JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 12 15 DECEMBER 2002 Influence of x-ray beam spatial coherence on the diffuse scattering from multilayer mirrors V. A. Chernov Institute of Catalysis, Novosibirsk, Russia and Siberian Synchrotron Radiation Center, Budker Institute of Nuclear Physics, 11 Lavrentiev Prospect, Novosibirsk, Russia V. I. Kondratiev Siberian Synchrotron Radiation Center, Budker Institute of Nuclear Physics, 11 Lavrentiev Prospect, Novosibirsk, Russia N. V. Kovalenko Budker Institute of Nuclear Physics, 11 Lavrentiev Prospect, Novosibirsk, Russia S. V. Mytnichenkoa) and K. V. Zolotarev Institute of Solid State Chemistry, Novosibirsk, Russia and Siberian Synchrotron Radiation Center, Budker Institute of Nuclear Physics, 11 Lavrentiev Prospect, Novosibirsk, Russia Received 2 April 2002; accepted 10 September 2002 The improved spatial coherence of a synchrotron radiation beam was shown experimentally to stimulate additional diffuse scattering of x rays diffracted from x-ray multilayer mirrors. Although the large-scale tens of microns roughness does not affect Bragg diffraction from multilayers, its presence causes phase shifts at the wave packet front. This leads to partial decay of the coherent wave packet and creates additional diffuse scattering. Additional scattering from this mechanism was observed at angles of incidence corresponding to the Bragg and Kiessig maximum angles. The properties of this scattering caused by large-scale roughness, observed due to improved x-ray beam spatial coherence, were shown experimentally to be different from those of diffuse scattering previously reported when the incoming or outgoing angle is equal to the Bragg angle. Typical breaks in the diffuse scattering intensity due to the standing-wave effect are absent, and there is obvious asymmetry of the diffuse scattering cross section around the incoming and outgoing angles. Due to the small angle of incidence, the coherently irradiated area has very different dimensions parallel and perpendicular to the beam, which leads to the observed scattering being concentrated in the specular diffraction plane defined by the incident and reflected wave vectors. © 2002 American Institute of Physics. DOI: 10.1063/1.1518131 I. INTRODUCTION the outgoing angle equal to the Bragg angle were observed Diffuse scattering, which inevitably accompanies specu- independently by two groups.4,5 A theoretical explanation of lar reflection, is an undesirable phenomenon that hampers the these phenomenona was found by extending the distorted development of x-ray multilayer optics. On the other hand, wave Born approximation DWBA , previously used to cal- x-ray diffuse scattering measurements provide a useful tool culate diffuse scattering from single surfaces,8 to the case of for surface and interfacial roughness studies that has aroused multilayers.9 Finally, it is necessary to cite works7,10,11 where much interest in the last decade. A brief survey of scientific the diffuse scattering was studied as a function of the mo- progress in x-ray diffuse scattering from multilayers starts mentum transfer normal to the specular diffraction plane. with Refs. 1 and 2 in which the replication of rough We think, however, that much work is still required on multilayer interfaces was shown to cause resonant amplifica- the diffuse scattering technique both from the point of view tion of diffuse scattering resulting in the observation of a of theory and of experiment. One of the reasons is that dif- ``quasi-Bragg sheet'' of diffuse scattering. The earliest ex- fuse scattering experiments are usually carried out at experi- perimental observations of quasi-Bragg diffuse scattering mental facilities that were designed for conventional specular were seen by several groups.3­6 Special features arise in the measurements. But what is sufficient for usual specular mea- diffuse scattering intensity when the incoming or outgoing surements proves to be inadequate for a diffuse scattering angle is nearly equal to the Bragg angle. When the first case study of x-ray multilayer mirrors XMMs . In this work we incoming angle nearly equal to the Bragg angle was studied focus on an important aspect of the experimental measure- experimentally,7 the features observed in the diffuse scatter- ments, namely, the spatial coherence of the incident x-ray ing intensity were explained by the location of the standing beam. Progress in synchrotron radiation SR source devel- wave that appeared as a result of interference of the incident opment has led to continual improvement of the x-ray beam and specularly reflected fields. Diffuse scattering features for spatial coherence which, in turn, has increased the require- ments on the XMM quality, making this problem highly rel- a Electronic mail: s.v.mytnichenko@inp.nsk.su evant. 