Angle Of Total External Reflection Research Articles

Performance study of polycapillary optics for hard x rays

In order to investigate the feasibility of using Kumakhov capillary x-ray optics for high energy x-ray applications, measurements have been performed on the behavior of capillary optics from 10 to 80 keV. Transmission efficiencies of straight polycapillary fibers of different types have been measured as a function of source location and x-ray energy. The measurements are analyzed using a geometrical optics simulation program, which includes roughness and waviness effects. Despite the low critical angle for total external reflection at high energies, capillary x-ray optics appear promising for many hard x-ray applications. Transmission measurements at high energies have also proven to be a very sensitive tool in capillary quality analysis.

The domain structure of LB multilayers prepared from fatty acid salts

Langmuir-Blodgett (LB) multilayers from fatty acid salts can be characterized by finite sized scattering aggregates. High-resolution atomic force microscopy maps reveal a substructure of molecular ordering. These blocks are to be considered as 3D domains. Furthermore, macroscopic holes and scratches appear at the surface. These defect structures have to be taken into account when interpreting observed X-ray and neutron reflectivity curves. The density loss due to the holes can be detected from the angular shift of the critical angle of total external reflection. Offdiagonal scans demonstrate a slight inclination of domains relative to each other. Neutron reflectivity patterns of sequentially deuterated and hydrogenated carbon chains provide information about the disorder of the organic chains. In the second part of the paper a structure model of the molecular order within the domains is developed using 16 in-plane Bragg peaks and their truncation rods measured by X-ray grazing incidence diffraction. The refined 3D unit cell contains at least four monolayers in a herringbone arrangement of the hydrocarbon chains. Its stability is given by the inter-chain coupling between two neighbouring monolayers.

Highly asymmetric differential X-ray reflectometry of multilayer films

Bragg scattering of X-ray radiation in a highly asymmetric geometry from Langmuir-Blodgett films was investigated. A complex multi-peak structure was observed in the angular distribution of the scattered X-rays. The proposed simple explanation and the corresponding expressions for the peak positions are in good agreement with the experimental results. The same interpretation is successfully applied to experimental results for multilayer films of a quite different origin, the crystalline W/Si superstructures. Based on this agreement and the generalization of the results obtained we propose a new method of monitoring of angular distribution of X-rays propagating in the film at very small angles. Combined with the expressions obtained, it can be applied, in particular, to the determination of the critical angle of total external reflection from multilayer films which provides additional information compared with a conventional technique. Possibilities to study film imperfections are also outlined.

Enlarged quantum well in a semiconductor superlattice studied by depth resolved grazing incidence x-ray diffraction

A lattice matched {InP/GaInAs}30/InP[001] superlattice containing an enlarged quantum well (EQW) was investigated by means of grazing incidence x-ray diffraction (GID) using synchrotron radiation. The in-plane (220) rocking curve was measured choosing a grazing angle for the incident beam with respect to the surface, αi. At the angular position of maximum intensity we recorded the intensity distribution of the reflected beam normal to the surface (rod scan) using a position sensitive detector. The rod contains information about the density variation towards the surface normal. Instead of a single superlattice Bragg peak we found a double peak which can be explained by the phase shift of the partial x-ray waves scattered at the two superlattices sandwitching the EQW. For fixed αithe intensity ratio of the two peaks is a measure of the EQW thickness. An additional advantage of the GID technique is that this ratio can be modified by changing the penetration depth of the probing x-ray beam into the sample. This is performed by keeping αi smaller or larger than the critical angle for total external reflection. The EQW thickness and its position below the surface is determined by simulation of the recorded rod scans using the kinematic approach of the GID. Both quantities are obtained with monolayer accuracy.

Properties of grazing-angle X-ray standing waves and their application to an arsenic-deposited Si(111) 1 × 1 surface

Grazing-angle diffraction of X-rays by crystal planes normal to a surface generates dynamical (lattice-modulated) standing waves, which are used in this paper to determine the in-plane structure of arsenic adatoms on an Si (111) surface of the 1 × 1 structure. The X-ray field, formed by the interference of the incident, specular-reflected and Bragg-diffracted beams above the surface, has two components with and without intensity modulation in the direction of the reciprocal-lattice vector parallel to the surface. The two components behave differently as a function of X-ray glancing incidence angle on the surface in the vicinity of the critical angle for total external reflection. This property has been exploited to determine the ordering of the As atoms accurately using X-ray fluorescence signals observed from a sample in ultra-high vacuum at a synchrotron source. The data show highly ordered As atoms occupying the threefold-coordinated sites on the bulk-like Si (111) surface. Displaced arsenic positions are not supported by the observation. The conclusion is fairly insensitive to the vertical height of the overlayer atoms used in the analysis, in accordance with the slow variation of the field profile along the surface normal. The grazing-angle X-ray standing-wave method allows model-independent determination of the registry of foreign atoms at a crystal surface with a positional accuracy of a few hundredths of an A.

