Dilution and cluster contributions to hopping transport in a bias field

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Abstract
Hole transport in molecularly doped polymers (MDPs) is modeled as random walks on fixed donors (Ds) embedded in a polymer matrix. Dilution p<1 corresponds to placing individual Ds, dimers D2, or tetramers D4 randomly on a fraction p of sites in a face-centered-cubic lattice. Monte Carlo simulations of the drift velocity vD(E) in a bias field E have maxima in dilute (p=8%) systems of D2 or D4 that are related to the formation and polarization of clusters of nearest-neighbor donors. Marcus or small-polaron hopping rates with fixed parameters account for the concentration, field, and temperature dependencies of the mobility, μ(E,T)=vD(E,T)/E, of D=TTA (tritolylamine) in polystyrene and of related systems with D2 or D4 in PS. The compensation temperature is lower for D2 than for D at p=20%, consistent with stronger positional disorder for dimers. The anomalous broadening of photocurrents in D4 with increasing E is due to cluster polarization. The parameter σ=700 K for energetic disorder is used throughout and is ∼25% smaller than in the Gaussian disorder model. Spatially correlated energies yield the characteristic field dependence of μ(E,T). Although not quantitative, the comprehensive treatment of dilution in TTA:PS and related MDPs clearly supports Marcus hopping rates and stronger geometrical than energetic disorder.