Pergamon Solid State Communications, Vol. 108, No. 10, pp. 769­773, 1998 1998 Elsevier Science Ltd. All rights reserved 0038­1098/98 $ - see front matter PII: S0038­1098(98)00430-X COMBINATION OF SPECULAR AND OFF-SPECULAR LOW-ANGLE X-RAY DIFFRACTION IN THE STUDY OF METALLIC MULTILAYERS A. de Bernabe´,a,b,* M.J. Capita´n,b H.E. Fischer,c C. Quiro´s,d C. Prieto,a J. Colino,a F. Mompea´na and J.M. Sanzd aInstituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cienti´ficas, Cantoblanco, 28049-Madrid, Spain bEuropean Synchrotron Radiation Facility, B.P. 220, 38043-Grenoble, France cInstitut Max von Laue-Paul Langevin, B.P. 156, 38042-Grenoble, France dDepartamento de Fi´sica Aplicada (C-XII), Universidad Auto´noma de Madrid, 28049-Madrid, Spain (Received 13 February 1998; in revised form 20 July 1998; accepted 25 August 1998 by J. Joffrin) The use of resonant low-angle X-ray diffraction, combining specular and off-specular scans, has been used to characterize accurately and self- consistently the mesoscopic structure and the quality of interfaces for a set of magnetron sputtered Co/Cu multilayers. In addition, the use of a simulation program to fit experimental patterns, which is based on the Distorted Wave Born Approximation has permitted to confirm its validity in the region of total external reflection in a system having a high degree of complexity. 1998 Elsevier Science Ltd. All rights reserved Keywords: A. magnetic films and multilayers, A. surfaces and interfaces, C. X-ray scattering. 1. INTRODUCTION and overlayer [5]; and off-specular scans (q-rock or The explanation of physical properties of metallic multi- rocking curves and 2v-rocks or detector scans) allow layers (ML), such as giant magnetoresistance (GMR) [1], the reconstruction of the height­height correlation is directly related to the interfacial structure of these function of the roughness [6­8]. systems [2]. Therefore, a precise and reliable structural The most reliable way of obtaining information from characterization becomes essential. The most widespread reflectivity patterns consists of simulating reflectivity technique used to probe the structure of these materials curves using a matricial calculation [5, 9­11]. Through is probably X-ray diffraction. For highly crystalline this method, an accurate and self-consistent structural systems, high-angle X-ray diffraction is used to obtain determination can be achieved when specular scans are a global measure of the sample's structure [2, 3] how- completed by off-specular scans (q-rock and 2v-rock ever, for polycrystalline samples the use of low-angle curves), which probe the in-plane structure of the ML X-ray diffraction provides very useful results to the and not simply the average electron density profile (r(z)) knowledge of the interfaces [4]. probed by specular scans. Such simulations are based on At low-angle X-ray diffraction, two kind of experi- the Distorted Wave Born Approximation (DWBA) ments can be performed: specular scans, which provide whose validity was reported in a previous work for information about the dimension perpendicular to near perfect semiconductor heterostructures in the the surface of the multilayer (ML), allowing thus the Si/Ge system [8]. In that paper, Schlomka et al. studied determination of the layer thicknesses and root-mean- the specular and off-specular scans of several samples square (r.m.s.) roughness of the substrate (j), interfaces with an increasing degree of complexity. The DWBA reproduced perfectly the off-specular scans taken at different wavevector transfer, in the region of total external reflection, for a Ge layer, a Ge/Si bilayer and * Corresponding author. finally a Ge/Si/Ge trilayer. 769 770 LOW-ANGLE X-RAY DIFFRACTION IN METALLIC MULTILAYERS Vol. 108, No. 10 In metallic multilayers, however, the growth mode is 3. RESULTS AND DISCUSSION quite far from the epitaxial and quasiperfect obtained in semiconductor heterostructures. We have aimed then to Figure 1 shows the experimental reflectivity patterns prove the validity of the DWBA in a highly complex obtained using synchrotron radiation, making use of the system, such as polycrystalline Co/Cu MLs. In addition, Co resonant dispersion for which the incident energy was the combination of specular and off-specular scans has selected to be 7704 eV. The hollow points represent the resulted in the obtention of a single set of self-consistent experimental data and lines are the mean square fits parameters which describe the mesoscopic structure of using the simulation program described ahead. Patterns our system. correspond to four different samples with bilayer thick- nesses ranging from 18 