230 P. Merc`ere et al. Wave-front measurement Closed loop X-ray Hartmann wave-frontsensor Flat deflection mirror Imaging optic Visible CCD camera Focal spot imaging 1 2 3 4 Removable YAG:Ce crystal Kirkpatrick - Baez active optic Command device Imaging system 36 36.33 36.63 38.22 Dista nce (m ) from the undulator source 38.62 X - ray beam Visible beam Hole array X-ray CCD camera Fig. 15.9. Beamline LUCIA end station with the KB active optical system and the soft X-ray HWS (b)(a) Fig. 15.10. Absolute residual wavefront measurements (single CCD image treatment) (a)beforeand(b) after closed-loop correction of the photon beam was tuned down to 700 eV to ensure a large illumination of the sensor with the central Airy disk. A closed-loop correction was then performed at E =3.64 keV (λ = 0.34 nm), the spatial filter pinhole having been removed. In a single itera- tion, we succeeded in correcting the phase distortions from 7.7 nm rms and 30.9 nm PV down to 0.8 nm rms and 4.6 nm PV (Fig. 15.10). With the KB system correctly aligned, we performed knife-edge scans in both dimensions to characterize the beam. At the focal spot position, the beam sections were measured at 2.4 × 2.86 μm 2 FWHM (Fig. 15.11). These dimensions are close to the theoretical limit given by the source size, the geometry of the beamline, and the slope errors of the KB mirrors (measured about 1.1 μrad). The performance of HWS at these high energies, in particular, the signal- to-noise ratio and the accuracy of the sensor, is strongly limited by shot noise, 15 Hartmann and Shack–Hartmann Wavefront Sensors 231 Fig. 15.11. Beam knife-edge measurements at the focal spot position after closed- loop correction with HWS from the photon-to-electron conversion process in CCDs. The residual wave- front that can be observed after correction in Fig. 15.10b is, for example, only the result of shot noise. To overcome this problem, accumulation of several images is required. The signal-to-noise ratio and the repeatability of wave- front measurements were studied at 2.1 keV as a function of the number of images integrated. To achieve a signal-to-noise ratio of about 100, at least 50 CCD images had to be integrated. By integrating 500 CCD images per wave- front measurement, we improved the repeatability of the sensor to better than 0.04 nm rms. Therefore, high-readout rate CCD cameras may be preferred in the soft to hard X-ray spectral ranges, when an optimal performance of HWS is required. 15.4.3 Conclusion In the EUV spectral range, wavefront measurements were performed over a wide wavelength range from 7 to 25 nm. The accuracy of the sensor was proved to be better than λ EUV /120 rms (λ EUV =13.4 nm), and the sensitivity better than λ EUV /600 rms, demonstrating the high metrological performance of this system. In the soft X-ray range, HWS was successfully used to align a 4-actuator Kirkpatrick–Baez (KB) active optical system. A wavefront closed-loop cor- rection was performed at E =3.64 keV, which led to beam focusing down to 2.4×2.86 μm 2 FWHM in a single iteration. Variation of the KB focal length is easily possible by the addition of a curvature term to the closed-loop wavefront target. Today, HWS are routinely working between 6 eV (193 nm) and 8 keV (0.155 nm), with accuracies as good as 0.04 nm rms. The use of high readout rate CCD cameras for fast accumulation of images and the use of luminescent screens for a visible Hartmann analysis of the beams, especially for energy ranges above 10 keV, are currently under investigation. The coupling of HWS 232 P. Merc`ere et al. with mechanical and bimorph multiactuator deformable mirrors should also be done in a very near future, to allow easy correction of higher frequency distortions on synchrotron beamlines. Acknowledgements The authors are greatly indebted to “REGION ILE DE FRANCE” for fund- ing part of the SH-LTP development project. The authors would like to thank the scientific and technical staffs of ALS beamline 12.0 and SLS beamline LUCIA (including Markus Janousch) for their support. Finally, the authors would like to thank several contributors to these works, including Sylvain Bro- chet, Samuel Bucourt, Gilles Cauchon, Guillaume Dovillaire, Thierry Moreno, Fran¸cois Polack, Muriel Thomasset, and Philippe Zeitoun. References 1. W.H. Southwell, J. Opt. Soc. Am. 70, 998 (1980) 2. M. Thomasset, S. Brochet, F. Polack, in Advances in Metrology for X-Ray and EUV Optics, ed. by L. Assoufid, P. Takacs, J. Taylor. Proc. SPIE, vol. 5921 (2005), p. 12 3. M. Otsubo, K. Okada, J. Tsujiuchi, Opt. Eng. 33, 608 (1994) 4. F. Siewert et al., Third International Workshop on Metrology for X-Ray Optics, Daegu, Korea, 2006 5. D. Attwood, P.P. Naulleau, K.A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E.M. Gullikson, M. Koike, H. Medecki, J.H. Underwood, IEEE Quantum Electron. 