Conventional X-ray Reflectivity Research Articles

Analysis of surface roughness correlation function by X‐ray reflectivity

X‐ray reflectivity (XRR) is a powerful tool for the analysis on surface and interface roughness. In the conventional XRR analysis, the reflectivity was calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot–Croce. We have developed an improved XRR formalism which derives more accurate surface and interface roughness. In this study, we introduced the effective roughness depending on the incidence angle of X‐rays. The newly developed XRR formalism, which derives more accurate surface and interface roughness, is found to be dependent on the size of coherent X‐rays probing area, and further derives the roughness correlation function as well as the lateral correlation length. Copyright © 2016 John Wiley & Sons, Ltd.

Recent Developments in the X-ray Reflectivity Analysis

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.

Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation

X-ray reflectivity (XRR) is usefull tool to estimate surface and interface roughness. In the conventional XRR analysis, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behavior due to the fact 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. 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) and XRR. The results of analysis show that the effective roughness measured by xrrmay depend on the angle of incidence. In this paper, it shows that new improved XRR formalism which derives more accurate surface and interface roughness with depending on the size of the probing area of coherent X-rays.

Improvement of surface and interface roughness estimation on X-ray reflectivity

In the conventional X-ray reflectivity (XRR) analysis, the reflectivity is calculated based on the Parratt formalism, incorporating the effect of the interface roughness according to Nevot and Croce. However, the results of calculations of the XRR have shown strange outcomes, where interference effects increase at a rough surface because of a lack of consideration of diffuse scattering within the Parratt formalism. Therefore, we have developed a new improved formalism in which the effects of the surface and interface roughness are included correctly. In this study, for deriving a more accurate formalism of XRR, we tried to compare the measurements of surface roughness of the same sample by atomic force microscopy (AFM) and XRR. It is found that the AFM result could not be completely reproduced even with the improved XRR formalism. By careful study of the AFM results, we determined the need for an additional effective roughness term within the XRR simulation that depends on the angle of incidence of the beam.

Improvement of X-ray reflectivity calculation on surface and interface roughness

In the conventional X-ray reflectivity (XRR) analysis for the estimation of multilayer surface, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behaviour due to the fact 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. In this study, we show applying of new improved formalism using a transmission electron microscope (TEM) observation result. The result of interfacial roughness by using the conventional XRR formulae showed large difference with the TEM result, and derived wrong structure of surface. While, the result by new improved formalism reproduce the TEM result well, but need appropriate parameters in transmission coefficient. It shows that new improved XRR formalism derives more accurate analysis of the XRR, but the reduced Fresnel coefficients with physical grounds in the reflectivity equation are need in further research.

Chemical selective microstructural analysis of thin film using resonant x-ray reflectivity

Strong modulations of the reflected x-ray intensities near the respective absorption edges of the constituent materials promise to determine layer composition of thin film structures along with spectroscopic like information. Near the absorption edge, the orders of magnitude more contrast beyond the pure electron density distributions of materials find an approach to overcome the low density difficulty of the conventional x-ray reflectivity technique. These aspects are explained by experimental studies on partially decomposed boron nitride thin films. Chemical composition profile is determined from free surface to the embedded buried layer with depth resolution in nanometer scale. The results of resonant reflectivity for chemical analysis are correlated with depth dependent x-ray photo electron spectroscopy.

Application of kinoform lens for X-ray reflectivity analysis

In this paper the first practical application of kinoform lenses for the X-ray reflectivity characterization of thin layered materials is demonstrated. The focused X-ray beam generated from a kinoform lens, a line of nominal size approximately 50 microm x 2 microm, provides a unique possibility to measure the X-ray reflectivities of thin layered materials in sample scanning mode. Moreover, the small footprint of the X-ray beam, generated on the sample surface at grazing incidence angles, enables one to measure the absolute X-ray reflectivities. This approach has been tested by analyzing a few thin multilayer structures. The advantages achieved over the conventional X-ray reflectivity technique are discussed and demonstrated by measurements.

Instrumentation for X-ray reflectivity in micro area: present status and future outlook

X-ray reflectivity is sensitive to slight structural changes along the depth of layered materials in the order of sub-nanometers or even smaller. This property is extremely promising for the observation of buried interfaces, but the conventional X-ray reflectivity technique unfortunately lacks spatial resolution. The method looks at quite a large area, typically mm2∼ cm2of the sample, and this often makes it difficult to analyze realistic problems in modern nano sciences and technologies. The present article discusses instrumentation for upgrading the X-ray reflectivity technique to give it a much higher spatial resolution. Recent preliminary results with high-energy white X-rays are reported.

