Electrical transport across pulsed laser deposited zinc oxide (ZnO)/aluminum nitride (AlN)/Si(100) thin film structures has been studied using conducting atomic force microscopy. Current versus voltage spectroscopy performed on the samples with varying AlN layer thickness (t), revealed asymmetric nonlinear behavior with a finite zero current region. The effective barrier height of the system is found to be (∼0.2 eV). The width of the zero current region was found to decrease exponentially with respect to t finally attaining the bulk band gap value. Density functional theory based calculations were carried out on the AlN and AlN–ZnO composite surface to investigate the band gap variation and ZnO adsorption on AlN. Results obtained by these calculations are in harmony with the experimental findings. Calculated values of the bulk cohesive energy explain the growth of the ZnO in an axis perpendicular to the surface supporting the experimentally observed results. Constant voltage current scans studies on the same sample showed the existence of current leakage spots. Current scans performed with varying bias voltages described an unambiguous growth profile of current leakage spots. These leakage spots were observed to evolve in a self similar pattern with the bias, which implied a possible existence of fractal dimension in the pattern of their growth. Mass fractal analysis is therefore carried out to model the growth pattern. Evolution of the mass-fractal with respect to the applied bias is found to be a case of Rayleigh distribution on a two-dimensional Poisson field, in the limiting case.