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Comparative monochromator studies for a soft x-ray microfocus beamline for BESSY-II
Journal of Electron Spectroscopy and Related Phenomena 101–103 (1999) 1003–1012
Comparative monochromator studies for a soft x-ray microfocus beamline for BESSY-II M.R. Weiss*, R. Follath, F. Senf, W. Gudat BESSY-GmbH, Lentzeallee 100, D-14195 Berlin, Germany
Abstract We present a comparative study for a microfocus beamline at the U41 undulator, the most brilliant source at BESSY-II. High flux and an illuminated sample spot size between 1 and 10 mm are the primary design goals to bridge the spatial resolution gap attainable with imaging photoelectron emission microscopy and microspectroscopy applications. The basic layout of the beamline consists of a monochromatisation and a subsequent refocusing stage. For the former, a focused spherical grating monochromator (FSGM) design and a collimated plane grating monochromator (PGM) were optimised. Both monochromator make use of the same refocusing stage: For limited spatial resolution but large working distance between the last mirror chamber and focal spot, a horizontal deflecting toroid will give a spot of 10320 mm 2 . The second system, a Kirkpatrick–Baez arrangement of bent plane-elliptical mirrors is expected to reach a 1 3 1 mm 2 spot. The plane grating monochromator was finally chosen for its high flux and versatility. Ray trace calculations indicate a photon flux of ca. 3310 13 photons / s at a spectral resolution E /DE above 2300. 1999 Elsevier Science B.V. All rights reserved. Keywords: Microspectroscopy; Collimated PGM; FSGM
1. Introduction Highly brilliant undulator sources at the newly built third generation synchrotron facilities provide the necessary flux density for fast spatially resolved electron spectroscopy. Consequently, many microspectroscopy beamlines are under construction or already in operation in the VUV and soft x-ray region [1–4]. At the 1.7-GeV electron storage ring facility BESSY-II a photoemission electron microscope with advanced electron
*Corresponding author. Correspondence address: Rudower Chaussee 5, D-12489 Berlin, Germany. Tel.: 149-30-6392-2941; fax: 149-30-6392-4850. E-mail address: [email protected] (M.R. Weiss)
optics is under construction aiming at a spatial resolution of 5 nm [5]. An optimised beamline for this microscope needs to focus the radiation into a field of view of 5 mm [6]. The beamlines for high spectral resolution will provide focal spots on the sample with sizes ranging from 20 mm to 200 mm. This leaves a spatial resolution gap in the intermediate range from 100 nm to 20 mm. It is therefore planned to build a beamline that is optimised for a microfocus with 1-mm spotsize and high flux. The concomitant demagnification requires that the last optical element has to be placed close to the sample position. Therefore, a second configuration is designed with more space for experiments with a microspot in the 10-mm range. To find the best suited monochromator for high flux microspectroscopy we compared two design concepts, the focused spherical grating mono-
0368-2048 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 98 )00380-6
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chromator (FSGM) and the collimated plane grating monochromator (PGM). The FSGM is a spherical grating monochromator (SGM) that allows changing of the included angle with an additional plane mirror in front of the spherical grating [7]. Thus, the focus in the dispersion plane can always be kept at the exit slit position. No real entrance slit will be used to provide the highest flux possible. The PGM is a development based on the Petersen type monochromators [8] at BESSY [9] at which the light is collimated in front of the grating. This allows the free adjustment of the fix-focus constant without movement of the exit slit. In Section 2 we will give information on the predesign considerations that are independent of the type of monochromator. The detailed description of FSGM and PGM are to be found in Sections 3 and 4. Finally, in Section 5 we will compare the performance and advantages or disadvantages of the two concepts.
2.1. U41 undulator source characteristics The source of this beamline is the U41 undulator which will be installed in a low beta section of the BESSY-2 storage ring [10]. It is a N 5 80 periods linear undulator of l0 5 41 mm period length. The expected photon beam was calculated for selected energies using the program SMUT [11] with the following electron beam characteristics: g 5 3326.81, Iring 5 100 mA, electron beam size sx 5 76 mm and sy 5 15 mm, electron beam divergence s x9 5 68 mrad and s 9y 5 10 mrad (at 3% coupling). The photon energy was selected such that the photon flux of the undulator harmonic is at a maximum. This occurs roughly at energies that are 1 /N times below the theoretical position of the harmonics. Datafiles of the source were produced that contain the photon intensity as a function of the emission angles. Table 1 shows the corresponding harmonic, K-value, photon energy, spectral flux, source size (FWHM) and divergence (FWHM).
2.2. Methods for performance calculation 2. Basic predesign considerations The primary design goals for this microfocus beamline are optimised spatial resolution and flux in the energy range from ca. 150 eV to 1500 eV which is served by an undulator (U41) for linearly polarised radiation. For the spatial resolution two different values should be reached:
• A resolution of 1 mm with a working distance as required for optimised focusing, and • A moderate resolution of 10–20 mm with large working distance of ca. 750 mm between last mirror and sample position. Other requirements have also to be met, namely:
1. The space requirements at the BESSY-II storage ring because of minimum source distance of 17 000 mm and the use of a premirror is required; 2. Spectral resolution is given less importance than flux, therefore E /DE above 2000 suffices.
Two methods were used for the calculations described in this paper: Analytic expressions for slope error and aberrations were used for large parameter searches which were performed for the optimisation of the two-step demagnification optics (Section 2.5). The slope errors were included as Gaussian distributed deviations of the reflected beam. The aberrations were approximated by the well known development of optical path function [12]. For simplification, only the dominant aberrations were used. Ray tracings were used to get realistic values of the expected performance utilising the program RAY [13] developed at BESSY for beamline design. It is a Monte-Carlo type ray tracing program that allows selection of mirrors and crystals with standard surfaces eg. planes, spheres, toroids, ellipsoids, etc. Surface characteristics such as microroughness and slope errors, both Gaussian distributed are taken into account. The reflectivity of metal coatings as well as grating surfaces is calculated for each element individually. The above described source files of the undulator were used as input files for the ray tracings. Many of the results will be discussed in
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Table 1 Undulator harmonic, K-value, spectral flux, source dimension (Dx, Dy) and beam divergence (Dx9, Dy9) for the U41 at energies which were used for the ray tracings Harmonic 1 1 1 1 3 1 3 5 3 5 3 5
K 2.5 2.0 1.5 1.0 2.5 0.5 2.0 2.5 1.5 2.0 1.0 1.5
Energy 160.81 221.01 312.31 442.02 485.30 587.61 667.30 810.36 939.30 1113.50 1340.40 1573.40 [eV]
Spectral flux 15
1.313 ? 10 1.226 ? 10 15 1.088 ? 10 15 0.776 ? 10 15 0.911 ? 10 15 0.294 ? 10 15 0.737 ? 10 15 0.447 ? 10 15 0.430 ? 10 15 0.326 ? 10 15 0.048 ? 10 15 0.145 ? 10 15 phot [ ]]]] ] s 100 mA 0.1% BW
terms of the fix focus constant c ff as defined by Petersen [8].
