398 M. Jergel et al. (a) (b) Fig. 24.2. Cross-sectional HR TEM images of the as-deposited (a) and collapsed (b) Ni/C ML whose XRR and GIXDS simulation parameters are given in Table 24.2. Black bars at the bottom correspond to 10 nm (a) and 20 nm (b) energy-dispersive X-ray and electron diffraction analyses while the matrix is formed by C and a small fraction of fine granular fcc Ni. Obviously, the annealing stimulates the growth and coalescence of the original Ni grains found in the as-deposited state, which governs also interface morphology as reflected in an increase of the lateral correlation length and a decrease of the vertical correlation of the interface roughness (decay of interface conformity). As soon as Ni grains are well developed and the ML becomes discontinuous, diffusion of C along Ni grain boundaries may also contribute to the ML break- down. A complete diffusion of C into Ni layers was reported in the past [21]. The observed thermal stability is comparable to sputtered and PLD Ni/C mirrors [18,19,25]. It is worth noting that the ML period steadily increases and C layer den- sities decrease when increasing the temperature above 100 ◦ C. Similar effects were reported in sputtered Ni/C MLs with larger periods [21, 42] and were attributed to a transformation of the amorphous into the graphitic-like struc- ture. Although we were not able to trace this effect directly by HR TEM or X-ray diffraction due to very thin C layers, the observed growth and coales- cence of Ni grains connected with a long-distance collective diffusion of Ni atoms across C regions may induce graphitization. It was shown that such a metal-driven graphitization is preferred to carbide formation when C is in excess [43] which explains also the absence of carbide formation in the tem- perature range applied. Once initiated, the graphitization due to Ni diffusion proceeds even at RT as evidenced by ≈8% increase of the ML period which was observed on the sample annealed at 300 ◦ C after a 16-month RT storage. 24 Multilayers with Ultra-Short Periods 399 Table 24.3. The XRR simulation parameters of the as-deposited Ni/B 4 C ML (400 periods) t Ni t B 4 C Λσ eff Ni-on-B 4 C σ eff B 4 C-on-Ni (nm) (nm) (nm) (nm) (nm) 0.78 0.81 1.59 0.28 0.26 Ni/B 4 C MLs prepared by DECR do not suffer from agglomeration effects in Ni as a ML with a period below 2 nm and an extremely small interface width below 0.3 nm could be deposited (Table 24.3). Obviously, much higher adatom mobilities with DECR sputtering than with UHV deposition have a healing effect on the geometrical interface roughness and layer continuity at small thicknesses which goes along with the amorphous character of the layers as confirmed by X-ray and electron diffraction. On the other hand, the presence of compound layers does not favour mixing effects. Significantly, substitution of C by B 4 C has no detrimental effect on the theoretical optical contrast. Due to very smooth interfaces, a large number of periods (N = 400) was necessary to visualize GIXDS effects in RSM. Only the GIXDS around the first ML Bragg maximum is visible (Fig. 24.3a) as the second maximum emerges directly from the instrumental background and the higher orders cannot be seen at all. This fact is a consequence of the ultra-short ML period when the measurements of RSM are especially instructive. A concentration of GIXDS in the form of a sheet around the Bragg peak (resonant diffuse scattering) is a clear sign of a partial vertical correlation of the interface roughness while its distinct asymmetry is exceptional. HR TEM revealed that the interfaces are wavy and partly copy each other. The as-deposited Ni/B 4 C ML was first exposed to several isothermal annealings at 300 ◦ C up to 8 h of total time with no significant changes of XRR but a slight improvement of the peak reflectivity on the first Bragg maximum. Contrarily, an additional annealing at 400 ◦ C for 2 h destroyed the ML completely and the Bragg peak disappeared. Therefore, an intermediate 350 ◦ C/2 h annealing, which brought about a decrease of the peak reflectiv- ity by ≈1 order of magnitude, was done independently. Such a pre-annealed sample was then processed by a series of 5- or 10-min RTAs with a step-like increase of temperature up to 520 ◦ C which resulted in a further severe reduc- tion of the peak reflectivity and a reduction of the ML period from 1.59 to 1.54 nm, the first Bragg maximum being still well resolved. This reduction may be attributed to the annealing-out of the excess free volume typical for amorphous structure. HR TEM inspection showed that the layered