0021-8979/2002/92(12)/7593/6/$19.00 7593 © 2002 American Institute of Physics Downloaded 15 May 2003 to 148.6.178.88. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 7594 J. Appl. Phys., Vol. 92, No. 12, 15 December 2002 Chernov et al. Roughness in XMMs may vary over a wide range of length scales from the atomic ( 10 10 m) up to the macro- scopic ( 10 3 m). The reasons for the appearance of the interfacial roughness are also varied. At the microscopic scale (10 10­ 10 7 m) the roughness mainly appears as a result of the chemical and physical processes which take place during the XMM deposition. On shorter length scales reproduction of the roughness at successive interfaces is im- perfect. But the contribution of roughness on this length scale to the diffuse scattering cross section is very small, at least in the case of XMMs. On a macroscopic scale (10 7­ 10 3 m) roughness at the interfaces is well replicated from one layer to another and FIG. 1. Origin of the additional diffuse scattering arising as a result of is mainly determined by the roughness of the substrate sur- distortion of the coherent wave packet front caused by macroroughness. The face. At the micron and shorter length scales, modern sub- nature of such diffraction is quite usual. The term ``distortion of the coherent strate preparation technology for XMMs is able to produce a wave packet front'' was used to emphasize that the transverse coherence surface quality that is practically ideal. But unfortunately this component considerably exceeds the longitudinal component. Clearly dem- onstrated is the anisotropy of the coherently irradiated XMM area. Due to is not the case at longer length scales. Moreover, at these the small value of the incident angle the size of this area in the direction scales conventional methods of XMM quality control using lying in the specular diffraction plane increases as L / 0 and can consid- x-ray tubes are simply unable to detect imperfections. erably exceed its size in the perpendicular direction. When crystals are used as monochromators the degree of monochromatization / is usually about 10 4. For the wavelength 0.154 nm (Cu K line this corresponds to a It is usual to use the following form of roughness corre- longitudinal coherence length of L lation function to model the x-ray diffuse scattering data:8 2/ 1 m. An- other important diffraction parameter is the average track C r 2 exp r/ 2h , length of the x-ray photon on Bragg diffraction from the XMM, L where is the rms roughness, h is a coefficient connected 2 / B , where is the extinction depth. For typi- cal XMMs the value of L with the fractal dimension D 3 h and is an effective is of about 1 m. Roughness on a scale longer than this will not affect Bragg diffraction from cut-off length for the self-affine roughness induced for many the XMM. physical reasons, including beam coherence. There is some No specular reflection is possible unless there is an ideal discrepancy in the literature concerning the interpretation of surface at the micron and shorter length scales. For this range . Some authors consider as the characteristic roughness literature values of the root mean square rms roughness are length. At the same time other authors point out the impor- of the order of a few tenths of a nm for typical XMMs. The tance of incident beam coherence. requirements on XMM quality at longer length scales are not In the XMM case this discrepancy may be overcome in so stringent. the following manner. It is reasonable to introduce a critical Nevertheless, because the transverse coherence length is value Lc so that at length scales shorter than Lc / 0 the given by XMM interfaces are practically ideal and C(r) can describe their roughness. Thus, if L is smaller than Lc , the value of L L D/2s, is not so important and reflects a real property of the roughness. Otherwise (L Lc) instead reflects the value where D is the source-sample distance and s is the source of L . In this case radical modifications to the diffuse scat- size, the fact that the roughness is on a length scale longer tering will be caused by roughness at the longest length than L scales ( Lc / 0). Moreover, the true specular reflection suf- and L does not mean that diffraction from this roughness will be absent. Indeed, the diffraction pattern from fers ``mosaic-like'' spreading. this roughness will be observable due to distortion of the Numerical modeling of diffuse scattering due to distor- coherent wave packet front Fig. 1 . This phenomenon is tion of the coherent wave packet front is beyond the scope of similar to the well-known observation of a diffuse halo this work. Nevertheless, proceeding from the general physi- speckle structure when