Platinum and gold thin films have been fabricated by filtered vacuum arc deposition perpendicularly on rough silicon and glass substrates. Four sets of samples have been prepared with different thickness (d). Two sets were very thin films of Pt (1.31 ≤ d ≤ 11.66 nm ) and Au (1.77 ≤ d ≤ 10.46 nm ) and two sets were thicker films also of Pt (7 ≤ d ≤ 80 nm ) and Au (34 ≤ d ≤ 200 nm ). The roughness mean-square ω of the films have been measured, as a function of the film thickness d, by scanning tunneling microscopy (STM). We verified that the dynamical scaling relation ω(t) ~ t^β, where β is the growth exponent, is obeyed for the thicker films but it is not obeyed for the very thin films. These cases are analyzed taking into account the films growth theory.