JOURNAL OF APPLIED PHYSICS VOLUME 84, NUMBER 4 15 AUGUST 1998 Study of interfaces in Co/Cu multilayers by low-angle anomalous x-ray diffraction A. de Bernabe´ Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cienti´ficas, 28049 Cantoblanco, Spain and European Synchrotron Radiation Facility, B.P. 220, 38043 Grenoble, France M. J. Capita´n European Synchrotron Radiation Facility, B.P. 220, 38043 Grenoble, France H. E. Fischer Institut Max von Laue-Paul Langevin, B.P. 156, 38042 Grenoble, France C. Prietoa) Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cienti´ficas, 28049 Cantoblanco, Spain Received 19 February 1998; accepted for pubication 5 May 1998 The innovative method of combining specular and off-specular low-angle x-ray diffraction, along with the anomalous scattering effect, has been used to characterize magnetron-sputtered Co/Cu multilayers. The anomalous dispersion of Co is employed to increase the electron density contrast between the cobalt and copper layer. The use of a simulation program has been proven to be a straightforward and reliable method to analyze x-ray low-angle diffraction patterns in such a nonperfectly ordered metallic multilayer system. This method has been successfully applied to data obtained from synchrotron experiments and the results compared with those performed using a standard laboratory diffractometer. The combination of both specular and off-specular scans has ensured the obtention of a single set of simulation parameters for the structure of the multilayer and its interfaces. In addition, the off-specular scans have permitted us to confirm, in a rather complex system, the validity of the distorted wave born approximation. The mesoscopic structure of this multilayered system has been accurately and self-consistently characterized. © 1998 American Institute of Physics. S0021-8979 98 00816-0 I. INTRODUCTION mean-square rms roughness of the substrate , interfaces For the purpose of explaining the unusual properties ex- and overlayer.12 Off-specular scans rock or rocking hibited by the different types of superlattices, such as curves, and 2 rocks or detector scans allow the reconstruc- metal/metal,1,2 or semiconductor/semiconductor,3,4 a precise tion of the height­height correlation function of the structural characterization has been essential. The role played roughness.13­16 by interfaces seems to be very important, especially in the There are two fundamental ways of obtaining the infor- context of giant magnetoresistance GMR ,5­8 where there is mation from the reflectivity patterns. One of them is the use need of an accurate determination of interfacial structure. of the Fourier analysis of data based on the Born approxima- Among the multiple techniques used to characterize the tion. This method permits us to obtain the autocorrelation structure of multilayers such as nuclear magnetic resonance, function of the derivative of the sample's electron density Rutherford backscattering spectroscopy, neutron and x-ray profile. It has been proven to be quite useful in some diffraction, and scanning electron microscopy or SEM the cases,17,18 however it must be used very cautiously and in most widespread is probably x-ray diffraction.9­11 X-ray dif- some cases the results may not be easy to interpret. When the fraction is a nondestructive technique and gives a global system to be characterized is almost perfect high degree of measure of the sample's structure unlike SEM . At high crystallinity and sharp interfaces as in semiconductor super- angles, x-ray diffraction yields information about a system at lattices , the pattern obtained after the Fourier transform will a crystallographic scale: structure, strains and domain sizes, be quite clear. However for thick metallic superlattices a while at small angles it yields information related to the me- great variety of growth defects may appear such as high soscopic structure of the material. At low angle x-ray diffrac- roughnesses or variations in the layer thicknesses . In this tion, two kinds of experiments can be performed: specular case, the Fourier analysis does not give much information on scans which provide information about the dimension per- the sample's structure. pendicular to the surface of the multilayer ML permitting Alternatively, one can simulate reflectivity curves using thus the determination of the layer thicknesses and root- a matricial calculation.12,19­21 Through this method, an accu- rate and self-consistent structural determination can be a Electronic mail: cprieto@icmm.csic.es achieved when specular scans are completed by off-specular 0021-8979/98/84(4)/1881/8/$15.00 1881 © 1998 American Institute of Physics Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 1882 J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. scans rock and 2 rock curves , which probe the in-plane structure of the ML and not simply the average electron den- sity profile z probed by specular scans. Our