Monte Carlo Simulations of non-linear evolution of materials resistivity

We developed an experimentally motivated Monte Carlo simulation to calculate the conductance materials and the effect of charged dopant concentration and applied this method to investigate the non-linear evolution of the resistivity with annealing time in oxygen deficient thin films. The model consists of an N x N square lattice with hydrogenic atoms placed at each lattice site. The valence electrons are bound to their respective lattice site via a harmonic potential, and electrons at different sites are allowed to interact via a screened Coulomb potential. At each Monte Carlo step, electrons attempt to slightly change their position with respect to their lattice site. Additionally, electrons attempt to transition between conducting and non-conducting states. We found nonlinear dependence of the resistance as a function of dopant concentration. The dopants act as electron traps where they lower the energy of nearby electrons and increase the energy requirement to transition to the conducting state. As more dopants are added, this effect increases, further suppressing the conductivity. This would indicate that the inclusion of the charged dopants advances the percolative evolution of such a phase transition.