a coherent laser beam penetrates cal criteria it is possible to make a few remarks concerning through a nonuniform medium.The importance of transverse the character of the scattering from long-range roughness. coherence increases for the component which lies in the 1 The cross section of this scattering is directly propor- specular diffraction plane. This is due to the fact that in this tional to the specular reflectivity coefficient of the XMM case the small value of the incident angle ( 0) will cause the at the corresponding angle of incidence. Thus, the scat- coherently irradiated sample area to increase as 1 0 in the tering discussed is closely associated with the diffuse corresponding direction Fig. 1 . Note that in contrast to the scattering features at 0 B ( B is the Bragg angle values of L and L , transverse coherence can vary over a previously observed by Kortright and co-worker5,7 and very wide range depending on the experimental setup. Its by Savage et al.4 value can amount to tens of microns when a modern SR 2 The long length scale of the roughness does not mean source is used. that the diffraction angles will be small since it is not the Downloaded 15 May 2003 to 148.6.178.88. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 92, No. 12, 15 December 2002 Chernov et al. 7595 size of the region of roughness itself but the size of its projection onto the wave packet front that is important: 1 /L 0, where 1 is the deviation of the outgoing angle 1 from the specular value and L is the length of a typical roughness feature. Since, as discussed above, in the spa- tial range 1 m the XMM surface and interfaces are ideal, the diffuse scattering discussed must be in a re- stricted range of angles. So at 0 3° and 0.154 nm the angles of scattering 1 0.2°. 3 Because of the small value of the incident angle the size of the coherently irradiated XMM area in the direction of the specular diffraction plane increases as L / 0 and significantly exceeds its size in the perpendicular direc- tion even if the transverse coherence components in both directions are comparable. This leads to the diffuse scat- tering discussed being concentrated in the specular dif- fraction plane. 4 Since the length scale of long range roughness exceeds FIG. 2. AFM surface pictures of the fused silica substrate at the submicron the value of L this type of scattering excludes the typi- upper and tens of micron lower spatial scales. The upper picture above cal intensity dependence on the standing wave phase un- demonstrates a high substrate quality with a roughness dispersion of 0.1 der the dynamical diffraction conditions. The role of nm at the submicron scale. This is not the case at the tens of microns spatial scale. Roughness waves with amplitude of 1 nm and period of 30 m Bragg diffraction is very simple: this type of scattering is are easily observed. The spikes in the lower picture are an artifact caused presented when the incident beam is efficiently reflected by dust particles on the sample surface. and otherwise it is absent. This article presents experimental data for x-ray diffuse III. RESULTS AND DISCUSSIONS scattering from a W/Si XMM that depends on the spatial The diffraction maps of the first Bragg reflection from coherence of the incident beam. the W/Si XMM are shown in Fig. 3. The measurements were performed in the vertical plane so that the crystal monochro- II. EXPERIMENT mator, XMM and the secondary crystal collimator Ge 111 were placed in , , geometry. The vertical angular reso- The W/Si XMM was deposited by magnetron sputtering lution was determined by a crystal collimator 15 18 in. . onto a flat fused silica substrate. The substrate was prepared The vertical component of the transverse coherence was es- by nanodiamond polishing12 followed by ion beam13 polish- timated to have a value of about 5 m. The maps represent ing. It should be emphasized that the surface of the substrate sets of transverse scans scans . 0 1 qx /k B , where used here is of the highest quality. The rms roughness was qx is the in-plane projection of the momentum transfer and k 0.3­0.4 nm according to x-ray reflectivity data and the flat- is the wave vector, is plotted parallel to the x axis and the ness was 250 nm/2 cm i.e., 10 5) according to interfer- total angle of diffraction ( 0 1 qz /k) is parallel to the ometry data. However, we studied the surface of a typical vertical axis. The q ranges of the upper map are 3.7 substrate using atomic force microscopy AFM . The data 10 3 nm 1 qx 3.7 10 3 nm 1 and 4.13 nm 1 qz obtained are shown in Fig. 2 and one can clearly see the 4.42 nm 1. Specular scans correspond to the vertical lines presence of ``roughness waves'' with amplitude of 1 nm at 0 1 0. and period of d 30 m. For the upper map in Fig. 3 angular resolution of 0.05° The number of bilayers forming the XMM was 200. A in the azimuthal direction was provided by a set of slits and least-squares fitting of the x-ray reflectivity data 0.154 the diffuse scattering signal was integrated over qy in the nm was performed to calculate the XMM optical parameters range of 2 10 2 nm 1 qy 2 10 2 nm 1. In the using Parrat's recursive dynamical method.14 The XMM pe- case of the lower map in Fig. 3 a knife was inserted to block riod was 1.47 nm ( B 3°), 0.5 and 0.6 nm. This last scattering in the specular diffraction plane (qy 0) and the value reflects both the roughness and the presence of mixed corresponding integration range was reduced to 1 layers. 