Influence of roughness distributions and correlations on x-ray diffraction from superlattices

Abstract

Interfacial roughness in superlattices is currently a topic of significant interest as a result of its impact on device applications and its influence on thin-film phenomena. In this work we examine the effects of interfacial roughness on x-ray diffraction from superlattices. By means of a Taylor expansion of the amplitude reflection coefBcient of the multilayer, we present general expressions for the specular, diffuse, and total diffracted intensity from a rough multilayer and examine how these quantities are influenced by roughness distributions and correlations among the interfaces. We present analytical solutions for exemplary structures including superlattices with no roughness, correlated roughness, uncorrelated roughness, and partially correlated roughness. We also present a model for cumulative roughening in multilayers and characterize its diffraction signature. We show how specific configurations of interfacial roughness give rise to a variety of additional features in diffraction spectra beyond the customary pseudo-Debye-Wailer attenuation. Specifically, we illustrate how roughness distributions induce broadening of the diffraction features, and how modulations in the diffuse scattering result directly from interfacial roughness correlations. We also show that partial correlation of interfacial roughness constitutes a second important source of peak broadening.

Experimental analysis of the surface roughness evolution of etched glass for micro/nanofluidic devices

“…Figure 5 shows representative histograms of AFM roughness height data at different etching times in horizontal etching. Statistical distribution of etched material surface has been assumed to be Gaussian in published literature [17,18]. However, Figure 5 shows that the histogram of the AFM surface height data appears to be more heavy-tailed than Gaussian.…”

“…In most studies random roughness is assumed to possess a Gaussian or Uniform distribution [17][18][19][20][21][22]. Relatively few works attempt to experimentally verify this assumption for the processed surfaces involved.…”

Multiple order parameter configurations in superconductor/ferromagnet multilayers

“…The data were fitted using the Parrat and Nevot-Croce recursion relation, which takes into account the electron density height fluctuations at the interface. 11,12 Within the fit procedure the roughness of each single layer was supposed to be independent on the roughness of other layers (the case of uncorrelated roughness 13 …”

Depth Resolved Structural Studies in Multilayers Using X-ray Standing Waves

“…Therefore, the diffuse scattering from the uncorrelated part of the roughness does not depend upon the scattering angle, while that due to correlated part of the roughness varies with the scattering angle, being maximum at the Bragg angle (due to constructive interface between various amplitudes). Thus the diffuse scattering measurements at Bragg peak is dominated by the correlated part of the roughness while that at scattering angle corresponding to a minimum in the reflectivity is dominated by the uncorrelated part of the roughness [17,19]. Therefore, in Figure 3 curve (a) gives the in-plane correlation length of the correlated part of the roughness as 300 nm, while curve (b) gives that of the uncorrelated part of the roughness as 50 nm.…”