Nuclear Instruments and Methods in Physics Research A 470 (2001) 155­157 The use ofquasi-Bragg diffuse scattering for express measurement ofchanges in multilayer d-spacing V.A. Chernova, N.V. Kovalenkob, S.V. Mytnichenkoc,* a Siberian SR Centre at Budker Institute of Nuclear Physics, 11 Lavrentyev Avenue, 630090 Novosibirsk, Russia b Budker Institute of Nuclear Physics, 11 Lavrentyev Avenue, 630090 Novosibirsk, Russia c Institute of Solid State Chemistry, 18 Kutateladze Str., 630128 Novosibirsk, Russia Abstract The possibility ofthe use ofquasi-Bragg diffuse scattering for express measurements ofchanges in multilayer d- spacing was studied. The error ofthis method was shown to be minimal, ifthe incident or scattered angles are sufficiently far from the critical total external reflection or Bragg angles. As an example, the measurements of the W/Si multilayer mirror with linearly varying d-spacing are presented. r 2001 Elsevier Science B.V. All rights reserved. PACS: 68.55.@a; 61.10.Kw Keywords: X-ray diffuse scattering; Multilayer mirror 1. Introduction experimental technique. Secondly, moderately large changes in the multilayer structure can cause Development ofX-ray multilayer optics requires significant changes in diffraction behavior due to improvement ofthe methods to control the quality strong dynamic effects. That is very difficult to ofmultilayers. The usual control method is X-ray take into account during experimental data treat- small-angle diffraction, which allows one to ment. This disadvantage is not important ifthe determine local values ofmultilayer d-spacing, studied multilayer mirror structure is uniform over thickness ratio ofthe layers ofa bilayer, roughness the sample square, and only very small changes in dispersion, intermixed layer thickness and so on. multilayer structure have to be controlled. If Nevertheless, this method has two important the studied multilayer mirror has a varying disadvantages. Firstly, it is necessary to perform structure, the discussed effect can be sufficiently exact adjustment ofthe sample at every measure- important. ment point which sufficiently complicates the From our point ofview, the use ofquasi-Bragg scattering [1­3] can be a more preferable method *Corresponding author. Siberian SR Centre at Budker ofcontrol. This scattering is caused by the Institute ofNuclear Physics, 11 Lavrentyev Avenue, 630090 interfacial roughness imperfections, coherently Novosibirsk, Russia. Tel.: +7-3832-394013; fax: +7-3832- repeating from one layer to another, and occurs 342163. E-mail address: s.v.mytnichenko@inp.nsk.su at the total scattered angle equal to double Bragg (S.V. Mytnichenko). angle (2yB) independent ofthe incident angle. 0168-9002/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 0 1 5 - 4 156 V.A. Chernov et al. / Nuclear Instruments and Methods in Physics Research A 470 (2001) 155­157 This technique has advantages over the conven- tional specular diffraction technique. Indeed, on the one hand, the diffuse scattering intensity dependence on the incident angle is very fine if its value differs remarkably from the Bragg angle or critical angle oftotal external reflection. Thus, no exact adjustment is necessary in this case. On the other hand, the kinematic approximation suits well for the theoretical description of this scatter- ing, which greatly simplifies data treatment. Finally, it is very important that the quasi-Bragg scattering behavior depends on the multilayer Fig. 1. The principal scheme ofthe experiment. Quasi-Bragg structure in a very simple manner. The difficulties scattering occurs at the total scattered angle equal to double ofthe quasi-Bragg scattering modeling are caused Bragg angle (2yB), independent ofthe incident angle. by the nontrivial theoretical description ofthe interfacial roughness, which in many cases is completely determined by the substrate surface primary channel-cut single-crystal Si(1 1 1) mono- (for a moderately high lateral momentum transfer chromator and a Ge(1 1 1) crystal-collimator ofthe this fact is always true). Thus, if the substrate ``anomalous scattering'' station was used [4]. The surface roughness is assumed to be uniform over measured angular broadening ofthe diffract- the sample square, the changes in quasi-Bragg ometer had a full-width at half-maximum scattering are directly connected to the local (FWHM) of1500. A scintillation detector based changes in the multilayer structure. on an FEU-130 photomultiplier with a NaI(Tl) This paper describes the measurements ofthe scintillator was used. The dynamic range ofthe W/Si multilayer d-spacing with the use ofquasi- detector