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Fe superlattices probed at different length scales
Thin Solid Films 366 (2000) 51±62 www.elsevier.com/locate/tsf
Structure of Ag/Fe superlattices probed at different length scales G. Gladyszewski a,*, K. Temst b, K. Mae b,1, R. Schad b,2, F. BelieÈn b,3, E. Kunnen b, G. Verbanck b, Y. Bruynseraede b, R. Moons c, A. Vantomme c, S. BlaÈsser c, G. Langouche c a
Department of Experimental Physics, Institute of Physics, Technical University of Lublin, ul.Nadbystrzycka 38, 20-618 Lublin, Poland Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium c Instituut voor Kern- en Stralingsfysika, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium
b
Received 7 March 1999; received in revised form 17 January 2000; accepted 22 January 2000
Abstract We report on the growth and structure of Ag(001)/Fe(001) superlattices studied in situ by re¯ection high-energy electron diffraction (RHEED) and ex situ by Rutherford backscattering and channeling spectroscopy (RBS/C), X-ray diffraction (XRD) and atomic force microscopy (AFM). These complementary characterization methods have been compared and applied to a detailed investigation of the epitaxial quality and the interface roughness. The apparent inconsistency in the results is explained by the difference in length scale probed by the four characterization techniques. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Epitaxy; Multilayered structures; Structure characterization; Ag/Fe superlattices
1. Introduction Recent experimental and theoretical investigations have shown that the properties of metallic multilayers differ considerably from those of bulk materials (for a review see e.g. Ref. [1]). Observed changes in the structural [2] and transport [3] properties, as well as the discovery of giant magnetoresistance (GMR) phenomena [4] have generated a renewed interest. Understanding the origin of these effects requires multilayered ®lms that are structurally well characterized, since the quality at an atomic scale of the composition and interface of the superlattice may drastically in¯uence its properties. Ultrathin ®lms, bilayers as well as multilayers of the Ag/ Fe system have been extensively studied, both theoretically and experimentally [5±22]. This fcc/bcc superlattice has a very attractive epitaxial relationship Ag(001)k100l// Fe(001)k110l leading to a small in-plane mismatch equal to 0.8% and allowing the growth of high quality epitaxial
* Corresponding author. Tel.:148-81-538-1510; fax:148-81-525-9385. E-mail address: [email protected] (G. Gladyszewski) 1 Present address: Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan. 2 Present address: Center for Materials for Information Technology, Box 870209, Tuscaloosa, AL 35478-0209, USA. 3 Present address: Philips Research Laboratories, NL-5656 AA Eindhoven, The Netherlands.
superlattice ®lms (particularly on MgO(001)). At the same time the out-of-plane mismatch in the Ag/Fe superlattice is very large and equal to 42.5%. This fact makes u ±2u XRD pro®les extremely sensitive to any changes occurring in the interface regions. Structural investigations reported a substantial increase in hardness properties of Ag(001)/ Fe(001) multilayers [14], while X-ray diffraction measurements were used to investigate the structure and solid-state reactions of laser-deposited and sputtered Ag/Fe multilayers [15]. Concerning the magnetic properties of the Ag/Fe system, it was reported that the Fe magnetic moments may be considerably enhanced compared to the bulk value [16,17]. With regard to interlayer magnetic coupling effects, the have been several papers describing the simultaneous presence of bilinear and biquadratic exchange coupling [18,19]. Recently GMR in sputtered Ag/Fe multilayers and its anomalous temperature dependence were presented, suggesting the presence of interfacial superparamagneticlike spins [20]. Finally, the transition from in-plane to outof-plane magnetization was shown to have an interesting relaxation behaviour [21]. A detailed understanding of these physical properties depends critically on a good insight in the sample quality and, in particular, on the interface structure. It is, therefore, the aim of this paper to study in detail the growth, layer structure, and interface roughness of Ag/Fe superlattices. Different complementary methods have been employed to achieve this goal: Rutherford backscattering and channeling
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(00)00888-9
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spectroscopy (RBS/C), atomic force microscopy (AFM), re¯ection high-energy electron diffraction (RHEED) and X-ray diffraction (XRD). The Ag/Fe multilayers are a test case in order to show that the different depth and lateral resolutions offered by these characterization methods contribute to a better understanding of the multilayer quality. The structure and interface modi®cation of Ag/Fe superlattices caused by ion irradiation and annealing treatments, as well as their in¯uence on transport and magnetic properties, are presented elsewhere [23,24]. 2. Experimental The Ag/Fe superlattices were prepared in a Riber MBE system (2 £ 10211 Torr base pressure) by sequential deposition of Ag and Fe from a Knudsen cell and an e-beam gun, respectively. The residual gas pressure during the evaporaÊ /s tion was 5 £ 10210 Torr. The evaporation rate of ,1 A was stabilized and controlled by a feedback system (using a quadrupole mass spectrometer) with an accuracy of 1%. All the samples were deposited onto MgO(001) substrates (obtained from Kelpin Co., Germany) held at room temperature. Before deposition the substrate was heated at 6008C for 10 min. If Ag is the ®rst layer grown on MgO, polycrystalline layers are produced (see Section 3.4); starting the growth on MgO by Fe leads to epitaxial layers. The notation [Ag(x)/Fe(y)]xN will be used throughout this paper for the multilayers consisting of N periods of silver and iron sublayers; x and y are thicknesses of Ag and Fe sublayers, respectively. In-situ 10 keV RHEED measurements were used to monitor the growth of the superlattice. The main advantages of RHEED are its simplicity and a large sensitivity to structural changes at the surface [25,26]. However, in order to extract more information about the roughness as well as the arrangement of atoms on the surface, whole RHEED patterns have been recorded and interpreted. In our system a regular Sony video camera was used. The spatial resolution on the RHEED ¯uorescent screen was about 0.08 mm, which is very small compared to the intrinsic width of a typical RHEED spot on the screen. Temporal resolution is limited by the refresh rate of the camera (0.02 s) and the speed of the frame-capture card in the PC (on order of 0.1 s), but again much faster than the changes which could occur in the RHEED pattern due to the ®lm growth (in that time we Ê of a deposited would typically deposit only about 0.1 A layer). Initial ex situ information concerning the composition, layer thickness, crystallinity and epitaxial orientation of the superlattices was obtained using 4He backscattering/ channeling spectrometry. From backscattering spectra taken with random beam incidence, the composition of the multilayer can be determined as a function of depth. When carefully aligning the a -beam, a channeling effect is
observed in directions perpendicular to the sample surface, as well as in off-normal crystal axes. In the ®rst geometry crystalline quality of the individual layers is obtained. In the latter geometry an estimate of the tetragonal distortion (determined by the elastic strain) of the layers can be deduced. An incident beam energy of 1.97 MeV and a scattering angle of either 1358 or 1558 were selected in order to obtain an optimal compromise between mass and depth resolution. Analysis of the spectra was done using the basic relations of backscattering spectrometry [27] and by comparison to RUMP simulations [28]. Scanning probe microscopy [29] has evolved into a very versatile and powerful tool for the investigation of the topography of thin ®lm surfaces. One of its variants, atomic force microscopy [30] (AFM) offers the advantage that it is also applicable to study the structure of non-conducting samples, although with a slightly smaller resolution than scanning tunneling microscopy. The initial stages of the growth process, granularity, and roughness of the layers can be imaged in great detail. AFM provides the additional advantage that the surface roughness can be measured directly as a function of the scan length, enabling a determination of the fractal dimension of the surface and the lateral roughness correlation length on the surface [31]. The AFM measurements were carried out using a Digital Instruments NanoScope III microscope at room temperature and in ambient atmosphere. All experiments were performed in the contact mode using 200-mm wide cantilevers with 0.12 N/m spring constant. Apart from recording the sample topology the root mean square (rms) surface roughness was measured in detail as a function of the lateral scan length using the built-in analysis software. X-ray diffraction is one of extensively applied techniques for the structure characterization of thin ®lms and superlattices. This technique is commonly used in the u ±2u geometry where the scattering vector is perpendicular to the sample surface and only `one-dimensional' information (in the growth direction) is obtained. Nevertheless, a speci®c superlattice XRD pro®le allows one to deduce some additional structural parameters by ®tting the measured intensity pro®les with model calculations [32±35]. In these models not only relative intensities of superlattice peaks and their positions are taken into account, but whole XRD pro®les including line pro®les are used to quantitatively determine lattice constants, disorder parameters, interface roughness, etc. However, it is necessary to keep in mind that only `one-dimensional' information is directly available and all other parameters are only estimated and deduced, and may vary from model to model. For this reason we have decided to use two different models based on different approaches but of course leading to the same goal ± the superlattice structure characterization. Both models have already been described in detail: one based on the analytical formula and re®nement (the SUPREX program [32]), the second based on a Monte Carlo method (the SLERF program [35]). The application of these two
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different models should provide us with the same structural parameters. The XRD measurements were carried out using a 12 kW Rigaku DMax rotating anode diffractometer with Ê ) and a thin ®lm attachment Cu Ka radiation (lx 1:5418 A goniometer with a post-sample graphite (0002) crystal monochromator in the Brag±Brentano con®guration. The source divergence slit was of 1/68 while a detector slit was of 0.6 mm. Samples were examined in both specular (small (0±158) and large (30±708) angle u ±2u geometry) and nonspecular (small- and large-angle v -scans, v ±2u offscans) conditions [36] in order to determine the superlattice period, the layering quality, the epitaxial relationships as well as deviations from the bulk lattice parameters. 3. Results and discussion A large amount of experimental data will be presented according to the characterization techniques used. First, the in-depth structure characterization using the RBS/C technique is described, after which the surface topography obtained by AFM is discussed. This last method allows characterization of the roughness of consecutive bilayers at different lateral length scales, which is impossible with the other methods. Therefore, we treat the image obtained from AFM as `reference-data' which chart the surface roughness as a function of the lateral length. The AFM measurements, however, are limited to Ag surfaces only, because the measurements were performed ex situ and the image of the Fe layers could be strongly affected by oxidation. The results obtained from RHEED concern Ag as well as Fe sublayers. Finally, the results from XRD are shown and structure parameters are determined. 3.1. Rutherford backscattering spectrometry Fig. 1 shows the experimental (circles) and simulated Ê )/Ag (solid line) backscattering spectra of an [Fe(145 A Ê )]x5 superlattice deposited on top of a MgO substrate. (220 A An incident He beam of 1.97 MeV is used, and the scattering angle of the detected particles is 1558. For the simulation, perfect interfaces between the various layers are assumed. The yield from the Ag (1.5±1.75 MeV) and Fe (1.25±1.5 MeV) signal drastically decreases when the incident He beam is aligned with the normal crystal axis of the MgO substrate (a phenomenon called channeling). The ratio of this aligned backscattering spectrum (dashed line in Fig. 1) to the spectrum measured with random beam incidence (circles) is referred to as the minimum yield for channeling, x min, and gives an indication of the crystal perfection of the thin ®lm structure: the lower x min, the lower the concentration of lattice imperfections. The value of this minimum yield is about xmin 13% in the top Fe layer and 20% in the top Ag layer, indicating a very good alignment of the multilayered structure. These minimum yield values markedly increase with the depth of the layers, both for Fe and Ag, up to values of about 60% in the bottom Fe layer and
Ê )/Fe(145 A Ê )]£5 Fig. 1. 97 MeV 4He backscattering spectra for the [Ag(220 A superlattice with random (circles) and MgOk001l aligned (dashed line) beam incidence, along with a RUMP simulation (solid line). The scattering angle of the detected particles was 1558.