to 66 A , in which the intensity position has been shifted in order to plot all of them 2. EXPERIMENTAL together. Samples were grown on a Si (1 0 0) oxidized substrate The small oscillations present in the spectra, using a DC-operated magnetron sputtering system with a correspond to sample-size oscillations (usually called residual pressure of 5 10¹7 mbar. The Ar pressure Kiessig fringes). They arise from multiple interference used for deposition was 4:8 10¹3 mbar at a constant between beams reflected at the top interface and at the substrate temperature of 60 C. The substrate was placed multilayer­substrate interface. Superimposed to the 8 cm away from magnetrons in order to get a good Kiessig fringes, appear the multilayer peaks (they are in-plane homogeneity of the sample. The deposition Bragg-like peaks coming from the chemical modulation rates obtained were 2 nm/min for Co and 3 nm/min for of the sample) which account for the periodicity of the Cu. Specially designed stainless steel screens were used ML. The number of Kiessig fringes between each pair to avoid mixing of Co and Cu during growth. The total of Bragg peaks is 2n ¹ 1, ``n'' being the number of sample thickness for the whole set was kept nearly deposited bilayers. Finally, some long wavelength constant around a value of 70 nm, for which the oscillation can be observed in some samples. Their number of bilayers was varied; no buffer was used for nature is due to the uppermost Co layer which oxidizes growth. The samples grown, with a Co/Cu thickness ratio and forms a thin oxide overlayer. equal to unity, are represented as [mCu/mCo]n, where m is the layer thickness in A and n the number of layers. Experiments were carried out on the four circle goniometer setup at DCI D23-beamline (Laboratoire pour l'Utilization du Rayonnement Electromagnetique, Orsay, France) [12]. The beamline is equipped with a double crystal (Si(1 1 1)) monochromator with fixed exist and sagittal focusing. The experiments were performed 5 eV under the Co absorption K-edge, which was determined previously by recording the Near Edge X-ray Absorption Structure spectrum, to obtain the edge precisely. The detection was done combining an avalanche photodiode with a Ge(1 1 1) crystal analyzer tuned at the incident beam wavelength. The use of the analyzer permits to increase the angular resolution and the signal to background ratio by suppressing fluores- cence. On the other hand, the avalanche photodiode has a good dynamic range (up to 50 000 counts/s). The instabilities of the incident beam were monitored through the diffuse scattering from a kapton film, recorded and corrected automatically in the data acquisition program. The experimental resolution function (a convolution of the slits used, beam divergence and the resolution of the detector) obtained from a rocking curve was 40 arcsec Fig. 1. Specular reflectivity patterns of Co/Cu multilayers with an incident beam dimensions of 0:1 6 mm. A set recorded at an incident energy just under the Co of secondary slits placed just before the detector was set absorption K-edge (7704 eV). Points correspond to to 200 mm so as to get rid of diffuse scattering queues the experimental patterns and solid lines have been present in the q-scans. calculated by the simulation program. Vol. 108, No. 10 LOW-ANGLE X-RAY DIFFRACTION IN METALLIC MULTILAYERS 771 Fig. 2. Rocking curves taken at constant values of 2v Fig. 3. 2v-rock curves with their fit. The value of q was placed at a Kiessig maximum around 2v held constant and around 0.66 . The variable used is M ¼ 1:32 . For the sake of clarity Dq ¼ q ¹ v D2v ¼ 2v ¹ 2v M has been taken as the M. For the simulations only the diffuse variable. The fits to the experimental patterns are intensity has been taken into account. based on the DWBA. The specular peak has not been reproduced in the simulations. spectrum corresponding to (33Co/33Cu)10 sample there is an important increase in the oscillation at 2v ¼ 1:6 , Figure 2 shows the rocking curves corresponding this comes from an intensity leakage of the first Bragg to four samples. They have been taken at somehow peak of the multilayer, as can be seen from a glance at different values of 2v in order to be placed at a secondary Fig. 3. In all the scans, the amplitude of the oscillations (Kiessig) maximum in all of them and have an optimal (related to vertical correlation length) as well as the contrast. They have been taken near the total reflection intensity tendency (coming from the horizontal correla- angle in order to see the dynamic effects in the MLs. tion length) are well reproduced, what permits to rely on Such effects are seen, in addition