aim in the present paper is threefold: first, we want to emphasize the need for using the anomalous dispersion techniques for systems in which the electron density contrast is very low. Only by using the anomalous resonant disper- sion effect can a pattern with sufficient contrast and extent within the wave vector q region be obtained; second, the fit of the experimental results with a computer simulation pro- gram is the method that gives the most complete and reliable characterization of the system; and finally, the combination of specular and off-specular experiments results in the obten- tion of a single set of self-consistent parameters which de- scribe the system. This all has been proven in a set of Co/Cu multilayers in which the mesoscopic structure has been com- pletely characterized. II. EXPERIMENT Samples were grown on a Si 100 oxidized substrate using a dc-operated magnetron sputtering system with a re- sidual pressure of 5 10 7 mbar. The Ar pressure used for deposition was 4.8 10 3 mbar at a constant substrate tem- FIG. 1. Specular reflectivity patterns of Co/Cu multilayers recorded at an incident energy of 8052 eV. Points correspond to the experimental patterns perature of 60 °C. The substrate was placed 8 cm away from and solid lines have been calculated by the described simulation program. magnetrons in order to get a good in-plane homogeneity of the sample. The deposition rates obtained were 2 nm/min for Co and 3 nm/min for Cu. Specially designed stainless steel with a Ge 111 crystal analyzer tuned at the incident beam screens were used to avoid mixing of Co and Cu during wavelength. The use of the analyzer permits us to increase growth. The total sample thickness for the whole set was the angular resolution and the signal to background ratio by kept nearly constant around a value of 70 nm, for which the suppressing fluorescence. On the other hand, the avalanche number of bilayers was varied; no buffer was used for photodiode has a good dynamic range up to 50 000 counts/ growth. The samples grown with a Co/Cu thickness ratio s . The instabilities of the incident beam were monitored equal to unity are represented as mCu/mCo n , where m is through the diffuse scattering from a kapton film, recorded the layer thickness in Å and n the number of layers. The and corrected automatically in the data acquisition program. samples presented in this paper are: 50 Cu/50 Co 7, 33 The experimental resolution function a convolution of the Cu/33 Co 10 , 24 Cu/24 Co 13 , 19 Cu/19 Co 17 , 17 Cu/17 slits used, beam divergence and the resolution of the detec- Co 20 and 9 Cu/9 Co 40 . tor obtained from a rocking curve was 40 arcsec with an The early x-ray specular-reflectivity measurements were incident beam dimensions of 0.1 6 mm. A set of secondary performed on a standard Siemens D-500 two-circle diffrac- slits placed just before the detector was set to 200 m so as tometer. The wavelength used was the K radiation line of to get rid of diffuse scattering queues present in the scans. Cu ( 1.54 Å with a graphite analyzer before the detector Using the standard D-500 diffractometer only specular to avoid the K 2 radiation line of copper. Incident and col- scans were performed. While using synchrotron radiation at lection slits were chosen to be 0.3°, which gave the best energies near the Co edge three kind of experiments were product signal resolution. The Cu target was operated at 40 done: specular scans - ; rocking curves or rocks taken keV and with a tube current of 25 mA. The dynamic range of at a constant 2 and 2 rocks in which is constant . For the detector could not allow the recording of the entire re- the rocking curves, the detector was placed at an angle 2 flectivity patterns, as a consequence of which reflectivity pat- coinciding with a secondary maximum Kiessig fringe at terns from the standard diffractometer were saturated at very around 1.3°. They were chosen to be on a secondary maxi- low angles. mum near the critical angle to obtain the highest contrast and X-ray resonant low-angle diffraction experiments were good detail. carried out on the four circle goniometer setup at D23 beam- line LURE-DCI, Orsay, France .22 The beamline is equipped with a double crystal Si 111 monochromator III. EXPERIMENTAL DATA with fixed exit and sagittal focusing. The experiments were Figures 1 and 2 show the experimental reflectivity pat- performed 5 eV under the Co absorption K edge, which was terns obtained using a standard diffractometer with an inci- determined previously by recording the near edge x-ray ab- dent energy of 8052 eV and synchrotron radiation in order sorption structure spectrum, to obtain the edge precisely. The to make use of the Co anomalous dispersion the incident detection was done combining an avalanche photodiode23 energy was 7704 eV . In both of them, the hollow points Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. 