50% in the bottom Ag layer. This means that the crystalline quality of the layers increases as more layers are grown. However, a small dechanneling contribution from mis®t dislocations (and other lattice imperfections), possibly present at the interfaces, cannot be excluded. The fact that the minimum yield results in a much higher value close to the substrate±superlattice interface, especially in the case of Fe, is believed to be due to the relatively large mis®t (~3%) between the MgO substrate and the ®rst iron layer. Between the various layers of the superlattice, the much smaller lattice mismatch (~0.8%) results in a much lower density of mis®t dislocations, and consequently in a lower defect density in the layers. Further proof of the epitaxial nature of the layers is obtained from the backscattering spectra taken with the incoming He beam aligned along the Agk011l axis, which is located at an angle of 458 with respect to the k001l normal axis (the geometry is schematically shown in the inset of Fig. 2). Due to this large tilt angle, the signal of the bottom Ag layer overlaps with the signal of the top Fe layer. Fig. 2 shows the spectrum for a Agk011l-aligned beam incidence (dashed line), along with a random spectrum taken while continuously rotating the sample azimuthally. Since the bcc lattice structure of Fe does not contain a major crystal axis in this direction, no signi®cant decrease of the backscattering yield is observed for the Fe signal. The slightly lower yield observed is due to so-called planar channeling along the Fe(110) plane. Hence, Fig. 2 illustrates a k011l axial channeling in Ag layers and a (011) planar channeling in Fe layers. Moreover, channeling is observed in the MgO substrate, indicating that the k011l Ag axis is aligned with the k011l MgO axis. This situation changes when the sample is rotated over 458 around the surface normal (spectra not shown): (011) planar channeling from the MgO substrate as well as from all Ag layers is observed (higher x min compared to the values shown in Fig. 2), whereas k011l axial channel-
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3.2. Atomic force microscopy
Ê )/Fe(145 Fig. 2. 1.97 MeV 4He backscattering spectra for the [Ag(220 A Ê )]£5 superlattice with random (circles) and MgO k011l aligned (dashed A line) beam incidence. The scattering angle of the detected particles was 1358.
ing is found for the Fe layers (lower x min values than those shown in Fig. 2). These observations prove that the Ag/Fe heterostructures are epitaxially oriented on the MgO substrate: the Ag layers are fully aligned with the MgO substrate whereas the Fe layers are rotated by 458. The exact position of the axes can be determined by measuring the backscattering yield as a function of the angle of incidence, i.e. by performing an angular scan. The minimum of the k011l scan for MgO is found at an angle c 45800 with respect to the k001l surface normal, as expected for this cubic lattice. On the other hand, the minima of the angular scans from the Ag layers are observed at c 45815, for all layers, indicating the presence of strain in these cubic lattices. From the value Dc 0815, a tetragonal distortion is derived, as 1T dk 2 d' =d' 0:52%. Assuming an isotropic in-plane stress distribution, the ratio between the perpendicular (1 ') and in-plane (1 k) strain can be estimated as ' 1 2n 1 k 1 12n where n is the Poisson coef®cient (nAg 0:37), and therefore 1' Ag 0:28%. Within the experimental uncertainties, a similar Dc value is measured for the Fe layers, suggesting the same tetragonal distortion is present throughout the multilayer. The possible errors are, however, larger for Fe than for Ag, since no corresponding substrate axis is found for the Fe measurement (cf. above), making a direct measurement of Dc impossible (therefore, in the case of Fe no quantitative analysis is done). Consequently, both the Fe and Ag layers are under tensile strain in the plane of the interfaces, which can be attributed to the relatively large mis®t between the MgO substrate and both superlattice components (,3%).
Fig. 3a shows a three-dimensional view of the surface Ê )/Fe(30 morphology of the Ag top layer of a [Ag(30 A Ê A)]£10 sample. The granular nature of the layers is clearly visible in this picture, from which an average grain size of Ê can be deduced. Although the top surface of a about 600 A single grain is smooth, there are rather deep valleys in between the grains and there can be considerable height differences between the surfaces of neighboring grains. The rms roughness measured over a 1 £ 1 mm 2 area is of the order of 2 nm. Fig. 3b shows a scan covering 1 mm 2 on the surface of a sample with 20 bilayers, with the same sublayers thicknesses as for the sample shown in Fig. 3a and grown under identical circumstances. The most obvious observation which can be made from this AFM image is the fact that the surface roughness is much smaller than for the sample with 10 bilayers. The qualitative observations discussed above can be analyzed in more detail by plotting the rms roughness data as a function of the lateral scan length, as shown in Fig. 4. For this purpose, the roughness of an area L £ L is averaged
Fig. 3. Atomic force microscopy topographs showing three-dimensional Ê )/Fe(30 A Ê )]£N views of 1 £ 1 mm 2 areas on the surface of the [Ag(30 A superlattices with N 10 (a) and N 20 (b). Note the difference between the vertical scales in a and b.
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reciprocal lattice points; the patterns are comparable to those obtained in transmission electron microscopy. Experimentally observed RHEED patterns are usually the superposition of these two cases. Fig. 6 shows the RHEED patterns which were taken after the growth of the ®rst, the second and the 20th Ag and Fe layers, respectively. The surface of the ®rst Fe layer is rather rough because we observe discrete diffraction spots due to electrons which feel the three dimensional periodicity of the lattice when they are transmitted through protrusions on the rough surface. The lateral island size can be roughly estimated by the simple kinematic theory of diffraction [37]. The one-dimensional diffracted intensity pro®le I(kx) is written as the so-called Laue function 2 Nakx sin 2 2 I kx akx sin2 2 Fig. 4. Evolution of the rms roughness obtained from the AFM data as a Ê )/Fe(30 A Ê )]£N multilayers function of the scan length L for the [Ag(30 A with N 10 (circles) and N 20 (squares).
over 10 different random positions on the sample surface in order to minimize the in¯uence of local topographic variations. The difference in overall roughness values between the N 10 and N 20 sample is quite clear from Fig. 4. For both samples an increase of the rms roughness with increasing scan length can be observed, re¯ecting the different roughness regimes which are probed by the AFM. For very small scan lengths L, the rms roughness is mainly determined by the surface quality of a single grain; for large scan lengths the height differences between adjacent grains are more in¯uential and cause an increase of the rms roughness. It should also be noted that the rms roughness of the N 10 sample already reaches its saturation value for scan lengths of about 300 nm, while the roughness of the sample with 20 bilayers does not yet reach full saturation even for scan lengths of 12 mm. This indicates that the lateral roughness correlation length is considerably larger in the N 20 sample than in the N 10 sample.
where kx is the scattering vector component, a is the atomic row spacing, and N is the number of atomic rows in the island in the considered direction. Strong diffraction peaks appear when kx 2ph=a, where h is an integer. The distance between the neighboring diffraction peaks is equal to 2p=a. The full width at half maximum (FWHM) of the diffraction peak is roughly equal to 2p=Na. The
3.3. Re¯ection high-energy electron diffraction RHEED patterns taken after the deposition of each Fe(30 Ê ) and Ag(30 A Ê ) layer indicate that Fe and Ag grow with the A well known epitaxial relationship of Ag(001)k100l// Fe(001)k110l//MgO(001)k100l. A schematic picture of the RHEED pattern to be expected in the present geometry is depicted in Fig. 5. If a surface is ¯at, the directions in which electrons are re¯ected are determined by cross sections between the Ewald sphere and the reciprocal lattice rods, so the diffraction spots align on semicircles centered on the shadow edge. On the other hand, when the surface is rough the diffractions are determined by the Ewald sphere and
Fig. 5. Schematic picture for interpretation of the RHEED pattern from the Ag and Fe (001) surface. The incident azimuth corresponds to the k100l for Ag and k110l direction for Fe. Positions of the spots corresponding to the transmission diffraction are indicated as solid and open circles for Ag and Fe, respectively. Cross sections between the 0th Laue circle and twodimensional reciprocal lattice rods characteristic for the re¯ection diffraction are indicated as crosses.
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Fig. 6. RHEED patterns measured during the growth of the Ag/Fe multilayer after the ®rst Ag layer (a), the second Ag layer (b), the 20th Ag layer (c), the ®rst Fe layer (d), the second Fe layer (e) and the 20th Fe layer (f).
number of atomic rows N which contribute to the diffraction can be deduced from the ratio of the distance between the neighboring diffraction peaks to the FWHM of the peak. In our experiment the width of a diffraction spot after the ®rst Fe layer deposition is about one-tenth of the distance to the next spot, which means N < 10. The k110l atomic rows of Ê . The size of the Fe islands can be Fe are separated by 2.02 A Ê . One can see also diffractherefore estimated as about 20 A tion spots due to the transmission for the ®rst Ag layer, but the positions of the spots move because of the different (001) plane interlayer distances of Fe and Ag. Such diffraction spots are still seen for the second Fe and Ag layers but the intensities are reduced. No diffraction spot due to the transmission of the electron beams is observed in the RHEED pattern for the 20th Ag layer, which indicates the surface has become two-dimensional. For the Fe layer nonzero intensities still remain observable at the position of the three-dimensional diffraction spots, even after the growth of the 20th layer, although the streak pattern indicates that the surface is much ¯atter than in the initial stages. Figs. 7 and 8 show changes in the intensity distribution along (00) and (01) streaks for Ag and Fe, respectively. In Fig. 7a one can see the largest peak shifts towards the shadow edge as the ®lm grows. The intensity at the (004) diffraction spot position decreases and the intensity of the specular beam increases. The contributions of the (004) diffraction spot and of the specular beam to the large peak are not clearly separated because the incident angle of the beam is close to the in-phase condition. Therefore we cannot unambiguously say whether the shift of the peak is due to the increase of the intensity of the specular beam or is due to the change of the Ag interplanar distance. One can also see the small peak from the (006) diffraction spot vanishing as the ®lm grows. This indicates also that a momentary Ag
Fig. 7. Intensity distribution along the (00) (a) and (01) (b) streaks of Ag surface measured for different numbers N of grown layers.
