We show how it is possible to perform a full calculation of the frequency-dependent hopping conductivity of a disordered array of semiconductor crystallites once their statistical distribution is known. We first apply this to a weakly disordered distribution of silicon spheres connected by silicon bridges and show the importance of the topology in determining the activation energy characteristic of the temperature dependence. We then use a model distribution to simulate the case of porous silicon and from this get a coherent description of various related properties. Finally, we emphasize the applicability of the method to determine the hopping conductivity of artificially built semiconductor nanostructures.

• Received 27 July 1998

DOI:https://doi.org/10.1103/PhysRevB.58.12044