35, 709 (1999) 6. K.A. Goldberg, Ph.D. Dissertation, University of California, Berkeley, 1997 7. D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation – Principles and Applications (Cambridge University Press, Cambridge, England, 1999) 8. Imagine Optic patent, PCT/FR02/02495, July 2002 9. P. Merc`ere et al., Opt. Lett. 28(17), 1534 (2003) 10. M. Janousch, R. Abela, Th. Schmidt, J.F. van der Veen, R. Wetter, A M. Flank, P. Lagarde, G. Cauchon, PSI Scientific Report 2002, Volume VII (2002) 11. O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A.K. Freund, Proc. SPIE, vol. 4499-19 (2001) 12. H.A. Padmore, M.R. Howells, S.C. Irick, T. Renner, R. Sandler, Y M. Koo, Proc. SPIE, vol. 2856 (1996), p. 145 13. P. Merc`ere et al., Opt. Lett. 31(2), 199 (2006) 16 Extraction of Multilayer Coating Parameters from X-Ray Reflectivity Data D. Spiga Abstract. Detailed analysis of X-ray reflectivity (XRR) angular scans of multilayer coated samples has been recognized as a powerful tool to investigate their stack structure. Even though the interpretation of multilayer XRR scans is made com- plex by the difficulty of managing the large number of parameters that characterize the stack, computer programs can be used to address the problem of the multi- parametric fit of experimental XRR scans of multilayers. This chapter describes a possible strategy to extract the layer thickness values of a multilayer coating from accurate fitting of XRR scans, based on the Python Program for Multilayers coded. The results of a best-fit analysis of XRR with transmission electron microscopy data are also discussed. 16.1 Introduction The development of multilayer structures intended to enhance the reflection of radiation with wavelengths in the range of 10–0.01nm, from extreme ultra- violet to X-rays, and of thermal neutrons, is at present being very actively pursued. In particular, the use of wideband multilayer coatings is foreseen in the next generation of soft (E<10 keV) and hard X-ray (E>10 keV) telescopes with imaging capabilities, like SIMBOL-X [1], Constellation-X [2], XEUS [3]. The reflection process in multilayers is a complex one, arising from the interference of the radiation reflected at each interface, beyond the crit- ical angle for total external reflection. The reflection/focusing performance over a wide energy band depends essentially on the thickness precision of all layers and on the smoothness, homogeneity, and sharpness of all interfaces. It is therefore easy to understand how, in order to improve deposition tech- niques, methods to investigate the internal structure of multilayer stacks are needed, and criteria to evaluate the feasibility of the adopted process in terms of repeatability, uniformity, smoothness, durability must be established. In this chapter we will compare two techniques that can be used to achieve a detailed characterization of a multilayer coating: the stack section imag- ing with TEM (transmission electron microscope) and the analysis of the 234 D. Spiga XRR (X-ray reflectivity) curves by means of a powerful computer program, PPM (Pythonic Program for Multilayers), developed by A. Mirone at ESRF (European Synchrotron Radiation Facility, Grenoble, France). Although the usefulness of the XRR curves are already recognized as important diagnostic tools for multilayers, the exact interpretation is made difficult by their com- plexity and by the large number of parameters characterizing a multilayer. Therefore, the matching between the experimental and a modeled XRR curve with manually adjusted parameters can be only qualitative in most cases. Consequently, the description of the stack structure is often a poorly detailed approximation of the real one. On the other hand, the application of PPM to the analysis of XRR data returns very detailed fits and a realistic description of the multilayer stack. The advantages of this technique are an effective, quick, nondestructive, in-depth probing of the distribution of thicknesses throughout the stack. In the following sections we review some features of X-ray reflection from multilayers. Then we describe some methods that can be used to extract information from the XRR curves and apply PPM to the reflectivity data of a multilayer. Finally, the PPM results are compared with those of TEM and the difficulties that can arise in such a comparison, due to artifacts in TEM images, are discussed. 