10 2 nm 1 qy 2 10 2 nm 1. The dynamical ranges X-ray diffuse scattering measurements were performed of the measurements were different for these maps: using SR from the VEPP-3 storage ring at a wavelength 105­ 106 for the upper map and 103­ 104 for the lower. 0.154 nm. A channel-cut Si 111 crystal was used as the The horizontal streaks in Fig. 3 are the quasi-Bragg scat- monochromator ( / 2 10 4) in all cases. A scintilla- tering due to the coherent replication of roughness from one tion detector based on an FEU-130 photomultiplier with a layer to another.2 Note that because of the experimental ge- NaI Tl scintillator was used. Other experimental details will ometry, the vertical streak in the lower map is not the true be described as appropriate below. specular scattering. This ``quasispecular'' diffuse scattering Downloaded 15 May 2003 to 148.6.178.88. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 7596 J. Appl. Phys., Vol. 92, No. 12, 15 December 2002 Chernov et al. FIG. 4. Intensity distribution of the diffuse scattering along the inclined streak corresponding to 0 B in the upper map of Fig. 3. short-range 1 m roughness dominates in this case as opposed to in our case. As a result the diffuse scattering features observed in Ref. 5 show evidence of standing-wave effects as breaks in the diffuse scattering intensity. In our data this effect only becomes apparent as an inclined light streak in the case of the lower map in Fig. 3 where the diffuse scattering discussed provided by the long-range 1 m roughness was suppressed. In the upper map the contri- bution of macroscopic-scale roughness dominates and this effect is not visible. It is necessary to point out the evident asymmetry of our data in the intensity of the ``incoming'' ( 0 B) and ``out- going'' ( 1 B) streaks. In our case the incoming streak is absolutely dominant, in contrast to in Ref. 5, where these features have approximately equal intensities. This difference is not accidental and can be qualitatively explained using basic physical principles. The symmetry of the diffuse scat- FIG. 3. Diffraction maps of scattering from a W/Si XMM near the first tering cross section relative to exchanging the incoming and Bragg reflection obtained using a three-crystal diffractometer. The intensity outgoing angles ( is shown on a logarithmic scale. The main distinction in the experimental 0 1) is known as the reciprocity setup of these maps was that in the case of the lower map the diffuse theorem8 and is an indispensable exclusive attribute of the scattering signal close to the specular diffraction plane was excluded by the Born including DWBA approximation. The forced conser- use of an additional shield. vation of the incident wave energy and violation of the opti- cal theorem by the Born approximation provide this symme- try. Thus, when energy dissipation through the incoherent is another dynamical effect in the diffraction from the rough diffuse scattering channel can be neglected, the diffuse scat- XMM. Mention of this effect can be found in Ref. 15. The tering data should reveal the symmetry discussed photoab- diffuse scattering under discussion is seen as inclined sorption as another important channel is omitted in this dis- streaks. This scattering is most strongly pronounced at inci- cussion . This situation was realized in Ref. 5. The long- dent angles near the Bragg angle. The rest of the inclined range roughness essentially increases the diffuse scattering streaks are due to Kiessig modulations. The absence of in- cross section the incoherent diffuse scattering channel is clined streaks in the lower map demonstrates well that the dominant in our case and, consequently, causes breakdown diffuse scattering discussed is concentrated in the specular of the Born approximation.16 Finally, the weak presence of diffraction plane. the outgoing streak in Fig. 3 can be explained by the higher It is very interesting to compare our data with those ob- dynamic range of the measurements of Ref. 5. tained from a W/C XMM by Kortright.5 As mentioned Figure 4 