structure without mixed regions but with many topological defects was still preserved. The RSM (Fig. 24.3b) exhibits substantial changes in comparison with the as- deposited state. Though it was not possible to simulate RSM with common correlation functions presented in the previous section, a qualitative change due to the annealing could be simulated when doubling the lateral correlation 400 M. Jergel et al. (a) (b) Fig. 24.3. Reciprocal space maps of the (a) as-deposited and (b) annealed up to 520 ◦ CNi/B 4 C ML around the first Bragg peak. In the first map, the shadow of a beam stopper protecting a position-sensitive detector hides the XRR whose simulation parameters are shown in Table 24.3. The second map was measured with a point detector. The labels denote the logarithms of the extreme values of the intensity length from 10 to 20 nm. This increase cannot be attributed to the grain growth as in the case of Ni/C couple as no crystallization inside the ML was observed. However, large re-crystallized regions in the substrate at the interface with the ML, presumably Ni silicide grains, could be seen locally by TEM. After the ML breakdown, the original layered structure was trans- formed into an inhomogeneous amorphous-like structure with only one diffuse ring in electron diffraction pattern. This collapsed ML still keeps a sharp interface with the substrate. HR TEM revealed a rare occurrence of crys- tallographically ordered regions, probably (111) planes of fcc Ni. This fact suggests that Ni diffusion controls the ML breakdown as in Ni/C couple but the mechanism of decay of the compound layers is unclear in the absence of a 24 Multilayers with Ultra-Short Periods 401 Table 24.4. The XRR and GIXDS simulation parameters of the as-deposited Sc/Cr ML (250 periods) t Sc (nm) t Cr (nm) Λ(nm) σ Cr-on-Sc (nm) σ Sc-on-Cr (nm) ξ(nm) L vert (nm) H 0.83 0.93 1.76 0.28 0.25 7 35 1 crystalline phase formation. Nevertheless, any deviation from the compound stoichiometry, which is common in extremely thin layers, may affect thermal stability of Ni/B 4 C mirror adversely. Ultra-short periods could be achieved and many periods (N = 250) were deposited also for the Sc/Cr couple using ECR ion source. Similarly as for Ni/B 4 C, only the region around the first Bragg maximum could be used for GIXDS analysis due to the ultra-short ML periods (Table 24.4). The presence of the resonant diffuse scattering sheet in RSM (Fig. 24.4a) suggests here as well a partial vertical correlation of the interface roughness. In contrast to previous cases, where the lateral correlation function according to (24.1) was used, PSD given by (24.2) proved to be convenient to simulate GIXDS for Sc/Cr MLs (Table 24.4; Fig. 24.4b). Different cuts throughout the calculated RSM gave a good quantitative agreement with particular scans measured sep- arately. The vertical correlation length represents only ≈8% of the total ML thickness. The σ eff and σ values are practically identical with a slight asym- metry between Sc/Cr and Cr/Sc interfaces, showing no mixing as expected because of the negligible miscibility of the elements. No mixing and a high reg- ularity of the ML stack were confirmed by HR TEM and TEM, respectively. Electron diffraction showed only one ring typical for an amorphous struc- ture but narrower than that for Ni/B 4 C which implies a higher short-range ordering. Thermal stability tests were performed on a ML with a period of 1.25 nm repeated 150 times. The sample was first exposed to several isothermal anneal- ings at 280 ◦ C up to 33 h of total time which brought about a decrease of the peak reflectivity on the first Bragg maximum by ≈25%. This decrease was connected with an increase of the initial interface roughness of 0.28 nm to the final value of 0.30nm for Cr-on-Sc interfaces while a similar increase from 0.26 to 0.29 nm was observed for Sc-on-Cr interfaces. Simultaneously, the ML period increased to 1.28 nm which may be ascribed to a structural ordering inside the layers. A further 450 ◦ C/4 h annealing decreased the peak reflec- tivity by one order of magnitude and a subsequent 650 ◦ C/4 h one destroyed the layered structure completely, as reflected in the disappearance of the ML Bragg maxima. No crystalline phase could be detected by X-ray diffraction. Presumably, a fine granular structure typical for immiscible components was formed. 