X-ray reflectivity of multilayers with non-continuous interfaces

Abstract

X-ray specular reflectivity and diffuse scattering calculated using the traditional multilayer model, which assumes continuous, non-intersecting interfaces, are capable of fitting the experimental data obtained on multilayers with non-continuous interfaces. However, wrong refined electron densities and interface roughness are the consequence of an inappropriate structure model. A modification of the Parratt optical formalism combined with the application of the distorted-wave Born approximation was suggested for evaluation of the small-angle x-ray scattering in multilayers with non-continuous interfaces. The influence of the multilayer discontinuity on the small-angle x-ray scattering is characterized by modified Fresnel reflection and transmission coefficients of individual interfaces and by changes in the optical paths in individual layers. The suggested theoretical approach is illustrated on Fe/Au multilayers. Parameters of the structure model obtained from the small-angle x-ray scattering were verified by comparison with results of transmission electron microscopy.

GISAXS study of the alignment of oriented carbon nanotubes grown on plain SiO2/Si(100) substrates by a catalytically enhanced CVD process

“…However, given that the major contribution to our GISAXS signal steams from the high reflectivity of our samples, we must account for this reflectivity. Therefore the problem was tackled with an approach using the recursive layer-by-layer Parrat formalism [23,[25][26][27][28][29][30] which is briefly recalled in Section 3.3) to evaluate the Fresnel coefficients. A log-normal size distribution function for the height accounted for the perpendicular disorder.…”

“…The reflectivity coefficients used in the DWBA formalism are calculated within recursive layer-by-layer Parrat formalism [23,[25][26][27][28][29][30], which is briefly recalled in Section 3.3). Thus, the total scattered intensity is:…”

“…The specular reflectance of our discontinue multilayer system (structure) consisting in four interfaces (Vacuum/Co, Co/C, C/SiO 2 and SiO 2 /Si) with interfacial roughness is calculated by use of a recursive classical exact layer by layer method, based on Fresnel coefficients within the Parratt optical formalism and the dispersion model [23,[25][26][27][28][29][30] (Figs. 3 and 4).…”

Thermally activated crystallization of Nb2O5 grown on Pt electrode

“…The free parameters of the multilayer model were the electron densities and thicknesses of individual layers, the root-mean-squared (rms) roughness of the interfaces and the rms roughness of the sample surface. For the calculation, the classical optical theory of Xray reflection [22][23][24] in the implementation from [25] was used.…”

Co layer fragmentation effect on magnetoresistive and structural properties of nanogranular Co/Cu multilayers

“…37 The progressive decrease in the NM/M optical contrast and of the best-fit quality following the decrease in t Co could be possibly due to Co-Cu interdiffusion or to the fragmentation process of the layers. 38 However, layers undulations 39,40 may appear during sample growth due to, e.g., shadowing effects. 9,41 In our case, these undulations are actually observed ͓see Fig.…”