Dimensional crossover in the conductivity of coevaporated Pb-Ge films

The resistance of coevaporated Pb-Ge films was measured during their deposition onto room-temperature glass substrates. The dependence of the conductivity on thickness for several concentrations was analyzed according to the theory of interdimensional crossover in order to determine the percolation exponents $t_2$ (in two dimensions) and $t_3$ (in three dimensions) of the conductivity and ${\nu }_3$ (in three dimensions) of the correlation length. This method has several advantages over the usual procedure of preparing samples of different concentration and constant thickness. It also measures film uniformity. The measured values of $t_2$, $t_3$, and ${\nu }_3$ are consistent with accepted values.