Invited Paper EL+AS+EM+MS+TF-FrM5
Roughness beyond Bruggeman's Effective Medium Approximation

Friday, October 22, 2010, 9:40 am, Room Cochiti

Surface roughness is regularly characterized with ellipsometry, which is especially sensitive for the short length scale roughness. Because of this, the roughness can be treated as a heterogeneous material modelled with an Effective Medium Approximation (EMA). The EMA layer thickness determined is often successfully related to the root mean square roughness from microscopy. A breakdown of this correspondence was recently shown [1]. This was attributed to the non-negligible influence of the characteristic length scale of the roughness. This typical characteristic length scale can approach the wavelength of the light used for many cases of surface roughness. In thus violates an important prerequisite of EMA, i.e. a variation limited to a length scale much smaller than the wavelength of light. This not only results in off-specular scattering, but also to a change in the polarization of the specular reflected light beam as probed with ellipsometry.

The applicability of an EMA to describe small surface roughness can be evaluated with the Rayleigh-Rice (RR) perturbation. In this perturbation method, the surface roughness is incorporated via its power spectral density function. Ohlidahl and co-workers [2] extensively compared Gaussian roughness distributions with EMA results. They reported that Bruggeman’s equation describes the roughness well in many situations. However, the correspondence between EMA and RR breaks down for surface heterogeneity if noble metals are involved. For example for deposited colloids, the resonance energy of the induced surface plasmon is not correct [3]. Also the optical spectra calculated with EMA for a rough silver surface can only be reproduced by RR if a very specific power spectral density is used, showing a quite large characteristic length scale.

Roughness with various length scales created by oblique incidence ion sputtering on Ag(001) were experimentally studied with normal incidence ellipsometry, also known as Reflection Anisotropy Spectroscopy [4]. The observed plasmon resonances are the result of anisotropy in the local length scale. This system allows to probe quantitatively the adequacy of the RR. One of the limits discussed is the inability to discriminate between roughness and roughness length scale for small scale roughness. The ability to monitor in-situ the evolution of the anisotropy of the roughness distribution will be addressed.

[1] B. Sperling and J. Abelson, J. Appl. Phys. 101 024915 (2007).

[2] D. Franta and I. Ohlidahl, Opt. Commun. 248 459 (2005).

[3] H. Wormeester, E.S. Kooij and B. Poelsema, Phys. Stat. Sol. A205 756 (2008).

[3] F. Everts, H. Wormeester and B. Poelsema, Phys. Rev. B 78 155419 (2008).