Surface-Induced Shift of the Hexagonal-to-Isotropic Phase Transition in a Lyotropic System Studied by X-ray Reflectivity

X-ray reflectivity measurements of the free surface of a C 12 E 5 + water mixture at a mass fraction of the surfactant of 0.4 are presented. This system forms a hexagonal LC-phase at ambient temperatures. At a temperature of T = 23.82°C the typical Bragg pattern for hexagonal symmetry is no longer observed when the angle of incidence of the beam is larger than the critical angle of total external reflection, α c . If the angle of incidence is smaller than α c , well-pronounced reflexes are observed at the same temperature. This shows that the anisotropic phase is stable to higher temperatures at the surface as compared to the bulk.

Core excitons in silicon and silicon oxides

Using a newly developed reflectometer we have measured the reflectivity at the silicon K edge for different silicon compounds. Combining these measurements with silicon L edge reflectivity measurements carried out on a different reflectometer we determined the binding energy of core excitons at the L edge. The results show that it is possible to carry out reflectivity measurements with the resolution necessary for the determination of the exciton parameters. Comparison with literature values shows that a rigid Kramers–Kronig analysis is not needed when the angle of incidence is well below the critical angle of total external reflection.

Synchrotron-radiation plane-wave GID topography (abstract)

X-ray-diffraction topography is a traditional tool for investigating the real structure of crystals and provides high sensitivity to lattice constant variations with good space resolution. However, recent advances in technology and the growing importance of surface regions of single-crystal and multilayer systems require new approaches to this method, which are made possible by the high brightness and wide tunability of synchrotron radiation. In this work the SR plane-wave grazing-incidence diffraction (GID) topography is discussed as an effective tool for depth-resolved investigations of near-surface defect structures in single crystals and epitaxial layers. The favorable properties of synchrotron radiation enable one to avoid the usual limitations on applicability of this diffraction geometry and investigate all classes of defects in real materials. The experiments were performed at the beamlines ROEMO1 and CEMO of HASYLAB, using double-crystal Ge/asymmetric Si monochromators. The image formation of near-surface dislocations and the effects of refraction on rough surfaces were investigated. Oblique diffraction planes were used to compare the topography in skew incoplanar and coplanar geometries. The latter is shown to be more effective, as it utilizes the wavelength tunability of SR and allows one to vary the diffraction conditions in a wide range from usual highly asymmetric to grazing incidence below the critical angle of total external reflection (and the penetration depth from hundreds to tens of nanometers) without off-plane rotations and provides pictures free of complicated geometrical distortions. The dislocation images at different diffraction conditions proved to be qualitatively the same for near-surface defects, while the structure distortions, produced by the defects in the underlying layers, become invisible at grazing incidence, due to both depth resolution of the method and inevitable loss of lattice-parameter resolution. This might be a substantial advantage for characterization of films on substrates with a low perfection. Thus SR based plane-wave GID topography provides all the features of usual asymmetric topography and has substantial advantages for surface defect analysis.

Grazing incidence X-ray photoemission and its implementation on synchrotron light source X-ray beamlines

Grazing incidence X-ray photoemission spectroscopy provides a method of obtaining information about surface chemical composition as well as the variation of composition with depth. Photoemission spectra are taken as X-rays are directed onto a surface over a range of incidence angles near the critical angle for total external reflection. The technique is particularly suited to the study of surface layers in the thickness range 10–40 Å, using X-rays in the energy range of 1–2 keV. We have implemented the technique in a geometry that minimizes distortion of the spectral lineshape by keeping a fixed relationship between the sample and the electron spectrometer. We present data taken in the laboratory that illustrate its application to the study of oxide films on Ge. The counting time for a spectrum would be shortened considerably by implementing the method on a soft X-ray beamline at a synchrotron light source. We present a method for doing so that retains the advantages of a fixed geometry between the sample and the electron spectrometer.