shows the intensity distribution along the main above, the diffuse scattering discussed here and that ob- inclined streak of the discussed diffuse scattering in the up- served in Ref. 5 are closely associated. They are described by per map of Fig. 3. The angular range of the diffuse scattering the same term R0T1 in the DWBA9 and have an entirely is in rather good agreement with the above estimate. At dynamical nature. Nevertheless, within the context of this present we are unable to give a complete explanation of the article the situation realized in Ref. 5 is opposite to our situ- origin of the distinct asymmetry of the intensity distribution. ation. The reported high value of the incident beam angular Nevertheless, it is interesting to note that in the case of the spread 0.125° leads to a low value of beam spatial coher- Kiessig streaks the diffuse intensity is symmetric with re- ence. Thus, it is reasonable to expect that the contribution of spect to the specular reflection. This fact allows one to con- Downloaded 15 May 2003 to 148.6.178.88. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 92, No. 12, 15 December 2002 Chernov et al. 7597 FIG. 6. Experimental setup a in the normal vertical geometry source size about 250 m, transverse coherence value about 5 m and b in the horizontal geometry source size about 3 mm, transverse coherence value FIG. 5. Map of the scattering near the first Bragg reflection from a W/Si about 5 m . In b the diffuse scattering due to coherent wave packet front XMM for incident angle exceeding the Bragg angle by a value of 0.1°. The distortion must be either absent or substantially suppressed, and this is what map was obtained using an image plate. The horizontal axis is the azimuthal is observed in Fig. 7. angle, qy /k, and the vertical axis is the deviation of the total scattering angle ( 0 1 qz /k) from 2 B . The intensity is shown on a logarithmic scale. The dynamical range of the measurements was of about 104. The extended horizontal streak in the center is quasi-Bragg scattering. The upper Bragg angles were observed. These features were explained spot is the specular reflection located at the intersection of two streaks: the as an experimental artifact connected with the use of a horizontal streak is the quasispecular scattering and the vertical streak is the position-sensitive detector. We also observed similar inclined diffuse scattering discussed. diffuse streaks in the study of a Ni/C XMM.18 The unex- pected features in the diffuse scattering disappeared during low-temperature annealing that was accompanied by a clude that the asymmetry discussed is caused by wave ex- mosaic-like widening of the specular reflection. tinction under dynamical Bragg diffraction from the XMM. Although the above experimental data are in good agree- Another type of map obtained using an image plate is ment with the suggestions made, more direct proof of the shown in Fig. 5. The secondary crystal collimator was not suggested nature of the observed diffuse scattering would be used in this case. The angular resolution in the azimuthal the dependence of the scattering intensity on the magnitude direction of about 0.02° was provided by a set of primary of transverse coherence. Assuming the undulating character collimators 100 100 m2 placed in front of the XMM. of the long-range roughness, an estimation of the critical The vertical component of the transverse coherence was es- value of transverse coherence can be obtained by timated to be the same as in the previous case. The horizontal axis in Fig. 5 is the azimuthal angle ( q Lc d 0/4, y /k), and the vertical axis is the deviation of the total scattering angle and at 0 3°, 0.154 nm and d 30 m, the value of ( 0 1 qz /k) from 2 B . The qy range in Fig. 5 is Lc 0.5 m. 0.43 nm 1 qy 0.43 nm 1. The diffuse scattering dis- The spatial characteristics of the VEPP-3 SR source al- cussed is presented in Fig. 5 as the Kiessig modulated verti- lowed us to perform such experiments. The vertical size per- cal streak. Note that Kiessig modulations of the scattering pendicular to the orbit plane of the electron bunch is about were not observed in the case of 0 B Fig. 4 . Obviously, 250 m and the horizontal size is about 3 mm. Thus by their absence in Fig. 4 is caused by wave extinction due to measuring the diffuse scattering in the horizontal plane Fig. dynamical diffraction. Finally, the data in Fig. 5 allow one to 6 it is possible to considerably worsen the transverse coher- conclude that the inclined streaks of diffuse scattering ence of the incident beam. In the experiment the source­ present in Fig. 3 are not an experimental artifact caused by sample distance was about 16 m and the entrance slits 100 the use of the secondary crystal collimator. m were