Coherent x-ray scattering from an optical gratingBinhua Lin, Mark L. Schlossman, Mati Meron, Scott M. Williams, Zhengqing Huang, and P. James Viccaro Citation: Applied Physics Letters 73, 906 (1998); doi: 10.1063/1.122033 View online: http://dx.doi.org/10.1063/1.122033 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/73/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Preface to Special Topic: Selected Papers from The Eleventh International Conference on Surface X-Ray andNeutron Scattering J. Appl. Phys. 110, 102101 (2011); 10.1063/1.3661159 Fast CCD camera for x-ray photon correlation spectroscopy and time-resolved x-ray scattering and imaging Rev. Sci. Instrum. 75, 4383 (2004); 10.1063/1.1808913 Grazing incidence small angle x-ray scattering from free-standing nanostructures J. Appl. Phys. 86, 6763 (1999); 10.1063/1.371724 Coherent soft x-ray scattering from InP islands on a semiconductor substrate J. Vac. Sci. Technol. B 17, 1728 (1999); 10.1116/1.590816 Nanometer surface gratings on Si(100) characterized by x-ray scattering under grazing incidence and atomicforce microscopy J. Appl. Phys. 81, 1212 (1997); 10.1063/1.363864

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Coherent x-ray scattering from an optical gratingBinhua Lina)

The James Franck Institute and the Center for Advanced Radiation Sources, The University of Chicago,Chicago, Illinois 60637

Mark L. SchlossmanDepartment of Physics and Department of Chemistry, The University of Illinois (M/C 273),Chicago, Illinois 60607

Mati MeronThe James Franck Institute and the Center for Advanced Radiation Sources, The University of Chicago,Chicago, Illinois 60637

Scott M. WilliamsDepartment of Physics and Department of Chemistry, The University of Illinois (M/C 273), Chicago,Illinois 60607

Zhengqing Huang and P. James ViccaroThe James Franck Institute and the Center for Advanced Radiation Sources, The University of Chicago,Chicago, Illinois 60637

~Received 15 April 1998; accepted for publication 11 June 1998!

X-ray speckles due to scattering of partially~transverse! coherent x rays from an optical reflectiongrating are observed. The speckles indicate the presence of surface inhomogeneities of the gratingthat are otherwise undetectable with either visible laser light or transversely incoherent x-rayscattering. Qualitative analysis of the speckle patterns provide information on the surfacemorphology of the grating. The underlying order due to the periodicity of the grating enhances thedetection of the speckles. ©1998 American Institute of Physics.@S0003-6951~98!01733-1#

The availability of high brilliance third-generation x-raysources has motivated the investigation of applications oftransverse-coherent x rays in several areas including detailedstructure determination and studies of dynamics.1–5 Applica-tion of dynamic x-ray scattering promises to probe the dy-namics in processes that occur over length scales as small asthe order of the x-ray wavelength. Increasing the transversecoherence lengthl tc of x rays also allows for the investiga-tion of structure over longer spatial correlation lengths whilemaintaining atomic scale resolution.

The degree of the transverse coherence of x rays is de-termined by the effective angular and spatial extent of thesource. We have demonstrated previously, using two limitingapertures and a focusing mirror, how to produce and charac-terize x rays of variable degrees of transverse~vertical!coherence.6,7 Here, we report the coherent scattering from anoptical reflection grating using this well-characterized par-tially coherent beam. X-ray speckles are observed as finestructure superposed on the grating diffraction maxima.These speckles probe surface inhomogeneities that cannot bedetected with either visible laser light or transversely inco-herent x rays.

The experiments were performed at bending magnetbeamline X19C@NSLS, Brookhaven National Laboratory~BNL!#. A 1:1 vertical and horizontal focusing mirror in thecenter of the beam line is followed by a pair of x-ray slits~aperture!, S2, that is followed by a horizontally reflectingmonochromator@Si~111!# placed ;1 m upstream of thesource image. Due to the 2 mrad horizontal acceptance, the

energy bandwidth is approximately 0.3% at the chosenwavelength,l51.54 Å. Another pair of slits, S3, is placed3.5 m downstream of S2 and near the mirror focal point. Thecombination of these apertures, S2 and S3, with appropri-ately chosen gaps define an angular divergence and effectivesource size equivalent to a diffraction-limited source for thewavelength used.6,7