2.3. Structure of the design problem A focus of 1 mm requires a demagnification of approx. 200 horizontally and 20 vertically. Since all photon energies in the required range should be accessible, grazing incidence optics is the only possible choice for this monochromator. Unfortunately, demagnification with this kind of optics is limited to values below 50 for aspheric surfaces and even limited to below 10 in favourable cases if spherical surfaces are used. In addition, since an exit slit is required for selection of the desired photon energy, refocusing optics between slit and sample is unavoidable. Therefore, the microfocus beamline was separated in a monochromatisation stage and a subsequent refocusing and demagnification stage. In addition, the monochromatisation stage is planned to focus both horizontally and vertically at the exit slit. This gives the advantage that the refocusing stage can later be replaced by other focusing concepts such as microzone-plates, bragg-fresnel lenses etc. which gives the beamline a higher versatility.
2.4. General considerations for the monochromatisation stage The monochromatisation stage serves two purposes: it provides the monochromatisation and it is also the first demagnification step in the beamline.
Dx
Dx9
Dy
Dy9
77.1 76.8 76.5 76.4 76.4 76.3 76.3 76.2 76.2 76.2 76.1 76.1 [mm]
212 202 176 174 172 169 164 162 167 157 168 151 [mrad]
19.7 18.5 17.5 16.9 16.7 16.4 16.3 16.0 15.9 15.8 15.6 15.5 [mm]
119 106 85 76 76 75 68 61 74 54 39 42 [mrad]
A general design goal for the monochromatisation stage is to provide a monochromatised beam without decreasing the beam quality, i.e. its spectral brilliance. There are two major sources for brilliance losses in a monochromator: slope errors (SE) and aberrations. These two contributions are interconnected since aspherical elements (ellipsoids) contain higher slope errors than spherical elements, which in turn give higher aberrations. Losses due to the SE are only dependent on the source distance of the imaging system. If aberrations such as coma are present an additional loss in brilliance occurs e.g. for high demagnification ratios for spherical and toroidal mirrors. Still, a demagnification of up to six can be reached without severe brilliance losses at source sizes and beam divergences as encountered here. An ellipsoidal mirror, although affected by higher SE, is constant in loss of brilliance and will be the better choice for demagnification above a factor of ten. Based on this consideration we decided to use spherical optics with the best SE possible at the smallest possible source distance for the monochromatisation stage. In addition, to avoid aberrational losses, only a small demagnification ratio will be used.
2.5. General considerations for the refocusing stage The refocusing stage has two purposes: transfer of the photons from exit slit to sample and further
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demagnification. The requirement of brilliance conservation, as it was discussed in the Section 2.4, is not valid here since spotsize and not divergence is of importance at the sample. Therefore, the spotsize depends almost completely on aberrations and slope errors as long as it has the smallest diameter.
2.5.1. Optics for refocusing Presently, there are several possibilities for grazing incidence refocusing. Ellipsoidal mirrors provide the best means for point-to-point imaging since they show no aberrations in this imaging geometry. Unfortunately, these turned out to be very difficult to produce, which led to unacceptably large slope errors [14,15]. A possible solution is to reduce the image distance which in turn leads to very small radii and therefore additional problems for the manufacturer. Only spherical mirrors and derived shapes such as cylindrical and toroidal mirrors can be obtained with a small enough slope error. But if one wants to achieve demagnifications in excess of ten, coma increases dramatically. Recently, Padmore et al. demonstrated that plane mirrors can be bent to elliptical shape by tailoring their width. By arranging two mirrors at 908 (Kirkpatrick–Baez arrangement) they achieve a spot of about 1-mm diameter [3] at a demagnification ratio of up to 20 and 40. This is only possible due to the small SE of about 1 mrad (RMS) [3]. These are impressive performance figures. However, it is not without practical problems. Due to the fact that the bent plane mirrors focus only in the longitudinal direction, they tend to become very long. Since the mirrors have to be placed one after the other the demagnification of the first mirror is rather small. One also has to be aware of the fact that space for the bending mechanism has to be added leading to even longer distances. For this study we shall use bent elliptical mirrors in the Kirkpatrick–Baez arrangement for the 1-mm microfocus. For the moderate microspot at large distance, we will use a a toroidal mirror as refocusing optics since this type of mirror is both readily available and low priced. The required microspot allows the large image distance at which the SE does not deteriorate the focus overly. Rather aberrations are expected which are still manageable for the required demagnification. An incidence angle with respect to the surface of
28 was chosen so that even the 1500-eV photons are reflected with high efficiency.
2.5.2. Optimisation of the refocusing stage Refocusing of the monochromatised spot starting at the exit slit depends on its size and the beam divergence there. Therefore, the refocusing optics cannot be optimised without knowledge of the monochromatisation stage. This stage, however, can be designed within a wide range of demagnification factors. Therefore, one should rather optimise the two-step demagnification of monochromatisation and refocusing stage. The first stage is provided by the monochromatisation stage which uses toroids and cylinders (for PGM) and spheres (for FSGM). The second stage consists either of the two bent elliptical mirrors or a toroidal mirror. The optimisation of this two-step demagnification was done for the horizontal and vertical direction independently. Slope errors as well as aberrations were included, the latter using the analytic expressions of the development of the optical path function for toroids and spheres [12]. The aberrations of the mirrors in the first stage and the toroid of the second stage were calculated separately where absolute values were added quadratically. This, of course, is an upper estimate of the expected error since there is in general the possibility that aberrations annihilate each other. The values for source size and divergence were chosen for the lowest energy (size: 77.1319.7 mm 2 , divergence: 2123119 mrad 2 ).