16.2 A Review of X-Ray Multilayer Coatings Properties The usefulness of multilayer coatings resides in their capability of reflecting radiation with wavelength λ in the nanometer/sub-nanometer range when the incidence angle and the energy exceed the conditions for total external reflection. The X-ray amplitude reflectivity, r, of a single interface between two layers with a difference in refractive index, Δn, decays rapidly with increase in incidence angle ϑ i (measured from the surface plane): r(λ) ≈ Δn(λ) 2sin 2 ϑ i . (16.1) Owing to the very small deviation of the real part of n from unity in X- rays (δ =10 −4 ÷10 −5 , depending on the photon energy and the composition of the reflecting coating), r is usually very small when the incidence angle is larger than the critical one. However, if the spacing of the interfaces of layers in a multilayer is properly conceived, the constructive interference of reflected rays at each interface enhances the reflectivity at definite photon energies. The reflectance of a multilayer with 2N layers with thickness t 1 ,t 2 , t 2N and refractive indexes n 1 ,n 2 , n 2N can be computed by recursive applica- tion of the single-layer reflection formula [4]: R m+1 = r m,m+1 + R m exp(−iΔφ m ) 1+r m,m+1 R m exp(−iΔφ m ) . (16.2) 16 Extraction of Multilayer Coating Parameters 235 In the last equation, r m,m+1 is the reflectance of the electric field amplitude at the mth/(m + 1)th layer interface, Δφ m =4πn m t m sin ϑ m /λ is the phase shift between reflected rays at the mth and the (m + 1)th interface, R m is the amplitude reflectivity of the first m layers. The final X-ray reflectance of the multilayer is |R 2N+1 | 2 . The d-spacing d j (j =1 N) is the total thickness of the jth couple of layers (bilayer). Multilayers with constant d-spacing, d j = d,aresuited to reflect narrow bands of the spectrum, whose locations are approximately (neglecting the beam refraction) determined by Bragg’s law, 2d sin ϑ i ≈ kλ. (16.3) In (16.3), k is an integer and λ is the wavelength of the radiation in use. Multilayers able to reflect a continuous energy band are characterized by a variable d-spacing throughout the stack (graded multilayers). Radiation with wavelength λ is reflected when it propagates across bilayers whose d-spacing satisfies approximately Bragg’s law. A well known possibility is to decrease gradually the d-spacing according to a power-law [5]: d(j)= a (j + b) c . (16.4) We denote with j =1, 2 N the index of the jth bilayer, ordered from the multilayer outer surface. Wide-band multilayers of the described type, initially developed to reflect neutron beams, are called supermirrors and are utilized also for X-ray mirrors, although in this case the absorption is more severe than that for neutrons. The coefficients a, b, c,aswellasthenumberofbilayers,N, and the ratio high-Z material/d-spacing, Γ , have to be optimized in order to obtain the desired reflectivity as a function of the photon energy. For graded multilayers Γ can be constant or slowly variable in order to maximize the reflection efficiency over the energy band to be reflected, i.e., to find the best trade-off between constructive interference and photoelectric absorption. As an example, we show in Fig. 16.1 a comparison of the reflectivity as a function of the photon energy at 0.2 ◦ grazing incidence for a constant d-spacing W/Si multilayer with 200 bilayers, d =8.7nm,Γ=0.46 and a supermirror with 200 bilayers, a =12nm,b=1.85,c=0.3, and con- stant Γ =0.46. The supermirror stack was especially designed to provide a reflectivity as uniform as possible in the energy band 1–70 keV. The reflec- tivity is improved at low energies by adding a capping layer of tungsten and a final layer of carbon [6]. Multilayer stacks of the described type [5, 7] are foreseen for the optics of future hard X-ray