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Fig. 8. Intensity distribution along the (00) (a) and (01) (b) streaks for Fe surface measured for different numbers N of grown layers.
surface tends to two-dimensionality. Flattening of the surface is more clearly recognized by a change of the intensity distribution along the (01) streak in Fig. 7b. It is clear that the (024) and (026) diffraction spots vanish and the intensity increases near the crossing point between the zero Laue circle and the (01) streak, which is close to the shadow edge. In Fig. 8 the (004) and (114) diffraction spots from the Fe surface disappear as the ®lm grows. The peaks from the (002) and (112) diffraction shift towards the shadow edge after growth of the third layer. This is probably due to an expansion of the interplanar distance by relaxation of the structure. In order to evaluate the changes of the surface roughness, we introduce a simple qualitative parameter, R I b =I s . In the case of Fe, Ib is the intensity at the (002) diffraction spot and Is is the intensity at the point where the specular beam is expected; in the case of Ag, Ib is the intensity at the (024) diffraction spot and Is is the intensity near the cross section between zero Laue circle and the (01) streak for Ag. We choose the different de®nition of R for Ag from that for Fe because the specular beam and the (004) diffraction spot for Ag are too close in position to distinguish the individual intensities. Although the de®nitions of R for Fe and Ag are different, one can still discuss the surface roughness qualitatively using R, because the diffraction spots related to the Laue circles change their intensities having positive relations among each other as the surface roughness changes and so do the three dimensional diffraction spots. As shown in Fig. 9, an exponential decay of R for Ag indicates that smoothening of the Ag surface is more pronounced in the ®rst few bilayers. The growing surface of the Ag layer is ¯attened as more bilayers are grown. For Fe the value of R
increases gradually after an initial large decrease, which means that the Fe surface is ¯attest in the second or third layer and is gradually roughened afterwards. This can be explained as follows. The ®rst Fe layer on the MgO substrate is considered to be much rougher than those on the Ag layers from a comparison between the surface energy differences between Fe and MgO, and between Fe and Ag. The surface energies of Fe, Ag, and MgO are 2.939, 1.302,
Fig. 9. Changes of the roughness parameter R I b =I s observed for different numbers of grown layers. Larger values of R corresponds to a rougher surface.
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Ê )/Fe(5 A Ê )]£20 Fig. 10. Large-angle u ±2u XRD pro®les of the [Ag(50 A Ê )/Fe(15 A Ê )]£20 superlattice (b). superlattice (a) and the [Ag(50 A
and 1.15 J/m 2 [38,39], respectively. The roughness of Fe layers decreases until smoothing by Ag layers mostly compensates the initial large Fe roughness. Step density on Ag layers seems to play an essential role in the roughness increase of the successive Fe layers. The separation between Fe islands grown on a ¯at Fe substrate with micrometer wide terraces at around room temperature is about 5 nm [40]. The distance between Cr islands grown on a Ag(100) substrate at room temperature is also several nanometers [41]. Fe on a Ag layer seems to have a similar nucleation density if terraces of the Ag layer are wide enough. If the terrace width is smaller than this, step density determines the nucleation density and the island size, because steps provide nucleation sites. The terrace width on the ®rst few Ag layers is considered to be apparently smaller than several nanometers because the island size of the ®rst Fe layer is estimated as a few nanometers by RHEED. The size of three-dimensional islands of Fe is con®ned by the Ag steps in the beginning. As the number of bilayers increases and the Ag surface becomes ¯atter, the nucleation density of Fe decreases and the island size increases both laterally and vertically, which is considered to be observed as the increase of R in the RHEED measurement. We conclude from the RHEED measurements that the growth of Fe roughens the surface, but that deposition of Ag ¯attens the surface. The surface becomes ¯atter as more bilayers are grown.
parameters to obtain high quality epitaxial samples is the minimum sublayer thickness. We therefore prepared samples with a ®xed thickness of one material and different thicknesses of the second. Fig. 10 shows XRD pro®les of Ê )/Fe(x)]£20 superlattices. For a small Fe sublayer [Ag(50 A thickness (see Fig. 10a) the multilayers grow with closepacked Ag(111) and Fe(011) planes parallel to the substrate. In such a case the in-plane lattice mismatch in the Agk110l/ Fek100l direction is very small and equal to 0.8%, but in the direction it is rather large and equal to Agk1 12l/Fek0 11l 21%, preventing epitaxial multilayer growth and therefore only textured polycrystalline multilayers can be grown. For thicker Fe sublayers, however, Ag(001)//Fe(001) epitaxy becomes possible. In another set of samples we ®xed the Ê and prepared samples with Fe sublayer thickness at 20 A different Ag sublayer thicknesses. Fig. 11 shows the XRD Ê )]£20 superlattices. For very thin pro®le of [Ag(x)/Fe(20 A Ag layers the superlattice satellites are not resolved, leading to the conclusion that the Ag/Fe interfaces are too rough and Ê epitaxial growth only for Ag sublayers thicker than 10A occurs. Quite an unusual (for metallic superlattices) epitaxÊ )/Fe(70 A Ê )]£10 ial quality has been reached for the [Ag(500 A multilayer shown in Fig. 12. For such large superlattice Ê ) the satellite peaks are periods L (in this case L 570 A usually not resolved. As shown in the inset of Fig. 12, the satellite peaks do appear and point to a very high layering quality. The asymmetric X-ray diffraction measurements were performed for the Ag(113) and Fe(112) planes. First, the corresponding v ,2u conditions were set and then the sample was turned around the axis perpendicular to the ®lm. When one of the Ag(113) family planes (or (112) planes in the case of the iron) satis®ed the Bragg condition a drastic increase
3.4. X-ray diffraction X-ray diffraction measurements allow to optimize the conditions of the superlattice growth. One of the critical
Ê )]£20 superFig. 11. Large-angle u ±2u XRD pro®les of the [Ag(x)/Fe(20 A Ê (a), x 10 A Ê (b), x 15 A Ê (c) and x 20 A Ê (d). lattices for x 5 A
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Ê )/Fe(70 A Ê )]£10 Fig. 12. Large-angle u ±2u XRD pro®le of the [Ag(500 A superlattice. The satellite peaks are shown in the inset.
of diffracted intensity was observed, proving a high epitaxial quality of the samples. For the detailed investigation of the interface roughness, interdiffusion, and other structure parameters we have Ê )/Fe(18.5 A Ê )]£20 superlattice sample chosen the [Ag(25 A with the XRD pro®les shown in Fig. 13. Small angle XRD peaks (Fig. 13a) are very sharp and indicate smooth interfaces without interdiffusion and highly ordered at the long range scale. The peak positions allow to determine the Ê. multilayer period L 44 A The small angle rocking curve taken around the second order peak (Fig. 13a, inset) is very sharp and indicates that the ®lm is well oriented, parallel to the substrate. The largeangle XRD pro®le (Fig. 13b) reveals well-de®ned sharp
Fig. 13. Small- (a) and large-angle (b) u ±2u XRD pro®le of the [Ag(25.5 Ê )/Fe(18.5 A Ê )]£20 superlattice. In the insets small- and large-angle rocking A scans performed for the peaks positions indicated with arrows are shown.
59
satellite peaks. Only the peak at 2u 66:98 has a nearly twice as large half-width as the others. However, a largeangle rocking scan shows clearly that this peak consists in fact of two different peaks: one is a superlattice peak (with a rocking scan half-width ,18) and the second is a `forbidden' MgO(003) peak (with a rocking scan half-width ,0.188). The appearance of a `forbidden' peak may take place also for other monocrystalline substrates [42,43]. Note that the intensity of this `forbidden' peak is three orders of magnitude lower than the MgO(002) peak. To extract quantitative information about the superlattice structure we have used two different models which allow us to determine independently structural parameters such as the number of monolayers in the superlattice unit cell, interplanar distances of each material, rms roughness of the interface, possible interdiffused interface thickness, average grain size in the growth direction, etc. First we have used the SUPREX program. A ®tting procedure available in this program is very ef®cient in determining the interplanar distances which do not need to be exactly the same as in the bulk materials. The average number of Ag and Fe monolayers in the superlattice unit cell, nAg and nFe, as well as the interdiffused interface thickness and other structural parameters were also estimated. The in¯uence of the MgO(002) peak (2u 43:98) made it impossible, however, to ®t the whole pro®le because the substrate peak had nearly the same position as the most intense superlattice satellite. The best ®t to the experimental pro®le is shown in Fig. 14a and was obtained with the parameters given in Table 1. To avoid the in¯uence of the `forbidden' MgO(003) peak the experimental large-angle XRD pro®le was measured as a 0.38 off-scan. In such a case (see the inset in Fig. 13) it is still possible to measure a superlattice pro®le whereas MgO(003) is out of the specular condition. However, it was not possible to completely avoid the presence of the MgO(002) peak because this peak is much more intense than MgO(003). Therefore during the ®tting procedure the range of the XRD pro®le which coincides with the substrate peak was not taken into account. The SUPREX program allows one to use in the ®tting procedure many different structural parameters, but we stress that in this work their number was restricted to a minimum. The SLERF program does not contain a ®tting procedure; therefore it is necessary to determine some of the parameters in another way or to change their values and to look for the best agreement between simulated and experimental pro®les. As a matter of fact such parameters like average numbers of monolayers nAg, nFe, standard deviations of number of monolayers sig nAg, sig nFe and interdiffused interface thickness s init are rather easy to ®nd, because they all have their particular in¯uence on the XRD pro®le. The interplanar distances dAg and dFe are more dif®cult to determine, because changing slightly nAg and nFe it is always possible to get the same L for considerably different values of dAg and dFe. The exact value of the limited grain size Dg in the growth direction (described by a Gaussian distribution with standard devia-
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also given in Table 1 and the corresponding XRD pro®les are shown in Fig. 14b. Both programs give nearly perfect ®ts to the experimental pro®le and the obtained structure parameters are very similar. In both cases the interplanar distances are slightly smaller than those for the bulk materials (as suggested by RBS channeling measurements). Also, the average numbers of monolayers as well as the superlattice period are very close. There are, however, also some differences. The SUPREX program suggests single crystal superlattice growth, whereas the Monte Carlo simulation provides a better agreement of the peak half-widths with the experimental pro®le if we assume that the superlattice also consists of very large well-oriented in-plane and out-ofplane columnar grains, with an average thickness smaller than the total thickness of the ®lm. The existence of such `grains' cannot be con®rmed nor ruled out by any of the methods used in this work. High-resolution transmission electron microscopy (HRTEM) studies could be interesting to shed light on this problem. For both models the standard deviations of number of monolayers are similar, very small, and sig nAg , sig nFe. These parameters are not only related to the ¯uctuation of the number of monolayers considered in the growth direction, but also with height differences between interfaces when crossing from one column to another in-plane [44]. Therefore, the fact that sig nAg , sig nFe may indicate that the long-range rms roughness of Ag interfaces is smaller than that of Fe. Also s init has small values that indicate that only two monolayers are initially intermixed. However, this result may be also interpreted as a maximum two monolayers short-range rms roughness, because for X-rays it is dif®cult to distinguish between an interdiffused and a rough interface considered inside one coherent crystal [45]. Table 1 Ê )/Fe(18.5 A Ê )]£20 superlattice Structural parameters of the [Ag(25.5 A obtained from the SUPREX [32] and the SLERF [35] programs
Ê )/Fe(18.5 A Ê )]£20 Fig. 14. Large-angle u ±2u XRD pro®le of the [Ag(25.5 A superlattice. Together with the experimental scans (circles) the pro®les obtained from the SUPREX (a) and SLERF (b) model calculations are shown.