3. Focused spherical grating monochromator design The FSGM allows adjustment of the included angle at the grating such that the diffracted order is focused at the fixed exit slit, as described already in the introduction. The basic layout for this type of monochromator as it is proposed in this study will be described in the following Section 3.1.
3.1. General layout The required premirror is a horizontally deflecting sphere which focuses horizontally onto the exit slit (see Fig. 2b). It is placed at minimum distance from
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the source (17 000 mm) to minimise the brilliance losses. The refocusing optimisation for the elliptical refocusing mirrors required a distance to the exit slit of 2000 mm which cannot be met due to the space problems. Therefore, the distance was set to the minimum allowable distance of 7500 mm. The vertically deflecting spherical grating provides the dispersion and focuses the source vertically onto the exit slit. The line density of the grating is chosen to be as small as possible to meet the high flux requirement. Still, the mechanically allowed angles have to be observed that lead to a grating with 300 l / mm. A lamellar grating profile with 10.0-nm groove depth and a groove width to spacing ratio of 0.6 was chosen for good efficiency over the range of energy and small higher order content. Considering a c ff value of 0.8 to 0.36, the image distance was chosen to be 3500 mm. The c ff values as a function of photon energy which is required for the focusing condition is shown in Fig. 1, bottom, as dot-dashed line. The plane mirror is placed after the grating to decrease the influence of its slope error. The detailed list of parameters of the FSGM monochromatisation stage is shown in Table 2. The refocusing optics is either a toroidal mirror at 3000 mm after the exit slit. It deflects sideways and
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Table 2 Parameters of the various optical elements for the FSGM monochromatisation stage Optical element shape
M1 Spherical
M2 Plane
Grating Spherical
Deflection Optical active surf. (mm 2 ) Coating Angle of incidence Source distance (mm) Image distance (mm) Radius R (mm) Groove density Groove depth (nm) Groove width to period ratio
Horizontal 270 3 10 Au 888 17 000 7500 298 233 – – –
Vertical 300 3 20 Au Variable – – – – – –
Vertical 90 3 15 Au Variable 21 000 3500 220 000 300 10.0 0.6
forms the image at 750 mm. A second refocusing optics is based on bent elliptical mirrors. The first mirror deflects vertically and is placed 5000 mm after the exit slit. The second mirror deflects horizontally and will be 115 mm after the previous mirror. The mirrors are bent such that the image is formed at 85 mm after the last mirror. The detailed list of parameters of the refocusing system is shown in Table 3. The optical layout of the elliptical refocusing system is also shown in Fig. 2c). The performance of the monochromator, as de-
Fig. 1. Diffraction efficiency calculations for a blaze grating with 600 l / mm, 0.88 blaze in gold as a function of photon energy and c ff . c ff -paths are shown for the PGM (dashed) and FSGM (dot-dashed). Left: First order efficiency; center: second order diffraction divided by first order; right: third order diffraction, divided by first order. The dashed curve shows a path that is optimised for flux.
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Table 3 Parameters of the toroidal (M t ) and Kirkpatrick–Baez bent elliptical (M e,1 , M e,2 ) refocusing systems Optical element shape
Mt Toroidal
M e,1 Elliptical
M e,2 Elliptical
Deflection Optical active surf. (mm 2 ) Coating Angle of incidence Source distance (mm) Image distance (mm) Long. radius R (mm) Sag. radius r (mm)
Horizontal 40 3 2.5 Au 888 3000 750 34384 41.88
Vertical 120 3 10 Au 888 5000 200 – –
Horizontal 70 3 10 Au 888 5115 85 – –
termined by ray tracing, shows the required spot sizes for both refocusing systems. The flux and energy resolution values are shown in Fig. 3, top, for the fist, third, and fifth harmonic and will be discussed in Section 5.
4. Petersen-type monochromator design As second choice we investigated the PGM. The general layout of this monochromator will be discussed shortly in the following Section 4.1 and is show in Fig. 2a.
4.1. General layout The premirror provides vertical collimation and a horizontal focusing of the undulator source onto the exit slit. To meet the requirement for conservation of the brilliance the horizontal focusing is done by this mirror (Section 2). Consequently, the premirror is of a toroidal shape. The next element is the grating which deflects vertically. The distance between premirror and grating is chosen as short as the dimension of the grating chamber and neighbouring beamline allows. The type of grating and line density will be discussed in more detail below. After the grating a plane mirror with vertical deflection is placed which allows one to freely choose the total deflection angle of the grating. The settings of grating and plane mirror can be completely described by the photon energy and c ff .
Following the plane mirror, a horizontally deflecting focusing mirror is placed, that focuses the collimated beam vertically onto the exit slit. This mirror does not contribute to the horizontal focusing and is therefore of cylindrical shape (Table 4).
4.2. c ff for optimised performance The fix-focus constant can be chosen freely for a collimated PGM, which can be used to optimise the monochromator. Therefore, if one uses a blaze grating one can stay on blaze for all desired energies. Still, other optimisation goals are accessible, even while scanning the monochromator. Within this section we will give some details on the calculations that were performed to select the best grating parameters. For these calculations, the REFLEC program [16] was used which is based on the method of Neviere [17]. We determined the first, second and third order grating efficiency for energy values ranging from 50 eV to 1500 eV, c ff from 0.1 to 0.85 (outside order diffraction) and blazes of 0.88, 1.08, and 1.28 on gold. From these results we determined also the ratio between first order and the higher orders which give the higher order content of the light. The result for 0.88 which is shown in Fig. 1, bottom, can be used to find an optimised c ff for each energy. If flux is to be optimised, one should follow the ridge in Fig. 1, left, which is shown as a dashed line. This will result in severe higher order content as can be seen from the higher content in Fig. 1, center and right. Note, that the higher order content is also reduced by the reduced reflectivity of the mirrors in the beamline for higher photon energy. If, on the contrary, higher diffraction orders are not desired, a path to the left of the dashed curve can be taken, that gives somewhat less diffraction efficiency by greatly reduced higher order content. Finally, any arbitrary curve through this parameter space can be chosen, if the experiment requires so. The performance of the monochromator, as determined by ray tracing, shows the required spot sizes for both refocusing systems (Fig. 3, bottom). Flux and energy resolution values for the first, third, and fifth harmonic are also shown in Fig. 3, center, and will be given a closer look in Section 5.
