J. Wollschlager et al., DIFFRACTION CHARACTERIZATION OF ROUGH FILMS FORMED UNDER STABLE AND UNSTABLE GROWTH-CONDITIONS, Physical review. B, Condensed matter, 57(24), 1998, pp. 15541-15552
Characterizing the roughness of epitaxial films by diffraction techniq
ues with respect to the step density and the rms roughness is well est
ablished. For self-affine surfaces the morphology of growing films, ho
wever, is often characterized by the correlation length xi of the heig
ht-height correlation and the roughness exponent a governing the behav
ior at small lateral distances. Recently, it has been emphasized that
for unstable growth conditions, characteristic lengths (average pyrami
d sizes) appear that produce an oscillating character of the height-he
ight correlation. Here we investigate the influence of both kinds of c
orrelations on the diffraction spots. The oscillating correlation caus
es 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 roughn
ess exponent a. The correlation length 5 and the characteristic length
can be evaluated from the satellite half-width and position at the ou
t-of-phase scattering condition taking into account the rms height w.
This model has been applied to the statistical growth of Ag adlayers o
n Ag(lll) at low temperatures where the satellites of the diffuse shou
lder point to the formation of pyramids. From the phase dependence we
obtain the roughness exponent alpha=1/2. The step density and the corr
elation length 5 increase with increasing coverage while no coarsening
of the pyramid sizes is observed.