This well-characterized transverse~in the vertical direc-tion! partially coherent beam is directed downward at a graz-ing angle of 0.3° onto the horizontal grating surface~placed40 mm downstream of S3, see Fig. 1!. The grating surfaceruling is a one-dimensional sinusoid produced by laser inter-ferometry ~period 10 mm, amplitude 0.1 mm, overall1 in.31 in.), and coated with 0.1mm of gold. The gratinggrooves are perpendicular to the propagation of the x raysand the diffraction patterns were measured along the plane ofincidence. A scintillator detector immediately after a pair ofslits, S4, ~1.3 m downstream of the grating! measures thescattering of the grating in the plane of incidence~the verti-

a!Electronic mail: binhua@rainbow.uchicago.eduFIG. 1. Schematic of the experimental setup for the measurement of diffrac-tion from a one-dimensional optical grating.

APPLIED PHYSICS LETTERS VOLUME 73, NUMBER 7 17 AUGUST 1998

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cal plane!. The grating diffraction is measured using an in-cident beam with a transverse coherence lengthl tc;11mmand a symmetric beam profile with an angular full width athalf maximum of;20 mrad ~produced with S2v>50mmand S3v>20mm). Using a characterized partially coherentbeam allows us to take full advantage of the available coher-ent flux by optimizing the x-ray coherence of the beam re-quired for this experiment. The projection of this coherencelength onto the grating surface corresponds to a region con-sisting of 200 grooves. Nearly 400 grooves of the grating areilluminated by the full incident beam. Due to absorption andthe small incident angle, x rays scatter off only the upperportion of the grating grooves~the peaks of the sinusoid!.This nonsinusoidal x-ray form factor leads to diffraction athigher orders than the single lowest order observed in dif-fraction with visible radiation.

Figure 2 shows the individual diffraction maxima fromthe zero to the sixth order. Fine structure, or x-ray speckles,in each diffraction maximum is observed. Since a perfectgrating would produce a single peak in each diffractionmaximum, the speckles apparently result from surface im-perfection. As shown in Fig. 3 the speckle pattern varies asdifferent regions of the grating are illuminated. This indi-cates that the surface imperfection varies across the surfaceof the grating.

To demonstrate that the diffraction fine structure is dueto coherent scattering, we made the same measurement withan incident beam of much smaller coherence length. If thecoherence length is small, the x rays probe only a very shortrange of correlation of the surface imperfection. To producean x-ray incident beam with a much shorterl tc but with asimilar beam divergence~; 20mrad! and comparable energybandwidth~0.3%! used in the coherent scattering, we substi-tuted a multilayer monochromator for the Si~111! monochro-mator. When the multilayer is used in the monochromator,l tc

is reduced to 1–3mm and the energy bandwidth is about0.5%. Figure 4 shows diffraction maxima of the zero to thesixth order produced by such a beam, and no fine structure isobserved. Interestingly, the speckles are also not observedwith laser~visible! light, indicating that the surface defect ison a length scale much smaller than visible light wave-

lengths. It is not surprising that an essentially perfect opticalgrating may be imperfect at the x-ray length scale.

Since the speckle separations~as observed with the par-tially coherent x rays! are much smaller than that of thegrating diffraction maxima of different order, and the inten-sities of all the speckles in each diffraction order are compa-rable, we conclude that the variation of the surface inhomo-geneity is of lower frequency than that of the gratingsinusoid and is correlated over a long range. Consistent withthese observations, we assume that the grating consists ofmany domains, each varying slightly from neighboring do-mains, each with a length scale on the order of a few tens tohundreds of microns~several to tens of grooves of the grat-ing!.

The three simplest possible morphological defects forthe domains are~1! the surfaces of neighboring domains arenot parallel ~slightly slanted domains!, ~2! the height ofneighboring domains varies, and~3! the period of the

FIG. 2. Individual x-ray diffraction maximum of the grating from the zeroto the sixth order~bottom to top!, using an incident beam withl tc

>11mm. The maxima are plotted as a function ofuz2uz,n , whereuz,n isthe position for thenth order maximum, and the intensity of the maxima isnormalized and shifted vertically for clarity. The solid lines are guides to theeye.