1883 FIG. 2. Specular reflectivity patterns of Co/Cu multilayers recorded at an FIG. 3. Rocking curves taken at constant values of 2 placed at a Kiessig incident energy just under the Co absorption K edge 7704 eV . Points maximum around 2 M 1.32°. For the sake of clarity M has correspond to the experimental patterns and solid lines have been calculated been taken as the variable. The fits to the experimental patterns are based on by the simulation program. the DWBA. The specular peak has not been reproduced in the simulations. represent the experimental data, and lines are the mean the so-called Yoneda wings24 which are broad maxima at square fits using the below described simulation program. both extrema of the plots after which the intensity drops Patterns correspond to six different samples with bilayer sharply . They arise from interferences of the diffuse scatter- thicknesses ranging from 18 to 100 Å, in which the intensity ing by different interfaces and they are not reproducible position has been shifted in order to plot all the patterns within the Born approximation. The spectrum 17 Co/17 together. Let us note that while in Fig. 2 patterns start at an Cu 20 may be the most inaccurate probably due to a lower angle 2 0°, in Fig. 1 they are plotted from 2 1°. The quality of the ML something which matches well with the reason for that is nothing but the saturation of the standard specular pattern , while the spectrum corresponding to 19 diffractometer detector, which did not allow to go to lower Co/19 Cu 17 manages to reproduce perfectly the structure angles. and the Yoneda wings. The small oscillations present in the spectra correspond The last type of scans are the 2 rocks. They are done at to sample-size oscillations usually called Kiessig fringes . a constant value of , which is half of the value of 2 at They arise from multiple interference between beams re- which the rocking curves were taken. This scan geometry flected at the top interface and at the multilayer­substrate permits us to see the reciprocal space in both the x and z interface. Superimposed to the Kiessig fringes, the multilayer directions. Figure 4 shows the spectra corresponding to the peaks appear they are Bragg-like peaks coming from the four samples from which rocks were taken. In the spec- chemical modulation of the sample which account for the trum corresponding to the 33 Co/33 Cu 10 sample there is an periodicity of the ML. The number of Kiessig fringes be- important increase in the oscillation at 2 1.6°. This comes tween each pair of Bragg peaks is 2n 1, `` n'' being the from an intensity leakage of the first Bragg peak of the number of deposited bilayers. An inspection of these fringes multilayer, as can be seen from a glance at Fig. 4. In all the permits us to check that the number of bilayers used in the scans, the amplitude of the oscillations related to vertical simulation is correct. Finally, some long wavelength oscilla- correlation length as well as the intensity tendency coming tion can be observed in some samples, which can be attrib- from the horizontal correlation length are well reproduced, uted to a thin oxide overlayer. allowing us to rely on the values of the correlation lengths. Figure 3 shows the rocking curves corresponding to four samples. They have been taken at somehow different values IV. DATA ANALYSIS AND DISCUSSION of 2 in order to be placed at a secondary Kiessig maxi- mum in all of them and have an optimal contrast. They have A. Anomalous diffraction been taken near the total reflection angle in order to see the As it can be observed from a direct comparison between dynamic effects in the MLs. Such effects are seen, in addi- Figs. 1 and 2, there is a remarkable difference in their pat- tion to the small oscillations near the central peak, through terns arising from the change in the electron density contrast Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 1884 J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. FIG. 4. 2 rock curves with their fit. The value of was held constant and FIG. 5. Experimental and calculated reflectivity spectra for the 33 Co/33 around 0.66°. The variable used is 2 2 2 Cu M . For the simulations 10 sample. Spectra A and C are the experimental patterns taken at 7704 only the diffuse intensity has been taken into account. and 8052 eV, respectively fits have been plotted by using a continuous line . The B curve is a simulation with the same parameters obtained from the A spectrum fit, but for an energy of 8052 eV. The D curve is a simula- between Co and Cu at the two incident energies used. To see tion with the same parameters obtained from the C spectrum fit except that the Co and Cu absorption values have been taken equal for both of them it more clearly, we present next the scattering cross section contrary to the situation at 8052 eV where the C spectrum was performed . of a rough interface, which was calculated for the first time The inset shows the absorption coefficients and the electron