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Fig. 2. Schematic views of the beamline layouts: (a) top and side view of the collimated PGM as described in Section 4 with toroidal refocusing mirror; (b) top and side view of the FSGM as described in Section 3; (c) refocusing optics using two plane elliptical mirrors.
5. Comparison The optimisation work done for this comparative study revealed advantages and disadvantages of either concept which will be discussed here. It also became apparent, that the differences are small with regard to many aspects. The placement
and distances and therefore the demagnifications of the optics are very similar. The range of c ff values is almost identical. The differences in the refocusing optics were so small that finally the same values are used. Finally, for both monochromators only one grating is necessary for the whole energy range due to limited requirement for the spectral resolution.
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Fig. 3. Result of the performance calculations for the PGM and FSGM. The top graphs show photonflux (a) and spectral resolution (b) for the FSGM with toroidal (s) and bent elliptical (앳) refocusing system. The center figures show photonflux (c) and spectral resolution (d) for the PGM with toroid (s) and bent ellipses (앳). The expected spots on the sample are shown in the bottom row for the bent elliptical focusing mirrors (e) and the toroidal refocusing mirror (f) for the collimated PGM at 160.8 eV.
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Table 4 Parameters of the various optical elements of collimated PGM monochromatisation stage Optical element shape
M1 Toroidal
M2 Plane
M3 Cylindrical
Grating Plane
Deflection Optical active surf. (mm 2 ) Coating Angle of incidence Source distance (mm) Image distance (mm) Long. radius R (mm) Sag. radius r (mm) Groove density Blaze
Horizontal 270 3 10 Au 888 17 000 6900 / ` 281 267 1186.58 – –
Vertical 300 3 20 Au Variable – – – – – –
Horizontal 80 3 10 Au 888 ` 2000 ` 139.60 – –
Vertical 90 3 15 Au Variable – – – – 600 0.88
5.1. Advantages and disadvantages of the FSGM design The strongest advantage of the FSGM beamline is obvious: it uses one element less than the PGM. Therefore, the monochromator stage is cheaper. This is even more the case since plane and spherical surfaces are used which are additionally easier (and cheaper) to produce and easier adjusted. Easier production means also less slope error for these mirrors which leads to a smaller focus. Another advantage is the c ff path with regard to aberrations (see Fig. 1, dot-dashed curve). It leads to a small vertical demagnification at low energies (c ff ¯ 0.4) and strong demagnification at high energies (c ff ¯ 0.8). This in turn gives reduced aberrations for the low energies where source divergence is large. The results in Fig. 3, top, reveal the major disadvantage of the FSGM. The spectral resolution changes largely over the energy range. In addition, a grating that works over the whole energy range gives only poor performance for the low energy part. Therefore, gratings for the low, middle, and upper energy region are required, which annihilates the low cost advantage that is stated above. Finally, the c ff -path cannot be changed. Therefore, optimisation of the grating angles for e.g. on-blaze or decreased higher order content is not possible.
5.2. Advantages and disadvantages of the PGM design The PGM is the more expensive monochromator design. It not only requires the additional focusing
mirror, it also contains toroids and cylinders which are more expensive to produce. In addition, these kinds of elements have higher SE. On the other hand, c ff can be chosen freely within the limits of the grating and plane-mirror mount. This gives the advantage, that e.g. the on-blaze condition for a blaze grating can be fulfilled. Thus, much higher grating efficiencies can be achieved which leads to higher spectral flux in the sample spot. The on blaze c ff -path has also the nice property that the relative energy resolution is almost constant on the energy range. Other c ff paths are possible that optimise the performance targeted on other qualities, e.g. higher order suppression (see Fig. 1).
6. Conclusion From the optimisation work that is described in this paper, we draw the conclusion that the collimated PGM is better suited as a microfocus monochromator. This type of beamline will be more expensive but provides higher spectral flux on the sample and allows the freedom to change c ff which opens the opportunity for other optimisation goals. The refocusing optics, based on a toroid, which is identical for both monochromator concepts will provide a 10 3 20 mm spot with large working distance. A second refocusing optics with bent elliptical mirrors will reach a 1 3 1 mm micro-spot. The latter is only possible with the small distance between the last mirror and the sample which has to be considered for the design of the experimental chamber. The stigmatic focusing monochromator
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also allows the use of different refocusing systems, e.g. micro zone plates. If a c ff path is chosen for optimised flux at the sample position, values are expected to exceed 3 3 10 13 phot / s 100 mA for low energies and using the toroidal refocusing. About 1 3 10 13 phot / s 100 mA are attainable for the elliptical refocusing system. Towards 1500 eV the flux is still as high as 1 3 10 12 phot / s100 mA which allows access to the deeper electron levels, e.g. for spatial resolved magnetic dichroism spectroscopy. The spectral resolution (E /DE) on this c ff -path changes only a little, around 2000 and 4000, respectively.
[5]
[6] [7] [8] [9] [10] [11]
References [12] [1] J. Welnak, Z. Dong, H. Solak, J. Wallace, F. Cerrina, M. Bertolo, A. Bianco, S. DiFonzo, S. Fontana, W. Jark, F. Mazzolini, R. Rosei, A. Svoia, J.H. Underwood, G. Margaritondo, Rev. Sci. Instrum. 66 (1995) 2273. ¨ [2] M. Marsi, L. Casalis, L. Gregoratti, S. Gunther, A. Kolmakov, J. Kovac, D. Lonza, M. Kiskinova, J. Electr. Spectrosc. Relat. Phenom. 84 (1997) 73. [3] H. Padmore, Proceedings of the 17th XAS, 1996, Hamburg Germany [4] T. Warwick, H. Ade, A.P. Hitchcock, H. Padmore, E.G.