tion sig Dg) is also not easy to determine because ¯uctuations of sublayer thickness have similar in¯uence on XRD pro®les. We did not put in the interplanar distances derived from the SUPREX ®tting procedure because we wanted to avoid any inter-model in¯uences. Therefore, during the interpretation of the XRD pro®le using the SLERF program the structure parameters were optimized independently in order to get the best agreement between experimental and simulated pro®les. The parameters estimated in this way are
Parameter
SUPREX
SLERF
Ê) dAg (A Ê) dFe (A nAg (ML) nFe (ML) sig nAg (ML) sig nFe (ML) Ê) dint (A Ê) Dg (A Ê) sig Dg (A s init (ML) Ê) L (A
2.0407 1.4311 12.54 12.87 0.34 0.46 1.7359 a 880 b ± 2.36 c 44.01
2.0356 1.4270 12.60 12.87 0.3 0.4 1.7313 a 260 105 2.1 c 44.01
a
Fixed parameter dint dAg 1 dFe =2. Columnar growth is assumed in the model. Then the average grain size Dg is set to be equal to the total ®lm thickness. c The SUPREX program considers a linear shape of the interface, whereas the SLERF program assumes `an error function' shape of the interface. Therefore the latter takes into account the distance between the 84% and 16% concentrations of one of the elements. b
G. Gladyszewski et al. / Thin Solid Films 366 (2000) 51±62
Fig. 15. Two hypothetical surfaces having the same rms roughness, but different lateral dimensions of terraces. A 3D RHEED picture would be observed for surface a, and 2D for surface b.
In presenting the experimental data we did not try to correlate them. It is clear, however, that they do not simply provide a single and consistent image of the superlattice structure. The RBS/C and XRD data are characteristic for high-quality epitaxial superlattices. Both methods provide similar information about the interplanar distances. From RBS measurements the perpendicular distortion of Ag layer 1' Ag 0:28% can be calculated. This value is very close to that derived from XRD - averaging dAg parameters obtained from the SUPREX and the SLERF programs leads to 1' Ag 0:25%. At the same time RHEED and AFM provide ample evidence for a three-dimensional growth character and rather rough interlayer surfaces. In the interpretation of these results it is important to address the issue of the depth and lateral resolution inherent to the used techniques, i.e. how large is the volume from which we gather structural information. AFM is the only method which explicitly yields roughness data as a function of lateral length scale. A drawback is, of course, that AFM is only sensitive to the surface of the layers, which does not necessarily need to be the same as the interfaces buried in the superlattice. RHEED is generally assumed to make an average over a Ê , but this size depends on the lateral scale of about 1000 A dimensions of the terraces formed on the sample surface. It is also a misconception to associate three-dimensional (3D) and 2D growth modes observed in RHEED patterns with rough and smooth surfaces, respectively. The observed 3D character of Fe growth and 2D character of Ag growth does not imply that Fe is automatically rougher than Ag. This is illustrated by the two hypothetical surfaces shown in Fig. 15, which both have the same rms roughness, but nevertheless would produce two distinctly different RHEED pictures. In the case of surface (a) transmission electron beam diffraction, and hence a 3D picture, would occur via small short range terraces. The large terraces present at
61
surface (b) would give rise to 2D RHEED patterns due to the fact that the electron beam cannot traverse barriers [46] Ê . It remains, however, virtually impossible wider than 100 A to obtain quantitative information from the RHEED data alone. X-ray diffraction has the important feature that it makes an average over all interfaces. Recent work clearly showed that large-angle XRD measurements allow to characterize the interface roughness on a scale limited to the lateral dimension of individual columnar grains [44,47]. Height differences between different grains do not contribute to the probed short range interface roughness. This explains why a 3D growth as seen in RHEED does not necessarily exclude the existence of an excellent large-angle XRD pro®le; it is suf®cient that the superlattice is well developed within each of the islands. Keeping this in mind, a consistent picture does emerge when we compare the AFM, RHEED and XRD results on Ê average grain the common lateral length scale, i.e. the 600 A dimension. From the AFM data we derive a roughness Ê depending on the number of ranging between 1.5 and 5 A bilayers, while ®ttings of the XRD data suggest that the rms roughness inside one coherent grain may be equal or smaller Ê. than 3.7 A 4. Conclusions Finally, we can construct the following image of the studied Ag/Fe multilayers: From the very beginning the layers grow with the Ag(001)k100l//Fe(001)k110l// MgO(001)k100l epitaxial relationship. The height differences between different crystals are reduced as more layers are grown. Inside the columns the multilayer structure corresponds to highly ordered layers and reveals the relatively small interface roughness. Both the Fe and Ag layers are tensely strained in-plane. Due to the fact that RHEED patterns typical for 3D growth were observed for Fe and 2D for Ag, we may conclude that a momentary surface during the multilayer deposition grows with large Ag terraces and small Fe islands. The rms roughness, however, is probably Ê as obtained from ®tting similar and not larger than 3.7 A XRD pro®les. Each method provides information in its characteristic length scale and the conclusions drawn from them should not be extended to all scales. Therefore, we see that basing only on one of the methods it could not be possible to characterize the structure properly. Combining the four techniques RBS/C, AFM, RHEED and XRD have allowed us to characterize the structure of the Ag/Fe superlattices in detail. Acknowledgements This work was ®nancially supported by the Belgian Concerted Action and the Belgian Interuniversity Attraction Poles Programs. K.M. is a Research Fellow of the Katho-
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lieke Universiteit Leuven. K.T. is a Postdoctoral Researcher of the Fund for Scienti®c Research ± Flanders, Belgium (F.W.D.). E.K. is supported by the Flemish Institute for the promotion of research in industry (I.W.T.). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
For a review see for instance, J. Magn. Magn. Mater. 1±3 (1996) 156. I.K. Schuller, A. Fartash, M. Grimsditch, MRS Bull. 15 (1990) 33. J.M. Valles Jr., R.C. Dynes, Proc. MRS Symp. Proc. 195 (1990) 375. M.N. Baibich, J.M. Broto, A. Fert, et al., Phys. Rev. Lett. 61 (1988) 2472. R. Richter, J.G. Gay, J.R. Smith, Phys. Rev. Lett. 54 (1985) 2704. C.L. Fu, A.J. Freeman, T. Oguchi, Phys. Rev. Lett. 54 (1985) 2700. J.E. Ortega, F.J. Himpsel, Phys. Rev. B 47 (1993) 16441. F. Pan, B.X. Liu, J. Phys.: Condens. Matter 5 (1993) L315. A.M. Mazzone, Thin Solid Films 216 (1992) 145. F.J. Himpsel, Phys. Rev. Lett. 67 (1991) 2363. B. Heinrich, K.B. Urquahart, A.S. Arrott, J.F. Cochran, K. Myrtle, S.T. Purcell, Phys. Rev. Lett. 59 (1987) 1756. Z.Q. Qiu, J. Pearson, S.D. Bader, Phys. Rev. Lett. 70 (1993) 1006. D.P. Pappas, C.R. Brundle, H. Hopster, Phys. Rev. B 45 (1992) 8169. M.R. Scanlon, R.C. Cammarata, D.J. Keavney, J.W. Freeland, J.C. Walker, C. Hayzelden, Appl. Phys. Lett. 66 (1995) 46. Y. Luo, H.-U. Krebs, J. Appl. Phys. 77 (1995) 1482. F. Pan, T. Yang, K. Tao, B.X. Liu, J. Phys.: Condens. Matter 4 (1992) 519. C.L. Wooten, J. Chen, G.A. Mulhollan, J.L. Erskine, J.T. Markert, Phys. Rev. B 49 (1994) 10023. Z. Celinski, B. Heinrich, J.F. Cochran, J. Appl. Phys. 73 (1993) 5966. M. SchaÈfer, S. Demokritov, S. MuÈller-Pfeiffer, R. SchaÈfer, M. Schneider, P. GruÈnberg, W. Zinn, J. Appl. Phys. 77 (1995) 6432. C. Yu, S. Li, W. Lai, M. Yan, Y. Wang, Z. Wang, Phys. Rev. B 52 (1995) 1123. A. Berger, H. Hopster, Phys. Rev. Lett. 76 (1996) 519. S. Li, C. Yu, W. Lai, Y. Wang, M. Yan, J. Appl. Phys. 78 (1995) 405. G. Gladyszewski, J. Barnas, K. Temst, et al., J. Magn. Magn. Mater. 156 (1996) 381. Y. Bruynseraede, K. Temst, R. Schad, et al., Thin Solid Films 275 (1996) 1.