densities for Co using the distorted wave Born approximation DWBA by and Cu. Vertical lines have been plotted at the energies at which the experi- Sinha et al.13 and later extended by Holy´ and Baumbach14,15 ments were performed. to layered systems. For a surface between two media with an electron density contrast of , the scattering cross section is difference in the electron density. In fact, at 8052 eV, the given by:13 Bragg peak comes just from the absorption difference be- A 2 tween Cu and Co. To see it more clearly and in order to 1 S 2 q T 2 T 2 e 2 2 q¯ *2 z q¯z compare the advantages of using the anomalous scattering of q2z atoms, four spectra have been plotted in Fig. 5. In this figure spectra A and C show the experimental patterns with their dx dy e q¯z 2C R e i qxx qyy , 1 fits for 33 Co/33 Cu 10 sample using synchrotron radiation at 7704 eV for the A spectrum and using the standard dif- where T( ) T( ) is the transmission coefficient of that fractometer at an incident energy of 8052 eV for the C spec- interface for the grazing angle of incidence collection ; A is trum , where the electron density contrast is lower. Let us the illuminated area; q is the scattering wave vector; is the note that in the C spectrum, we have extended the wave rootmean-square roughness of the surface and C(R) is the vector region to q 0 in order to get a clearer comparison. height­height correlation function R is the lateral position , The difference between both spectra is evident: in the A which describes the morphology of the surface.25 For a spectrum the Bragg peaks can be observed up to the third multilayer, the total scattered intensity must account for the order and the Kiessig fringes are perfectly seen over all the intensity scattered at each interface of the ML, which will spectrum; on the other hand, in the C spectrum only one depend on the electron density contrast between the elements multilayer peak can be observed, with a lower contrast in forming the ML. The consequence of this result is that the the Kiessig fringes too and only background noise is seen intensity of the Bragg peaks arising from the additional pe- from q 0.15Å 1. Along with these two plots, the B spec- riodicity of a multilayer is proportional to the square of the trum permits us to see the differences in the reflectivity pat- refraction index contrast between its elements. As the inset tern coming from the advantage of the anomalous dispersion in Fig. 5 shows, at the energy of Cu K radiation, E 8052 or from the use of a different characterization source syn- eV, the electron density contrast between the Co and the Cu chrotron radiation versus standard diffractometer . Looking is almost zero, while there exists a high difference in their at the B spectrum, one may think that a third order Bragg absorption coefficients. On the contrary, just under the Co peak may also be seen; however the intensity decreases two absorption edge, E 7704 eV, the contrast is given by the orders of magnitude from q 0.2 Å 1 and a contrast even Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. 1885 higher than that obtained would be needed to distinguish the peaks from the background. As it can be in the inset, at 8052 eV the Co and Cu electron densities are practically equal vertical line marked as Eb), therefore the Bragg peaks ob- served in the C curve come just from the difference in their absorption coefficients. To see this better, the D spectrum has been plotted. It is a simulation which has been calculated with exactly the same parameters obtained in the fit of the C one but equal to the absorption of Co and Cu ( Cu Co 385 cm 1). As it can be seen, the Bragg peak has totally disappeared and the only remaining feature is a slight decrease of the intensity just at the former peak angle. Fig. 5 proves how the anomalous dispersion permits us to obtain higher quality results which help us to determine more accurately the structural parameters of the ML. B. Fourier transform As explained in Sec. I, one way to analyze x-ray reflec- tivity patterns is to perform the Fourier transform FT of the experimental results. This analysis is based on the fact pointed out in the literature17 that the reflectivity can be ap- proximately expressed, for wave vectors larger than the criti- cal, as: FIG. 6. Fourier transform as indicated in Eq. 4 where R(q) has been dn obtained by simulation of a 33 Cu/33 Co 10 multilayer with three different interface roughnesses. dz eiqzdz 2 R q q4 , 2 where q is the scattering wave vector and n the refractive responding to multiples of the single layer thickness around index. The autocorrelation function ACF of the derivative 33 Å . In addition, a broad and intense peak appears at of the density profile around 660 Å, arising from the first layer­substrate inter- (z) , defined as: face. As the roughness is increased, the oscillations are re- n n duced. At about 8 Å, no information about the layer z thicknesses