High entropy alloy (HEA) thin films of CrCoCuFeNi are grown on stainless steel substrate using radiofrequency (RF) magnetron sputtering method at different sputtering times (30, 60 and 90 min), substrate temperatures (room temperature, 100 and 200 deg. Celsius) and RF powers (100, 150 and 200 W). The nanoscale morphology and topography of the thin films are obtained using an atomic force microscopy (AFM) method. The average surface roughness, interface width, fractal and multifractal characteristics of the films are presented. It is shown that the average surface roughness and interface width decrease with the time of deposition while considering the combination of the other factors. The autocorrelation and height-height correlation functions reveal that these surfaces are self-affine and exhibit fractal characteristics. The increase in sputtering power, with different combinations of time and temperature, is related to large fractal dimension and small lacunarity coefficient. The increase in substrate temperature (for different combinations with time and RF power) is shown to enhance the spatial roughness of the HEA thin films. A multifractal analysis undertaken using generalized fractal dimension, mass exponent against moment order and multifractal spectrum reveal that all the films have a multifractal character; and the films deposited at high temperatures and powers exhibit the strongest multifractal behaviour.