Comparison between experimental and theoretical rocking curves in extremely asymmetric Bragg cases of X-ray diffraction

Double-crystal rocking Curves from a highly perfect silicon crystal were taken in extremely asymmetric schemes, in which the glancing angles of the incident X-rays were very close to the critical angle of total external reflection. The experimental rocking curves were compared with theoretical calculations based both on an ordinary dynamical theory of diffraction and also on an extended dynamical theory, which uses a more exact solution of the fundamental equation of the dynamical theory and takes the effect of specular reflection into account. It is demonstrated from such a comparison that, in the case of extremely asymmetric diffraction, the ordinary treatment of the dynamical theory of diffraction is not valid; in contrast, the extended theory explains the rocking curve very well.

Scattering by locally periodic one-dimensional potentials

One-dimensional scattering by an arbitrary finite periodic potential is considered. Closed expressions for reflection and transmission (tunneling) amplitudes and probabilities are obtained. Equations determining the positions of transmission resonances are derived. The appearance of a band structure of the energy eigenspectrum as the number of barriers increases is investigated. The application of the results for the description of the reflection of X-rays incident under an angle slightly above the critical angle for total external reflection on the superlattice structures is discussed.

The influence of specular interface reflection on grazing incidence X-ray diffraction and diffuse scattering from superlattices

Superlattices (SL) with a large difference in the refractive index between the alternating layers give rise to specular reflection from the intrinsic interfaces of the SL which proves very efficient for small incident or exit angles near the critical angle of total external reflection. This influences the intensity of grazing incidence X-ray diffraction (GID) and non-specular X-ray scattering (NSXR). Additional peaks were found besides the common features. They are explained by waves scattered in transmission geometries and measured above the sample surface due to subsequent specular interface reflection. The experimental findings are interpreted by Umweganregung in terms of the distorted wave Born approximation (DWBA).

Near-surface region characterization by extremely asymmetric Bragg reflection topography

Near-surface regions of Cd1−xMnxTe and Hg1−xCdxTe epilayers (down to tens of angstroms) on (001) GaAs substrates have been characterized by extremely asymmetric Bragg reflection topography (EABRT) with the laboratory x-ray source condition and a Lang camera, using x-ray grazing incidence angles less than the critical angle for total external reflection. The experimental topographs obtained in the present work illustrate the potential of the EABRT technique for nondestructive characterization of near-surface regions of crystals. The resolution of an image in EABRT is discussed in detail.

Determination of residual stress in Cr-implanted Al2O3 by glancing angle x-ray diffraction

We report x-ray diffraction measurements of residual stress in sapphire crystals implanted with Cr+ ions. Stress is determined by measuring both in-plane and out-of-plane lattice constants. Bragg peak positions are measured to determine average stress, while peak widths are measured to determine its variation. Using angles of incidence close to the critical angle for total external reflection of x rays, we compare measurements confined to within ∼2.5 nm of the surface and measurements over the ∼80 nm thickness of the implanted region. These x-ray residual stress determinations are consistent with those based on indentation crack length, but were less by a factor of 10 than reports based on cantilever bending.

X-ray scattering from interfacial roughness in multilayer structures

A quantitative theory of the nonspecular scattering of x rays from multilayer structures having rough interfaces is presented. The results are valid for arbitrary polarization and angles of incidence (measured from the normal) less than the critical angle for total external reflection. A structural model is adopted wherein each interface is assumed to be described by a surface having statistically random roughness with a well-behaved power spectrum. In addition, the model accounts for arbitrary correlation of the roughness between different interfaces. Calculations are presented for a variety of roughness configurations to investigate the dependence of the nonspecular scattering on the fundamental structural parameters. In particular, it is shown that the scattering from correlated roughness exhibits characteristic resonance behavior (quasi-Bragg diffraction).

Environments of ion-implanted As and Ga impurities in amorphous silicon.

Glancing-angle x-ray-absorption fine-structure experiments are reported for arsenic and gallium implants in amorphous silicon. Total impurity concentrations range from 5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ to ${10}^{21}$ atoms ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. The effects of hydrogen and chemical compensation have been explored. The hydrogen concentration in the films has been derived from the critical angle for total external reflection. Evidence is found for extra hydrogen bound to impurities. The presence of phosphorus causes gallium to adopt fourfold-coordinated sites. From the shape of the fine-structure envelope, more than one impurity site has been established. In particular, both arsenic and gallium exhibit a minority well-ordered site that we propose provides the source of electronically active centers. This assertion is supported by structural differences resulting from chemical compensation and also thermal annealing of ion-implanted films. As the impurity dilution increases, an approximate correspondence has been found between the densities of these well-ordered sites and those reported for dangling-bond silicon states in hydrogenated amorphous silicon.

