In this work, the fractal dimensions and electric properties of carbon films embedded by nickel nanoparticles annealed at different temperature 300, 500 and 800 ◦C were investigated. A detailed analysis in terms of small polaron hoping (SPH) parameters is used to correlate electrical transport properties with annealing temperature in the range 150–300 K. It can be seen that with increasing annealing temperature up to 500 ◦C the polaron radius (rp) decrease and has a minimum value 4.58 × 10−8 cm then from 500 ◦C to 800 ◦C it increased to 6.13 × 10−8 cm. The polaron hopping energy (WH) at 500 ◦C has minimum value 0.017 eV while the density of states N(EF) at the Fermi level has maximum value 5.43 × 1021 eV−1 cm−3. It can be seen that polaron hopping energy, density of state at Fermi energy and carrier mobility of films correlate with fractal dimensions of films which obtained from the power spectral densities (PSDs) analyses. It can be seen that there are a fluctuation in the polaron mass (mp) and at 500 ◦C which correspond to maximum value of fractal dimension, has minimum value. With increasing fractal dimensions, carrier mobility of films decreases and have minimum value 1.2 × 10−10 s−1 V−1 cm2.
