In general, roughness evolution during the growth/etching process can be described in frames of the scaling theory. According to it, static roughness exponent determines the asymptotical behaviour of power spectrum at high spatial frequencies while dynamic exponent determines the relation between "growth-induced" roughness term and speed of deposition/etching.

For the details see: Stanley, Barabasi "Fractal concepts in surface growth"; also Majaniemi et al, "Kinetic roughening of surfaces", Phys. Rev. B 1996, 53:8071-82.

http://dx.doi.org/10.1103/PhysRevB.53.8071

For an experimental case, see e.g. Peverini et al. "Dynamic scaling of roughness at the early stage of tungsten film growth", Phys. Rev. B 2007, 76:045411

http://dx.doi.org/10.1103/PhysRevB.76.045411

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