Pseudo-percolation of charge carriers in molecularly doped polymers: A Monte Carlo study

Abstract

Motivated by the recent work of Santos Lemus and Hirsch and of Pai, Yanus and Stolka on the concentration dependence of hole transport in selected molecularly doped polymers, a Monte Carlo computer study has been conducted. It predicts that transport should in principle exhibit percolative features without, however, showing a well-defined percolation threshold (“pseudo-percolation”). A threshold concentration c ₀ for pseudo-percolation will be defined. In a van der Waals solid with exponential wavefunction overlap it decreases with decreasing wavefunction localization because of non-nearest-neighbour jumps. A relation between c ₀ and the effective coordination number of the lattice, defined via overlap, is established. For c < c ₀ the carrier mobility remains finite and follows approximately a power law, μ∝c ^m, in accord with experiment. The exponent m increases with increasing localization of the wavefunction which depends on the energetic separation between the transport levels of dopant and host.