Diffraction characterization of rough films formed under stable and unstable growth conditions

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Characterizing the roughness of epitaxial films by diffraction techniques with respect to the step density and the rms roughness is well established. For self-affine surfaces the morphology of growing films, however, is often characterized by the correlation length $\ensuremath{\xi}$ of the height-height correlation and the roughness exponent $\ensuremath{\alpha}$ governing the behavior at small lateral distances. Recently, it has been emphasized that for unstable growth conditions, characteristic lengths (average pyramid sizes) appear that produce an oscillating character of the height-height correlation. Here we investigate the influence of both kinds of correlations on the diffraction spots. The oscillating correlation causes a splitting of the diffuse shoulder into satellites. The satellite position and half-width show characteristic oscillations depending on the scattering condition. From the latter one can determine the roughness exponent $\ensuremath{\alpha}$. The correlation length $\ensuremath{\xi}$ and the characteristic length can be evaluated from the satellite half-width and position at the out-of-phase scattering condition taking into account the rms height $w$. This model has been applied to the statistical growth of Ag adlayers on Ag(111) at low temperatures where the satellites of the diffuse shoulder point to the formation of pyramids. From the phase dependence we obtain the roughness exponent $\ensuremath{\alpha}=$$\frac{1}{2}$. The step density and the correlation length $\ensuremath{\xi}$ increase with increasing coverage while no coarsening of the pyramid sizes is observed.