imaging telescopes (SIMBOL-X, Constellation-X, XEUS). Imperfections of the interfaces, such as microroughness and layers interdif- fusion, cause a broadening of the interface width. When the two effects can be 236 D. Spiga Fig. 16.1. Calculated X-ray reflectivity of a constant d-spacing W/Si multilayer (dashed line) and a W/Si supermirror (solid line) in the energy range 1–70 keV at the grazing incidence angle 0.2 ◦ . The computation supposes zero roughness considered to be independent of each other, the total interface width, σ,canbe computed as the quadratic sum of the roughness, σ r , and the interdiffusion, σ d : σ 2 = σ 2 r + σ 2 d . (16.5) One of the effects of interface broadening is the exponential reduction of the “specular” reflectivity (reflection angle equal to the angle of incidence), following the N´evot–Croce formula [8]: R σ = R 0 exp  − 16π 2 σ 2 n h n l sin ϑ h sin ϑ l λ 2  . (16.6) In this formula, n l ,n h are the refractive indexes and ϑ l ,ϑ h are the incidence angles in the two components of the multilayer. The two angles are not equal due to beam refraction. The reduction is much more severe for high energies (small λ). The interfacial roughness, σ r , has also another effect, the X-ray Scattering in directions around the specular one. This effect has an important role in the degradation of imaging quality of X-ray optics. High precision in the thickness of the layers and a low roughness are required to ensure a good reflectivity in the energy band of interest. Deviations of the thickness of the layers from the nominal ones can destroy the ordered phase shift distribution that generates the high reflectivity or/and the energy resolution, e.g., for narrow-band multilayers used as monochromators. There- fore, the reflectivity scan of a multilayer is very sensitive to thickness drifts and irregularities, and it is easily understood how the deposition facility has to be carefully calibrated. Furthermore, the deposition rate has to be very steady. As we shall see in the next section, the sensitivity of X-ray reflectance to small deviations of the multilayer thickness from the nominal one makes X-ray reflectivity scans a powerful tool for the investigation of the internal structure of a multilayer, and consequently, for the evaluation of the improvement of 16 Extraction of Multilayer Coating Parameters 237 a deposition technique. We shall, moreover, see how a detailed description of the multilayer can be extracted by means of PPM. 16.3 Determination of the Layer Thickness Distribution in a Multilayer Coating 16.3.1 TEM Section Analysis A possible technique that can be used to visualize the structure of a multi- layer coating is the use of a Transmission Electron Microscope (TEM). In TEM images, the high-density layers appear dark, whereas the low-density layers are bright. For instance, we show in Fig. 16.2 the TEM sections of a Pt/C multilayer deposited by e-beam evaporation onto a Si wafer (σ ≈ 0.3 nm) sub- strate at Media-Lario technologies (Bosisio Parini, Italy); the layered structure is clearly visible and the thickness of single layers can be directly measured. For example, the TEM image in Fig. 16.2 highlights the presence of a much thicker carbon layer due to an instability of the electron beam evaporator. Indeed, the increase of Pt layers at the right side is an image artifact. It will be explained in Sect. 16.3.3. The information provided by the TEM analysis is often useful in helping to improve the stability of the deposition system. For example, this sample was a very important test because it constituted the final calibration of the deposition facility for the manufacturing of a hard X-ray optic prototype [9]. In addition to the layers thickness of the multilayer, TEM images also provide useful information concerning the crystallization state of the layers, the interdiffusion between adjacent layers, and sometimes the undulations of Fig. 16.2. TEM section of a Pt/C multilayer deposited by e-beam evaporation onto a Si wafer. Pt layers are the dark bands. The section thickness, perpendicular to the page, decreases from the right to the left side. The growth direction is from bottom to top (image by L. Lazzarini and C. Ferrari, IMEM-CNR, Parma, Italy) 238 D. Spiga the interfaces due to the microroughness growth (see Fig. 16.8). This is a well-known phenomenon, resulting from the combined effect of the replication of topography of the underlying layers and the random fluctuations of the deposition process [10]. The TEM images presented in this work are obtained from a JEOL-2000- FX installed at IMEM-CNR (Parma, Italy). The accuracy in layers thickness measurements is ∼0.5 nm for multilayers with abrupt interfaces. 