Monolithic Monochromator Research Articles

On the design of a monolithic 4-bounce high resolution X-ray monochromator

A monolithic monochromator (+n, −n, −m, +m) made of a single block of Ge crystal designed for CoKα1 radiation was developed and tested numerically and experimentally by means of X-ray diffraction. The advantage of monolithic devices is their mechanical stability and the alignment of such optics is much easier than with polylithic optics, but the development of these devices is rather demanding. The presented monochromator belongs to a group of coplanar in-line devices, which means that the input beam is parallel with the output beam. For the estimation of the spectral and angular properties of a diffracted beam of this monochromator (such as bandpass width, output divergence and input acceptance) we used a numerical approach which we call spectral-angular function. It takes into account both the vertical and the horizontal divergence of the input radiation and uses two-beam X-ray dynamical theory of diffraction. Experimentally, the monochromator was tested by means of X-ray diffraction (synchrotron radiation testing) and the results from this characterization are presented. The influence of the vertical divergence on the spectral distribution of the diffracted beam is discussed and compared with previously published analytical results.

X-Ray Monochromators: I. Theory

X-ray cyclic monochromators, which are particular cases of X-ray resonators, are considered. Conditions for the existence of a resonance wavelength in the Co-K α1 line spectral interval in monolithic cyclic monochromators and polylithic tunable cyclic monochromators are discussed. Maximum reflectivity for a four-reflection monolithic monochromator is achieved when each reflection is symmetric. For a two-monolith four-reflection polylithic monochromator, maximum reflectivity is achieved when the asymmetry of one reflection in one monolith is the inverse of the other reflection in the same monolith.

Energy-selective (+, +) monolithic monochromator and relative lattice-spacing measurement of Si wafers with synchrotron radiation

X-ray optic systems have been developed at beamline BL-3C2 of the Photon Factory, KEK, for the study of the relative lattice spacings of Si wafers using synchrotron radiation. Since synchrotron radiation has no characteristic (wavelength) spectral lines, unlike an X-ray tube, a new tool has been introduced into the system as a wavelength-selective device – a (+, +) high-resolution channel-cut monolithic monochromator. Using two types of monolithic monochromator, two schemes are proposed and applied to the study of the lattice spacings of Si wafers. The lattice-spacing differences are determined in the sub-p.p.m range; for example, in scheme 1 and scheme 2 we obtain 0.6 p.p.m. and 0.2 p.p.m., respectively. One of the practical advantages of this system is that it can be applied for a fast and precise measurement of the lattice-spacing changes due to the doping and defects in Si, GaAs and other single crystals.

A monolithic monochromator–collimator for high-resolution X-ray diffraction

The possibility of finding, for a given X-ray wavelength, the conditions for obtaining multiple coplanar reflections in a single block of crystal is investigated. It is found that by introducing a small relative tilt between two parts of the crystal, the conditions for a high-resolution X-ray monochromator for conventional and synchrotron X-ray sources can be obtained. The design of a new high-resolution monochromator–collimator based on a single crystal, which takes advantage of the existence for almost any wavelength ofnandmplanes in the single crystal that lie near the Bragg condition, is presented. A weak link between the two reflecting surfaces is used to align the crystal planes and to obtain efficient reflections in the dispersive configuration. DuMond diagrams are used to evaluate the total diffracted intensity and the resolution of such a monochromator. The experimental results obtained from prototypes made of single crystals of silicon and germanium are in good agreement with theoretical predictions. This new type of monochromator offers the advantages of a compact design and simple alignment.

Precise X-ray relative measurement of lattice parameters of silicon wafers by multiple-crystal Bragg-case diffractometry. Computer simulation of the experiment

A feasibility study of an X-ray experiment is presented by which the lattice parameter of a silicon wafer relative to that of a perfect reference silicon crystal can be measured with a precision of 10 -7. A multicrystal geometry in the symmetric Bragg case is proposed, using a monolithic monochromator as a beam splitter. Sample and analyser crystals are aligned with respect to the monochromator and the rotation of the analyser around its Bragg position produces two diffraction peaks. Their separation is related to the difference between the lattice parameters of monochromator and sample. The sample can be a piece of any commercial slice, generally cut from the ingot with an angle between the surface normal and the nominal crystallographic orientation and bent due to the mirror finishing on only one side. Moreover, the bending can be induced by layers grown on the surface by the processes of planar technology. Miscutting angle and curvature influence the diffraction peak position. The X-ray tracing and the procedure chosen for measurement eliminate these effects.

Lattice spacings of LEC-grown and MLEC-grown GaAs crystals

Lattice spacings ( d) were measured with an accuracy of 5.9 x 10 -6 in terms of Δ d/ d, using a diffractometer with a Si monolithic monochromator. For crystals with 10 4 -10 5 cm -2 order of dislocation density, the lattice spacing varied in the 10 -5 order of magnitude. This variation was attributed to the residual strains in the crystals. There was no definite evidence to prove that lattice spacings depend either on initial melt compositions or on dislocation density.

