from 10² to 10⁸ Hz.