can be extracted from the pattern. Furthermore, if z t z t z dt 3 in addition to the roughness there are other kind of inhomo- can be written, taking into account its definition and Eq. 2 , geneities in the sample, such as fluctuations in the layer as thicknesses, the patterns become quite difficult to interpret. We have then followed this method to have a prelimi- z q4R q eiqzdq, 4 nary overall picture of our multilayers. In Fig. 7 we have represented four FT patterns corresponding to two samples. which is just the FT of the reflectivity pattern multiplied by The numbers in each plot refer to the corresponding peak the wave vector q to the fourth power. When the multilayer position. A and B plots correspond to sample 50 Co/50 Cu 7 has perfect interfaces, the ACF is a Dirac delta, but when but at the two incident energies used, 7704 and 8052 eV, there is roughness, the Dirac function turns into a Gaussian respectively. Both yield interface positions very similar to distribution which is nothing but the FT of the derivative of one another, yet have the former higher contrast and extent an error function . of the oscillations. The values corresponding to the first Even it the FT of the reflectivity profile is a quite simple peaks in the FT are given within the plot and match quite method; when the superlattice deviates from an ideal case, well the expected results 50 Å for each layer thickness . C the obtained results as well as the interpretation are not and D plots correspond to the sample 33 Co/33 Cu 10 , at trivial. To illustrate this assertion, we have performed several 7704 and 8052 eV, respectively. Even if the peak positions simulations for a 33 Cu/33 Co 10 multilayer with different in the C plot correspond approximately to the expected in- roughnesses, increasing from no roughness 0 to 8 Å. terfaces an estimation from the Bragg peak positions yield We have then applied the FT as in Eq. 4 to the simulations. 66 Å for the bilayer thickness , the contrast is very low, The obtained results are presented in Fig. 6. In the lowest indicating that the roughness is high and the homogeneity of graph 0 , the peaks corresponding to each interface are the layer thickness is not perfect. On the other hand, the D perfectly reproduced indeed, as explained previously, they plot does not reproduce the ML modulation wavelength. This should correspond to Dirac functions, something which does is understood since in the reflectivity pattern there is only not happen because of the process used to perform the FT, one ML peak, making this method unuseful. The rest of the which is also responsible for the ``side loves'' appearing at samples present a similar behavior under the FT yielding no the bottom of the peaks . These peaks appear at depths cor- useful information. Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 1886 J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. different tables Sasaki, Henke, . . . ; second, the Co oxide produced at the surface may be of various kinds. In our fits, the electron density calculated for Co ( Co e 1.737 Å 3 at E 7704 eV gives a critical angle that matches quite well the experimental one. For the oxide layer a compound Co3O4 seems to be the most frequent and stable for thin films at ambient temperature,29 while in bulk form it is CoO the usual stoichiometry. Calculations of their electron density yield 1.36 and 1.40 Å 3 for Co3O4 and CoO, at the incident energy of E 7704 eV, respectively. An input parameter for the electron density of the oxide layer of 1.3 Å 3 has been used and the value fitted by a least square procedure. The obtained result, slightly under 1.40 Å 3, lies between the expected electron densities of both oxides, suggesting that the possibility of existence of both oxides cannot be ne- glected. The fitting procedure was the next: once the parameters had been obtained from the specular patterns, they were used to simulate the off-specular scans in which only x , z , h and the roughnesses were varied. If no good fit could be obtained, the new roughness values were introduced into the reflectivity simulations and varied to obtain a better fit. Again, those parameters were used to do the off-specular FIG. 7. Fourier transform as indicated in Eq. 4 of the experimental reflec- simulations and the processes repeated until a single set of tivity. a Data obtained for 50 Co/50 Cu 7 at incident energy of 7704 eV. roughness parameters was obtained. This process was per- b The same sample at 8052 eV. c Data obtained for 33 Co/33 Cu 10 at formed only in the four samples having both specular and incident energy of 7704 eV. d The same sample at 8052 eV. off-specular scans. In the off-specular scans, the x obtained in the rocks was used to simulate the 2 rocks and z was This reinforces the following ideas: first, the need for then varied until a good fit was reached. using anomalous diffraction to obtain more multilayer Bragg To obtain the error bars, once