to the small oscillations the values of the correlation lengths (terms explained near the central peak, through the so-called Yoneda ahead in the section). wings [13] (which are broad maxima at both extrema The simulations present in Figs 2 and 3 do not of the plots after which the intensity drops sharply). They reproduce the central peak since only the diffuse scattering arise from interferences of the diffuse scattering by term has been considered in their calculation. different interfaces and they are not reproducible In order to obtain a quantitative and precise charac- within the Born Approximation. Spectrum (17Co/ terization of samples, measured patterns have been fitted 17Cu)20 is the most inaccurate which may be due to a using the following simulation program (a detailed lower quality of the ML (something which matches description is in preparation [14]). For specular scans, well with the specular pattern), while the spectrum the formalism given by Vidal and Vincent [10] has been corresponding to (19Co/19Cu)17 reproduces perfectly used and the patterns have been fitted by a least square the structure and the Yoneda wings. procedure. The Distorted Wave Born Approximation as The last type of scans are the 2v-rocks. They are done presented by Daillant and Be´lorgey [15] has been used at a constant value of q, which is half of the value of 2v at for the off-specular simulations. The computer program, which the rocking curves were taken. This scan geometry takes into account a great number of parameters permits to see the reciprocal space in both the x and z which influence the reflectivity pattern obtained: layer directions. Figure 3 shows the spectra corresponding to thicknesses, roughnesses, deviations from the ideal the four samples from which q-rocks were taken. In the cases (a linear and a Gaussian variation of the layer 772 LOW-ANGLE X-RAY DIFFRACTION IN METALLIC MULTILAYERS Vol. 108, No. 10 thicknesses, a linear stretch of the roughnesses,...), as distance between horizontal bumps. It allows to deter- well as the roughness correlation lengths yx and yz and mine if there exists interdiffusion (yx 15 A ) or inter- parameter h. face roughness (yx 15 A ). On the other hand, the The electron densities and the absorption coefficients vertical correlation length (yz) gives an idea of the of the substrate, Co, Cu and the oxide layer, have been vertical distance throughout which the interfaces can be taken from the Sasaki tables [16]. Special attention has correlated. The Hurst parameter (h) ranges from 0 to 1 been paid to the oxide layer (thickness and roughness) and gives an idea of the type of interface [17]. A value since it became essential when trying to fit the experi- near zero will be characteristic of a jagged interface mental patterns. The fitting procedure was the following: while a value near one is typical of flat and wide bumps once the parameters had been obtained from the specular in the interface. patterns, they were used to simulate the off-specular The simulation results are summarized in Table 1. It scans in which only yx, yz, h and the roughnesses were should be remarked from these results that, while at a varied. If the obtained fit is not satisfying, new roughness bilayer thickness (L) up to 38 A the roughness of Co and values are then introduced into the reflectivity simulations Cu are equal, at a value of L ¼ 66 A there exists a and varied to obtain a better fit. Again, those parameters difference in their roughness values, being lower for were used to perform the off-specular simulations and Cu. This is in agreement with the observed different the process repeated until a single set of roughness growth behavior for Co and Cu. Co grows on Cu (1 1 1) parameters was obtained. In the off-specular scans, the forming islands up to a thickness of about 5 MLs after yx obtained in the q-rocks was used to simulate the which it grows layer-by-layer [18]. Something interest- 2v-rocks and yz was then varied until a good fit was ing, as well, is the decreasing tendency of the oxide layer reached. roughness as the oxide layer thickness increases. This To obtain the error bars, once the optimal fit had been behaviour, has been explained in a previous work and its reached by a root-mean-square process, the fit para- reason attributed to the process of oxidation itself [19]. meters were varied manually. When an appreciable It seems worth at this point remarking on the validity change between the calculated and the experimental of the Distorted Wave Born Approximation (DWBA), patterns had been observed, the difference was taken as that it can perfectly reproduce the off-specular scans