WO2021209083A1

WO2021209083A1 - Diffraction grating and method for using the diffraction grating

Info

Publication number: WO2021209083A1
Application number: PCT/DE2021/000073
Authority: WO
Inventors: Andrey SOKOLOV; Florin Radu
Original assignee: Helmholtz-Zentrum Berlin für Materialien und Energie Gesellschaft mit beschränkter Haftung
Priority date: 2020-04-14
Filing date: 2021-04-12
Publication date: 2021-10-21
Also published as: DE102020110173A1; DE102020110173B4

Abstract

The method relates to a diffraction grating and to the use thereof, as is used, for example, in monochromators for X-rays. The diffraction grating according to the invention comprises at least one substrate (S) having a surface which has grating lines, and is characterised in that the grating lines have a regular spacing and form a trapezoidal angle y in the range of from 5° to 90° in profile, comprising a line spacing (p) in the range of from 6.1 μm to 7.1 μm, an upper groove width (G) in the range of from 3.66 μm to 4.97 μm and a line depth (GD) in the range of from 55 nm to 65 nm. The ratio of the upper groove width (G) to the line spacing (p) is in the range of from 0.6 to 0.7. The diffraction grating according to the invention and the use thereof cause efficient higher-order diffraction suppression while simultaneously having good efficiency of the first-order diffraction.

Description

description

Diffraction Grating and Method of Using the Diffraction Grating Description

The invention relates to a diffraction grating of the type used for diffraction of X-rays, for example in a monochromator, and an associated method.

State of the art

A diffraction grating of the type according to the invention is a so-called plane grating. Planar grids of the type according to the invention are, for example, in article 1 by G. Reichardt and F. Schäfers (Laminar versus trapezoidal grating profiles: AFM measurements and efficiency simulations, Grating and Grating Monochromators for Synchrotron Radiation, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 3150, 1997, pp. 121-129). A plane grid essentially consists of a flat substrate in which there are parallel, straight grooves, the so-called grid lines. The substrate can be coated or made up of several layers. Layers and coatings also have a functional character, for example to influence the reflective properties of the grating. The grid lines have a spacing, a width and a depth which are suitable for diffracting electromagnetic radiation and, in particular, X-ray radiation of a predetermined wavelength upon incidence at an angle determined by the Bragg condition. In the case of a simple diffraction grating, the distance between the grating lines has a periodicity, ie it is regular. The distance also determines the line density, lines / mm. The Bragg condition for diffraction at a grating is given by: nλ = p (sina + sinβ), with n = diffraction order, λ = wavelength, p = grating period (distance between the grooves), α = angle between the incident

Ray and grating normal, given here by the substrate normal and β = angle between the bent (emerging) ray and the grating normal.

The parameter c _ff , which results from the following ratio c _ff = (cos β / cos α), engl. As "constant or fix focal distance" (constant distance from the focal plane) or "plane grating-focus condition" is usually considered when using a plane grating in a monochromator. In particular, it influences the focusing properties of the plane grating and is a function of the wavelength (energy), the diffraction order and the grating period. When using a plane grating in the monochromator, in particular those that are also equipped with mirrors, c _{ff is set} by the orientation of the plane grating in relation to the incident X-ray beam and optimized as required. Also influenced by c _ff are, for example, parameters of the monochromator such as resolution and transmission.

The substrate in the plane grids to be considered according to the invention is flat. The surface can be treated to improve the diffraction properties, e.g. by polishing or coating. The grid lines can be designed from planar grid to planar grid, as required, by grooves of different profiles, with only grooves with a rectangular profile to be considered with regard to the grid according to the invention. The spacing of the grid lines on a given substrate can also change continuously in one direction, in which case it is a so-called variable line spacing (VSL) grid.

Diffraction gratings are often used due to the property of selective diffraction to monochromatize radiation and are used in spectrometers, X-ray optics and other devices. An overview of diffraction gratings for the monochromatization of soft X-rays is given in article 2 by H. Petersen et. al. (Review of plane grating focusing for soft x-ray monochromators, Review of Scientific Instruments, Vol. 66 (1), 1995, pp. 1-14).