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Rightor, B.P. Tonner, J. Electr. Spectrosc. Relat. Phenom. 84 (1997) 85. R. Fink, M.R. Weiss, E. Umbach, D. Preikszas, H. Rose, R. Spehr, P. Hartel, W. Engel, R. Degenhardt, W. Erlebach, K. ¨ Ihmann, R. Schlogl, A.M. Bradshaw, G. Lilienkamp, Th. Schmidt, E. Bauer, H. Kuhlenbeck, R. Wichtendahl, H.-J. Freund, G. Benner, J. Electr. Spectrosc. Relat. Phenom. 84 (1997) 231. C. Jung, U. Flechsig, J. Bahrdt, M.R. Weiss, Proceedings of SPIE, in: 1997. H.A. Padmore, Rev. Sci. Instrum. 60 (1989) 1608. H. Petersen, Ch. Jung, C. Hellwig, W.B. Peatman, W. Gudat, Rev. Sci. Instrum. 66 (1995) 1. R. Follath, F. Senf, Nucl. Instr. Meth. A390 (1997) 388. J. Bahrdt, A. Gaupp, G. Ingold, M. Scheer, W. Gudat, J. Synchrotron Radiation 5 (1998) 443. Jacobsen C. SMUT-Undulator spectrum code with finite electron beam dimensions. Lawrence Berkeley Laboratory, Center for X-Ray Optics. W.B. Peatman, Gratings, Mirrors and Slits, Gordon and Breach Science Publishers, Amsterdam, 1997. ¨ F. Schafers, BESSY Technical Report 202 / 96, Berlin, 1996 J. Voss, J. Electr. Spectrosc. Relat. Phenom. 84 (1997) 29. ¨ M.R. Weiss, V. Wustenhagen, R. Fink, E. Umbach, J. Electr. Spectrosc. Rel. Phenom. 84 (1997) 9. ¨ F. Schafers, Michael Krumrey, BESSY Technical Report 201 / 96, Berlin, 1996. M. Neviere, P. Vincent, R. Petit, Nouv. Rev.: Opt. 5 (1974) 65.
Comparative monochromator studies for a soft x-ray microfocus beamline for BESSY-II M.R. Weiss*, R. Follath, F. Senf, W. Gudat BESSY-GmbH, Lentzeallee 100, D-14195 Berlin, Germany
Abstract We present a comparative study for a microfocus beamline at the U41 undulator, the most brilliant source at BESSY-II. High flux and an illuminated sample spot size between 1 and 10 mm are the primary design goals to bridge the spatial resolution gap attainable with imaging photoelectron emission microscopy and microspectroscopy applications. The basic layout of the beamline consists of a monochromatisation and a subsequent refocusing stage. For the former, a focused spherical grating monochromator (FSGM) design and a collimated plane grating monochromator (PGM) were optimised. Both monochromator make use of the same refocusing stage: For limited spatial resolution but large working distance between the last mirror chamber and focal spot, a horizontal deflecting toroid will give a spot of 10320 mm 2 . The second system, a Kirkpatrick–Baez arrangement of bent plane-elliptical mirrors is expected to reach a 1 3 1 mm 2 spot. The plane grating monochromator was finally chosen for its high flux and versatility. Ray trace calculations indicate a photon flux of ca. 3310 13 photons / s at a spectral resolution E /DE above 2300. 1999 Elsevier Science B.V. All rights reserved. Keywords: Microspectroscopy; Collimated PGM; FSGM
1. Introduction Highly brilliant undulator sources at the newly built third generation synchrotron facilities provide the necessary flux density for fast spatially resolved electron spectroscopy. Consequently, many microspectroscopy beamlines are under construction or already in operation in the VUV and soft x-ray region [1–4]. At the 1.7-GeV electron storage ring facility BESSY-II a photoemission electron microscope with advanced electron
*Corresponding author. Correspondence address: Rudower Chaussee 5, D-12489 Berlin, Germany. Tel.: 149-30-6392-2941; fax: 149-30-6392-4850. E-mail address: [email protected] (M.R. Weiss)
optics is under construction aiming at a spatial resolution of 5 nm [5]. An optimised beamline for this microscope needs to focus the radiation into a field of view of 5 mm [6]. The beamlines for high spectral resolution will provide focal spots on the sample with sizes ranging from 20 mm to 200 mm. This leaves a spatial resolution gap in the intermediate range from 100 nm to 20 mm. It is therefore planned to build a beamline that is optimised for a microfocus with 1-mm spotsize and high flux. The concomitant demagnification requires that the last optical element has to be placed close to the sample position. Therefore, a second configuration is designed with more space for experiments with a microspot in the 10-mm range. To find the best suited monochromator for high flux microspectroscopy we compared two design concepts, the focused spherical grating mono-
0368-2048 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 98 )00380-6
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chromator (FSGM) and the collimated plane grating monochromator (PGM). The FSGM is a spherical grating monochromator (SGM) that allows changing of the included angle with an additional plane mirror in front of the spherical grating [7]. Thus, the focus in the dispersion plane can always be kept at the exit slit position. No real entrance slit will be used to provide the highest flux possible. The PGM is a development based on the Petersen type monochromators [8] at BESSY [9] at which the light is collimated in front of the grating. This allows the free adjustment of the fix-focus constant without movement of the exit slit. In Section 2 we will give information on the predesign considerations that are independent of the type of monochromator. The detailed description of FSGM and PGM are to be found in Sections 3 and 4. Finally, in Section 5 we will compare the performance and advantages or disadvantages of the two concepts.
2.1. U41 undulator source characteristics The source of this beamline is the U41 undulator which will be installed in a low beta section of the BESSY-2 storage ring [10]. It is a N 5 80 periods linear undulator of l0 5 41 mm period length. The expected photon beam was calculated for selected energies using the program SMUT [11] with the following electron beam characteristics: g 5 3326.81, Iring 5 100 mA, electron beam size sx 5 76 mm and sy 5 15 mm, electron beam divergence s x9 5 68 mrad and s 9y 5 10 mrad (at 3% coupling). The photon energy was selected such that the photon flux of the undulator harmonic is at a maximum. This occurs roughly at energies that are 1 /N times below the theoretical position of the harmonics. Datafiles of the source were produced that contain the photon intensity as a function of the emission angles. Table 1 shows the corresponding harmonic, K-value, photon energy, spectral flux, source size (FWHM) and divergence (FWHM).
2.2. Methods for performance calculation 2. Basic predesign considerations The primary design goals for this microfocus beamline are optimised spatial resolution and flux in the energy range from ca. 150 eV to 1500 eV which is served by an undulator (U41) for linearly polarised radiation. For the spatial resolution two different values should be reached:
• A resolution of 1 mm with a working distance as required for optimised focusing, and • A moderate resolution of 10–20 mm with large working distance of ca. 750 mm between last mirror and sample position. Other requirements have also to be met, namely:
1. The space requirements at the BESSY-II storage ring because of minimum source distance of 17 000 mm and the use of a premirror is required; 2. Spectral resolution is given less importance than flux, therefore E /DE above 2000 suffices.