Resonant soft x-ray reflectivity of organic thin films

At photon energies close to absorption edges in the soft x-ray range, the complex index of refraction, n=1−δ−iβ, of organic materials varies rapidly as a function of photon energy in a manner that strongly depends on the chemical moieties and functionalities present in the material. The authors present details of how these molecular structure specific variations in the complex index of refraction can be utilized to enhance and tune the contrast in reflectivity experiments of organic films. This near edge contrast enhancement mimics the specific contrast achieved through deuterium labeling in neutron reflectivity (NR). This relatively new x-ray approach, resonant soft x-ray reflectivity (RSoXR), thus combines aspects of NR and conventional x-ray reflectivity (XR), yet does not require special chemical procedures. The capabilities of RSoXR are exemplified using a number of polymeric bi- and multilayers. Furthermore, a direct comparison of RSoXR to conventional x-ray reflectivity and NR for polystyrene and poly(methyl methacrylate) bilayers verifies that RSoXR is an excellent alternative tool for the characterization of organic thin films. The influence of the longitudinal and transverse coherence properties as well as the divergence of the x-ray or neutron beam on the capabilities and limitations of each reflectivity variant is discussed.

Phasing of resonant anomalous X-ray reflectivity spectra and direct Fourier synthesis of element-specific partial structures at buried interfaces

A formalism for model-independent determination of element-specific partial structures at buried interfaces using the phase-dependent behavior of resonant anomalous X-ray reflectivity (RAXR) data is described. Each RAXR spectrum (i.e.reflectivityversusenergy at a fixed momentum transfer near the absorption edge of interest) is uniquely constrained by the amplitude and phase of the resonant partial structure factor with pre-determined non-resonant total structure factor and anomalous dispersion corrections of the resonant species. The element-specific partial density distribution is then imaged by discrete Fourier synthesis with the partial structure factor. The utility of this approach is demonstrated in the comparison of Rb+and Sr2+distributions at muscovite (001)–aqueous solution interfaces derived by model-independent and model-dependent approaches. This imaging method is useful for rapid determination of complex buried interfacial structures where element-specific atomic distributions are poorly constrained by conventional X-ray reflectivity analysis.

Time-resolved energy dispersive x-ray reflectometry measurements on ruthenium phthalocyanine gas sensing films

The energy dispersive (ED) variant of the conventional x-ray reflectivity (XR) provides an atomic scale determination of the morphological characteristics of thin films, such as their thickness and surface roughness. We report on the in situ EDXR measurements of the (minimal) morphological changes of ruthenium phthalocyanine gas sensing thin films. A series of reflectivity spectra have been collected, during the exposure of the films to a gas flux of nitrogen oxides (NOx) molecules. The measurements allowed a very high density time sampling of the evolution of the two morphological parameters, providing important information on the gas-film interaction.

Transition radiation from electrons: Application to thin film and superlattice analysis

The transition radiation from nonrelativistic electrons moving in periodical nanostructures is discussed in view of its application to surface and interface analysis and thickness measurements. The spectrum of this radiation is shown to deliver information on the investigated sample that is similar to that provided by conventional x-ray reflectivity methods. An analytical expression for the intensity of electromagnetic radiation from the electrons passing through the periodical multilayers has been derived. Numerical examples of radiation spectra are given for some typical sample models, and general conditions for the observation of these spectra with a background of bremsstrahlung are discussed.

Grazing incidence X-ray studies of twist-bonded Si/Si and Si/SiO 2 interfaces

Twist-bonded Si/Si (0 0 1) and Si/SiO 2 interfaces have been investigated by grazing incidence X-ray scattering methods. For Si/Si (0 0 1) bonding, conventional X-ray reflectivity reveals the good quality of the interfaces in terms of flatness and roughness. In-plane grazing incidence diffraction measurements around the (2 2 0) reflection show satellite peaks close to the substrate and the layer diffraction peaks. These sharp satellites are produced by a periodic displacement resulting from a very regular buried dislocation network. The Si/SiO 2 bonding has been studied with X-ray reflectivity within a transmission geometry. The analysis of the data shows the high quality of both bonded Si/SiO 2 and thermal oxide SiO 2/Si interfaces.

X-ray scattering studies of thin films and surfaces: thermal oxides on silicon

A triple-axis X-ray spectrometer has been used to examine the reflectivity and surface scattering from silicon wafers with various thicknesses of oxide surface layers (from 10 to 100 AA). The X-ray techniques provide accurate information on the thickness of the surface oxide layer, the electron density of the roughness of both the surface interface and the substrate to layer interface. The use of a triple-axis spectrometer has two important advantages over the more conventional X-ray reflectivity techniques. It allows accurate reflectivity measurements to be carried out on samples which are, macroscopically, far from flat, such as semiconductor wafers in preparation for device fabrication. It also enables the intensity of the specularly reflected X-ray beam to be measured without contamination from the appreciable small-angle scattering which can occur from a microscopically rough surface. To illustrate this point, reflectivity measurements from a high-quality glass optical flat are also described.