Scaling exponents and growth mechanisms of W/Si multilayers determined 
by diffuse x-ray scattering from interface roughness

T. Salditt, T. H. Metzger, D. Lott and J. Peisl

Sektion Physik der Ludwig - Maximilians - Universitaet Muenchen,
Geschwister - Scholl - Platz 1,  80539 Muenchen, Germany

We have investigated the interfacial roughness of amorphous W/Si multilayers
produced by sputter deposition at varying Ar pressure.  Changing the Ar
pressure from a low value to a high one, above the thermalization threshold,
causes the energy of the impinging atoms to change from some eV to thermal
energies and the distribution of the angle of incidence to vary from near
normal to random incidence, respectively.  The evolving interface roughness
correlations have been investigated by diffuse, nonspecular x ray scattering
in the geometry of grazing incidence and exit (GID geometry).  Only this
technique allows for the full range of parallel momentum transfer necessary to
determine both the self- and cross -correlation functions from the structure
factor of the diffuse scattering for rough interfaces.

For the multilayers produced at low Ar pressure the average self- correlation
function shows the logarithmic scaling behaviour (H=3D0) predicted by the
Edwards-Wilkinson (EW) equation [1].  The curvature driven smoothening term in
this equation does not directly allow to reveal a microscopic smoothening
mechanism.  Since no driving force is present we propose resputtering of the
adsorbed ad-atoms to be the relevant mechanism, since the impinging atoms have
enough energy to cause desorption from energetically less favored sites.  On a
mesoscopic scale such resputtering is described by the term proportional to
the local curvature (Laplace term) in the EW equation.

Multilayers sputter-deposited at large Ar pressure evolve to a very distinct
roughness morphology.  On the micrograph obtained by TEM a columnar structure
is observed that is well replicated through the top ten bilayers.  This
conformal roughness is analyzed quantitavely by diffuse x-ray scattering.
Both the static (H=3D0.7) and dynamic scaling exponents (z=3D1.37) are
determined and are found to agree well with the growth mechanism following the
Huygens principle, proposed by Tang et al [2].  A simple explanation is given
why this growth behavior is observed rather than that discribed by the
Kadar-Parisi-Zhang (KPZ) equation.  It is based on the fact that at high Ar
pressure the sputtered atoms are thermalized by collisions with the Ar atoms
and arrive at the substrate surface under random incidence, thus leading to
the observed "cusps" caused by shadowing effects.

[1] T. Salditt, T. H. Metzger, and J. Peisl, Phys. Rev. Lett. 73 (16), 2228 (1994)
[2]  C. Tang, S. Alexander and R. Bruinsma, Phys. Rev. Lett. 64(7),772 (1990)