Nonspecular x-ray scattering in a multilayer-coated imaging system

Stearns, D. G.; Gaines, D. P.; Sweeney, Donald W.; Gullikson, Eric M.

doi:10.1063/1.368098

Cited by 141 publications

(108 citation statements)

References 43 publications

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“…(6) and (7) and the growth parameters shown in the figure. The growth parameters used are in agreement with those obtained from smooth substrates and values in the literature [8].…”

Section: Multilayer Deposition and Characterizationsupporting

confidence: 79%

“…We describe a rough surface by its 2-dimensional power spectral density PSD(f), [6][7][8][9][10] which is a function of spatial frequency f=(f ,f ), where f=1/7 , and 7 is a spatial period on the surface. During film growth, particles or atoms x y s s arrive randomly at the substrate during deposition, and this random rain of particles produces roughness with a flat white noise power spectrum: where S is the particle volume and d the film thickness with a rms film roughness…”

Section: Multilayer Growth Modelmentioning

confidence: 99%

“…One set of 6 glass substrates of 5 cm diameter was polished in the Livermore optical shop, and each of them was characterized by AFM over square areas of 10 µm x 10 µm and 1 µm x 1 µm. The PSD and roughness were calculated from all pictures by 2-D Fourier transform [7][8][9][10]. For another set of 20 substrates of 2.5 cm diameter only 2 were characterized by AFM.…”

Section: Figmentioning

confidence: 99%

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<title>Smoothing of mirror substrates by thin-film deposition</title>

et al. 1999

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L a w r e n c e L i v e r m o r e N a t i o n a l L a b o r a t o r y UCRL-JC-135146 Smoothing of Mirror Substrates by Thin-Film DepositionE. Spiller S. Baker E. Parra C. Tarrio August 3, 1999This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author. PREPRINT ABSTRACTSuperpolished optical flats with high spatial frequency roughness below 0.1 nm have been commercially available for years. However, it is much more difficult to obtain figured optics of similar quality. We have obtained and tested the finish of figured optics from different vendors by atomic force microscopy and optical profilometry and have investigated how the substrate quality can be improved by the deposition of thin films. We have determined the growth parameters of several thin-film structures. From these parameters we can determine how the surface topography of a coated mirror differs from that of the substrate, select the best thin-film structure, and predict the possible improvement.

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“…(6) and (7) and the growth parameters shown in the figure. The growth parameters used are in agreement with those obtained from smooth substrates and values in the literature [8].…”

Section: Multilayer Deposition and Characterizationsupporting

confidence: 79%

Section: Multilayer Growth Modelmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

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<title>Smoothing of mirror substrates by thin-film deposition</title>

et al. 1999

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“…26 Several interface profile functions were investigated, including the exponential, linear, sinusoidal, step, and error-function profiles described in Refs. 24 and 26.…”

Section: Experimental and Data Analysis Techniquesmentioning

confidence: 99%

Growth, structure, and performance of depth-graded W/Si multilayers for hard x-ray optics

Windt

Christensen

Craig

et al. 2000

Journal of Applied Physics

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We describe the development of depth-graded W/Si multilayer films prepared by magnetron sputtering for use as broad-band reflective coatings for hard x-ray optics. We have used specular and nonspecular x-ray reflectance analysis to characterize the interface imperfections in both periodic and depth-graded W/Si multilayer structures, and high-resolution transmission electron microscopy ͑TEM͒ and selected area electron diffraction ͑SAED͒ to characterize the interface structure and layer morphology as a function of depth in an optimized depth-graded multilayer. From x-ray analysis we find interface widths in the range ϭ0.275-0.35 nm for films deposited at low argon pressure ͑with a slight increase in interface width for multilayers having periods greater than ϳ20 nm, possibly due to the transition from amorphous to polycrystalline metal layers identified by TEM and SAED͒, and somewhat larger interface widths ͑i.e., ϭ0.35-0.4 nm͒ for structures grown at higher Ar pressures, higher background pressures, or with larger target-to-substrate distances. We find no variation in interface widths with magnetron power. Nonspecular x-ray reflectance analysis and TEM suggest that the dominant interface imperfection in these films is interfacial diffuseness; interfacial roughness is minimal ( r ϳ0.175 nm) in structures prepared under optimal conditions, but can increase under conditions in which the beneficial effects of energetic bombardment during growth are compromised. X-ray reflectance analysis was also used to measure the variation in the W and Si deposition rates with bilayer thickness: we find that the W and Si layer thicknesses are nonlinear with the deposition times, and we discuss possible mechanisms responsible for this nonlinearity. Finally, hard x-ray reflectance measurements made with synchrotron radiation were used to quantify the performance of optimized depth-graded W/Si structures over the photon energy range from 18 to 212 keV. We find good agreement between the synchrotron measurements and calculations made using either 0.3 nm interface widths, or with a depth-graded distribution of interface widths in the range ϭ0.275-0.35 nm ͑as suggested by 8 keV x-ray and TEM analyses͒ for a structure containing 150 bilayers, and designed for high reflectance over the range 20 keV ϽEϽ70 keV. We also find for this structure good agreement between reflectance measurements and calculations made for energies up to 170 keV, as well as for another graded W/Si structure containing 800 bilayers, designed for use above 100 keV, where the peak reflectance was measured at Eϭ212 keV to be Rϭ76.5Ϯ4% at a graze angle of ϭ0.08°.

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“…In calculation of the intensity of X-ray scattering by multilayer gratings, one customarily resorts to layer boundary profiles obtained in scaling an initial to the final profile in the framework of various relevant models Peverini et al, 2007;Stearns et al, 1998). Quite frequently, these calculations are not based on accurate information even on the initial or final boundary profile, which markedly complicates fitting the profiles of inner boundaries (Goray & Seely, 2002).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings

Goray

Lubov

2013

J Appl Cryst

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It is shown that taking into proper account certain terms in the nonlinear continuum equation of thin-film growth makes it applicable to the simulation of the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The proposed model describes smoothing and displacement of Mo/Si and Al/Zr boundaries of gratings grown on Si substrates with a blazed groove profile by magnetron sputtering and ion-beam deposition. Computer simulation of the growth of multilayer Mo/Si and Al/Zr gratings has been conducted. Absolute diffraction efficiencies of Mo/Si and Al/Zr gratings in the extreme UV range have been found within the framework of boundary integral equations applied to the calculated boundary profiles. It has been demonstrated that the integrated approach to the calculation of boundary profiles and of the intensity of short-wave scattering by multilayer gratings developed here opens up a way to perform studies comparable in accuracy to measurements with synchrotron radiation, at least for known materials and growth techniques.

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Nonspecular x-ray scattering in a multilayer-coated imaging system

Cited by 141 publications

References 43 publications

<title>Smoothing of mirror substrates by thin-film deposition</title>

<title>Smoothing of mirror substrates by thin-film deposition</title>

Growth, structure, and performance of depth-graded W/Si multilayers for hard x-ray optics

Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings

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