402 M. Jergel et al. (a) (b) Fig. 24.4. Measured (a)andsimulated(b) reciprocal space maps of the Sc/Cr ML around the first Bragg peak. The simulation parameters are shown in Table 24.4. The labels denote the logarithms of the extreme values of the intensity 24.5 Conclusions and Outlook The ability to form thermally stable ultra-short period MLs was tested for material couples of different compositions and miscibilities. Such periods are inherently required for high-quality imaging in the water window or for very hard X-rays and put strong requirements on the interface quality. The Cu/Si couple is attractive for very hard X-rays because it is low absorbing and forms very regular ML stacks easily down to small periods. On the other hand, it is a miscible pair of materials. We found a limit of ≈2nmfor the ML period which still yields a well-resolved ML Bragg peak in the XRR curve for UHV-deposited MLs and which compares well with dc-sputtered 24 Multilayers with Ultra-Short Periods 403 ones prepared previously. Thermal stability restricts their use to below 100 ◦ C and therefore does not qualify this material pair to be used for ML mirrors working in high heat load conditions. Ni/C mirrors were studied mostly for applications below the C–K edge (284 eV) or for hard X-rays of several keV (e.g. G¨obel mirrors). A shift to ultra- short periods would render them useful for applications close to 100 keV with a low-absorption coefficient. A better thermal stability than for the Cu/Si couple may also be expected due to a low mutual solubility of Ni and C. We found a minimum limit of ≈2.5 nm for the ML period imposed by agglomeration effects in polycrystalline Ni layers. Such a ML is stable up to 300 ◦ C, the breakdown being controlled by the growth and coalescence of Ni grains and Ni-induced graphitization of C. The thermal stability is comparable to that of Ni/C MLs with larger periods studied previously, which suggests that it is independent of the ML period when continuous layers are formed. Vertical correlation of the interface roughness is much weaker than for Cu/Si MLs with positive implications for their use when a good specular imaging contrast is required. From the technological point of view, UHV deposition with an in situ substrate heating proved to be a cost-effective promising alternative to in situ ion-beam etching for Cu/Si and Ni/C couples. Nevertheless, ultra-short periods down to 2 nm or less are not accessible with them. An ultra-short ML period far below 2 nm could be achieved by a sub- stitution of C by B 4 C in Ni/C MLs and application of DECR sputtering for deposition of Ni/B 4 C MLs. A high adatom energy allows formation of extremely smooth amorphous layers which are continuous at very small thick- nesses. The presence of compound layers enhances thermal stability to 350 ◦ C on a long-term annealing and above 500 ◦ C on RTA. The amorphous character of the layers plays also some role as it excludes fast grain boundary diffusion. The mirror collapses by Ni diffusion and decomposition of B 4 C layers without formation of a well-developed crystalline phase. The Sc/Cr couple is also able to provide MLs with an ultra-short period far below 2 nm using ECR sputtering. The MLs have excellent quality and good thermal stability up to 500 ◦ C as expected for the elements with neg- ligible miscibility. The vertical correlation length of the interface roughness constitutes less than 10% of the total ML thickness, so that its detrimen- tal effect on the specular imaging contrast is minimized. The ML breakdown is presumably controlled by the formation of fine granular phase typical for immiscible elements. For the future, new material combinations suitable for ultra-short period ML mirrors aimed at specific applications have to be tested in detail in a way similar to that demonstrated in this work. In particular, material pairs yielding structures with minimum interface roughness have to be searched for. It has to be stressed that even traditional material pairs represent new challenges for technology when MLs with layer thicknesses below 1 nm and several hundred periods have to be deposited. At present, an optimization of 404 M. Jergel et al. the reflectivity in UHV electron-beam evaporated ML stacks is done in situ by ion milling and partial material removal after deposition of each layer. In this way the layers, which have been deposited thicker than nominal values, are thinned to optimum thicknesses with in situ control. For the mirrors deposited by sputtering, a high quality of the ML stack is achieved by employing stable sputtering parameters and a precise control of the motion of the sample with respect to the targets. ECR sputtering with the inert gas pressure far below the thermalization threshold proves to be superior to other techniques in