the optimal fit had been peaks and higher contrast in the reflectivity patterns; second, reached by a rms process, the fit parameters were varied the use of a simulation program to obtain the information manually. When an appreciable change between the calcu- becomes necessary to obtain complete information of the lated and the experimental patterns had been observed, the system or even just when its complexity is rather high. difference was taken as the error bar. Some special features should be taken into account to fit a particular sample, for instance 33 Co/33 Cu C. Simulation methods 10 sample in Fig. 2, the fact that the second order at about 3° is seen In order to obtain a quantitative and precise character- while even orders should not be seen since the Co and Cu ization of samples, obtained patterns have been fitted using thicknesses are equal and that the third one at 4.5° is so the following simulation program a detailed description will weak and double, means that there is a deviation from the be reported elsewhere26 . For specular scans, the formalism ideal case. For the fit a Gaussian distribution of the layer given by Vidal and Vincent19 has been used and the patterns thickness centered at bilayer thickness 33 Å and with a have been fitted by a least square procedure. The DWBA full width at half maximum equal to 0.2 Å has been used. presented by Daillant and Be´lorgey27 has been used for the For other samples a linear stretch of the roughness or a off-specular simulations. The computer program permits us thickness gradient should be taken into account. In 17 Co/17 to take into account a great number of parameters which Cu 20 after the ML peak, the Kiessig oscillations cannot be influence the reflectivity pattern obtained: layer thicknesses, seen anymore. The broadening undergone by the Bragg peak roughnesses, deviations from ideal cases a linear and a points toward a slight variation in the layer thicknesses. In Gaussian variation of the layer thicknesses, a linear stretch of the simulation, a linear thickness gradient of 0.2%/mm has the roughnesses, . . . , as well as the roughness correlation been included, which improved the fit considerably. This lin- lengths x and z and parameter h, explained later in the ear variation of the layer thicknesses during growth can be section. understood as a monotonously continuous change of growing The electron densities and the absorption coefficients of conditions. Finally, in 9 Co/9 Cu 40 a linear stretch of the the substrate, Co, Cu and the oxide layer, have been taken Cu and Co roughnesses ( N 0 / 0) has been used in the from the Sasaki tables.28 They have been used as input pa- fit, yielding 16% for Co and 13% for Cu ( 18 Å . rameters and then refined with the simulation program. Spe- Even if the specular reflectivity patterns provide very cial attention has been paid to the Co and its oxide electron good and precise structural parameters of the system when density for two reasons: first, close to the absorption edge the dealing with roughness, more than one possible solution may values for the Co scattering factor differ slightly among the be obtained if diffuse scattering data were not accounted for. Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. 1887 TABLE I. Values obtained by the least square fit at two different energies: at 8052 eV, with a standard diffractometer, and at 7704 eV, using synchrotron radiation. Horizontal Vertical Thickness of Thickness of Co rms Cu rms Oxide layer Oxide layer Substrate correlation correlation Hurst Co layer Cu layer roughness roughness thickness roughness roughness length length parameter dCo dCu Co Cu dO O s x z Å Å Å Å Å Å Å Å Å h * 9 Co/9 Cu a 40 9.0 9.0 7 7 3 2.0 11 ¯ ¯ ¯ 8052 eV 0.3 0.3 1 1 2 0.5 2 9 Co/9 Cu 40 9.1 9.1 9 9 13 13. 13 6000 700 0.45 7704 eV 0.1 0.1 1 1 1 0.5 2 500 200 * 17 Co/17 Cu a 20 15.6 17.6 11 7 8 7.0 13 ¯ ¯ ¯ 8052 eV 0.5 0.5 1 1 2 0.7 2 17 Co/17 Cu 20 17.1 17.0 12 12 18 8.0 12 5000 650 0.45 7704 eV 0.2 0.2 1 1 2 0.5 2 2000 100 * 19 Co/19 Cu a 17 19.7 18.3 8 8 21 4.5 12 ¯ ¯ ¯ 8052 eV 0.4 0.4 1 1 4 0.3 2 19 Co/19 Cu 17 19.1 19.1 8 8 50 3.0 8 8000 900 0.4 7704 eV 0.2 0.2 1 1 2 0.2 2 2000 100 * 24 Co/24 Cu a 13 26.6 20.6 11 13 7 11 15 ¯ ¯ ¯ 8052 eV 0.4 0.5 1 1 2 3 2 * 24 Co/24 Cu 13 23.5 23.5 9 9 23 5 8 ¯ ¯ ¯ 7704 eV 0.2 0.2 1 1 2 1 2 * 33 Co/33 Cu a 10 32.2 32.2 12 12 6 12 17 ¯ ¯ ¯ 8052 eV 0.5 0.5 1 1 2 1 2 33 Co/33 Cu 10 33.0 33.0 12 6 33 4.5 10 8500 700 0.5 7704 eV 0.3 0.3 2 2 1 0.5 2 500 50 * 50 Co/50 Cu a 7 46.3 49.7 6 6 8 4 14 ¯ ¯ ¯ 8052 eV 0.4 0.4 1 1 1 2 2 * 50 Co/50 Cu a 7 49.8 49.8 7 6 45 2.5 14 ¯ ¯ ¯ 7704 eV 0.2 0.2 1 1 5 0.5 1 aSamples having an asterisk mean that only the specular scans have been used to obtain their parameters. From left to right, given values are: thickness of the Co layer, thickness of the Cu layer, Co rms roughness, Cu rms roughness, oxide layer thickness, oxide layer roughness, substrate roughness, horizontal correlation