ac conduction in bis [catena-poly(methylarsenic)]
John E. Lewis, Murtada Mohamed Edris · Physical review. B, Solid state · 1975
The dark complex impedance $Z=R+\frac{j}{\ensuremath{\omega}C}$ of $\mathrm{bis}$ [catena-poly(methylarsenic)], an organic ladder polymer, has been measured as a function of frequency (1.3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$-1.5 \ifmmode\times\else\texttimes\fi{} ${10}^{5}$ Hz) and temperature (77-400 K), with a 0.1-V rms ac signal. Conduction is due to a parallel combination of intrinsic excitation of carriers across an energy gap and ac-field-assisted carrier hopping between localized centers. The resistance $R$ falls smoothly from its dc value and at high frequencies ($\ensuremath{\gtrsim}{10}^{2}$ Hz) varies over many orders of magnitude as ${f}^{\ensuremath{-}n}$, with $n$ temperature dependent, typical of a carrier-hopping mechanism below the characteristic hopping frequency between centers. A temperature- and frequency-dependent activation energy is indicated for this process. The variation of $n$ suggests that single hops between pairs of identical centers predominates at low temperatures while single and multiple hops in a random distribution of centers is more appropriate above room temperature. At lower frequencies (and/or high temperature) $R$ varies exponentially with inverse temperature, with a frequency-independent energy gap ${E}_{ g}=1.5$ eV, typical of an intrinsic semiconductor. At high frequencies the capacitance $C$ varies as ${f}^{s}$, such that $s=n\ensuremath{-}1$, as required by the Kramers-Kronig relations. As the frequency is lowered, this relationship breaks down and $C$ increases apparently without limit. Temperature-dependent peaks at these low frequencies in the loss factor versus frequency plot are due to a Debye-type relaxation mechanism, having an activation energy of 0.73 eV, one-half the value of the intrinsic energy gap. Polarization phenomena at these low frequencies are also seen in the current-voltage characteristics of the material and in the response of the samples to step-function changes in the applied dc voltage. It is thought that this polarization is associated with losses in the intrinsic conduction mechanism.