Modeling of electrical conductance variation in substrate during initial growth of ultra thin film

Abstract
A model of the electrical conductance of a resistive or semiconductive substrate, as a function of the average thickness d of a deposited film in initial growth on the substrate is proposed. The total conductance has two terms: one proportional to d2/3 for three-dimension (3D) growth, and one proportional to d for 2D growth or for increasing number of islands. The model was applied to the conductance of a Sn film deposited on a SiOx substrate showing that the initial growth is dominated by 3D growth. The proposed model may be useful for in situ study of the growth of ultra thin films prior to the onset of tunneling conductance.