[25] P.K. Larsen, P.J. Dobson (Eds.), RHEED and Re¯ection Electron Imaging of Surfaces Plenum, New York, 1988. [26] Z. Mitura, P. Mazurek, K. Paprocki, P. Mikolajczak, Appl. Phys. A 60 (1995) 227. [27] W.-K. Chu, J.W. Mayer, M.-A. Nicolet (Eds.), Backscattering Spectrometry Academic Press, New York, 1978. [28] L.R. Doolittle, Nucl. Instrum. Methods B 9 (1985) 344. [29] S.M. Hues, R.J. Colton, E. Meyer, H.J. GuÈntherodt, Bull. January (1993) 41. [30] R.J. Behrn, N. Garcia, H. Rohrer (Eds.), Scanning Tunneling Microscopy and Related Methods NATO ASI Series E, 184, Kluwer, Dordrecht, 1990. [31] J. Krim, I. Heyvaert, C. Van Haesendonck, Y. Bruynseraede, Phys. Rev. Lett. 70 (1993) 57. [32] E.E. Fullerton, I.K. Schuller, H. Vanderstraeten, Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. [33] M.B. Stearns, C.H. Lee, T.L. Groy, Phys. Rev. B 40 (1989) 8256. [34] Z. Mitura, P. Mikolajczak, J. Phys. F 18 (1988) 183. [35] G. Gladyszewski, Thin Solid Films 204 (1991) 473. [36] G. Gladyszewski, Y. Bruynseraede, Phys. Rev. B 54 (1996) 11672. [37] M.G. Lagally, D.E. Savage, M.C. Tringides, in: P.K. Larsen, P.J. Dobson (Eds.), Re¯ection High-Energy Electron Diffraction and Re¯ection Electron Imaging of Surfaces, Plenum, New York, 1988 p. 139. [38] L.Z. Mezey, J. Giber, Jpn. J. Appl. Phys. 21 (1982) 1569. [39] A.R.C. Westwood, D.L. Goldheim, J. Appl. Phys. 34 (1963) 3335. [40] J.A. Stroscio, D.T. Pierce, R.A. Dragoset, Phys. Rev. Lett. 70 (1993) 3615. [41] A.J. Quinn, J.F. Lawler, R. Schad, H. van Kempen, Surf. Sci. 385 (1997) 395. [42] C. Templier, B. Boubeker, H. Garem, E.L. MatheÂ, J.C. Desoyer, Phys. Status Solidi A 92 (1985) 511. [43] G. Gladyszewski, Ph. Goudeau, A. Naudon, Ch. Jaouen, J. Pacaud, Mater. Lett. 12 (1992) 419. [44] G. Gladyszewski, Thin Solid Films 170 (1989) 99. [45] I.K. Schuller, Solid State Commun. 92 (1994) 141. [46] E. Miyazaki (Ed.), Introduction and Application of Surface Science Fuji Technosystem, Tokyo, 1991. [47] K. Temst, M.J. Van Bael, B. Wuyts, et al., Appl. Phys. Lett. 67 (1995) 3429.
Structure of Ag/Fe superlattices probed at different length scales G. Gladyszewski a,*, K. Temst b, K. Mae b,1, R. Schad b,2, F. BelieÈn b,3, E. Kunnen b, G. Verbanck b, Y. Bruynseraede b, R. Moons c, A. Vantomme c, S. BlaÈsser c, G. Langouche c a
Department of Experimental Physics, Institute of Physics, Technical University of Lublin, ul.Nadbystrzycka 38, 20-618 Lublin, Poland Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium c Instituut voor Kern- en Stralingsfysika, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium
b
Received 7 March 1999; received in revised form 17 January 2000; accepted 22 January 2000
Abstract We report on the growth and structure of Ag(001)/Fe(001) superlattices studied in situ by re¯ection high-energy electron diffraction (RHEED) and ex situ by Rutherford backscattering and channeling spectroscopy (RBS/C), X-ray diffraction (XRD) and atomic force microscopy (AFM). These complementary characterization methods have been compared and applied to a detailed investigation of the epitaxial quality and the interface roughness. The apparent inconsistency in the results is explained by the difference in length scale probed by the four characterization techniques. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Epitaxy; Multilayered structures; Structure characterization; Ag/Fe superlattices
1. Introduction Recent experimental and theoretical investigations have shown that the properties of metallic multilayers differ considerably from those of bulk materials (for a review see e.g. Ref. [1]). Observed changes in the structural [2] and transport [3] properties, as well as the discovery of giant magnetoresistance (GMR) phenomena [4] have generated a renewed interest. Understanding the origin of these effects requires multilayered ®lms that are structurally well characterized, since the quality at an atomic scale of the composition and interface of the superlattice may drastically in¯uence its properties. Ultrathin ®lms, bilayers as well as multilayers of the Ag/ Fe system have been extensively studied, both theoretically and experimentally [5±22]. This fcc/bcc superlattice has a very attractive epitaxial relationship Ag(001)k100l// Fe(001)k110l leading to a small in-plane mismatch equal to 0.8% and allowing the growth of high quality epitaxial
* Corresponding author. Tel.:148-81-538-1510; fax:148-81-525-9385. E-mail address: [email protected] (G. Gladyszewski) 1 Present address: Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan. 2 Present address: Center for Materials for Information Technology, Box 870209, Tuscaloosa, AL 35478-0209, USA. 3 Present address: Philips Research Laboratories, NL-5656 AA Eindhoven, The Netherlands.
superlattice ®lms (particularly on MgO(001)). At the same time the out-of-plane mismatch in the Ag/Fe superlattice is very large and equal to 42.5%. This fact makes u ±2u XRD pro®les extremely sensitive to any changes occurring in the interface regions. Structural investigations reported a substantial increase in hardness properties of Ag(001)/ Fe(001) multilayers [14], while X-ray diffraction measurements were used to investigate the structure and solid-state reactions of laser-deposited and sputtered Ag/Fe multilayers [15]. Concerning the magnetic properties of the Ag/Fe system, it was reported that the Fe magnetic moments may be considerably enhanced compared to the bulk value [16,17]. With regard to interlayer magnetic coupling effects, the have been several papers describing the simultaneous presence of bilinear and biquadratic exchange coupling [18,19]. Recently GMR in sputtered Ag/Fe multilayers and its anomalous temperature dependence were presented, suggesting the presence of interfacial superparamagneticlike spins [20]. Finally, the transition from in-plane to outof-plane magnetization was shown to have an interesting relaxation behaviour [21]. A detailed understanding of these physical properties depends critically on a good insight in the sample quality and, in particular, on the interface structure. It is, therefore, the aim of this paper to study in detail the growth, layer structure, and interface roughness of Ag/Fe superlattices. Different complementary methods have been employed to achieve this goal: Rutherford backscattering and channeling
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(00)00888-9
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spectroscopy (RBS/C), atomic force microscopy (AFM), re¯ection high-energy electron diffraction (RHEED) and X-ray diffraction (XRD). The Ag/Fe multilayers are a test case in order to show that the different depth and lateral resolutions offered by these characterization methods contribute to a better understanding of the multilayer quality. The structure and interface modi®cation of Ag/Fe superlattices caused by ion irradiation and annealing treatments, as well as their in¯uence on transport and magnetic properties, are presented elsewhere [23,24]. 2. Experimental The Ag/Fe superlattices were prepared in a Riber MBE system (2 £ 10211 Torr base pressure) by sequential deposition of Ag and Fe from a Knudsen cell and an e-beam gun, respectively. The residual gas pressure during the evaporaÊ /s tion was 5 £ 10210 Torr. The evaporation rate of ,1 A was stabilized and controlled by a feedback system (using a quadrupole mass spectrometer) with an accuracy of 1%. All the samples were deposited onto MgO(001) substrates (obtained from Kelpin Co., Germany) held at room temperature. Before deposition the substrate was heated at 6008C for 10 min. If Ag is the ®rst layer grown on MgO, polycrystalline layers are produced (see Section 3.4); starting the growth on MgO by Fe leads to epitaxial layers. The notation [Ag(x)/Fe(y)]xN will be used throughout this paper for the multilayers consisting of N periods of silver and iron sublayers; x and y are thicknesses of Ag and Fe sublayers, respectively. In-situ 10 keV RHEED measurements were used to monitor the growth of the superlattice. The main advantages of RHEED are its simplicity and a large sensitivity to structural changes at the surface [25,26]. However, in order to extract more information about the roughness as well as the arrangement of atoms on the surface, whole RHEED patterns have been recorded and interpreted. In our system a regular Sony video camera was used. The spatial resolution on the RHEED ¯uorescent screen was about 0.08 mm, which is very small compared to the intrinsic width of a typical RHEED spot on the screen. Temporal resolution is limited by the refresh rate of the camera (0.02 s) and the speed of the frame-capture card in the PC (on order of 0.1 s), but again much faster than the changes which could occur in the RHEED pattern due to the ®lm growth (in that time we Ê of a deposited would typically deposit only about 0.1 A layer). Initial ex situ information concerning the composition, layer thickness, crystallinity and epitaxial orientation of the superlattices was obtained using 4He backscattering/ channeling spectrometry. From backscattering spectra taken with random beam incidence, the composition of the multilayer can be determined as a function of depth. When carefully aligning the a -beam, a channeling effect is
observed in directions perpendicular to the sample surface, as well as in off-normal crystal axes. In the ®rst geometry crystalline quality of the individual layers is obtained. In the latter geometry an estimate of the tetragonal distortion (determined by the elastic strain) of the layers can be deduced. An incident beam energy of 1.97 MeV and a scattering angle of either 1358 or 1558 were selected in order to obtain an optimal compromise between mass and depth resolution. Analysis of the spectra was done using the basic relations of backscattering spectrometry [27] and by comparison to RUMP simulations [28]. Scanning probe microscopy [29] has evolved into a very versatile and powerful tool for the investigation of the topography of thin ®lm surfaces. One of its variants, atomic force microscopy [30] (AFM) offers the advantage that it is also applicable to study the structure of non-conducting samples, although with a slightly smaller resolution than scanning tunneling microscopy. The initial stages of the growth process, granularity, and roughness of the layers can be imaged in great detail. AFM provides the additional advantage that the surface roughness can be measured directly as a function of the scan length, enabling a determination of the fractal dimension of the surface and the lateral roughness correlation length on the surface [31]. The AFM measurements were carried out using a Digital Instruments NanoScope III microscope at room temperature and in ambient atmosphere. All experiments were performed in the contact mode using 200-mm wide cantilevers with 0.12 N/m spring constant. Apart from recording the sample topology the root mean square (rms) surface roughness was measured in detail as a function of the lateral scan length using the built-in analysis software. X-ray diffraction is one of extensively applied techniques for the structure characterization of thin ®lms and superlattices. This technique is commonly used in the u ±2u geometry where the scattering vector is perpendicular to the sample surface and only `one-dimensional' information (in the growth direction) is obtained. Nevertheless, a speci®c superlattice XRD pro®le allows one to deduce some additional structural parameters by ®tting the measured intensity pro®les with model calculations [32±35]. In these models not only relative intensities of superlattice peaks and their positions are taken into account, but whole XRD pro®les including line pro®les are used to quantitatively determine lattice constants, disorder parameters, interface roughness, etc. However, it is necessary to keep in mind that only `one-dimensional' information is directly available and all other parameters are only estimated and deduced, and may vary from model to model. For this reason we have decided to use two different models based on different approaches but of course leading to the same goal ± the superlattice structure characterization. Both models have already been described in detail: one based on the analytical formula and re®nement (the SUPREX program [32]), the second based on a Monte Carlo method (the SLERF program [35]). The application of these two
