Concentration dependence of hopping conduction in lightly doped semiconductor

We study the concentration dependence of hopping conduction using percolation method, specially the random site percolation problem and direct solution to Miller Abrahams random resistor networks. As an example, we first tested our method on a simple cubic lattice. We obtained both the bond percolation threshold and conductivity of the simple cubic random network. Then by comparing disorder averaged changes in the cluster size with increasing average number of connections between donors, we calculate the percolation threshold for a random site percolation problem. This value is used to determine the exponential dependence of hopping conductivity on donor concentration. To calculate the effective conductivity of the network, Kirchhoff's Equations built on the network were solved. In addition, we obtained the conductivity distributions in both the simple cubic resistor networks and random resistor site networks. Except in the vicinity of the percolation threshold, the conductivity distributions have a log normal form.