Models

where v and A are proportionality constants which can be interpreted physically [6], The solution of eq. (7) results in a = 0.5 and /? = 0.33 for Z>top = 2, a « 0.4 and ¡3 » 0.25 for Z>top = 3, and (a + aJP) = 2 for all ZW

On the other hand, according to the VW model [8] when smoothening is produced by surface diffusion, the equation of motion becomes dh(x,t)I dt = -vi V4/j + T](x,t) (8)

where rj(x,t) has a Gaussian distribution. Equation (8) leads to a = 3/2 and ¡3 = 3/7 for Dtop = 2 and a= 1 and/?= 0.25 for Z>top = 3.

The VLD model [10] included a surface diffusion term in Eq. (7). Thus, it follows that dh(x, t)/dt = - vi + X\ V2( VJi)2 + rfa t) (9)

where v\ and X\ are proportionality constants. Equation (9) leads to a = 3/2 and ¡3 = 0.34 for .Drop = 2 and to a = 2/3 and ¡3= 1/5 for Z>top = 3.

Values of a, ¡3, and z are suitable quantities for the comparison of experimental data and theoretical models. Therefore, the preceding summary of the dynamic scaling approach provides a way for determining the dominant mechanism for the rough surface growth mode, irrespective of whether the development of the rough surface results from the accumulation or the dissolution of the solid phase.

The equations derived from the dynamic scaling theory are valid for self-affine and self-similar surfaces. Accordingly, the theory provides information about fractal properties and growth mechanisms of rough surfaces.

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