With monochromatization it is meant here to reduce electromagnetic radiation with a spectral width incident on a grating, in the emerging, i.e. diffracted beam, in the spectral width. The spectral width to be achieved in the diffracted beam is a characteristic of a given plane grating. In general, the narrowest possible spectral width is aimed for in the emerging (monochromatized) beam, which is also rated as a good property of a monochromator.

In addition to the first order of diffraction, n = ± 1, higher order diffraction, n> | ± 1 |, is theoretically always possible. In particular in the case of applications in the X-ray range with wavelengths in the so-called range of soft X-rays (soft X-rays), essentially given by the wavelength range from 10 eV to 200 eV, this can lead to the wavelengths or energies belonging to the higher orders are present in the diffracted beam with a not insignificant intensity and interfere with spectral analyzes.

Various approaches are described in the prior art for suppressing higher orders. In essay 3 by Z.-Y. Guo et al. (A new method to suppress heigh-order harmonics for a Synchrotron radiation soft X-ray beamline, Chinese Physics C, Vol. 39, 2015, pp. 048002: 1-4), higher orders are achieved through a reduced included angle with a simultaneous lengthening of the Distance to an exit slit that cuts out a spatial region from a diffracted beam is suggested. In essay 4 by MR Howells (Plane grating monochromators for Synchrotron radiation, Nuclear Instruments and Methods 177, 1980, pp. 127-139), the use of mirrors in particular, but also various others Critically discussed proposals. The influence of the grid line spacing on the intensity of the higher orders in the diffracted beam is discussed in article 5 by R. Follath (The versatility of collimated plane grating monochromators, Nuclear Instruments and Methods in Physics Research A, Vol. 467-468, 2001, p . 418-425). Larger lattice spacings are suitable for suppressing higher orders, but this is to praise deteriorated spectral resolution.

The so-called blaze grids (from English sparkle, blaze) are also described in the prior art. Blaze gratings are characterized by the optimization of the diffraction efficiency of a diffraction order, contrary to the suppression of undesired diffraction orders, and consist of equidistant, inclined surfaces. These grids are very complex to manufacture, as e.g. the article 6 by R. K. Heilmann et al. (Advances in reflection grating technology for Constellation-X; Proceedings of SPIE Vol. 5168, 2004, pp. 271-282) can be found.

All devices known from the prior art for suppressing the higher orders during diffraction have disadvantages. They mean greater instrumental effort and / or at the expense of resolution and / or intensity.

Task

The object of the present invention is therefore to specify a device which causes a suppression of higher orders of diffraction while at the same time minimizing the instrumental complexity and good resolution and using the same. The object is achieved by the features of the subject matter of claim 1 and claim 4. Advantageous configurations are the subject matter of the dependent claims.

The device is given by the diffraction grating according to the invention, which comprises at least one substrate with a surface having the grating lines. The grid lines are parallel and regular. All materials with high reflectivity in the soft X-ray range, in particular silicon, in particular coated with gold, platinum or tantalum, as also corresponds to embodiments, come into consideration as the substrate. The substrate normal of the silicon advantageously corresponds to <100>, as it corresponds to an embodiment. The number of grid lines is large enough to ensure diffraction, which is theoretically the case from a number of two grid lines. The total number here is in particular greater than 50 and, in a particularly advantageous manner, greater than a total of 500.

The surface of the substrate preferably has a roughness that is less than sq <0.9 nm and in particular less than sq <0.6 nm (sq = mean square height).

The profile of the grating lines of the diffraction grating is ideally rectangular. However, from a manufacturing point of view, this cannot be achieved or can only be achieved with difficulty. The angles that characterize the profile are formed by the acute angle (g, trapezoidal angle) that is spanned by the walls of the profile and the base line in the profile (parallel to the base / surface of the substrate). The tolerable angular range for the grating according to the invention is 5 ° to, as a limit case of the acute angle, 90 °. The angle mentioned is referred to here with g and otherwise also as a trapezoidal or “slope” angle in the literature. Any unevenness that may occur due to production needs to be averaged out when looking at the angles. The line spacing of the grating lines (p), which corresponds to the grating period of the diffraction grating, is in the range from 6.1 μm to 7.1 μm. This corresponds to a line density in the range of 164 lines / mm and 141 lines / mm. The upper groove width (G), ie the distance between the profiles of the grid lines, is in the range from 3.66 μm to 4.97 μm and the line depth of the grid lines (GD) is in the range from 55 nm to 65 nm. The values for The upper groove width G and the line spacing of the grid lines p are designed in such a way that they form a ratio of the upper groove width G to the line spacing p, G: p, which is between 0.6 and 0.7. The values for G and p are to be selected accordingly when manufacturing the diffraction grating, taking the boundary conditions into account

