Impurity distribution and electronic states in doped conjugated polymers in the coherent-potential approximation

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Abstract
The electronic level structure and the dimerization order parameter are studied in doped conjugated polyamers when randomly distributed site-type impurities occupy different positions from those in previous investigations. Each impurity is assumed to be located at a lattice site. The number of impurities at the even-numbered sites is equal to that at the odd-numbered sites. It gives rise to both forward and backward scatterings of electrons. The generalized Takayama–Lin-Liu–Maki model is analyzed with the help of the coherent-potential approximation (CPA), using the assumption that the order parameter is uniform with one electron per site. The order parameter, the electronic level structure, and its phase diagram are obtained numerically. The characteristic CPA results obtained previously are found to be rather insensitive to the impurity positions. There are some quantitative differences. The isolated acceptor impurity band is closer to the valence band and the donor band to the conduction band at low impurity concentrations. The broadening of the density of states is reduced at high concentrations. Accordingly, the phase with an isolated impurity band becomes narrower. The phase with the vanishing energy gap also becomes narrower.