Gas and Percolation Models

Mobilities of all doped polymers are strongly dependent upon the donor or acceptor concentration, increasing with increasing concentration. There are two general explanations of the concentration dependence. The first involves the concept of a homogeneous lattice gas (Mott and Davis, 1971, 1979 Gill, 1972 Pfister, 1977 Hirsch. 1979). The second is based on percolation (Silver et al., 1979 Ries et al., 1986). 

In the lattice gas model, the hopping frequency of a carrier decreases exponentially with the hopping distance p as v = vQ exp(-2p/p0). Here, pQ is a wavefunction decay constant and vQ a frequency factor. From the Einstein relationship, the zero-field mobility is 

The lattice gas model is based on the assumption that the hopping distance can be described as p = (M/Ach) 9 where M is the molecular weight of the dopant 

In the original Scher-Montroll formalism, hopping was assumed to occur through a manifold of spatially disordered isoenergetic hopping sites. In the 

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