An X-ray monochromator system using successive reflection and its application to measurements of diffraction curves of annealed GaAs wafers

To measure local lattice deformation on crystal surfaces, a monolithic monochromator system for Mo Kα 1 radiation was designed which uses successive 444 and 022 reflections from an Si crystal. The angular spread of the monochromated beam is 1.7′′ and the wavelength spread (Δλ/λ) is 1.9 × 10−5. The system has been applied to precise measurement of the Bragg-case diffraction curve from Ge and GaAs crystals with a triple-crystal arrangement. The percentage reflection and half-width of the diffraction curve at various points on semi-insulating GaAs wafers were measured before and after annealing at 1123 K, with the results that annealing processes are found to be very effective for improving the quality of the crystal.

A class of condensing-collimating channel-cut monochromators for SAXS, XRPD, and other applications

We present design principles and examples for a new class of X-ray (and neutron) perfect-crystal monolithic monochromators which act to spatially condense and angularly collimate the resulting X-ray beam. Such condensing-collimating channel-cut (CCCC) monochromators can produce very narrow collimated beams and should prove very useful as beam concentrators for both synchrotron and conventional sources, and also in developing new types of high-resolution small-angle X-ray scattering (SAXS) and X-ray powder diffraction (XRPD) instruments, especially when these involve the use of position-sensitive detectors or imaging techniques.

A theoretical treatment of the Ge [440, \overline{2}20] monolithic monochromator

The calculated intensities of the X-ray beam behind the exit surface of the Ge [440, {\bar 2}20] dispersive monolithic monochromator for Co Kα1 radiation are presented. The reflections 440 and {\bar 2}20 resulting from Ge {000, 440, 260, {\bar 2}20} coplanar four-beam diffraction were taken into account and the influence of the π/2 reflection 260 is discussed. The four-surface arrangement of Ge [440, {\bar 2}20] providing the resultant beam parallel to the incident beam is considered. For comparison Ge [440, {\bar 2}20] in the two-beam approximation is solved. The obtained results demonstrate that the four-beam basis of diffraction affects the resultant beam. The quality of the X-ray beam evaluated behind the examined monochromators also provided the conditions for the use of such monochromators as wavelength standards.

A monolithic X-ray monochromator with fixed exit beam position

To avoid the inconvenient lateral movement of the monochromated beam in conventional, monolithic monochromators while the wavelength is changed, a new approach has been made. In principle the device is a channel cut single crystal where the walls of the groove are curved in such a way that the parallel displacement between the incoming and outgoing beams is independent of the wavelength. The analytical description of the shape of the mirrors is derived and different designs are discussed. Restrictions due to the asymmetric reflections are pointed out. The influence of deviations from the exact geometry are investigated as well as the consequences of misalignments with respect to the primary beam. Finally the successful fabrication with support by the CANON company and the first operation in the beam of the Photon Factory are reported. The result of an EXAFS experiment using this monochromator is presented.

A tunable, fixed-exit, monolithic X-ray monochromator for synchrotron radiation sources

A novel X-ray monochromator has recently been built and tested at the Cornell High Energy Synchrotron Source (CHESS). It features all the inherent advantages of monolithic monochromators but also has a fixed exit height with respect to the incident beam. Applications and extensions of this design to other monochromating systems will be discussed.

Absorption of X-rays by Coplanar Four-beam Reflections

Abstract The absorption effect in dispersion and reflection curves is shown for the a and n polarizations and for some wavelengths in the small wavelength interval in which the coplanar four-beam diffraction of x-rays exists. The investigated coplanar Ge[000, 440, 260, 2̄20] reflections appear in a Ge[440, 2̄20] monolithic monochromator working with CoKα1 radiation. It is shown that the absorption not only reduces the intensity in a complicated way but also changes the energy distribution between the participating reflections.

Order sorting, focusing and polarizing monolithic monochromators for synchrotron radiation

Two novel types of monochromators which eliminate higher orders usually present in crystal monochromatized synchrotron radiation beams have been used successfully in spectroscopic studies in the 1–4 Å X-ray range. The design of the monochromators is based on the refractive index correction's dependence on wavelength and relative orientation of crystal surface to reflecting Bragg planes. The monochromators can be used to select a particular order, eliminate higher orders, to decrease or increase the reflected beam cross section by Bragg focusing, and in one type, to manipulate the polarization state of the diffracted beam. The general theory and summary of operating experience with these monochromators in synchrotron radiation studies at the 12 GeV electron synchrotron at the Wilson Synchrotron Laboratory at Cornell University and the 1.8 GeV storage ring DCI at Orsay are presented.