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A percolation treatment of high-field hopping transport

A previous percolation theory for hopping conduction is extended to high fields, and applied specifically to the Mott (1969) model (a constant density of states). The importance of nearest-neighbour pair correlations, the local chemical potential, and certain spatial correlations are discussed. The directional constraints created by the spatial correlations and by the nature of the percolation cluster are included approximately. The effect of the local chemical potential is included in an approximation similar to the mean field approximation. The theory is worked out primarily in the moderate field regime. The conductance is found to be proportional to exp (-A+eFl/kT), where exp(-A) is the low field conductance, F the electric field, and l a fraction of the characteristic low-field hopping distance rm. For three dimensions, l=0.17 rm, and for two dimensions, l=0.18 rm. Expressions are also derived for the high-field limit, and agree functionally with derivations by others.