Two methods were used for the calculations described in this paper: Analytic expressions for slope error and aberrations were used for large parameter searches which were performed for the optimisation of the two-step demagnification optics (Section 2.5). The slope errors were included as Gaussian distributed deviations of the reflected beam. The aberrations were approximated by the well known development of optical path function [12]. For simplification, only the dominant aberrations were used. Ray tracings were used to get realistic values of the expected performance utilising the program RAY [13] developed at BESSY for beamline design. It is a Monte-Carlo type ray tracing program that allows selection of mirrors and crystals with standard surfaces eg. planes, spheres, toroids, ellipsoids, etc. Surface characteristics such as microroughness and slope errors, both Gaussian distributed are taken into account. The reflectivity of metal coatings as well as grating surfaces is calculated for each element individually. The above described source files of the undulator were used as input files for the ray tracings. Many of the results will be discussed in
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Table 1 Undulator harmonic, K-value, spectral flux, source dimension (Dx, Dy) and beam divergence (Dx9, Dy9) for the U41 at energies which were used for the ray tracings Harmonic 1 1 1 1 3 1 3 5 3 5 3 5
K 2.5 2.0 1.5 1.0 2.5 0.5 2.0 2.5 1.5 2.0 1.0 1.5
Energy 160.81 221.01 312.31 442.02 485.30 587.61 667.30 810.36 939.30 1113.50 1340.40 1573.40 [eV]
Spectral flux 15
1.313 ? 10 1.226 ? 10 15 1.088 ? 10 15 0.776 ? 10 15 0.911 ? 10 15 0.294 ? 10 15 0.737 ? 10 15 0.447 ? 10 15 0.430 ? 10 15 0.326 ? 10 15 0.048 ? 10 15 0.145 ? 10 15 phot [ ]]]] ] s 100 mA 0.1% BW
terms of the fix focus constant c ff as defined by Petersen [8].
2.3. Structure of the design problem A focus of 1 mm requires a demagnification of approx. 200 horizontally and 20 vertically. Since all photon energies in the required range should be accessible, grazing incidence optics is the only possible choice for this monochromator. Unfortunately, demagnification with this kind of optics is limited to values below 50 for aspheric surfaces and even limited to below 10 in favourable cases if spherical surfaces are used. In addition, since an exit slit is required for selection of the desired photon energy, refocusing optics between slit and sample is unavoidable. Therefore, the microfocus beamline was separated in a monochromatisation stage and a subsequent refocusing and demagnification stage. In addition, the monochromatisation stage is planned to focus both horizontally and vertically at the exit slit. This gives the advantage that the refocusing stage can later be replaced by other focusing concepts such as microzone-plates, bragg-fresnel lenses etc. which gives the beamline a higher versatility.
2.4. General considerations for the monochromatisation stage The monochromatisation stage serves two purposes: it provides the monochromatisation and it is also the first demagnification step in the beamline.
Dx
Dx9
Dy
Dy9
77.1 76.8 76.5 76.4 76.4 76.3 76.3 76.2 76.2 76.2 76.1 76.1 [mm]
212 202 176 174 172 169 164 162 167 157 168 151 [mrad]
19.7 18.5 17.5 16.9 16.7 16.4 16.3 16.0 15.9 15.8 15.6 15.5 [mm]
119 106 85 76 76 75 68 61 74 54 39 42 [mrad]
A general design goal for the monochromatisation stage is to provide a monochromatised beam without decreasing the beam quality, i.e. its spectral brilliance. There are two major sources for brilliance losses in a monochromator: slope errors (SE) and aberrations. These two contributions are interconnected since aspherical elements (ellipsoids) contain higher slope errors than spherical elements, which in turn give higher aberrations. Losses due to the SE are only dependent on the source distance of the imaging system. If aberrations such as coma are present an additional loss in brilliance occurs e.g. for high demagnification ratios for spherical and toroidal mirrors. Still, a demagnification of up to six can be reached without severe brilliance losses at source sizes and beam divergences as encountered here. An ellipsoidal mirror, although affected by higher SE, is constant in loss of brilliance and will be the better choice for demagnification above a factor of ten. Based on this consideration we decided to use spherical optics with the best SE possible at the smallest possible source distance for the monochromatisation stage. In addition, to avoid aberrational losses, only a small demagnification ratio will be used.
2.5. General considerations for the refocusing stage The refocusing stage has two purposes: transfer of the photons from exit slit to sample and further
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demagnification. The requirement of brilliance conservation, as it was discussed in the Section 2.4, is not valid here since spotsize and not divergence is of importance at the sample. Therefore, the spotsize depends almost completely on aberrations and slope errors as long as it has the smallest diameter.
2.5.1. Optics for refocusing Presently, there are several possibilities for grazing incidence refocusing. Ellipsoidal mirrors provide the best means for point-to-point imaging since they show no aberrations in this imaging geometry. Unfortunately, these turned out to be very difficult to produce, which led to unacceptably large slope errors [14,15]. A possible solution is to reduce the image distance which in turn leads to very small radii and therefore additional problems for the manufacturer. Only spherical mirrors and derived shapes such as cylindrical and toroidal mirrors can be obtained with a small enough slope error. But if one wants to achieve demagnifications in excess of ten, coma increases dramatically. Recently, Padmore et al. demonstrated that plane mirrors can be bent to elliptical shape by tailoring their width. By arranging two mirrors at 908 (Kirkpatrick–Baez arrangement) they achieve a spot of about 1-mm diameter [3] at a demagnification ratio of up to 20 and 40. This is only possible due to the small SE of about 1 mrad (RMS) [3]. These are impressive performance figures. However, it is not without practical problems. Due to the fact that the bent plane mirrors focus only in the longitudinal direction, they tend to become very long. Since the mirrors have to be placed one after the other the demagnification of the first mirror is rather small. One also has to be aware of the fact that space for the bending mechanism has to be added leading to even longer distances. For this study we shall use bent elliptical mirrors in the Kirkpatrick–Baez arrangement for the 1-mm microfocus. For the moderate microspot at large distance, we will use a a toroidal mirror as refocusing optics since this type of mirror is both readily available and low priced. The required microspot allows the large image distance at which the SE does not deteriorate the focus overly. Rather aberrations are expected which are still manageable for the required demagnification. An incidence angle with respect to the surface of
28 was chosen so that even the 1500-eV photons are reflected with high efficiency.