An in situ x-ray diffraction method for the structure of amorphous thin films using shallow angles of incidence

A technique for the structural characterization of thin amorphous films employing synchrotron radiation parallel beam x-ray optics at grazing angles of incidence is detailed. At incident angles near to the critical angle for total external reflection, sampling of specimens may be achieved via the evanescent mode. The parallel beam geometry allows the use of a technique in which a 2θ detector, incorporating a parallel plate collimator, scans diffraction data for a given incident angle. For a specified wavelength, the incident angle chosen will determine the penetration of the radiation into the sample (∼10–1000 Å). The data must be corrected for significant peak shifting resulting from x-ray refraction, as well as for the effects associated with conventional θ:2θ scans. Preliminary data resulting from the first application of this technique to amorphous hydrogenated silicon:carbon thin films, deposited onto crystalline silicon substrates, will be presented and discussed. Conventional θ:2θ powder diffraction data will also be presented as a comparative standard.

Characterization of porous silicon layers by grazing- incidence X-ray fluorescence and diffraction

X-ray fluorescence and diffraction has been performed on porous silicon samples at incidences near the critical angle for total external reflection. By fitting the X-ray fluorescence intensity as a function of the incidence angle, density and density variarations versus depth have been obtained for porouslayers prepared under different conditions. Good agreement with other techniques has been obtained. Grazing-incidence diffraction measurements show broad diffuse scattering around Bragg reflections, which is related to the pore structure. Therefore, structure information concerning the mean pore size, correlations between pores positions, the local lattice distortions within the porous silicon in relation to the existence of pore, has been demonstrated. Informations obtained from single measurement from the Full-Width at Half Maximum and from the tails of the diffuse scattering are discussed.

Grazing incidence diffraction of X-rays in semiconductor heterostructures: Application of the integral mode

The grazing incidence diffraction (GID) of X-rays enables to characterize thin subsurface layers in semiconductor heterostructures having a thickness smaller than 100 nm. The dynamical theory of X-ray diffraction is extended for the case of identical in plane lattice parameters at the heterointerface. Especially the variation in the specular diffracted (220) Bragg intensity measured with open detector (integral mode) is evaluated in dependence on the grazing angle Φ0 of the primary beam with respect to the (001) surface. Using a parallel beam an oscillation behaviour occurs at the high angle side Θc < Φ0≦0.50(Θc is the angle of total external reflection) of the diffraction curveI(Φ0) which can be related to the thickness of the perfect crystalline part of the epilayertK. Having an incident beam divergence and a small difference in the effective refractive indices of the layer and the substrate the oscillations are almost leveled. They are further visible in case of a minute inclination of the (220) lattice plane with respect to the surface normal. In the interval 0 < Φ0<Θc the slope of the integral curve depends on the thickness of the subsurface layertAwhich does not contribute to the Bragg diffraction. The integral mode is sensitive for layers of about 0<tA<15 nm and 15<tK<80 nm. The proposed theory working principally for multilayer structures is presently suplicated to interpret GID curves ofAIIIBvheterostructures.

Extreme asymmetric X-ray Bragg reflection of semiconductor heterostructures near the edge of total external reflection

Synchrotron radiation has been used to measure the rocking curves from a (GaIn)(AsP) single layer grown on an InP (100)-oriented substrate. For angles of incidence ΦB = (ΘB − ϕ) ≤ 0.7° measured at the Bragg angle ΘB (ϕ is the angle between the diffracting lattice plane and the surface), the rocking curve (RC) is very strongly influenced by total external reflection (TER). This causes a decrease in the full width at half-maximum (FWHM) and an asymmetrical shape for the RC for small ΦB. Both of these effects are due to the Bragg-angle shift from the actual incident angle Φ which is not considered in the conventional dynamical theory. In this paper the essential influence of TER on any thin-layer rocking curve is investigated using a numerical solution of the extended dynamical theory. The pattern can be interpreted up to ΦB ≥ ΘC (ΘC is the angle of TER) by semiempirical incorporation of the results of the extended theory with the coupling formalism of Barrels, Hornstra & Lobeek [Acta Cryst. (1986). A42, 539–545].