system was about 5 104. The photon Bragg scattering. As a test sample, a linearly energy was 8.048 keV. varying d-spacing multilayer mirror was chosen. The multilayer d-spacing values, which were obtained from quasi-Bragg diffuse scattering, were studied versus the incident angle in this work. The 2. Experimental studied sample was placed so that the d-spacing gradient axis was perpendicular to the specular A multilayer mirror with a linearly varying d- diffraction plane (Fig. 1). The incident beam was spacing was deposited by magnetron sputtering in 100 100 mm in size. For a given incident angle the Ar+ environment on a float glass substrate. In 2y-scan (total diffracted angle scan) (see Fig. 1) order to provide the desired gradient ofmultilayer was performed. After that, the d-spacing value was d-spacing, the substrate was moved over the W calculated from this diffraction profile. In this and Si targets with variable velocity. The move- manner, the d-spacing dependencies on the in- ment was performed by step motors under cident angle were obtained at several points ofthe computer control. The sputtering regime was sample. Finally, the d-spacing dependence along tuned so as to maintain the W-layer thickness to the gradient axis was obtained from the quasi- be constant and to ensure linear increase ofthe Bragg measurements. multilayer d-spacing due to the Si-layers thickness increase. The number ofbilayers was 50. The X-ray diffuse scattering measurements were 3. Results performed using SR of the VEPP-3 storage ring of the Siberian SR Centre at Budker INP, which An example ofd-spacing dependence on the off- operates at 2 GeV, with a maximum stored current specular angle, o (o ¼ y02y1, where y0 and y1 are of165 mA. The triple-axis diffractometer with a the incident and diffracted angles, respectively), V.A. Chernov et al. / Nuclear Instruments and Methods in Physics Research A 470 (2001) 155­157 157 Fig. 2. The multilayer d-spacing value measured at the same Fig. 3. The d-spacing values measured with the use ofquasi- sample point by quasi-Bragg scattering versus the off-specular Bragg scattering along the gradient direction. The black points angle, o. The central black point is the d-spacing value are values measured by the conventional specular diffraction. measured by the conventional specular diffraction. obtained from the quasi-Bragg scattering is shown 4. Conclusion in Fig. 2. The central black point (o ¼ 0) in Fig. 2 corresponds to the d-spacing value measured by The use ofquasi-Bragg scattering in order to the conventional specular diffraction. The depen- control the varying multilayer d-spacing was dence behavior at the ends ofthe curve is evidently shown to have advantages over the conventional caused by the total external reflection effects. specular diffraction technique. One ofthose is the The instability in the central narrow angle range simplicity ofthe experimental conditions as well as is not so evident. Nevertheless, this behavior is not ofdata treatment due to the kinematic nature of an artifact and is caused by the behavior of diffuse this scattering. scattering near the Bragg point [3]. The latter effect demonstrates well the advantage ofthe quasi- Bragg scattering over conventional specular dif- Acknowledgements fraction. Values ofmultilayer d-spacing measured with We would like to thank the staffs ofVEPP-3, the use ofquasi-Bragg scattering are shown in optical workshops, and SSRC at BINP for their Fig. 3. The smoothed changes in d-spacing are assistance. This study was supported by the caused by the real deviations in d-spacing from Russian Foundation for Basic Research, Grants linear behavior. As may be observed from Fig. 3, nos. 99-02-16671 and 00-02-17624. the technique errors do not exceed the errors ofthe conventional specular diffraction technique. It is necessary to mark the experimental simplicity of the discussed technique. So, only a few minutes References were needed to measure the presented experimen- tal data. [1] A.V. Andreev, A.G. Michette, A. Renwick, J. Mod. Opt. 35 The discussed method can be used in the case of (1988) 1667. a multilayer with curved surface. It needs to be [2] D.G. Stearns, J. Appl. Phys. 71 (1992) 4286. noted that the angle between the incident direction [3] V.A. Chernov, V.I. Kondratev, N.V. Kovalenko, and that normal to the multilayer surface can be S.V. Mytnichenko, Nucl. Instr. and Meth. A 470 (2001) 145, these proceedings. controlled by the measurement ofthe specular [4] Briefdescription ofthe SR Experimental Station, Preprint, diffracted beam (Fig. 1) in this case. INP, 90-92, Novosibirsk, 1990.