2.5.2. Optimisation of the refocusing stage Refocusing of the monochromatised spot starting at the exit slit depends on its size and the beam divergence there. Therefore, the refocusing optics cannot be optimised without knowledge of the monochromatisation stage. This stage, however, can be designed within a wide range of demagnification factors. Therefore, one should rather optimise the two-step demagnification of monochromatisation and refocusing stage. The first stage is provided by the monochromatisation stage which uses toroids and cylinders (for PGM) and spheres (for FSGM). The second stage consists either of the two bent elliptical mirrors or a toroidal mirror. The optimisation of this two-step demagnification was done for the horizontal and vertical direction independently. Slope errors as well as aberrations were included, the latter using the analytic expressions of the development of the optical path function for toroids and spheres [12]. The aberrations of the mirrors in the first stage and the toroid of the second stage were calculated separately where absolute values were added quadratically. This, of course, is an upper estimate of the expected error since there is in general the possibility that aberrations annihilate each other. The values for source size and divergence were chosen for the lowest energy (size: 77.1319.7 mm 2 , divergence: 2123119 mrad 2 ).
3. Focused spherical grating monochromator design The FSGM allows adjustment of the included angle at the grating such that the diffracted order is focused at the fixed exit slit, as described already in the introduction. The basic layout for this type of monochromator as it is proposed in this study will be described in the following Section 3.1.
3.1. General layout The required premirror is a horizontally deflecting sphere which focuses horizontally onto the exit slit (see Fig. 2b). It is placed at minimum distance from
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the source (17 000 mm) to minimise the brilliance losses. The refocusing optimisation for the elliptical refocusing mirrors required a distance to the exit slit of 2000 mm which cannot be met due to the space problems. Therefore, the distance was set to the minimum allowable distance of 7500 mm. The vertically deflecting spherical grating provides the dispersion and focuses the source vertically onto the exit slit. The line density of the grating is chosen to be as small as possible to meet the high flux requirement. Still, the mechanically allowed angles have to be observed that lead to a grating with 300 l / mm. A lamellar grating profile with 10.0-nm groove depth and a groove width to spacing ratio of 0.6 was chosen for good efficiency over the range of energy and small higher order content. Considering a c ff value of 0.8 to 0.36, the image distance was chosen to be 3500 mm. The c ff values as a function of photon energy which is required for the focusing condition is shown in Fig. 1, bottom, as dot-dashed line. The plane mirror is placed after the grating to decrease the influence of its slope error. The detailed list of parameters of the FSGM monochromatisation stage is shown in Table 2. The refocusing optics is either a toroidal mirror at 3000 mm after the exit slit. It deflects sideways and
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Table 2 Parameters of the various optical elements for the FSGM monochromatisation stage Optical element shape
M1 Spherical
M2 Plane
Grating Spherical
Deflection Optical active surf. (mm 2 ) Coating Angle of incidence Source distance (mm) Image distance (mm) Radius R (mm) Groove density Groove depth (nm) Groove width to period ratio
Horizontal 270 3 10 Au 888 17 000 7500 298 233 – – –
Vertical 300 3 20 Au Variable – – – – – –
Vertical 90 3 15 Au Variable 21 000 3500 220 000 300 10.0 0.6
forms the image at 750 mm. A second refocusing optics is based on bent elliptical mirrors. The first mirror deflects vertically and is placed 5000 mm after the exit slit. The second mirror deflects horizontally and will be 115 mm after the previous mirror. The mirrors are bent such that the image is formed at 85 mm after the last mirror. The detailed list of parameters of the refocusing system is shown in Table 3. The optical layout of the elliptical refocusing system is also shown in Fig. 2c). The performance of the monochromator, as de-
Fig. 1. Diffraction efficiency calculations for a blaze grating with 600 l / mm, 0.88 blaze in gold as a function of photon energy and c ff . c ff -paths are shown for the PGM (dashed) and FSGM (dot-dashed). Left: First order efficiency; center: second order diffraction divided by first order; right: third order diffraction, divided by first order. The dashed curve shows a path that is optimised for flux.
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Table 3 Parameters of the toroidal (M t ) and Kirkpatrick–Baez bent elliptical (M e,1 , M e,2 ) refocusing systems Optical element shape
Mt Toroidal
M e,1 Elliptical
M e,2 Elliptical
Deflection Optical active surf. (mm 2 ) Coating Angle of incidence Source distance (mm) Image distance (mm) Long. radius R (mm) Sag. radius r (mm)
Horizontal 40 3 2.5 Au 888 3000 750 34384 41.88
Vertical 120 3 10 Au 888 5000 200 – –
Horizontal 70 3 10 Au 888 5115 85 – –
termined by ray tracing, shows the required spot sizes for both refocusing systems. The flux and energy resolution values are shown in Fig. 3, top, for the fist, third, and fifth harmonic and will be discussed in Section 5.
4. Petersen-type monochromator design As second choice we investigated the PGM. The general layout of this monochromator will be discussed shortly in the following Section 4.1 and is show in Fig. 2a.
4.1. General layout The premirror provides vertical collimation and a horizontal focusing of the undulator source onto the exit slit. To meet the requirement for conservation of the brilliance the horizontal focusing is done by this mirror (Section 2). Consequently, the premirror is of a toroidal shape. The next element is the grating which deflects vertically. The distance between premirror and grating is chosen as short as the dimension of the grating chamber and neighbouring beamline allows. The type of grating and line density will be discussed in more detail below. After the grating a plane mirror with vertical deflection is placed which allows one to freely choose the total deflection angle of the grating. The settings of grating and plane mirror can be completely described by the photon energy and c ff .
Following the plane mirror, a horizontally deflecting focusing mirror is placed, that focuses the collimated beam vertically onto the exit slit. This mirror does not contribute to the horizontal focusing and is therefore of cylindrical shape (Table 4).