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53
different models should provide us with the same structural parameters. The XRD measurements were carried out using a 12 kW Rigaku DMax rotating anode diffractometer with Ê ) and a thin ®lm attachment Cu Ka radiation (lx 1:5418 A goniometer with a post-sample graphite (0002) crystal monochromator in the Brag±Brentano con®guration. The source divergence slit was of 1/68 while a detector slit was of 0.6 mm. Samples were examined in both specular (small (0±158) and large (30±708) angle u ±2u geometry) and nonspecular (small- and large-angle v -scans, v ±2u offscans) conditions [36] in order to determine the superlattice period, the layering quality, the epitaxial relationships as well as deviations from the bulk lattice parameters. 3. Results and discussion A large amount of experimental data will be presented according to the characterization techniques used. First, the in-depth structure characterization using the RBS/C technique is described, after which the surface topography obtained by AFM is discussed. This last method allows characterization of the roughness of consecutive bilayers at different lateral length scales, which is impossible with the other methods. Therefore, we treat the image obtained from AFM as `reference-data' which chart the surface roughness as a function of the lateral length. The AFM measurements, however, are limited to Ag surfaces only, because the measurements were performed ex situ and the image of the Fe layers could be strongly affected by oxidation. The results obtained from RHEED concern Ag as well as Fe sublayers. Finally, the results from XRD are shown and structure parameters are determined. 3.1. Rutherford backscattering spectrometry Fig. 1 shows the experimental (circles) and simulated Ê )/Ag (solid line) backscattering spectra of an [Fe(145 A Ê )]x5 superlattice deposited on top of a MgO substrate. (220 A An incident He beam of 1.97 MeV is used, and the scattering angle of the detected particles is 1558. For the simulation, perfect interfaces between the various layers are assumed. The yield from the Ag (1.5±1.75 MeV) and Fe (1.25±1.5 MeV) signal drastically decreases when the incident He beam is aligned with the normal crystal axis of the MgO substrate (a phenomenon called channeling). The ratio of this aligned backscattering spectrum (dashed line in Fig. 1) to the spectrum measured with random beam incidence (circles) is referred to as the minimum yield for channeling, x min, and gives an indication of the crystal perfection of the thin ®lm structure: the lower x min, the lower the concentration of lattice imperfections. The value of this minimum yield is about xmin 13% in the top Fe layer and 20% in the top Ag layer, indicating a very good alignment of the multilayered structure. These minimum yield values markedly increase with the depth of the layers, both for Fe and Ag, up to values of about 60% in the bottom Fe layer and
Ê )/Fe(145 A Ê )]£5 Fig. 1. 97 MeV 4He backscattering spectra for the [Ag(220 A superlattice with random (circles) and MgOk001l aligned (dashed line) beam incidence, along with a RUMP simulation (solid line). The scattering angle of the detected particles was 1558.
50% in the bottom Ag layer. This means that the crystalline quality of the layers increases as more layers are grown. However, a small dechanneling contribution from mis®t dislocations (and other lattice imperfections), possibly present at the interfaces, cannot be excluded. The fact that the minimum yield results in a much higher value close to the substrate±superlattice interface, especially in the case of Fe, is believed to be due to the relatively large mis®t (~3%) between the MgO substrate and the ®rst iron layer. Between the various layers of the superlattice, the much smaller lattice mismatch (~0.8%) results in a much lower density of mis®t dislocations, and consequently in a lower defect density in the layers. Further proof of the epitaxial nature of the layers is obtained from the backscattering spectra taken with the incoming He beam aligned along the Agk011l axis, which is located at an angle of 458 with respect to the k001l normal axis (the geometry is schematically shown in the inset of Fig. 2). Due to this large tilt angle, the signal of the bottom Ag layer overlaps with the signal of the top Fe layer. Fig. 2 shows the spectrum for a Agk011l-aligned beam incidence (dashed line), along with a random spectrum taken while continuously rotating the sample azimuthally. Since the bcc lattice structure of Fe does not contain a major crystal axis in this direction, no signi®cant decrease of the backscattering yield is observed for the Fe signal. The slightly lower yield observed is due to so-called planar channeling along the Fe(110) plane. Hence, Fig. 2 illustrates a k011l axial channeling in Ag layers and a (011) planar channeling in Fe layers. Moreover, channeling is observed in the MgO substrate, indicating that the k011l Ag axis is aligned with the k011l MgO axis. This situation changes when the sample is rotated over 458 around the surface normal (spectra not shown): (011) planar channeling from the MgO substrate as well as from all Ag layers is observed (higher x min compared to the values shown in Fig. 2), whereas k011l axial channel-
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3.2. Atomic force microscopy
Ê )/Fe(145 Fig. 2. 1.97 MeV 4He backscattering spectra for the [Ag(220 A Ê )]£5 superlattice with random (circles) and MgO k011l aligned (dashed A line) beam incidence. The scattering angle of the detected particles was 1358.
ing is found for the Fe layers (lower x min values than those shown in Fig. 2). These observations prove that the Ag/Fe heterostructures are epitaxially oriented on the MgO substrate: the Ag layers are fully aligned with the MgO substrate whereas the Fe layers are rotated by 458. The exact position of the axes can be determined by measuring the backscattering yield as a function of the angle of incidence, i.e. by performing an angular scan. The minimum of the k011l scan for MgO is found at an angle c 45800 with respect to the k001l surface normal, as expected for this cubic lattice. On the other hand, the minima of the angular scans from the Ag layers are observed at c 45815, for all layers, indicating the presence of strain in these cubic lattices. From the value Dc 0815, a tetragonal distortion is derived, as 1T dk 2 d' =d' 0:52%. Assuming an isotropic in-plane stress distribution, the ratio between the perpendicular (1 ') and in-plane (1 k) strain can be estimated as ' 1 2n 1 k 1 12n where n is the Poisson coef®cient (nAg 0:37), and therefore 1' Ag 0:28%. Within the experimental uncertainties, a similar Dc value is measured for the Fe layers, suggesting the same tetragonal distortion is present throughout the multilayer. The possible errors are, however, larger for Fe than for Ag, since no corresponding substrate axis is found for the Fe measurement (cf. above), making a direct measurement of Dc impossible (therefore, in the case of Fe no quantitative analysis is done). Consequently, both the Fe and Ag layers are under tensile strain in the plane of the interfaces, which can be attributed to the relatively large mis®t between the MgO substrate and both superlattice components (,3%).
Fig. 3a shows a three-dimensional view of the surface Ê )/Fe(30 morphology of the Ag top layer of a [Ag(30 A Ê A)]£10 sample. The granular nature of the layers is clearly visible in this picture, from which an average grain size of Ê can be deduced. Although the top surface of a about 600 A single grain is smooth, there are rather deep valleys in between the grains and there can be considerable height differences between the surfaces of neighboring grains. The rms roughness measured over a 1 £ 1 mm 2 area is of the order of 2 nm. Fig. 3b shows a scan covering 1 mm 2 on the surface of a sample with 20 bilayers, with the same sublayers thicknesses as for the sample shown in Fig. 3a and grown under identical circumstances. The most obvious observation which can be made from this AFM image is the fact that the surface roughness is much smaller than for the sample with 10 bilayers. The qualitative observations discussed above can be analyzed in more detail by plotting the rms roughness data as a function of the lateral scan length, as shown in Fig. 4. For this purpose, the roughness of an area L £ L is averaged
Fig. 3. Atomic force microscopy topographs showing three-dimensional Ê )/Fe(30 A Ê )]£N views of 1 £ 1 mm 2 areas on the surface of the [Ag(30 A superlattices with N 10 (a) and N 20 (b). Note the difference between the vertical scales in a and b.
G. Gladyszewski et al. / Thin Solid Films 366 (2000) 51±62
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reciprocal lattice points; the patterns are comparable to those obtained in transmission electron microscopy. Experimentally observed RHEED patterns are usually the superposition of these two cases. Fig. 6 shows the RHEED patterns which were taken after the growth of the ®rst, the second and the 20th Ag and Fe layers, respectively. The surface of the ®rst Fe layer is rather rough because we observe discrete diffraction spots due to electrons which feel the three dimensional periodicity of the lattice when they are transmitted through protrusions on the rough surface. The lateral island size can be roughly estimated by the simple kinematic theory of diffraction [37]. The one-dimensional diffracted intensity pro®le I(kx) is written as the so-called Laue function 2 Nakx sin 2 2 I kx akx sin2 2 Fig. 4. Evolution of the rms roughness obtained from the AFM data as a Ê )/Fe(30 A Ê )]£N multilayers function of the scan length L for the [Ag(30 A with N 10 (circles) and N 20 (squares).
over 10 different random positions on the sample surface in order to minimize the in¯uence of local topographic variations. The difference in overall roughness values between the N 10 and N 20 sample is quite clear from Fig. 4. For both samples an increase of the rms roughness with increasing scan length can be observed, re¯ecting the different roughness regimes which are probed by the AFM. For very small scan lengths L, the rms roughness is mainly determined by the surface quality of a single grain; for large scan lengths the height differences between adjacent grains are more in¯uential and cause an increase of the rms roughness. It should also be noted that the rms roughness of the N 10 sample already reaches its saturation value for scan lengths of about 300 nm, while the roughness of the sample with 20 bilayers does not yet reach full saturation even for scan lengths of 12 mm. This indicates that the lateral roughness correlation length is considerably larger in the N 20 sample than in the N 10 sample.
where kx is the scattering vector component, a is the atomic row spacing, and N is the number of atomic rows in the island in the considered direction. Strong diffraction peaks appear when kx 2ph=a, where h is an integer. The distance between the neighboring diffraction peaks is equal to 2p=a. The full width at half maximum (FWHM) of the diffraction peak is roughly equal to 2p=Na. The
3.3. Re¯ection high-energy electron diffraction RHEED patterns taken after the deposition of each Fe(30 Ê ) and Ag(30 A Ê ) layer indicate that Fe and Ag grow with the A well known epitaxial relationship of Ag(001)k100l// Fe(001)k110l//MgO(001)k100l. A schematic picture of the RHEED pattern to be expected in the present geometry is depicted in Fig. 5. If a surface is ¯at, the directions in which electrons are re¯ected are determined by cross sections between the Ewald sphere and the reciprocal lattice rods, so the diffraction spots align on semicircles centered on the shadow edge. On the other hand, when the surface is rough the diffractions are determined by the Ewald sphere and
Fig. 5. Schematic picture for interpretation of the RHEED pattern from the Ag and Fe (001) surface. The incident azimuth corresponds to the k100l for Ag and k110l direction for Fe. Positions of the spots corresponding to the transmission diffraction are indicated as solid and open circles for Ag and Fe, respectively. Cross sections between the 0th Laue circle and twodimensional reciprocal lattice rods characteristic for the re¯ection diffraction are indicated as crosses.