terms of yielding extremely smooth interfaces. To fabricate regular ML stacks with ultra-short periods, further progress is expected by making a still tighter con- trol of the deposition process including an in situ monitoring with a resolution below 10 −1 nm to provide feedback for subsequent correction procedures. Thermal stability requirements are also more critical with ultra-short peri- ods below 2 nm, particularly in view of the advent of free electron laser (FEL) sources whose brilliance is several orders of magnitude higher than that at present synchrotron beam lines. To set and manipulate thermal stability lim- its of ultra-short period mirrors working with femtosecond intense pulses, ML response to short-time power loads far below a second and with the ramp edge of several 100 K s −1 must be studied. Here, advanced time-resolved in situ diagnostics of the processes at the interfaces, like in situ ellipsometry with several ms read-out, must be applied. Though much knowledge has already been gained, the research and devel- opment of ultra-short period ML mirrors with the individual layer thicknesses on the sub-nanometre scale is still open to new creative ideas. The design and the production of mirrors with atomic level control will shift frontiers not only in the ML optics but also in nanotechnology as a whole. Acknowledgements The authors are grateful to M. Yamamoto from IMRAM Tohoku University, Sendai, for providing Sc/Cr ML samples and to V. Hol´y from Charles Uni- versity, Prague, for providing DWBA software. Z. Bochn´ıˇcek from Masaryk University, Brno, is acknowledged for X-ray reciprocal space measurements. Supports by COST P7 Action, Scientific Grant Agency VEGA (contracts no. 2/4101/26 and 2/6030/26) and Center of Excellence SAS project CE-PI I/2/2006 are acknowledged. References 1. M. Yamamoto, T. Namioka, Appl. Optics 31, 1622 (1992) 2. E. Spiller, Soft X-Ray Optics (SPIE Optical Engineering Press, Bellingham, 1994) 3. 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Djavanbakht, V. Carrier, J.M. Andre, R. Barchewitz, P. Troussel, J. Phys. IV 10, 281 (2000) 43. R. Sinclair, T. Itoh, R. Chin, Microsc. Microanal. 8, 288 (2002) 25 Specially Designed Multilayers J.I. Larruquert, A.G. Michette, Ch. Morawe, Ch. Borel, and B. Vidal Abstract. Periodic multilayers, utilising Bragg reflection at single angle or wave- length, are established as efficient reflectors from the hard X-ray down to the extreme ultraviolet (XUV) region of the electromagnetic spectrum. More recently, both lat- erally and depth-graded multilayers have been designed and fabricated; they allow either reflection of divergent beams or over a broad angular or wavelength range, or a combination of both. Recent developments in aperiodic structures, along with advances in ultra-short period and transmission mutilayers, are discussed in this chapter. Modelling methods to provide designs for specific purposes are described, as are advances in manufacturing techniques and quality control. In addition to peak reflectivity at a specific wavelength or angle, high integrated reflectivity over a given wavelength or angular range is considered, along with flat reflectivity profiles. Impor- tant potential applications of flat response mirrors are X-ray micro-spectroscopy, X-ray diffraction, XUV polarimetry, and any other technique requiring both high reflectivity and broad bandwidth. 25.1 Introduction Periodic multilayers, utilizing Bragg reflection at single angles or wavelengths, are established as efficient reflectors from the hard X-ray to the extreme ultraviolet (XUV) region of the electromagnetic spectrum. Recently, laterally graded multilayers allowing reflection of divergent beams and depth-graded multilayers providing broad angular or wavelength ranges have been designed and made; combinations having both types grading have also been considered. Recent developments in such aperiodic structures, along with advances in ultra-short period and transmission multilayers, are discussed in this chapter. Modeling methods to provide designs for specific applications are described, but manufacturing techniques and quality control are not discussed explicitly, as these are similar to those used for conventional multilayers. In addition to peak reflectivity at a specific wavelength or angle, high integrated reflectiv- ity over a given wavelength or angular range is considered, along with flat reflectivity profiles. [...]