The diffraction grating according to the invention is used in the suppression of diffraction of higher order,> | ± 1 |, in the diffraction of X-rays in the energy range from 10 eV to 200 eV.

The diffraction grating according to the invention of use comprises at least one substrate with a surface which has grating lines. The grid lines are parallel and regular. All materials with high reflectivity in the soft X-ray region, in particular silicon, in particular coated with gold, as also corresponds to embodiments, come into consideration as the substrate. The substrate normal of the silicon advantageously corresponds to <100>, as it corresponds to an embodiment. The number of grid lines is large enough to ensure diffraction, which is theoretically the case from a number of two grid lines. The total number here is in particular greater than 50 and, in a particularly advantageous manner, greater than a total of 500.

The profile of the grating lines in the diffraction grating is ideally rectangular. However, from a manufacturing point of view, this cannot be achieved or can only be achieved with difficulty. The angles that characterize the profile of the grid lines are formed by the acute angle (γ, trapezoidal angle) formed by the walls of the Profile and the baseline in the profile (parallel to the base / surface of the substrate) is spanned. The tolerable angular range for the grating according to the invention is 5 ° to, as a limit case of the acute angle, 90 °. The angle mentioned is referred to here as g and is otherwise also referred to in the literature as a trapezoidal or “slope” angle. Any unevenness that may occur due to production needs to be averaged out when looking at the angles.

The line spacing of the grating lines (p), which corresponds to the grating period, is in the range from 6.1 μm to 7.1 μm. This corresponds to a line density in the range of 164 lines / mm and 141 lines / mm. The upper groove width (G), ie the distance between the profiles of the grid lines, is in the range from 3.66 μm to 4.97 μm and the line depth of the grid lines (GD) is in the range from 55 nm to 65 nm. The values for The upper groove width G and the line spacing of the grid lines p are designed in such a way that they form a ratio of the upper groove width G to the line spacing p, G: p, which is between 0.6 and 0.7. The values for G and p are to be selected when manufacturing the diffraction grating, taking the boundary conditions into account, so that a corresponding ratio is set.

When using the diffraction grating, it is oriented with regard to the direction of an incident X-ray beam so that the plane grating condition c _{ff is} in the range between 1.2 to 1.7 and in particular in the range from 1.4 to 1.5 . The ideal value for c _ff , for the energy range of the X-ray beam in the range from 10 eV to 200 eV, is 1.45, the maximum efficiency is then 60 eV. The choice of the value for c _ff depends on the choice of energy to be used and can also be determined by optimizing the flow of the X-rays (flux).

Surprisingly, it was found at the Helmholtz Center Berlin that a grating according to the invention, with the specified parameters and below a suitable plane grating focus condition, c _ff , without the use of further aids, in particular optics, contrary to the prejudice that a large line spacing has a very negative effect on the grating properties, a suppression of higher order diffraction (> | ± 1 |) of up to to an efficiency of <0.025 for the energy range 10 eV to 200 eV, with an efficiency for the first order diffraction of up to> 0.32, with an energy of 60 eV (c _ff = 1.45). The plan grid focus condition c _ff is in the range between 1.2 and 1.7.

The diffraction grating according to the invention and the associated method enable a very efficient suppression of higher-order diffraction, while at the same time having good diffraction properties and with minimal instrumental expenditure. It is only necessary to use the diffraction grating.

Embodiment

The invention is to be explained in more detail in an exemplary embodiment and with reference to 3 figures.

The figures show:

Figure 1: Schematic representation of a section perpendicular to the

Grating lines of a diffraction grating (StdT);

FIG. 2: Diffraction efficiency of diffractions of different orders on a diffraction grating according to the invention when used according to the invention as a function of the energy;

FIG. 3: Quality factor of the transmission as a function of the energy of a diffraction grating according to the invention.