length, vertical correlation length and Hurst parameter. This observation, already stated in the literature16, led us to computing time diverges when the h parameter deviates from perform off-specular scans in our samples to obtain a single 0.5, we did not consider it worth going to lower h values. solution to the roughnesses. In addition, they have permitted Again only the diffuse scattering has been used to do the us to obtain the correlation lengths of the roughness profiles simulations. In three of the spectra all but the 17 Co/17 as well as the Hurst parameter, the combination of which Cu 20] there is a certain mosaicity, which can be clearly seen permits us to describe the morphology of the multilayer in- in the central peak. This is evident in the case of 9 Co/9 terfaces. The horizontal correlation length ( x), represents Cu 40 , where a double central peak is present. All the simu- approximately the distance between horizontal bumps. It al- lations manage to reproduce very well the 2 patterns except lows us to determine if there exists interdiffusion ( x 15 Å maybe after the critical angle. This is not surprising since the or interface roughness ( x 15 Å . On the other hand, the scans are taken at a grazing angle of about 0.7°, and at vertical correlation length ( z) gives an idea of the vertical very low positions of the detector (2 2 C), there may distance throughout which the interfaces can be correlated. exist border effects due to a slight misalignment, sample The Hurst parameter h ranges from 0 to 1 and gives an idea boarder effects or even a beam position shift let it be noted of the kind of interface. A value near zero will be character- that the shoulder present in the 2 scan of 33 Co/33 Cu 10 istic of a jagged interface while a value near one is typical of just under the critical value is exactly the same appearing in flat and wide bumps in the interface. its specular pattern . For the rocking curve simulations of Fig. 3, the diffuse The simulation results are summarized in Table I. This intensity has been taken into account. That is the reason why table contains the parameters obtained from both the spectra the central peak is not reproduced. Typically, the rocking taken with the standard diffractometer and those coming curves are very well reproduced by the simulation as in the from the synchrotron radiation source. Samples having an 9 Co/9 Cu 40 sample, except for the structure peaks which asterisk mean that only the specular scans have been used to are not resolved in the background due to a weak contrast . obtain their parameters. In Table I, even if the layer thick- In the sample 33 Co/33 Cu 10 , the oscillations due to the nesses are quite well reproduced, there exists some differ- structure are perfectly reproduced except near the Yoneda ence concerning the roughness. It has to be pointed out as wings . Nevertheless, the intensity fall after the critical angle well that there is a difference existing between the oxide would be reproduced better with a lower Hurst exponent h layer thicknesses obtained with the commercial diffracto- 0.5 , indicating that our interfaces are rather jagged. Since meter and using synchrotron radiation. The reason for this is Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 1888 J. Appl. Phys., Vol. 84, No. 4, 15 August 1998 de Bernabe´ et al. nothing more than the fact that experiments were done in have been compared by using a simulation program more different times and that samples had undergone a slight oxi- reliable and accurate than the FT method. Finally, the com- dation which affected only the uppermost layer.30 bination of specular and off-specular scans has ensured the Let it note that the values obtained from the reflectivity obtention of a single set of parameters which may be taken patterns at the two incident energies differ more than the as the actual solution to the system. The mesoscopic struc- error bars. However, the sum of both individual thicknesses ture of the Co/Cu multilayers has been accurate and unam- is almost exact and well within the estimated errors except biguously determined. maybe the 17 Co/17 Cu 20 sample for which the shoulder on the right side of the Bragg-like peak as well as its width ACKNOWLEDGMENTS yielded a larger error and mismatch between the multilayer The authors gratefully acknowledge Dr. Lefebvre and periods obtained at E 7704 and 8052 eV . The problem Dr. Bessie res from Line D23 at LURE for providing support here is obtaining the thicknesses of Co and Cu separately. for and during the experiments. One of us, A. de B., wishes This problem, already overcome at high angles11 has not, to acknowledge his stay at ESRF where he performed this our knowledge, been solved for low-angle patterns yet. At- work. This work has been partially supported by the CICyT tempts are currently being done to try to obtain both thick- under Contract No. MAT97/0725. nesses separately with a high degree of accuracy. In our E 7704 eV reflectivity patterns, nevertheless, 1 M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. there is clear evidence that the thicknesses of both Co and Cu Eitienne, G. Creuzet, A. Friedrich, and J. Chazelas, Phys. Rev. Lett. 61, are almost exact. It is a fact that the even orders of the 2472 1988 . 