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Fig. 6. RHEED patterns measured during the growth of the Ag/Fe multilayer after the ®rst Ag layer (a), the second Ag layer (b), the 20th Ag layer (c), the ®rst Fe layer (d), the second Fe layer (e) and the 20th Fe layer (f).
number of atomic rows N which contribute to the diffraction can be deduced from the ratio of the distance between the neighboring diffraction peaks to the FWHM of the peak. In our experiment the width of a diffraction spot after the ®rst Fe layer deposition is about one-tenth of the distance to the next spot, which means N < 10. The k110l atomic rows of Ê . The size of the Fe islands can be Fe are separated by 2.02 A Ê . One can see also diffractherefore estimated as about 20 A tion spots due to the transmission for the ®rst Ag layer, but the positions of the spots move because of the different (001) plane interlayer distances of Fe and Ag. Such diffraction spots are still seen for the second Fe and Ag layers but the intensities are reduced. No diffraction spot due to the transmission of the electron beams is observed in the RHEED pattern for the 20th Ag layer, which indicates the surface has become two-dimensional. For the Fe layer nonzero intensities still remain observable at the position of the three-dimensional diffraction spots, even after the growth of the 20th layer, although the streak pattern indicates that the surface is much ¯atter than in the initial stages. Figs. 7 and 8 show changes in the intensity distribution along (00) and (01) streaks for Ag and Fe, respectively. In Fig. 7a one can see the largest peak shifts towards the shadow edge as the ®lm grows. The intensity at the (004) diffraction spot position decreases and the intensity of the specular beam increases. The contributions of the (004) diffraction spot and of the specular beam to the large peak are not clearly separated because the incident angle of the beam is close to the in-phase condition. Therefore we cannot unambiguously say whether the shift of the peak is due to the increase of the intensity of the specular beam or is due to the change of the Ag interplanar distance. One can also see the small peak from the (006) diffraction spot vanishing as the ®lm grows. This indicates also that a momentary Ag
Fig. 7. Intensity distribution along the (00) (a) and (01) (b) streaks of Ag surface measured for different numbers N of grown layers.
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Fig. 8. Intensity distribution along the (00) (a) and (01) (b) streaks for Fe surface measured for different numbers N of grown layers.
surface tends to two-dimensionality. Flattening of the surface is more clearly recognized by a change of the intensity distribution along the (01) streak in Fig. 7b. It is clear that the (024) and (026) diffraction spots vanish and the intensity increases near the crossing point between the zero Laue circle and the (01) streak, which is close to the shadow edge. In Fig. 8 the (004) and (114) diffraction spots from the Fe surface disappear as the ®lm grows. The peaks from the (002) and (112) diffraction shift towards the shadow edge after growth of the third layer. This is probably due to an expansion of the interplanar distance by relaxation of the structure. In order to evaluate the changes of the surface roughness, we introduce a simple qualitative parameter, R I b =I s . In the case of Fe, Ib is the intensity at the (002) diffraction spot and Is is the intensity at the point where the specular beam is expected; in the case of Ag, Ib is the intensity at the (024) diffraction spot and Is is the intensity near the cross section between zero Laue circle and the (01) streak for Ag. We choose the different de®nition of R for Ag from that for Fe because the specular beam and the (004) diffraction spot for Ag are too close in position to distinguish the individual intensities. Although the de®nitions of R for Fe and Ag are different, one can still discuss the surface roughness qualitatively using R, because the diffraction spots related to the Laue circles change their intensities having positive relations among each other as the surface roughness changes and so do the three dimensional diffraction spots. As shown in Fig. 9, an exponential decay of R for Ag indicates that smoothening of the Ag surface is more pronounced in the ®rst few bilayers. The growing surface of the Ag layer is ¯attened as more bilayers are grown. For Fe the value of R
increases gradually after an initial large decrease, which means that the Fe surface is ¯attest in the second or third layer and is gradually roughened afterwards. This can be explained as follows. The ®rst Fe layer on the MgO substrate is considered to be much rougher than those on the Ag layers from a comparison between the surface energy differences between Fe and MgO, and between Fe and Ag. The surface energies of Fe, Ag, and MgO are 2.939, 1.302,
Fig. 9. Changes of the roughness parameter R I b =I s observed for different numbers of grown layers. Larger values of R corresponds to a rougher surface.
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Ê )/Fe(5 A Ê )]£20 Fig. 10. Large-angle u ±2u XRD pro®les of the [Ag(50 A Ê )/Fe(15 A Ê )]£20 superlattice (b). superlattice (a) and the [Ag(50 A
and 1.15 J/m 2 [38,39], respectively. The roughness of Fe layers decreases until smoothing by Ag layers mostly compensates the initial large Fe roughness. Step density on Ag layers seems to play an essential role in the roughness increase of the successive Fe layers. The separation between Fe islands grown on a ¯at Fe substrate with micrometer wide terraces at around room temperature is about 5 nm [40]. The distance between Cr islands grown on a Ag(100) substrate at room temperature is also several nanometers [41]. Fe on a Ag layer seems to have a similar nucleation density if terraces of the Ag layer are wide enough. If the terrace width is smaller than this, step density determines the nucleation density and the island size, because steps provide nucleation sites. The terrace width on the ®rst few Ag layers is considered to be apparently smaller than several nanometers because the island size of the ®rst Fe layer is estimated as a few nanometers by RHEED. The size of three-dimensional islands of Fe is con®ned by the Ag steps in the beginning. As the number of bilayers increases and the Ag surface becomes ¯atter, the nucleation density of Fe decreases and the island size increases both laterally and vertically, which is considered to be observed as the increase of R in the RHEED measurement. We conclude from the RHEED measurements that the growth of Fe roughens the surface, but that deposition of Ag ¯attens the surface. The surface becomes ¯atter as more bilayers are grown.
parameters to obtain high quality epitaxial samples is the minimum sublayer thickness. We therefore prepared samples with a ®xed thickness of one material and different thicknesses of the second. Fig. 10 shows XRD pro®les of Ê )/Fe(x)]£20 superlattices. For a small Fe sublayer [Ag(50 A thickness (see Fig. 10a) the multilayers grow with closepacked Ag(111) and Fe(011) planes parallel to the substrate. In such a case the in-plane lattice mismatch in the Agk110l/ Fek100l direction is very small and equal to 0.8%, but in the direction it is rather large and equal to Agk1 12l/Fek0 11l 21%, preventing epitaxial multilayer growth and therefore only textured polycrystalline multilayers can be grown. For thicker Fe sublayers, however, Ag(001)//Fe(001) epitaxy becomes possible. In another set of samples we ®xed the Ê and prepared samples with Fe sublayer thickness at 20 A different Ag sublayer thicknesses. Fig. 11 shows the XRD Ê )]£20 superlattices. For very thin pro®le of [Ag(x)/Fe(20 A Ag layers the superlattice satellites are not resolved, leading to the conclusion that the Ag/Fe interfaces are too rough and Ê epitaxial growth only for Ag sublayers thicker than 10A occurs. Quite an unusual (for metallic superlattices) epitaxÊ )/Fe(70 A Ê )]£10 ial quality has been reached for the [Ag(500 A multilayer shown in Fig. 12. For such large superlattice Ê ) the satellite peaks are periods L (in this case L 570 A usually not resolved. As shown in the inset of Fig. 12, the satellite peaks do appear and point to a very high layering quality. The asymmetric X-ray diffraction measurements were performed for the Ag(113) and Fe(112) planes. First, the corresponding v ,2u conditions were set and then the sample was turned around the axis perpendicular to the ®lm. When one of the Ag(113) family planes (or (112) planes in the case of the iron) satis®ed the Bragg condition a drastic increase
3.4. X-ray diffraction X-ray diffraction measurements allow to optimize the conditions of the superlattice growth. One of the critical
Ê )]£20 superFig. 11. Large-angle u ±2u XRD pro®les of the [Ag(x)/Fe(20 A Ê (a), x 10 A Ê (b), x 15 A Ê (c) and x 20 A Ê (d). lattices for x 5 A
G. Gladyszewski et al. / Thin Solid Films 366 (2000) 51±62
Ê )/Fe(70 A Ê )]£10 Fig. 12. Large-angle u ±2u XRD pro®le of the [Ag(500 A superlattice. The satellite peaks are shown in the inset.
of diffracted intensity was observed, proving a high epitaxial quality of the samples. For the detailed investigation of the interface roughness, interdiffusion, and other structure parameters we have Ê )/Fe(18.5 A Ê )]£20 superlattice sample chosen the [Ag(25 A with the XRD pro®les shown in Fig. 13. Small angle XRD peaks (Fig. 13a) are very sharp and indicate smooth interfaces without interdiffusion and highly ordered at the long range scale. The peak positions allow to determine the Ê. multilayer period L 44 A The small angle rocking curve taken around the second order peak (Fig. 13a, inset) is very sharp and indicates that the ®lm is well oriented, parallel to the substrate. The largeangle XRD pro®le (Fig. 13b) reveals well-de®ned sharp
Fig. 13. Small- (a) and large-angle (b) u ±2u XRD pro®le of the [Ag(25.5 Ê )/Fe(18.5 A Ê )]£20 superlattice. In the insets small- and large-angle rocking A scans performed for the peaks positions indicated with arrows are shown.
