In this work, silver thin films were prepared using sputtering at different deposition times with the nanoscale thickness. To investigate their surface morphology, atomic force microscopy (AFM) and scanning electron microscopy (SEM) were employed. The surface topography of the samples studied using the AFM. The results revealed that, the roughness of the thin films enhanced by increasing the sputtering time. The permutation entropy (PE) was introduced as an interesting parameter to characterize the surface morphology. At the best of our knowledge, it is the first time one uses the PE for characterizing the thin films. Although the roughness might always enhance by increasing the film thickness, it was not the case for PE. The PE was found to be an independent parameter for characterizing the surface of thin film.