Fig. 1 shows a schematic representation of a section perpendicular to the

Grating lines of a generic diffraction grating, as it is also from the State of the art, for example in article 1, is known. The illustration is not true to scale and only serves to illustrate the parameters of the diffraction grating. The diffraction grating is characterized by the uniform line spacing p of the grating lines, the depth of the profiles of the grating lines GD and their upper groove width G. The grating lines are introduced onto the surface of a substrate S. The trapezoidal angle γ is also marked.

In the exemplary embodiment, the substrate is made from silicon <100> and the grid lines are applied to the surface of the substrate using a grid dividing machine. The line spacing of the grid lines p is 6.7 μm, which corresponds to a line density of 150 lines / mm. The line depth GD is 60 nm and the upper groove width G is 4.36 μm and the ratio of G to p therefore corresponds to 0.65. The trapezoidal angle g i is 10 °.

The surface of the diffraction grating is gold-plated.

In FIG. 2, the suppression of the higher order diffraction (> | ± 1 |) using the diffraction grating of the exemplary embodiment is shown on the basis of the efficiency of the diffraction as a function of the energy. The efficiency results from the ratio of the intensity of the X-ray radiation incident on the diffraction grating to the intensity of the X-ray beam after diffraction. The suppression of the higher order diffraction (2, 3, 4, 5) is due to their very low efficiency (or low transmission) of up to <0.025 for the energy range 10 eV to 200 eV, with a

simultaneous efficiency for first order diffraction (■, -) of up to> 0.32, with an energy of 60 eV. The plan grid focus condition c _ff is 1.45.

A figure of merit (FOM) for the transmission, to be expressed also as the quality of the suppression of higher order (ie low transmission (efficiency) of the diffraction of higher order), with simultaneous optimized efficiency of the diffraction 1. Order, depending on the energy and for several values of c _ff are shown in FIG. 3 for the diffraction grating of the exemplary embodiment

The most favorable value for c _{ff in} each case can be determined experimentally if necessary, depending on the requirements. The FOM is defined as:. where Ef

f _i the efficiency (or transmission) of the

Denotes i-th order diffraction.

The illustrated embodiment shows the advantages of the diffraction grating according to the invention and the associated use. The diffraction grating and its use enable a very efficient suppression of the higher order diffraction while at the same time having good diffraction properties for the diffraction ± 1. Order and with minimal instrumental effort. Only the diffraction grating is used.

Claims

1. Diffraction grating, at least comprising a substrate (S) with a surface which has grating lines, characterized in that the grating lines have a regular spacing and a trapezoidal angle g in the range from 5 ° to 90 ° in profile, as well as a line spacing of the grating lines ( p) in the range from 6.1 μm to 7.1 μm, an upper groove width (G) in the range from 3.66 μm to 4.97 μm and a line depth (GD) in the range from 55 nm to 65 nm and where the Values for the upper groove width (G) and the line spacing of the grid lines (p) form a ratio, G: p, which is between 0.6 and 0.7.

2. Diffraction grating according to claim 1, characterized in that the substrate (S) is formed from silicon <100>.

3. Diffraction grating according to claim 1, characterized in that the surface of the substrate with gold. Platinum or tantalum is coated.

4. Use of a diffraction grating for suppressing diffraction with a diffraction order> | ± 1 |, of X-rays in the range from 10 eV to 200 eV, wherein the diffraction grating comprises a substrate with a surface that has grating lines, and wherein the grating lines are regularly spaced have and a trapezoidal angle g in the range from 5 ° to 90 ° in profile, and a line spacing p in the range from 6.1 μm to

7.1 μm, an upper groove width G in the range from 3.66 μm to 4.97 μm and a line depth GD in the range from 55 nm to 65 nm and where the values for the upper groove width (G) and the line spacing of the grid lines (p) a ratio, G: p, which is between 0.6 to 0.7, and the diffraction grating to a direction of an incident X-ray so oriented is that the plan grid focus condition c _ff lies in the range between 1.2 and 1.7.