4.2. c ff for optimised performance The fix-focus constant can be chosen freely for a collimated PGM, which can be used to optimise the monochromator. Therefore, if one uses a blaze grating one can stay on blaze for all desired energies. Still, other optimisation goals are accessible, even while scanning the monochromator. Within this section we will give some details on the calculations that were performed to select the best grating parameters. For these calculations, the REFLEC program [16] was used which is based on the method of Neviere [17]. We determined the first, second and third order grating efficiency for energy values ranging from 50 eV to 1500 eV, c ff from 0.1 to 0.85 (outside order diffraction) and blazes of 0.88, 1.08, and 1.28 on gold. From these results we determined also the ratio between first order and the higher orders which give the higher order content of the light. The result for 0.88 which is shown in Fig. 1, bottom, can be used to find an optimised c ff for each energy. If flux is to be optimised, one should follow the ridge in Fig. 1, left, which is shown as a dashed line. This will result in severe higher order content as can be seen from the higher content in Fig. 1, center and right. Note, that the higher order content is also reduced by the reduced reflectivity of the mirrors in the beamline for higher photon energy. If, on the contrary, higher diffraction orders are not desired, a path to the left of the dashed curve can be taken, that gives somewhat less diffraction efficiency by greatly reduced higher order content. Finally, any arbitrary curve through this parameter space can be chosen, if the experiment requires so. The performance of the monochromator, as determined by ray tracing, shows the required spot sizes for both refocusing systems (Fig. 3, bottom). Flux and energy resolution values for the first, third, and fifth harmonic are also shown in Fig. 3, center, and will be given a closer look in Section 5.
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Fig. 2. Schematic views of the beamline layouts: (a) top and side view of the collimated PGM as described in Section 4 with toroidal refocusing mirror; (b) top and side view of the FSGM as described in Section 3; (c) refocusing optics using two plane elliptical mirrors.
5. Comparison The optimisation work done for this comparative study revealed advantages and disadvantages of either concept which will be discussed here. It also became apparent, that the differences are small with regard to many aspects. The placement
and distances and therefore the demagnifications of the optics are very similar. The range of c ff values is almost identical. The differences in the refocusing optics were so small that finally the same values are used. Finally, for both monochromators only one grating is necessary for the whole energy range due to limited requirement for the spectral resolution.
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Fig. 3. Result of the performance calculations for the PGM and FSGM. The top graphs show photonflux (a) and spectral resolution (b) for the FSGM with toroidal (s) and bent elliptical (앳) refocusing system. The center figures show photonflux (c) and spectral resolution (d) for the PGM with toroid (s) and bent ellipses (앳). The expected spots on the sample are shown in the bottom row for the bent elliptical focusing mirrors (e) and the toroidal refocusing mirror (f) for the collimated PGM at 160.8 eV.
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Table 4 Parameters of the various optical elements of collimated PGM monochromatisation stage Optical element shape
M1 Toroidal
M2 Plane
M3 Cylindrical
Grating Plane
Deflection Optical active surf. (mm 2 ) Coating Angle of incidence Source distance (mm) Image distance (mm) Long. radius R (mm) Sag. radius r (mm) Groove density Blaze
Horizontal 270 3 10 Au 888 17 000 6900 / ` 281 267 1186.58 – –
Vertical 300 3 20 Au Variable – – – – – –
Horizontal 80 3 10 Au 888 ` 2000 ` 139.60 – –
Vertical 90 3 15 Au Variable – – – – 600 0.88
5.1. Advantages and disadvantages of the FSGM design The strongest advantage of the FSGM beamline is obvious: it uses one element less than the PGM. Therefore, the monochromator stage is cheaper. This is even more the case since plane and spherical surfaces are used which are additionally easier (and cheaper) to produce and easier adjusted. Easier production means also less slope error for these mirrors which leads to a smaller focus. Another advantage is the c ff path with regard to aberrations (see Fig. 1, dot-dashed curve). It leads to a small vertical demagnification at low energies (c ff ¯ 0.4) and strong demagnification at high energies (c ff ¯ 0.8). This in turn gives reduced aberrations for the low energies where source divergence is large. The results in Fig. 3, top, reveal the major disadvantage of the FSGM. The spectral resolution changes largely over the energy range. In addition, a grating that works over the whole energy range gives only poor performance for the low energy part. Therefore, gratings for the low, middle, and upper energy region are required, which annihilates the low cost advantage that is stated above. Finally, the c ff -path cannot be changed. Therefore, optimisation of the grating angles for e.g. on-blaze or decreased higher order content is not possible.
5.2. Advantages and disadvantages of the PGM design The PGM is the more expensive monochromator design. It not only requires the additional focusing
mirror, it also contains toroids and cylinders which are more expensive to produce. In addition, these kinds of elements have higher SE. On the other hand, c ff can be chosen freely within the limits of the grating and plane-mirror mount. This gives the advantage, that e.g. the on-blaze condition for a blaze grating can be fulfilled. Thus, much higher grating efficiencies can be achieved which leads to higher spectral flux in the sample spot. The on blaze c ff -path has also the nice property that the relative energy resolution is almost constant on the energy range. Other c ff paths are possible that optimise the performance targeted on other qualities, e.g. higher order suppression (see Fig. 1).
6. Conclusion From the optimisation work that is described in this paper, we draw the conclusion that the collimated PGM is better suited as a microfocus monochromator. This type of beamline will be more expensive but provides higher spectral flux on the sample and allows the freedom to change c ff which opens the opportunity for other optimisation goals. The refocusing optics, based on a toroid, which is identical for both monochromator concepts will provide a 10 3 20 mm spot with large working distance. A second refocusing optics with bent elliptical mirrors will reach a 1 3 1 mm micro-spot. The latter is only possible with the small distance between the last mirror and the sample which has to be considered for the design of the experimental chamber. The stigmatic focusing monochromator
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also allows the use of different refocusing systems, e.g. micro zone plates. If a c ff path is chosen for optimised flux at the sample position, values are expected to exceed 3 3 10 13 phot / s 100 mA for low energies and using the toroidal refocusing. About 1 3 10 13 phot / s 100 mA are attainable for the elliptical refocusing system. Towards 1500 eV the flux is still as high as 1 3 10 12 phot / s100 mA which allows access to the deeper electron levels, e.g. for spatial resolved magnetic dichroism spectroscopy. The spectral resolution (E /DE) on this c ff -path changes only a little, around 2000 and 4000, respectively.
[5]
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