16.3.2 X-Ray Reflectivity Analysis The TEM technique is expensive and the sample preparation is complex and destructive; therefore, it can be utilized only for selected samples. However, a large amount of information can be extracted from the analysis of the X-Ray Reflectivity (XRR) scan of the multilayer. This technique is a commonly performed test of the reflectance efficiency and consists of prob- ing the multilayer by means of a thin X-ray beam incident on the coating and measuring the reflectivity in the specular direction at different incidence angles. The usefulness of the XRR measurement as a diagnostic tool is also well known: the reflectivity as a function of the grazing incidence angle, resulting from the interference of the radiation reflected at each interface, is usually very sensitive to the details of the multilayer structure, namely all the values of thickness, density, and roughness of the layers. For instance, if the multilayer has a high periodicity and smooth, abrupt surfaces, it will generally exhibit high, sharp, clearly defined interference peaks (16.3). Conversely, irregularities of d-spacing will cause the peaks to be “spread” on the angular scale (see Fig. 16.3), whereas rough or diffuse interfaces will reduce the intensity of peaks (16.6). This technique is not destructive, it is quick, and it does not require any particular preparation of the sample. In addition, the probed surface is usually large (several cm 2 )evenwithverythinbeamsbecause the measurement is usually performed in grazing incidence. This reduces selection effects because local fluctuations of d-spacing are averaged out. The requirements for XRR measurements for deriving the multilayer structure are a monochromatic X-ray source with a small divergence (a few 10 arcsec) in order to guarantee a good angular resolution. In addition, the incident X-ray beam has to be very thin (a few tenth/hundredth microns, depending on the sample size) in order to be entirely collected by the sample at very small incidence angles (ϑ i > 500 arcsec). Interpretation of X-Ray Reflectivity Data Although the analysis of XRR curves is a widespread tool, their exact inter- pretation is a complex problem. Because of the sensitive dependence of XRR measurements on the thickness, density, roughness of all layers, the 16 Extraction of Multilayer Coating Parameters 239 Fig. 16.3. Comparison of the measured X-ray reflectivity scans of two Ni/C multi- layers with the same average value (9 nm), but different dispersion of the d-spacing (deposited in 2003 by e-beam evaporation at Media-Lario technologies). The smaller dispersion in the case of the solid line curve is made apparent by the narrower and more regular peaks. The approximate Γ factor is 0.2 for the solid line and 0.4 for the dashed line Fig. 16.4. Experimental X-ray reflectivity of the W/Si multilayer with 30 bilayers deposited by e-beam with ion assistance (grey dots). The black solid line is the initial reflectivity model, computed with the IMD package [11], assuming a multilayer with constant d-spacing interpretation of XRR scans is not trivial. The XRR of a multilayer with N bilayers can be computed by applying recursively (16.2) including (16.6) to account for the roughness/interdiffusion. However, to fit the reflectance modeling to the experimental dataset it would be necessary to handle 4N parameters, namely all the thickness and roughness values of all layers, assuming at least constant density values throughout the stack. We show in Fig. 16.4 an example we adopt in the following pages: the experimental XRR scan at 8.05 keV (measured at INAF/Osservatorio [...]... These devices are simple to align, offer a good working distance between the optics and the sample, and are expected to become standard elements in synchrotron beamlines instrumentation in general and in high energy X-ray microscopy in particular 17. 