Percolative transport in amorphous semiconductors

For phonon-assisted transport between localized electronic states in amorphous semiconductors, the conductance of the medium is known to be the same as that of an equivalent resistor network. If the impedances of the resistors between adjacent sites vary over several orders of magnitude, this conductance is determined mainly by the magnitude of the critical impedance Z_c such that a percolation path through the system of resistors with impedance less than Z₀ exists only if Z₀≥Z_c. The calculation of Z_c is complicated by the dependence of the impedance between a pair of sites on the energies of the states localized around them. Various methods for calculating Z_c, and its dependence on the parameters of the system, are compared for a model system in which all the states have one of two discrete energies. Our main conclusion is that, in the calculation of Z_c from the mean number of bonds per site, it can be very important to optimize the range of sites and bonds that are considered.