AVS 56th International Symposium & Exhibition
    Applied Surface Science Monday Sessions
       Session AS+EM+MS+TF-MoA

Paper AS+EM+MS+TF-MoA8
Universal Behavior of Light Scattering from Self-Affine Fractal Surfaces: A Quantitative Relationship between Roughness and EMA Models

Monday, November 9, 2009, 4:20 pm, Room C2

Session: Spectroscopic Ellipsometry II
Presenter: A. Yanguas-Gil, University of Illinois at Urbana-Champaign
Authors: A. Yanguas-Gil, University of Illinois at Urbana-Champaign
B.A. Sperling, University of Illinois at Urbana-Champaign
J.R. Abelson, University of Illinois, Urbana-Champaign
Correspondent: Click to Email
The effective medium approximation (EMA) is typically used to model the influence of roughness on the optical response of a surface or buried interface as measured by ellipsometry. Although the standard assumption of 50% material - 50% void provides useful results, the relationship between the EMA layer thickness and the surface topography is not fully understood. For example, in thin film deposition many authors have found a good correlation between the thickness of the EMA layer and the rms surface roughness measured by AFM, while others have found significant discrepancies between the time evolution of these two parameters.

Using first principles scattering models, we have analyzed the ellipsometric response of surfaces that exhibit a self-affine dependence of surface topography on the lateral scale of measurement. This type of surface roughness is found for a wide variety of real surfaces, including many deposited thin films. The calculations show that when the surface correlation length evaluated from the height-height correlation function or the power spectral density is much smaller than the incident wavelength, a universal behavior is found in the ellipsometric response. Both the amplitude of the reflected fields in the p- and s-polarizations, and the thickness of the EMA layer, depend on the product of the rms surface roughness times the average surface slope. Therefore, the linearity between roughness and the thickness of the EMA layer holds only as long as the average surface slope remains constant. That is the case when the growth obeys the predictions of dynamic scaling theory, i.e., the rms roughness and the correlation length change with time as σ ~ tβ and ξ ∼ tβ/α, where α and β are the roughness and the growth exponents, respectively. Results are presented for different materials whose optical properties cover a broad range from metals to dielectrics. An important consequence of this universality is that the ellipsometric response is mathematically separable into two independent functions, one depending only on the optical properties of the film and the other only on the surface topography.