59
satellite peaks. Only the peak at 2u 66:98 has a nearly twice as large half-width as the others. However, a largeangle rocking scan shows clearly that this peak consists in fact of two different peaks: one is a superlattice peak (with a rocking scan half-width ,18) and the second is a `forbidden' MgO(003) peak (with a rocking scan half-width ,0.188). The appearance of a `forbidden' peak may take place also for other monocrystalline substrates [42,43]. Note that the intensity of this `forbidden' peak is three orders of magnitude lower than the MgO(002) peak. To extract quantitative information about the superlattice structure we have used two different models which allow us to determine independently structural parameters such as the number of monolayers in the superlattice unit cell, interplanar distances of each material, rms roughness of the interface, possible interdiffused interface thickness, average grain size in the growth direction, etc. First we have used the SUPREX program. A ®tting procedure available in this program is very ef®cient in determining the interplanar distances which do not need to be exactly the same as in the bulk materials. The average number of Ag and Fe monolayers in the superlattice unit cell, nAg and nFe, as well as the interdiffused interface thickness and other structural parameters were also estimated. The in¯uence of the MgO(002) peak (2u 43:98) made it impossible, however, to ®t the whole pro®le because the substrate peak had nearly the same position as the most intense superlattice satellite. The best ®t to the experimental pro®le is shown in Fig. 14a and was obtained with the parameters given in Table 1. To avoid the in¯uence of the `forbidden' MgO(003) peak the experimental large-angle XRD pro®le was measured as a 0.38 off-scan. In such a case (see the inset in Fig. 13) it is still possible to measure a superlattice pro®le whereas MgO(003) is out of the specular condition. However, it was not possible to completely avoid the presence of the MgO(002) peak because this peak is much more intense than MgO(003). Therefore during the ®tting procedure the range of the XRD pro®le which coincides with the substrate peak was not taken into account. The SUPREX program allows one to use in the ®tting procedure many different structural parameters, but we stress that in this work their number was restricted to a minimum. The SLERF program does not contain a ®tting procedure; therefore it is necessary to determine some of the parameters in another way or to change their values and to look for the best agreement between simulated and experimental pro®les. As a matter of fact such parameters like average numbers of monolayers nAg, nFe, standard deviations of number of monolayers sig nAg, sig nFe and interdiffused interface thickness s init are rather easy to ®nd, because they all have their particular in¯uence on the XRD pro®le. The interplanar distances dAg and dFe are more dif®cult to determine, because changing slightly nAg and nFe it is always possible to get the same L for considerably different values of dAg and dFe. The exact value of the limited grain size Dg in the growth direction (described by a Gaussian distribution with standard devia-
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also given in Table 1 and the corresponding XRD pro®les are shown in Fig. 14b. Both programs give nearly perfect ®ts to the experimental pro®le and the obtained structure parameters are very similar. In both cases the interplanar distances are slightly smaller than those for the bulk materials (as suggested by RBS channeling measurements). Also, the average numbers of monolayers as well as the superlattice period are very close. There are, however, also some differences. The SUPREX program suggests single crystal superlattice growth, whereas the Monte Carlo simulation provides a better agreement of the peak half-widths with the experimental pro®le if we assume that the superlattice also consists of very large well-oriented in-plane and out-ofplane columnar grains, with an average thickness smaller than the total thickness of the ®lm. The existence of such `grains' cannot be con®rmed nor ruled out by any of the methods used in this work. High-resolution transmission electron microscopy (HRTEM) studies could be interesting to shed light on this problem. For both models the standard deviations of number of monolayers are similar, very small, and sig nAg , sig nFe. These parameters are not only related to the ¯uctuation of the number of monolayers considered in the growth direction, but also with height differences between interfaces when crossing from one column to another in-plane [44]. Therefore, the fact that sig nAg , sig nFe may indicate that the long-range rms roughness of Ag interfaces is smaller than that of Fe. Also s init has small values that indicate that only two monolayers are initially intermixed. However, this result may be also interpreted as a maximum two monolayers short-range rms roughness, because for X-rays it is dif®cult to distinguish between an interdiffused and a rough interface considered inside one coherent crystal [45]. Table 1 Ê )/Fe(18.5 A Ê )]£20 superlattice Structural parameters of the [Ag(25.5 A obtained from the SUPREX [32] and the SLERF [35] programs
Ê )/Fe(18.5 A Ê )]£20 Fig. 14. Large-angle u ±2u XRD pro®le of the [Ag(25.5 A superlattice. Together with the experimental scans (circles) the pro®les obtained from the SUPREX (a) and SLERF (b) model calculations are shown.
tion sig Dg) is also not easy to determine because ¯uctuations of sublayer thickness have similar in¯uence on XRD pro®les. We did not put in the interplanar distances derived from the SUPREX ®tting procedure because we wanted to avoid any inter-model in¯uences. Therefore, during the interpretation of the XRD pro®le using the SLERF program the structure parameters were optimized independently in order to get the best agreement between experimental and simulated pro®les. The parameters estimated in this way are
Parameter
SUPREX
SLERF
Ê) dAg (A Ê) dFe (A nAg (ML) nFe (ML) sig nAg (ML) sig nFe (ML) Ê) dint (A Ê) Dg (A Ê) sig Dg (A s init (ML) Ê) L (A
2.0407 1.4311 12.54 12.87 0.34 0.46 1.7359 a 880 b ± 2.36 c 44.01
2.0356 1.4270 12.60 12.87 0.3 0.4 1.7313 a 260 105 2.1 c 44.01
a
Fixed parameter dint dAg 1 dFe =2. Columnar growth is assumed in the model. Then the average grain size Dg is set to be equal to the total ®lm thickness. c The SUPREX program considers a linear shape of the interface, whereas the SLERF program assumes `an error function' shape of the interface. Therefore the latter takes into account the distance between the 84% and 16% concentrations of one of the elements. b
G. Gladyszewski et al. / Thin Solid Films 366 (2000) 51±62
Fig. 15. Two hypothetical surfaces having the same rms roughness, but different lateral dimensions of terraces. A 3D RHEED picture would be observed for surface a, and 2D for surface b.
In presenting the experimental data we did not try to correlate them. It is clear, however, that they do not simply provide a single and consistent image of the superlattice structure. The RBS/C and XRD data are characteristic for high-quality epitaxial superlattices. Both methods provide similar information about the interplanar distances. From RBS measurements the perpendicular distortion of Ag layer 1' Ag 0:28% can be calculated. This value is very close to that derived from XRD - averaging dAg parameters obtained from the SUPREX and the SLERF programs leads to 1' Ag 0:25%. At the same time RHEED and AFM provide ample evidence for a three-dimensional growth character and rather rough interlayer surfaces. In the interpretation of these results it is important to address the issue of the depth and lateral resolution inherent to the used techniques, i.e. how large is the volume from which we gather structural information. AFM is the only method which explicitly yields roughness data as a function of lateral length scale. A drawback is, of course, that AFM is only sensitive to the surface of the layers, which does not necessarily need to be the same as the interfaces buried in the superlattice. RHEED is generally assumed to make an average over a Ê , but this size depends on the lateral scale of about 1000 A dimensions of the terraces formed on the sample surface. It is also a misconception to associate three-dimensional (3D) and 2D growth modes observed in RHEED patterns with rough and smooth surfaces, respectively. The observed 3D character of Fe growth and 2D character of Ag growth does not imply that Fe is automatically rougher than Ag. This is illustrated by the two hypothetical surfaces shown in Fig. 15, which both have the same rms roughness, but nevertheless would produce two distinctly different RHEED pictures. In the case of surface (a) transmission electron beam diffraction, and hence a 3D picture, would occur via small short range terraces. The large terraces present at
61
surface (b) would give rise to 2D RHEED patterns due to the fact that the electron beam cannot traverse barriers [46] Ê . It remains, however, virtually impossible wider than 100 A to obtain quantitative information from the RHEED data alone. X-ray diffraction has the important feature that it makes an average over all interfaces. Recent work clearly showed that large-angle XRD measurements allow to characterize the interface roughness on a scale limited to the lateral dimension of individual columnar grains [44,47]. Height differences between different grains do not contribute to the probed short range interface roughness. This explains why a 3D growth as seen in RHEED does not necessarily exclude the existence of an excellent large-angle XRD pro®le; it is suf®cient that the superlattice is well developed within each of the islands. Keeping this in mind, a consistent picture does emerge when we compare the AFM, RHEED and XRD results on Ê average grain the common lateral length scale, i.e. the 600 A dimension. From the AFM data we derive a roughness Ê depending on the number of ranging between 1.5 and 5 A bilayers, while ®ttings of the XRD data suggest that the rms roughness inside one coherent grain may be equal or smaller Ê. than 3.7 A 4. Conclusions Finally, we can construct the following image of the studied Ag/Fe multilayers: From the very beginning the layers grow with the Ag(001)k100l//Fe(001)k110l// MgO(001)k100l epitaxial relationship. The height differences between different crystals are reduced as more layers are grown. Inside the columns the multilayer structure corresponds to highly ordered layers and reveals the relatively small interface roughness. Both the Fe and Ag layers are tensely strained in-plane. Due to the fact that RHEED patterns typical for 3D growth were observed for Fe and 2D for Ag, we may conclude that a momentary surface during the multilayer deposition grows with large Ag terraces and small Fe islands. The rms roughness, however, is probably Ê as obtained from ®tting similar and not larger than 3.7 A XRD pro®les. Each method provides information in its characteristic length scale and the conclusions drawn from them should not be extended to all scales. Therefore, we see that basing only on one of the methods it could not be possible to characterize the structure properly. Combining the four techniques RBS/C, AFM, RHEED and XRD have allowed us to characterize the structure of the Ag/Fe superlattices in detail. Acknowledgements This work was ®nancially supported by the Belgian Concerted Action and the Belgian Interuniversity Attraction Poles Programs. K.M. is a Research Fellow of the Katho-
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lieke Universiteit Leuven. K.T. is a Postdoctoral Researcher of the Fund for Scienti®c Research ± Flanders, Belgium (F.W.D.). E.K. is supported by the Flemish Institute for the promotion of research in industry (I.W.T.). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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