Frequency-dependent conductivity in bismuth-vanadate glassy semiconductors

The first measurements are reported for the frequency-dependent (ac) conductivity (real as well as imaginary parts) for various compositions of the bismuth-vanadate glassy semiconductors in the frequency range ${10}^2$–${10}^5$ Hz and in the temperature range 77–420 K. The behavior of the ac conductivity is broadly similar to what has been observed previously in many other types of amorphous semiconductors, namely, nearly linear frequency dependence and weak temperature dependence. The experimental results are analyzed with reference to various theoretical models based on quantum-mechanical tunneling and classical hopping over barriers. The analysis shows that the temperature dependence of the ac conductivity is consistent with the simple quantum-mechanical tunneling model at low temperatures; however, this model completely fails to predict the observed temperature dependence of the frequency exponent. The overlapping-large-polaron tunneling model can explain the temperature dependence of the frequency exponent at low temperatures. Fitting of this model to the low-temperature data yields a reasonable value of the wave-function decay constant. However, this model predicts the temperature dependence of the ac conductivity much higher than what actual data showed. The correlated barrier hopping model is consistent with the temperature dependence of both the ac conductivity and its frequency exponent. This model provides reasonable values of the maximum barrier heights but higher values of characteristic relaxation times.