2 X-Ray Microscopy The history of X-ray microscopy goes back to 1896, the year following the discovery of X-rays by Roentgen The method used to study the structural... of X-ray radiographs was called by P Goby as microradiography in 1913 [1] Beginning in the late 1940s, X-ray microscopy with grazing incidence mirror optics was proposed by P Kirkpatrick in order to surpass the optical microscope in resolution [2] As a branch of earlier developments in electron microscopy, projection microscopy was proposed by Cosslett and Nixon [3] and it became very popular since... nonabsorbing This enables imaging of specimens up to ∼10 μm thickness, with high intrinsic contrast using X-rays with a lateral resolution down to 15 nm [6] In recent years, considerable progress has been made in X-ray microscopy in the hard X-ray regime (E > 4 keV), as a result of the development of high brilliance, high energy X-ray sources coupled with advances in manufacturing technologies of focusing optics. .. studies including wide and small angle scattering In a microprobe, the strategy is to scan the beam over the sample and to measure a signal in diffraction, in fluorescence, or in absorption (XANES, EXAFS) for each beam position When combining scanning microscopy with tomographic techniques the inner structure of a sample can be reconstructed, including the distribution of different atomic species and even... spatial resolutions in imaging applications These methods fall into three broad categories: reflective, refractive and diffractive optics The basic principles and recent achievements are discussed for optical devices in each of these categories 17. 1 Introduction A summary of microfocusing optics and methods for hard X-rays is presented The hard X-ray region is taken as extending from about several keV... should be included Possible angular offsets in the experimental curves, instrumental noise, and the angular resolution of the measurement should be accurately evaluated and included in the calculations Finally, when comparing XRR analysis and TEM results, correct the thickness values obtained from TEM according to (16.9) These fitting methodologies were tested on several multilayer samples [26] in addition... for X-rays in the energy range 4–100 keV, as provided by synchrotron radiation sources The advent of third generation storage rings such as the ESRF, the APS and Spring-8 with X-ray beams of high brilliance, low divergence and high coherence has made possible efficient X-ray focusing and imaging The main emphasis is on those methods which aim to produce submicrometre and nanometre spatial resolutions in. .. and it became very popular since the 1950s In the early 1 970 s, several groups started new technological developments of X-ray optics, in particular, Fresnel zone plates, and the modern era of X-ray microscopy started In 1 974 , Schmahl and collaborators built a full-field transmission microscope at DESY (Deutsches Elektronen Synchrotron) in Germany [4] Kirz and Rarback at NSLS (National Synchrotron Light... (16.9) 1/2τ √ In (16.9) the factor 2 is the peak to rms ratio The root of the integral of the PSD is the rms roughness and 1/2τ is the minimum frequency being integrated, in other words, the minimum frequency with a maximum of the oscillation in a length τ The increase of Δz with τ is partly due to the enlargement of the frequency band and partly due to the rapid increase of P (f ) for decreasing frequencies... rings like ESRF, APS, and SPring-8 with radiation beams of high brilliance, low divergence, and high coherence makes possible efficient X-ray focusing and imaging X-ray microscopy techniques are presented first The main emphasis will be put on those methods that aim to produce nanometer resolution These methods fall into three broad categories: reflective, refractive, and diffractive optics The basic principles . ALS beamline 12.0 and SLS beamline LUCIA (including Markus Janousch) for their support. Finally, the authors would like to thank several contributors to these works, including Sylvain Bro- chet,. efficiency and consists of prob- ing the multilayer by means of a thin X-ray beam incident on the coating and measuring the reflectivity in the specular direction at different incidence angles. The usefulness. d-spacings: the outermost 20 bilayers are thicker and reflect soft X-rays, the innermost 75 bilayers are thinner and reflect the hardest X-rays. The reflectivity of the sample was measured using the