placed in immediate proximity to the sample. The It is possible that the scattering discussed was observed transverse coherence values were about 5 and 0.4 m in more than once in the literature. In Refs. 10 and 11 the azi- Figs. 6 a and b , respectively. The secondary slits 100 m muthal dependence of the diffuse scattering from a W/Si were placed 0.4 m from the sample. The total angular reso- multilayer was studied and a ``hump'' near the specular dif- lution of the measurements was about 0.01° Fig. 6 a and fraction plane was observed. This feature was explained as a 0.015° Fig. 6 b . The main goal of the experiment was to cross-correlation effect. At the same time the authors care- perform comparative measurements of the specular and dif- fully stated that this explanation has a preliminary character. fuse scattering intensities. Another example is the small-angle diffuse scattering study The experimental data Fig. 7 demonstrate the differ- of an AlAs/GaAs superlattice17 where intense diagonal ence in diffuse scattering behavior between the vertical and steaks in the qx­ qz diagram corresponding to the incident horizontal measurement geometries Fig. 6 . As can be seen Downloaded 15 May 2003 to 148.6.178.88. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 7598 J. Appl. Phys., Vol. 92, No. 12, 15 December 2002 Chernov et al. 3 SR studies of XMM microroughness necessitate the use of unusual experimental diffuse scattering geometries that allow one to avoid measurements of diffuse scatter- ing in the specular diffraction plane. ACKNOWLEDGMENTS The authors thank A. N. Artyushin, N. I. Chkhalo, I. B. Khriplovich, G. N. Kulipanov, A. V. Latushev, V. F. Pin- dyurin and W. Schwarzacher for their help and for useful discussions. This study was supported by the Russian Foun- dation for Basic Research, Grant Nos. 99-02-16671 and 00- 02-17624. 1 FIG. 7. Normalized intensity of diffuse scattering as a function of the inci- A. V. Andreev, A. G. Michette, and A. Renwick, J. Mod. Opt. 35, 1667 1988 . dent angle 0 at fixed total diffraction angles scans, 0 1 2 B 2 D. G. Stearns, J. Appl. Phys. 71, 4286 1992 . 0.2°) in the vertical a upper curve and horizontal b lower curve 3 A. Bruson, C. Dufour, B. George, M. Vergant, G. Marchai, and Ph. Man- geometries. The peaks at 0 3.1° are the specular reflections, the peaks on gin, Solid State Commun. 71, 1045 1989 . the left at 0 3.0° are the diffuse scattering discussed. The strong suppres- 4 D. E. Savage, J. Kleiner, N. Schimke, Y.-H. Phang, T. Jankowski, J. Ja- sion of this peak in b is in good agreement with the suggestions made. cobs, R. Kariots, and M. G. Lagally, J. Appl. Phys. 69, 1411 1991 . 5 J. B. Kortright, J. Appl. Phys. 70, 3620 1991 . 6 in Fig. 7 b low spatial coherence the diffuse scattering O. Renner, M. Kopecky, E. Krousky, F. Schufer, B. R. Muller, and N. I. Chkhalo, Rev. Sci. Instrum. 63, 1478 1992 . discussed in this article is strongly suppressed which is in 7 J. B. Kortright and A. Fischer-Colbrie, J. Appl. Phys. 61, 1130 1987 . good agreement with the above suggestions. 8 S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B 38, 2297 1988 . 9 IV. SUMMARY V. Holy and T. Baumbach, Phys. Rev. B 49, 10668 1994 . 10 T. Salditt, T. H. Metzger, and J. Peisl, Phys. Rev. Lett. 73, 2228 1994 . The experimental data obtained allowed us to make the 11 T. Salditt, D. Lott, T. H. Metzger, J. Peisl, G. Vignaud, J. F. Legrand, G. following conclusions. Grubel, P. Hoghoi, and O. Scharpf, Physica B 221, 13 1996 . 12 A. I. Volokhov, E. P. Kruglyakov, and N. I. Chkhalo, Surface 1, 130 1 At a sufficiently high degree of transverse coherence of 1999 . in Russian . 13 S. J. Sulyaev, N. V. Kovalenko, and V. A. Chernov, Surface 1, 74 2001 the x-ray incident beam, macroroughness with character- in Russian . istic length of the order of tens of microns may cause 14 L. G. Parrat, Phys. Rev. 95, 359 1954 . additional diffuse scattering. This scattering is all con- 15 S. K. Sinha, M. K. Sanyal, S. K. Satija, C. F. Majkrzak, D. A. Neumann, centrated in the specular diffraction plane and has the H. Homma, S. Szpala, A. Gibaud, and H. Morkoc¸, Physica B 198, 72 1994 . strongest intensity at the incident angle equal to the 16 D. K. G. de Boer, Phys. Rev. B 53, 6048 1996 . Bragg angle. 17 E. A. Kondrashkina, S. A. Stepanov, R. Opitz, M. Schimidbauer, R. 2 Rapid progress in SR source development makes im- Kohler, R. Hey, M. Wassermeier, and D. V. Novikov, Phys. Rev. B 56, provement of the XMM quality in the spatial range un- 10469 1997 . 18 V. A. Chernov, E. D. Chkhalo, N. V. Kovalenko, and S. V. Mytnichenko, der discussion highly relevant. Nucl. Instrum. Methods Phys. Res. A 448, 276 2000 . Downloaded 15 May 2003 to 148.6.178.88. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp