Abstract
X-ray reflectivity (XRR) is a powerfull tool for investigations on surface and interface structures of multilayered thin film materials. In the conventional XRR analysis, the X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. However, the calculated results have shown often strange behaviour where interference effects would increase at a rough surface. The strange result had its origin in a serious mistake that the diffuse scattering at the rough interface was not taken into account in the equation. Then we developed new improved formalism to correct this mistake. However, the estimated surface and interface roughnesses from the x-ray reflectivity measurements did not correspond to the TEM image observation results. For deriving more accurate formalism of XRR, we tried to compare the measurements of the surface roughness of the same sample by atomic force microscopy (AFM), high-resolution Rutherford backscattering spectroscopy (HRBS) and XRR. The results of analysis showed that the effective roughness measured by XRR might depend on the angle of incidence. Then we introduced the effective roughness with depending on the incidence angle of X-ray. The new improved XRR formalism derived more accurate surface and interface roughness with depending on the size of coherent X-rays probing area, and derived the roughness correlation function and the lateral correlation length. In this review, an improved XRR formalism, considering the diffuse scattering and the effective roughness, is presented. The formalism derives an accurate analysis of the x-ray reflectivity from a multilayer surface of thin film materials.
Highlights
X-ray scattering spectroscopy is a powerful tool for investigations on rough surface and interface structures of multilayered thin film materials, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] and X-ray reflectometry is used for such investigations of various materials in many fields. [15, 16, 20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] In many previous studies in X-ray reflectometry, the X-ray reflectivity was calculated based on the Parratt formalism, [1] coupled with the use of the theory of Nevot and Croce to include roughness
We show that the strange result has its origin in a currently used equation due to a serious mistake in which the Fresnel transmission coefficient in the reflectivity equation is increased at a rough interface, and the increase in the transmission coefficient completely overpowers any decrease in the value of the reflection coefficient because of a lack of consideration of diffuse scattering
We investigated the fact that the calculated result of the x-ray reflectivity based on Parratt formalism [1] with the effect of the roughness incorporated by the theory of Nevot-Croce[2] show a strange phenomenon in which the amplitude of the oscillation due to the interference effects increase in the case of the rougher surface
Summary
X-ray scattering spectroscopy is a powerful tool for investigations on rough surface and interface structures of multilayered thin film materials, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] and X-ray reflectometry is used for such investigations of various materials in many fields. [15, 16, 20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] In many previous studies in X-ray reflectometry, the X-ray reflectivity was calculated based on the Parratt formalism, [1] coupled with the use of the theory of Nevot and Croce to include roughness. [2] the calculated results of the X-ray reflectivity done in this way often showed strange results where the amplitude of the oscillation due to the interference effects would increase for a rougher surface. In contrast to previous calculations of the x-ray reflectivity, in the present analysis we consider the effect of a decrease in the intensity of penetrated x-rays due to diffuse scattering at a rough surface and rough interface. Croce’s treatment originates in the fact that the modified Fresnel coefficients were calculated based on the theory which contains the x-ray energy conservation rule at surface and interface In their discussion, the transmission coefficients were replaced approximately by the reflection coefficients by the ignoring diffuse scattering term at the rough interface, and according to the principle of conservation energy at the rough interface . The new improved XRR formalism derived more accurate surface and interface roughness with depending on the size of coherent X-rays probing area, and derived the roughness correlation function and the lateral correlation length. This article is the review article that summarized the research articles [33,34,35,36,37,38,39,40,41] and the later study
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