Percolation theory approach to the description of electrical conductivity near 3D-2D transition in thin polycrystalline SnO2 films

In order to simulate numerically the electrical properties of polycrystalline SnO₂ thin films a polycrystalline film material is substituted by a “plane” or “volume” resistor network. The reliability of the developed calculation procedure is based on the coincidence of our evaluations of the electroconductivity parameters such as critical concentration C* and electrical conductivity index t in the pure “plane” and “volume” situations with numerical results predicted by the percolation theory. A good agreement between calculated and experimental data is obtained, it is shown that the variation of relation between average grain size and film thickness may serve as an effective mean to control the electrical properties of semiconducting polycrystalline films including SnO₂ polycrystalline films