the error bar. even in the region of total external reflection. The Even if the specular reflectivity patterns provide very conclusions at which Schlomka et al. [8] arrived in good and precise structural parameters of the system, their: Ge/Si/Ge system are now supported by these when dealing with roughness, more than one possible results in a system having structural complications such solution may be obtained if diffuse scattering data are not as a linear stretch of the roughness or a Gaussian accounted for. This observation, already stated in the distribution of the interlayer roughness. The DWBA is literature [8], led us to perform off-specular scans in our a very good approach to calculate the X-ray scattering samples to obtain a single solution for the roughnesses. In cross section of rough interfaces near the critical angle. addition, they have permitted us to obtain the correlation lengths of the roughness profiles as well as the Hurst parameter, the combination of which permits to describe 4. CONCLUSIONS the morphology of the multilayer interfaces. The horizontal The combination of specular and off-specular resonant correlation length (yx), represents approximately the X-ray diffraction experiments has permitted to obtain Table 1. Values obtained by the fit procedure described in the text. From left to right, given values are: thickness of the Co layer, thickness of the Cu layer, Co r.m.s. roughness, Cu r.m.s. roughness, oxide layer thickness, oxide layer roughness, substrate roughness, horizontal correlation length, vertical correlation length and Hurst parameter dCo (A ) dCu (A ) jCo (A ) jCu (A ) dO (A ) jO (A ) jS (A ) yx (A ) yz (A ) h (9Co/9Cu)40 9.1 9.1 9 9 13 13.0 13 6000 700 0.45 0.1 0.1 1 1 1 0.5 2 500 200 (17Co/17Cu)20 17.1 17.0 12 12 18 8.0 12 5000 650 0.45 0.2 0.2 1 1 2 0.5 2 2000 100 (19Co/19Cu)17 19.1 19.1 8 8 50 3.0 8 8000 900 0.4 0.2 0.2 1 1 2 0.2 2 2000 100 (33Co/33Cu)10 33.0 33.0 12 6 33 4.5 10 8500 700 0.5 3 0.3 2 2 1 0.5 2 500 50 Vol. 108, No. 10 LOW-ANGLE X-RAY DIFFRACTION IN METALLIC MULTILAYERS 773 accurately and self-consistently a single set of parameters Bessie re, M., Nucl. Instrum. Methods, B97, 1995, describing the mesoscopic structure of magnetron- 402. sputtering Co/Cu multilayers. In addition to describing 5. Chason, E. and Mayer, T., Critical Review in Solid the structure of these multilayers with such detail as a State and Materials Science, 22, 1997, 1. Gaussian distribution of the interface roughness, the 6. Sinha, K., Sirota, E.B., Garoff, S. and Stanley, H.B., Phys. Rev., B38, 1988, 229. Distorted Wave Born Approximation, used in the data 7. Holy´, V. and Baumbach, T., Phys. Rev., B49, 1994, treatment, has been proved to be perfectly valid to 10668. calculate the diffuse scattering cross section in a region 8. Schlomka, P., Tolan, M., Schwalowsky, L., Seeck, within the total external reflection. O.H., Stettner, J. and Press, W., Phys. Rev., B51, 1992, 2311. 9. Parratt, L.G., Phys. Rev., 95, 1954, 359. Acknowledgements-We gratefully acknowledge Prof. 10. Vidal, B. and Vincent, P., Appl. Optics, 23, 1984, S. Lefebvre and Prof. M. Bessie res from LURE for 1794. providing support for and during the experiments. One 11. Lu, J.R., Lee, E.M. and Thomas, R.K., Acta. Cryst., of us, AdB, wishes to thank E.S.R.F. for the stay which A52, 1996, 11. allowed us to perform this work. This work has been 12. Elkaim, E., Lefebvre, S., Kahn, R., Berar, J.F., partially supported by the CICyT under contract no. Lemonnier, M. and Bessie re, M., Rev. Sci. Instrum., MAT97/0725. 63, 1992, 988. 13. Yoneda, Y., Phys. Rev., 131, 1963, 2010. REFERENCES 14. Fischer, H.E., Fisher, H. and Piecuch, M. (unpublished). 1. Baibich, M.N., Broto, J.M., Fert, A., Nguyen Van 15. Daillant, J. and Be´lorgey, O., J. Chem. Phys., 97, Dan, F., Petroff, F., Eminent, P., Croquet, G., 1992, 5824. Friederich, A. and Chazelas, J., Phys. Rev. Lett., 16. Sasaki Tables, National Laboratory for High 61, 1988, 2472. Energy Physics, Japan. 2. Fullerton, E.E., Kelly, D.M., Guimpel, J., Schuller, 17. Mandelbrot, B.B., The Fractal Geometry of Nature. I.K. and Bruynseraede, Y., Phys. Rev. Lett., 68, Freeman, New York, 1982. 1992, 859. 18. de la Figuera, J., Prieto, J.E., Ocal, C. and Miranda, 3. De Santis, M., De Andre´s, A., Raoux, D., Maurer, R., Phys. Rev., B47, 1993, 13 043. M., Ravet, M.F. and Piecuch, M., Phys. Rev., B46, 19. de Bernabe´, A., Capita´n, M.J., Fischer, H.E., 1992, 15465. Lequien, S., Prieto, C., Colino, J., Mompea´n, F., 4. Fischer, H.E., Fischer, H., Durand, O., Pellegrino, Lefebvre, S., Bessiere, M., Quiro´s, C. and Sanz, O., Andrieu, S., Piecuch, M., Lefebvre, S. and J.M., Vacuum (in press).