FIG. 3. ~a!–~c! The speckle patterns on diffraction maxima~the zero to thesecond order, bottom to top! from three different regions on the gratingobtained under the same experimental condition as for the measurementshown in Fig. 2, plotted the same way as in Fig. 2.

FIG. 4. The angular positions of the five speckles with respect to the nomi-nal diffraction maxima of the grating (uz,n

m 2uz,n0 ), as a function of the

diffraction ordern. The solid lines are determined by fits of Eq.~1! to thedata.

907Appl. Phys. Lett., Vol. 73, No. 7, 17 August 1998 Lin et al.

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grooves varies slightly from domain to domain. Straightfor-ward calculation shows that for the first two defects, thespeckle separation is largest at the zero order of the diffrac-tion maximum and becomes smaller as the order is in-creased. For the third defect the separation of the speckles iszero at the specular reflection and increases as the order isincreased.

The most striking aspect of the data~Fig. 2! is the in-crease in speckle separation with the increase of diffractionorder. This indicates that the dominant morphological defectis due to the variation in the groove period. However, thisdefect alone cannot fully explain the data as indicated by thebroadening of the lowest-order maxima~see also Fig. 3!. Formaxima n<2, the first and second morphological defectscontribute noticeably to the scattering.

We may determine the variation in the period of thegrating due to a variation in the groove period in the follow-ing way. There are essentially five speckle peaks resolvableat the higher order of the diffraction maxima, indicating theexistence of five discrete grating periods. These five peaks inFig. 2 are designated asm522 to m52, respectively, fromleft to right. The five peak positions are determined by amulti-Gaussian fit to the speckle patterns. The periods arethen obtained by fitting the peak positions to the equation forthe position of diffraction maxima

~uz,nm !25

2l

dmn1~uz,i

m !2, ~1!

whereuz,nm is themth speckle position at thenth diffraction

maximum, anddm is the grating period generating specklem~the fitted angle of incidence for each speckle,uz,i

m , from theexperimentally determined angle of incidence of about0.3%!. Figure 5 shows the fits~solid lines! of Eq. ~1! to the

positions~symbols! of the five speckles with respect to thenominal diffraction maxima of the grating as a function ofthe diffraction ordern. The deviations of the fitted periodsdm from the nominal value of the periodd0 (d0510mm)are, form522 to m52, ~within 60.01 mm! 0.06, 0.04, 0,20.02, and20.07mm, respectively. The large scatter in thedata forn<2 indicates that the speckles at the lower order ofthe maxima are not attributable solely to the variation in thegroove period.

In summary, we have demonstrated that transversely co-herent x rays can be used to detect surface defects that arenot observable by either visible laser light or transverselyincoherent x rays. The underlying periodicity of the gratingproduces a long-range correlation that enhances the detectionof the speckles, and, therefore, detection of surface imperfec-tions. In fact, this enhancement is also evident in other x-rayspeckle measurements involving substrates with underlyingorder,3 though not specifically mentioned by the authors. Ourresult suggests a method to enhance the resolution of x-rayspeckles that may prove useful in the study of dynamic pro-cesses at surfaces. This method may also be applied to thestudy of surface defects of nanometer-sized structures onsemiconductor surfaces, so-called ‘‘surface gratings’’ thatare potential candidates for electronic and optoelectronicdevices.8 Ideas for taking advantage of this enhancement inthe measurement of detailed surface structure~or surface re-construction! and surface/interface dynamics will be testedwith the high brilliance undulator x-ray source at the Ad-vanced Photon Source~at Argonne National Laboratory!.

This work was supported by a grant from the Universityof Illinois at Chicago, a grant from the Illinois Board ofHigher Education–Higher Education Cooperation Act, andpartially supported by the donors of the Petroleum ResearchFund ~M.L.S.!. The NSLS at BNL is supported by the De-partment of Energy.

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5S. K. Sinha, M. Tolan, and A. Gibaud, Phys. Rev. B57, 2740~1998!.6B. Lin, M. L. Schlossman, M. Meron, S. M. Williams, and P. J. Viccaro,Rev. Sci. Instrum.67, 1 ~1995!.

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FIG. 5. Individual x-ray diffraction maximum of the grating from the zeroto the sixth order~bottom to top!, using an incident beam withl tc<3 mm,plotted the same way as in Fig. 2.

908 Appl. Phys. Lett., Vol. 73, No. 7, 17 August 1998 Lin et al.

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