It is well known that the evaluation of the hopping conductivity reduces to the percolation problem, in which the existence of bonds between impurities depends not only on the distance between the impurities but also on the distribution of the impurity energies. It is shown that a constant activation energy can exist in a wide range of temperatures only if such a distribution is narrow. A method of small perturbations in the percolation theory is developed which can be used to calculate the activation energy for a given distribution of the impurity energies. In the simplest case, when all the energy distribution functions are uncorrelated and identical for all impurities, a Monte Carlo calculation was carried out on a computer which confirmed the results of the perturbation theory.
|Original language||English (US)|
|Number of pages||5|
|Journal||Sov Phys Solid State|
|State||Published - Jan 1 1975|