... response mirrors include X-ray microspectroscopy, X-ray diffraction, XUV polarimetry, and any other technique requiring both high reflectivity and broad bandwidth Importantly, in the recent years, the use of multilayer-based X-ray optics at third-generation synchrotron sources has seen a considerable growth [1,2] The principal applications are focusing or collimating optics and broadband monochromators... laterally graded multilayers can be combined into single devices providing fixed focus optics over broad energy intervals [5]; such optics have wide applicability in, e.g., microspectroscopy and diffraction experiments 25.2.1 Laterally Graded Multilayers Most multilayer-based synchrotron optics, including focusing and collimating devices using curved multilayers and flat monochromators [6], require lateral... 429 Reflectivity or Inreflectance This function involves, instead of the simple reflectivity modulus, the modulus raised to the power of inverse of the complex refractive index of the next (outer) layer, including an inclination term Thus inreflectance is not defined for the outermost layer Maximizing the inreflectance at every internal layer, proceeding sequentially outward, results in a multilayer with... Variation The algorithms described in Sects 25.4.1 and 25.4.2 may readily be extended to the design of a multilayer coating in which the refractive index varies continuously in depth In this case, an inhomogeneous coating with a refractive index profile can be optimized, in principle, at every thickness element to obtain the largest possible reflectivity at a given wavelength In practice, several difficulties... contrast across interfaces; the thickness of the element is calculated in terms of the refractive index increment at the interface The coating is optimized element by element starting from the substrate When the refractive index varies both continuously and smoothly, the thickness element is first order in the refractive index increment A convenient way to calculate the refractive index profile in depth is... 0.0746 0.0874 0.0848 0.1062 0.0909 0 .112 7 0 .113 5 0 .114 2 0 .114 9 0 .115 4 0 .115 70 0 .115 71 0 .115 72 2.412 2.814 2.585 2.986 3.014 3.443 3.358 3.298 3.317 3.1486 3.0692 3.0639 3.0632 426 J.I Larruquert et al provide a significant throughput enhancement The reflectivity after nine reflections at the target wavelength and integrated within the reflectance band are also shown in Table 25.2 At the design wavelength,... 0.534 0.535 0.536 In each case the combination of materials providing the largest Thereafter, the increases become smaller; for ten materials in each period the total increase, over two materials, is 20% The highest reflectivities are obtained when aluminum is the outermost material, and so the calculation should incorporate the effect of the thin oxide film that readily grows on aluminum in contact with... in contact with the atmosphere This was not taken into account in this example, since the purpose is to show the benefit of multimaterial SQWMs compared to standard two-material multilayers In this and other examples investigated, it was found that the increase in the number of materials does not necessarily affect the spectral bandwidth The intrinsic bandwidth depends more on the specific optical constants... at high energies crystal optics were (and still are) employed The problem was in the intermediate energy range; it was this gap that periodic multilayer mirrors were initially designed to fill Such coatings can, in principle, be deposited on substrates of any form and can be used as reflectors for energies of ∼0.01–10 keV at incidence angles ranging up to, in some cases, normal incidence Periodic multilayers... of different materials used The following summarizes the main details of the design of a multilayer coating consisting of m thin films of various absorbing materials deposited on an opaque substrate, assuming that the interfaces are abrupt and smooth Let ni be the refractive indices of the films and substrate (i = m + 1), the outer˜ most film corresponding to i = 1 In the most general case, all the ni . Non- periodic and laterally graded multilayers can be combined into single devices providing fixed focus optics over broad energy intervals [5]; such optics have wide applicability in, e.g., microspectroscopy. microspectroscopy and diffraction experiments. 25.2.1 Laterally Graded Multilayers Most multilayer-based synchrotron optics, including focusing and collimating devices using curved multilayers and flat monochromators. response mirrors include X-ray microspectroscopy, X-ray diffraction, XUV polarimetry, and any other tech- nique requiring both high reflectivity and broad bandwidth. Importantly, in the recent years,