2 S. S. Parkin, R. Bhadra, and K. P. Roche, Phys. Rev. Lett. 66, 2152 Bragg-like peaks do not appear in these patterns see for 1991 . example, near 2 3° for the 33 Co/33 Cu 3 P. Voisin, G. Bastard, C. E. T. Goncalves da Silva, M. Voos, L. L. Chang, 10 sample, or around 2 5° in the 19 Co/19 Cu and L. Esaki, Solid State Commun. 39, 79 1981 . 17 sample . At E 4 B. Abeles and T. Tiedje, Phys. Rev. Lett. 51, 2003 1983 . 8052 eV, however, the low contrast does not allow us to 5 E. E. Fullerton, D. M. Kelly, J. Guimpel, I. K. Schuller, and Y. Bruynser- obtain several low-angle diffraction orders and thus the to- aede, Phys. Rev. Lett. 68, 859 1992 . tally reliable parameter is the bilayer thickness. All these 6 H. E. Fischer, F. Petroff, F. Belie¨n, S. Lequien, G. Verbank, Y. Bruinser- considerations support, once again, the advantage of using aede, S. Lefebvre, and M. Bessie re, J. Phys. III 4, 121 1994 . 7 M. Suzuki, Y. Taga, A. Goto, and H. Yasuoka, Phys. Rev. B 50, 18 580 anomalus x-ray scattering. 1994 . At this point it seems worth mentioning the validity of 8 M. Ueda, O. Kitakami, Y. Shimada, Y. Goto, and M. Yamamoto, Jpn. J. the DWBA, which can reproduce perfectly the off-specular Appl. Phys., Part 1 33, 6173 1994 . 9 scans even near the critical angles. A quite remarkable work H. E. Fischer, H. Fischer, O. Durand, O. Pellegrino, S. Andrieu, M. Piecuch, S. Lefebvre, and M. Bessie re, Nucl. Instrum. Methods Phys. Res. by Schlomka et al.16 concerning this subject was done re- B 97, 402 1995 . cently. They studied the specular and transverse diffuse 10 E. E. Fullerton, Y. K. Schuller, H. Vanderstraeten, and Y. Bruynseraede, scans of several samples with an increasing degree of com- Phys. Rev. B 45, 9292 1992 . 11 plexity. The DWBA reproduced perfectly the off-specular M. De Santis, A. de Andre´s, D. Raoux, M. Maurer, M. F. Ravet, and M. Piecuch, Phys. Rev. B 46, 15 465 1992 . scans of a Ge layer, then a Ge/Si bilayer and finally a three 12 E. Chason and T. Mayer, Crit. Rev. Solid State Mater. Sci. 22, 1 1997 . layer system: Ge/Si/Ge, taken at different wave vector trans- 13 K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B 38, 2297 fer. In the present case, we are not dealing with a three layer 1988 . 14 epitaxial system, but with a more complicated ML. Our V. Holy´ and T. Baumbach, Phys. Rev. B 49, 10 668 1994 . 15 V. Holy´, J. Kube´na, I. Ohli´dal, K. Lischka, and W. Plotz, Phys. Rev. B 47, samples have between 10 and 20 bilayers, with increasing 15 896 1993 . roughnesses, varying thicknesses and with thick oxide layers. 16 P. Schlomka, M. Tolan, L. Schwalowsky, O. H. Seeck, J. Stettner, and W. Even so, the rocks manage to reproduce remarkably well Press, Phys. Rev. B 51, 2311 1995 . 17 F. Bridou and B. Pardo, J. Phys. III 4, 1523 1994 . the shape and position of the dynamic peaks. These results 18 M. Li, M. O. Mo¨ller, and G. Landwehr, J. Appl. Phys. 80, 2788 1996 . lead to the same conclusions as those from Schlomka and 19 B. Vidal and P. Vincent, Appl. Opt. 23, 1794 1984 . co-workers in their previous work, enabling us to support the 20 J. R. Lu, E. M. Lee, and R. K. Thomas, Acta Crystallogr., Sect. A: Found. validity of the DWBA as a very good approach for calculat- Crystallogr. 52, 11 1996 . 21 L. G. Parratt, Phys. Rev. 95, 359 1954 . ing the x-ray scattering cross section of rough interfaces near 22 E. Elkaim, S. Lefebvre, R. Kahn, J. F. Berar, M. Lemonnier, and M. the critical angle. Bessie re, Rev. Sci. Instrum. 63, 988 1992 . 23 M. Bordessoule, S. Lefebvre, and M. Bessie re unpublished . 24 V. CONCLUSIONS Y. Yoneda, Phys. Rev. 131, 2010 1963 . 25 B. B. Mandelbrot, The Fractal Geometry of Nature Freeman, New York, Anomalous x-ray reflectivity has been used to study a set 1982 . 26 of magnetron-sputtered Co/Cu multilayers. The use of the H. E. Fischer, H. Fischer, and M. Piecuch in preparation . 27 J. Daillant and O. Be´lorgey, J. Chem. Phys. 97, 5824 1992 . anomalous scattering and synchrotron radiation has allowed 28 Sasaki Tables National Laboratory for High Energy Physics, Japan . us to obtain higher contrast and a wider scanned angular 29 CRC Handbook of Chemistry and Physics, edited by D. R. Lide CRC, range, which have permitted us to determine accurately the London, 1994 . 30 structure parameters of the system. In addition, the two ways A. de Bernabe´, M. J. Capita´n, H. E. Fischer, S. Lequien, C. Prieto, J. Colino, F. Mompea´n, S. Lefebvre, M. Bessiere, C. Quiro´s, and J. M. Sanz, of obtaining information from an x-ray reflectivity pattern Vacuum in press . Downloaded 10 Sep 2002 to 148.6.178.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp