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Epitaxy of fcc and bcc Co, Ni, and Cu studied by X-ray photoelectron diffraction
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Surface Science North-Holland
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Epitaxy of fee and bee Co, Ni, and Cu studied by X-ray photoelectron diffraction J. Zhang, Z.-L. Han, S. Varma Department of Physics, University of Wisconsin-Milwaukee, 1900 East Kenwood Bhld., Milwaukee, WI 53211, USA
and B.P. Tonner Synchrotron Radiation Center, University of Wisconsin-Madison, Stoughton, WI 53589, USA Received
16 March
1993, accepted
for publication
20 March
1993
The structures of epitaxial transition-metal films with thicknesses of only a few monolayers were determined by X-ray photoemission diffraction (XPD) techniques. Ni ultrathin films were studied on two Cu single-crystal surfaces, and Cu/Ni multilayers (or “sandwich” structures) were also grown. On Cu(lOO), the initial Ni epitaxy is found to result in expansion of the Ni lattice constant to achieve lateral coherence with the substrate, along with a reduction in the Ni interplanar spacing perpendicular to the substrate, approximately maintaining a fixed Ni-Ni nearest-neighbor distance. This structure is a body-centered tetragonal distortion of the normal fcc(100) lattice. The behavior on Cu(l11) is different, in that the epitaxial Ni films retain the c/a axis relationship of bulk Ni(ll1). Films of Co, Ni, and Cu, which are normally fee or hcp crystals at room temperature, were grown on single-crystal Fe(100) substrates to induce bee ordering. Both Co and Ni grow as bcc(100) films on iron, but the Cu films are disordered. This is in contrast to epitaxy of Cu on strained layer Fe(100) films, which do support the growth of bee Cu(100). Modelling of ultrathin film XPD using multiple-scattering calculations was used for bond-length determinations with high accuracy, and for a determination of growth modes.
1. Introduction
Magnetic structures built up from epitaxial ultrathin films of transition metals are currently of great interest, due to the potential for applications in devices such as magnetic random-access memories, and magneto-resistive thin-film readwrite heads. In addition, there are still many open questions regarding fundamental magnetic properties of very thin films and multilayers of transition metals with local magnetic moments. The interplay between ferromagnetic ordering and crystallographic structure involves transitions between different lattice symmetries (such as fee to bee), and generally requires distinguishing be0039-6028/93/$06.00
0 1993 - Elsevier
Science
Publishers
tween lattice constants with accuracy better than 0.05 A. The techniques generally called X-ray photoemission (or photoelectron) diffraction (XPD), which includes X-ray-excited Auger electron diffraction, are particularly well suited to the study of the structure of very thin transition-metal films. There are at least two strong reasons for this. First, an XPD diffraction pattern or angular profile is collected from each chemical species in the sample independently. This can be very useful, say, for very thin layers of Ni on Cu which have nearly identical scattering power above about 100 eV. Secondly, the XPD pattern is a diffuse diffraction pattern, arising primarily from
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J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
the local structure of a few atomic shells surrounding the emitting atom, so that long-range order is not necessary. The physical origin of this feature is the localized nature of the electron emission process. A close similarity exists between XPD, electron-excited Auger electron diffraction (AED), and medium-energy electron diffraction (MEED) [l], but XPD and AED are chemical-state or atomic-species selective. Reviews of the experimental techniques used in X-ray photoemission diffraction (including Xray-excited Auger diffraction) are readily available [21. In our work, we use a multi-chamber ultra-high vacuum system, which includes a loadlocked growth chamber for epitaxial film growth, a digital-LEED system for complimentary structural studies of long-range order, and the dedicated XPD system, equipped with a twin-anode Mg/Al X-ray source [l]. In the present studies of metal-on-metal epitaxy, energy resolution of the electron detector is not a significant limitation, since only elemental separation of emission lines is needed to distinguish the overlayer from the substrate. However, angular resolution is of great importance, as the small, sharp interference effects that directly carry information about bond lengths can be easily smeared out in conventional XPS systems. Due to the Helmholtz-Lagrange law, the angular resolution of our electron lens improves along with the energy resolution, as the energy analyzer pass energy is decreased. The calculated angular resolution for 100 eV pass energy, as typically used, is f2” for the CuLVV Auger electron line at 914 eV [3]. This compares favorably with the measured fine-structure from Si(lOO), for example, where peaks with a full-width half-maximum of only 3” were seen at 1337 eV [41. In this paper we report on a series of related XPD determinations of structures of epitaxial first-row transition-metal ultrathin films. These include a study of Ni epitaxy on Cu(100) and Cu(ll1) surfaces, and a (Ill)-oriented Cu/Ni/Cu multilayer sandwich structure. We next discuss a comparative study of attempts to grow metastable bee films of Co, Ni, and Cu on different substrates, including strained-layer epitaxial films of Fe(lOO). Finally, we give an example of a quanti-
tative growth-mode study, as applied taxial growth of Co on Cu(ll1).
2. Tetragonal
to the epi-
Ni(100)
The bulk lattice constants of Cu (3.61 A) and Ni (3.52 A) differ by 2.5%, which is large enough to result in the formation of misfit dislocations in epitaxial films of Cu on Ni(lOO) after a critical layer thickness of only 15 A [5]. Chambers et al. [5] studied the Cu/Ni(lOO) system using angle-resolved Auger diffraction, and concluded that the copper overlayers adopted the lateral lattice constant of the substrate, and an expanded interlayer spacing that was a function vf film thickness up to a thickness of about 30 A. In the growth of multilayer “sandwiches” or superlattices of nickel and copper, the free surface is alternately a low free-energy (Cu) or high free-energy (Ni) surface, which may result in different growth modes at the two types of interface. Here we report results of a study of Ni epitaxy on Cu(lOO), using the XPD technique. As our reference structure, we use the XPD pattern from the single-crystal Cu(100) substrate. Fig. 1 shows the experimental Auger diffraction
Fig. 1. X-ray-excited LW Auger electron diffraction pattern from Cu(100) at high angular resolution (914 eV).
353
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
pattern from Cu(1001, taken with a higher angular resolution than in our previously published work [6]. This Auger pattern shows the rich and subtle structures that are present in the diffuse diffraction of photoelectrons. Many of the characteristics of these high-energy Auger diffraction patterns are also seen in quasi-elastic electron backscattering diffraction patterns (or “Kikuchi” patterns) [7], since the strongest features are dominated by final-state scattering and interference, and the influence of final-state angular momentum is small [S]. Diffraction patterns like those of fig. 1 are built up from individual polar-angle intensity plots at discrete azimuths spanning a segment of the hemisphere of possible emission angles. To reduce the effort of data collection, only those azimuths corresponding to unique directions are acquired, as shown in fig. 2 for a 10 ML film of Ni on Cu(lOO), and the complete diffraction pattern is then created by appropriate rotation and reflection operations. As shown in the example of Ni/Cu(lOO) (fig. 21, the locations of the high-symmetry azimuths ([loo] and [llO] in this case) are determined experimentally by taking additional polar plots surrounding each emission mirrorplane. This process also helps to eliminate possi-
Ni(lOML)
on
Cu(100)
A: n
,
Cu(100) I,
B: Ni film A,
+ <211>,
+ 410>
Fig. 3. Auger electron XPD intensity contour maps from a Cu(100) substrate reference crystal and from the 10 ML tetragonal Ni film. The symbols are located at angular positions corresponding to low-index crystallographic directions. The Ni-film intensity maxima are shifted towards higher angles (away from normal emission).
ble systematic errors from the symmetry operations. In the future, automated sample goniometers will facilitate full-hemisphere data collection and eliminate the need for symmetrizing the data. Iso-intensity contours created from the polar intensity profiles for the Cu(100) substrate and the Ni(100) 10 ML ultrathin film are found in fig. 3. The symbols locate the angular positions of low-index crystallographic directions of a bulk fee crystal, uncorrected for refraction effects (which are small on the scale of the symbols). It is characteristic of high kinetic energy XPD patterns that there is a close correspondence between intensity maxima and low-index crystallographic directions in real-space, as borne out by the Cu(100) data in fig. 3A [l]. This is a result of strong forward scattering at high energy, and is present in metals, semiconductors, and insulators
Dl.
Fig. 2. Polar-angle
intensity profiles of Ni Auger 10 ML Ni film on CutlOO).
XPD from a
The diffraction pattern from bulk Ni(100) would look very similar to bulk Cu(100) in fig. 3A (also see the NKllll case below). The ultrathin film of Ni(lOO), however, has a different diffraction pattern from that of the substrate, as shown in fig. 3B. The symbols on the Ni-film contour plot mark the same low-index directions as for the bulk Cu(100) contour (noting that forwardscattering peaks in all fee structures occur at the same angles). However, the location of the intensity maxima in the 10 ML Ni film data are uni-
_I.Zhang et al. / Epitaqv of fee and bee Co, Ni, and Cu studied by XPD
354 I
’
I 18.4”
0
’
I
’
I
45.0”
20 40 Polar Angie jdeg)
’ [loo]*
60
80
Fig. 4. XPD from the 10 ML Ni film, compared to a reference curve from single-crystal CuUOO), along the mirror-plane azimuths. Polar angle 4.5” on azimuth [loo] (top curves) corresponds to [llO] direction; polar angle 35.3” on azimuth [110] (bottom curves) corresponds to 11123direction.
formly shifted toward the perimeter of the diffraction pattern (see particularly the [l lo] and Ill21 maxima). This shift towards higher polar-angle (away from the sample normal) is emphasized in the polar plots for the two mirror-plane azimuths, found in fig. 4. The polar plot data is shown here (fig. 4) without correction for refraction, so we will consider primarily relative comparisons between the Cu and Ni diffraction profiles. The overall shape, number of intensity maxima, and relative peak intensities are similar between the single-crystal Cu(100) and the Ni epitaxial film data. The high intensity of the XPD features shows that the Ni film is well ordered, and the similarity in peak positions and shapes shows that the structure of the Ni film can be viewed as a distortion of the fee lattice structure of the substrate. There is a consistent displacement of the diffraction features from the Ni towards higher polar angle, along the [loo] azimuth near 45” ((110) direction), and near 35.3” and 54.7” in the (1101 azimuth. This is a direct result of lattice matching of the Ni film to the Cu substrate, in
the interface plane. This requires an expansion of the Ni lattice constant for the film, relative to bulk Ni. In response to this expansion, the Ni film interlayer spacing contracts, causing a shift of the peak positions towards higher polar angle. We can identify the internuclear axes that are primarily responsible for the intensity maxima at 45” along [loo], and at 35.3” and 54.7” along [llO]. We measure the angular displacement of the peaks in the Ni film, relative to that of bulk Cu, and use this displacement to determine the interlayer spacing and nearest-neighbor distance in the Ni film directly from geometric arguments. The polar-angle plots were collected with 0.5” step sizes, and with angular resolution below -&2”. Peak shifts can be determined easily to within a precision of 0.3” from the polar plots, and with higher precision by model calculations 191.A precision of 0.3” in the present case corresponds to an interlayer spacing accuracy of 0.02 A. The experimentally determined interlayer spacing d perp for 10 Mb Ni/Cu(lOO) is found to, be dperp = 1.73 + 0.01 A, as compared to 1.76 A in bulk Ni, and 1.805 A in bulk Cu. Since the lattice constant of Ni parallel to the surface is that of bulk Cu, the reduction in Ni interlayer spacing relative to Cu produces a distorted fee structure which is referred to as body-centered tetragonal (bet). We can determine the nearest-neighbor distance in bet Ni/Cu(OOl) from the same geometrical procedure, and get a value cf rNN = 2.50 A, which is to be compared to 2.49 A in bulk fee Ni. The bet distortion can therefore be interpreted as Ni atoms behaving like hard-spheres maintaining a constant interatomic distance. As the spacing parallel to the interface is increased, the interlayer spacing decreases. The same hardsphere model expiains the bet distortion of Cu on Nif 100) [S].
3. Epitaxial Ni(ll1)
and Cu/Ni
multilayers
The cases of Cu/Ni(lOO) and Ni/Cu(lOOI film growth were both found to exhibit lateral coherence (at the interface), with a corresponding expansion or contraction of the interlayer spacing to maintain an approximately constant nearest-
355
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
neighbor spacing. In both cases a distorted fee lattice results with two inequivalent lattice parameters. This pattern did not continue for epitaxy along the (111) direction, however, as we found in a study of Ni/Cu(lll) films, and Cu/Ni/Cu(lll) multilayer structures. As before, a reference study of the diffraction pattern from a Ni(ll1) substrate was done, and is shown in fig. 5. This diffraction pattern is very similar to that of Cu(1 ll), which can be found in ref. [l]. The structure of epitaxial Ni(ll1) films on Cu(ll1) for film thicknesses of 5, 10, and 15 ML is summarized in the polar-angle XPD profiles shown in fig. 6. These polar plots are for the two azimuths that comprise the mirror-plane of the fee (111) surface, and the XPD profiles from substrate Cm11 1) and Ni(l11) are shown for reference. The major forward-scattering peaks are marked with vertical lines. Note that normal emission (0”) does not correspond to a forwardscattering maximum in fee (111) structures. The most obvious result evident from fig. 6 is the close similarity, even for small details such as the region around normal emission, between the diffraction patterns from these materials. It can immediately be concluded that epitaxial Ni on
Fig. 5. LW
Auger
electron XPD substrate.
pattern
from
a Ni(ll1)
I
I
I
I
I
I
I
o;Bo Polar
Angle
B (deg)
Fig. 6. Auger electron polar-angle intensity profiles for Ni films of varying thickness on Cu(1 ll), along with reference curves from Cu(ll1) and NKlll) substrates. The profiles are taken in an azimuth corresponding to the surface mirror-plane.
Cu(ll1) is also in an fee (111) stacking sequence, with the same orientation as the substrate (not a twinned interface). This is substantively different from Co epitaxy on Cu(lll), which instead shows a complex stacking sequence which is fee only for the first two layers [lo]. Unlike the Ni/Cu(lOO) case, however, there are no peak position shifts in Ni(l11) films relative to the Cu(ll1) substrate. Furthermore, the Ni ultrathin films have peak positions and peak shapes that are nearly indistinguishable from bulk Ni(ll1). There are significant changes in the peak intensities from the films as compared to the substrate, which is due to a progressive roughening of the film surface with thickness. Relying on the data of fig. 6 alone, with no additional information, it is only possible to determine that the ratio of the lattice constant normal to the surface (c axis) and parallel to the surface (a axis) is identical in the films to that of ideal fcc(ll1). Therefore, epitaxy of Ni on Cu(l11) does not produce a distorted fee structure. This differs not only from Ni on the Cu(100) surface, but also from other fee (111) systems such as Cu/Ir(lll) [91, which produces a distorted fcc(ll1) Cu film. We suggest that the Ni/Cu(lll) interfaces in these films are not coherent, lattice-matched interfaces, and that films from 5 ML thickness on are fully relaxed bulk Ni(ll1) structures.
.I. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
4. Metastable
epitaxial
bee Co(lOO), Ni(lOO), and
Cu(100)
-80
-60
-40
-20
0
20
40
60
80
Polar Angle (deg) Fig. 7. Comparison of XPD from a Cu overlayer in a Cu/Ni/Cu(lll) multilayer structure (0, and the XPD from the Ni middle layer in this structure (B). The curve for a 15 ML Ni/Cu(lll) film is also shown for reference (A).
We further investigated the structure of 3 ML Cu/15 ML Ni/Cu(lll) multilayers using XPD. One interesting aspect of the XPD technique is that both the outer Cu layers and the middle Ni film structure can be simultaneously and independently measured. This is illustrated in fig. 7, which shows the XPD results for a 15 ML NKlll) film on Cu(lll), in comparison to the Ni underlayer and Cu overlayer XPD curves for the multilayer “sandwich” structure. When the 15 ML Ni film is coated with 3 ML of Cu (curve B), the only change to the XPD profiles is a general reduction in peak intensity, which is a result of scattering through Cu layers which have less order than the Ni middle layer. The reduction in intensity is not due to simply inelastic attenuation, since this effect is explicitly removed by the data normalization procedure. The 15 ML Ni film completely attenuates the substrate Cu emission, so that all of the copper signal that is seen when the 3 ML overlayer is deposited comes from the overlayer itself. This overlayer also shows an fee (111) structure (see curve 0, but with reduced order compared to either the Cu(ll1) substrate (fig. 6) or the 15 ML Ni film on Cu(ll1) (compare also the 5 ML Ni film in fig. 6). From this data, it can be concluded that the entire structure, Cu/Ni/ Cu(1 11) is in an ideal abcabc . . . fee (111) stacking sequence.
Epitaxial growth is a powerful method for producing thin films of metals with non-equilibrium crystal structures. Of particular importance in magnetism are the bee metastable phases of the first-row transition elements, which have been the subject of several theoretical investigations using local-density functional methods [ll]. Consider an fcc(100) thin film. To transform this structure into a bee lattice, it can be uniaxially compressed along the surface normal (100) direction. Alternatively, the (100) axes parallel to the surface can be expanded, while simultaneously contracting the interlayer spacing along the surface normal. This is the approach used in attempts to grow bee metastable films of Co, Ni, and Cu. We have previously studied the epitaxy of Co and Fe on Ag(lOO), and Co on strained bee Fe(100) grown epitaxially on Ag(100) [12]. With a 45” rotation in orientation of the surface (100) directions, there is a close lattice match between the silver substrate bond lengths and bulk Fe(100). Using XPD, Fe was shown to be bcc(100) on AdlOO), but Co formed a body-centered tetragonal (bet) structure with lattice constants intermediate between fee and bee. Co did form bcc(100) films on strained Fe/Ag(lOO) templates. In this work, we attempted to grow bee metastable films directly on Fe(100) substrates, which have a slightly smaller lattice constant than the strained bee films of Fe/Ag(lOO). We performed XPD structure measurements on clean Fe(100) single crystals, and on Co, Ni, and Cu films grown on this substrate. All depositions were done at room temperature, and the substrate temperature was at all times kept below 400°C to avoid the bee to fee phase transition of bulk Fe(100). A range of film thicknesses were investigated ranging up to about 15 ML. The specific data reported here are for films of approximately 20 A thickness, corresponding to 1416 layers. The experimental results are shown in fig. 8, which has the XPD polar plots for the [loo] and [llO] bee azimuths. At the top of the figure is the
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD 80 R
60
40
20
Azimuth:bcc[lOO]
0
80
60
40
20
0
Azimuth:bcc[llO]
Fig. 8. XPD polar-angle profiles for epitaxy of Co, Ni, and Cu on Fe(100) substrates. Co and Ni exhibit high-quality XPD intensities, consistent with the formation of metastable bee epitaxial films for these materials. Cu, in contrast, shows little evidence of ordering.
data from the clean Fe(100) substrate. There are three major XPD peaks identified, which are due to the major low-index direction of the bee lattice. These are at normal emission (bee [OOl]), 45” along the [loo] azimuth, and 54.7” along the [llOl azimuth. There is no mistaking an fee structure for a bee one, as the peaks for fee would be at 54.7” instead of 45”, and 45” instead of 54.7” in the respective azimuths. From the figure, we immediately conclude that the Co and Ni films both adopt the bee (1001 structure. There is a great deal of similarity between the XPD curves for the Fe substrate, and the Co and Ni films, both along the low-index directions and for the additional secondary peak structures. For both the Co and Ni films, the magnitude of the XPD intensities are comparable to those from the single-crystal substrate, indicating a high degree of long-range order in these metastable films. The relative peak heights of the XPD structures in the epitaxial films are similar to those for the substrate. This implies that the films do not grossly deviate from flat overlayers. The situation for the Cu/Fe(lOO) is very different. As displayed, the Cu XPD pattern is nearly isotropic (no peak structures), indicating that there is no epitaxial relationship between the film and the substrate. This Cu film is either polycrystalline or highly disordered. For the Co and Ni
351
experiments, all depositions produced bee XPD patterns, independent of film thickness (up to the maximum studied). In the case of Cu, however, there were noticeable variations between depositions, indicating a sensitive dependence on growth conditions. In some cases, deposition at slightly elevated substrate temperatures (loo-200°C) produced XPD patterns with weak features due to a bee structure. In other cases, weak evidence for fee XPD peaks were seen. This suggests that further study of growth rates and substrate temperatures might uncover conditions under which Cu could be reliably grown as a bee structure on Fe(100). From earlier work using Ag(100) substrates, it is known that bee Cu can be reproducibly grown on strained-layer bee Fe/Ag(lOO) films [13]. A bet distortion from bee was found for Cu grown directly on the Ag(100) surface [141. However, the slight difference in lattice constant between Fe/Ag(lOO) and bulk Fe0001 surfaces is enough to prevent room-temperature bee growth of Cu/Fe(lOO). A very similar relationship was found in the prior study of bee metastable film growth of Co [12]. The bee Co structure formed for Co(100) grown on strained Fe/Ag(lOO) films, but bee Co could not be grown directly on AdlOO). The difference in lattice constant between Fe/Ag(lOO) and bulk Fe(100) is less than 2%, which highlights the importance of quantitative lattice constant measurements with high precision.
5. Growth-mode
simulations
In order to use XPD quantitatively for solving structures, it is necessary at some point to compare the experiment to a model calculation. This is true both to improve the accuracy of interpretation of the forward-scattering peaks, and to attempt to get direct information about bond lengths. The angular position of forward-scattering peaks are due to bond angles, and in themselves do not reveal the bond-length information needed for solving a structure. This information resides in the more subtle interference modulations in the XPD polar plots, which are directly
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
358
influenced by the final-state angular momentum and kinetic energy. An additional requirement for more advanced quantitative use of XPD data arises in studies of the growth modes of epitaxial films [El. In trying to distinguish between ideal layer-by-layer growth and more complex growth modes that involve the nucleation of three-dimensional islands, it is necessary to interpret the relative intensities of XPD features quantitatively, rather than simply locating the angular positions of peak maxima. A quantitative theory of XPD peak intensities must include multiple-scattering effects, which are very strong in the forward-scattering directions for epitaxial metal films. Multiple-scattering calculations using exact Green’s functions in a real-space cluster model have been very successful in accurately reproducing experimental XPD data from single-crystal substrates, for which many layers of atoms contribute to the diffraction pattern, and multiplescattering effects are large [8]. Although such exact calculations are highly successful in identifying the origin of XPD peak positions, shapes, and intensities, the calculations typically require substantial computation times that make it infeasible to engage in extensive searches of model structures with several varying parameters. We have therefore developed alternative, approximate scattering methods that retain the essential physical concepts necessary to correctly account for multiple scattering, but are considerably faster computationally since they use only approximate forms for the free-electron propagator. One of the methods is based on the separable Green’s function approximation using the formalism of Rehr and Albers [16,171. An effective, spherical-wave-corrected atomic scattering factor is constructed from the formula f&r,
r’>
=$(Zi+l)
eiSl sin 6,P,(i.?‘)c,(r)c,(r’),
I=0 (1)
where k is the electron wavenumber, atomic scattering phase-shift corrected
6, is the for finite
temperature, r and r’ are the vectors defining the scattering event at a particular atom, and the cI(r) are the spherical-wave correction factors [16,18]. In the forward direction (zero-scattering angle), this effective scattering factor is identical to the Rehr and Albers [3 X 31 matrix scattering factor method. At finite scattering angles, it is similar to the [l x 11 approximation, with the following modification. Separable approximations can have numerical instabilities at large kinetic energy, which is related to the approximation of the Bessel function that appears in the free-electron Green’s function where x = [Z(1+ l)/‘(/’ + l)/ ;;,,‘$$‘;hl’ en kr is small (nearest neighbors), and either 1 or I’ is large, the replacement of J,, with unity is invalid. To compensate for this problem, we place an upper bound (I,,,) on the angular momentum sum in fCfr, instead of relying on the decreasing size of t, = eiS/ sin S, to attenuate the high angular momentum terms. This “semi-empirical” approach to fefr is calibrated by performing calculations for small clusters of atoms using the f,rf method and exact calculations, adjusting the value of I,,, for best agreement (for detailed examples, see ref. [19]>. The scattering amplitude for a particular path, resulting in an electron travelling in the direction P, is given by eikrl
X $%A
t-27 t-3) eikrN
x
. . . -
rN
feff(rN,
rm>
epik.‘~~N,
(2)
where ri is the bond-length between the atom at the origin and the first scattering atom in the sequence, and rON is the vector from the origin to the terminal atom in the sequence. The final-state angular momentum appears in the spherical harmonic YL,,,where L = (I,m). IneIastic damping is included by introducing an imaginary component to the electron wavevector k. An additional approximation that is made for XPD at electron energies above a few hundred
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
eV is the “negligible back-scattering (NBS) approximation”, for which scattering paths with scattering angles above some maximum value are neglected. For cases such as the LVV Auger diffraction patterns of Co, Ni, Cu, and Fe, we find that a scattering angle of less than 90” is usually sufficient to reproduce all measurable features. If the atom cluster is visualized as being constructed from shells of atoms, this constraint is the same as only considering shell-to-shell multiple scattering in the forward direction, while neglecting intrashell multiple scattering. Finally, for Auger diffraction patterns, we use the s-wave final-state approximation to the angular momentum, since angular-momentum effects have been found to be small (though detectable) at high energy [Bl. Fig. 9 shows a comparison between the feff NBS calculation and a full multiple-scattering calculation by Xu and Van Hove [20], using the Taylor-series magnetic quantum number expansion method, for atomic clusters of nickel atoms and copper Auger electron emitters. The singlescattering calculations are identical, as expected, and the multiple-scattering calculations differ in only relatively minor details. The NBS path-formalism calculations have been found to work well for metal substrates and thin films [4,9,10], and for semiconductor substrates [21]. Some of the most important scattering effects that are used in determining a film growth mode by XPD can be seen in multiple-scattering calculations for chains of atoms, as shown in fig. 10 for a chain of copper atoms embedded in a uniform medium, simulating the [llO] forward-scattering direction in a Cu(100) single crystal. In a growthmode study, the intensity of forward-scattering peaks are compared as a function of film thickness, to determine the local coverage and geometry of (possible) islands in the film. As shown in fig. lOA, single-scattering calculations greatly overestimate the contribution of scattering from deep atoms, relative to those near the surface. Multiple-scattering effects limit the “visibility” of atoms along high-density chains to only a few layers (note, however, that some features in an XPD pattern from metals arise from as much as 10 layers deep).
(A)
rr 0
0
,& s
I” (W
.G
a
2
B (Cl 63.4” 1 2MLNi 1 MLCU
0
20 40 60
0 20 40 60 80
Polar Angle
Polar Angie
Fig. 9. Comparison of a forward-multiple-scattering spherical-wave approximation calculation (left), with full multiple-scattering calculations, using from ref. [20] the TS-MQNE approximation (right). (A) Single scattering, 8 atoms; (B) multiple scattering, 8 atoms; (Cl multiple scattering, 3 layers.
In the usual situation, it is the integrated intensity from several atomic layers that is measured (as opposed to an isolated buried layer), a case which is simulated for a chain in fig. 10B. Again, significant differences are seen between the single- and multiple-scattering calculations. The total intensity in the forward-scattering peak reaches a saturation value for chain lengths of only 4 atoms, which shows that the forwardscattering component of XPD is primarily a probe of the outer-layer structure of a film. The angular peak-width of the forward-scattering feature decreases in the multiple-scattering simulation at a faster rate than found in single-scattering. The intensity of XPD peaks along low-index directions, for both a substrate and an overlayer film of varying thickness, can be used to determine growth modes. In the simplest examples,
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
360
certain forward-scattering peaks only appear at a particular local coverage (say three layers), so that a growth mode can be established when the average coverage can be accurately determined by other means. We have calculated the rate of rise in XPD intensity along three directions for a Cu(ll1) substrate, and for a Co(l11) fee film of varying thickness. The calculation, which used an atomic cluster assuming ideal layer-by-layer
Co !2 0
Coverage
(ML)
Fig. 11. A growth-mode determination using XPD for epitaxy of Co on Cu(ll1). The theoretical curves (open symbols) are for an assumed ideal layer-by-layer growth mode. Solid symbols are experimental data. Significant deviations are seen for the overlayer emission (right); smaller effects are visible from the substrate (left).
B c E4 h 2 i 2 (4 -70
0 0
Angle
off
70
Normal
ti =: .r( E W
-70
@I
0
Angle
0
off
70
Normal
Fig. 10. Single- and multiple-scattering calculations for a chain of copper atoms embedded in a uniform medium. The chain is oriented 45” off the surface normal; the inter-nuclear distance is 2.55 A, and the mean free path 10 A. (A) Intensity from individual emitter atoms at the end of a chain; (B) sum of intensity for all emitters.
growth, is shown in fig. 11. The substrate forward-scattering intensities for all three directions show rather similar behavior, noting that the trivial inelastic loss attenuation is removed from the data before comparison. There are noticeable differences between directions for the overlayer, however. The thresholding behavior, for which a forward-scattering peak only is observed above a specific layer thickness, can be seen in the [112] direction calculation (open symbols). Notice as well how the XPD anisotropy saturates after only 4-5 monolayers along the [loo] and [llO] directions, but continues to rise along [112] which has a different atomic density. The growth of Co on Cu(ll1) turns out to be more complex than, say, Co on Cu(100) [lo]. Growth begins initially in fee stacking sequence, but hcp stacking faults begin to occur as early as the third layer. This unfortunately complicates the interpretation of the growth-mode curves of fig. 11. The substrate XPD features appear to follow the theoretical curves for up to 5 ML along the [loo] and [112] directions, but this should
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
probably be interpreted as indicating that the substrate diffraction features are not as reliable for growth-mode studies as the overlayer peaks. It is clear from the Co overlayer experimental diffraction data (filled symbols) that ideal fee layer-by-layer growth does not continue beyond the third layer.
6. Conclusion Structural studies of epitaxial layers using XPD at high kinetic energy benefit from several factors intrinsic to the technique, such as elemental and chemical-state specificity, and no requirement for long-range order. In addition, computational methods are available that yield excellent agreement between experiment and theory, in terms of absolute peak positions, intensities and lineshapes. The trend toward quantitative XPD analysis of ultrathin film and interface structure continues to show that XPD is capable of tetermining structures with an accuracy of 0.02 A, limited at this time in part by experimental angular smearing of XPD fine-structure.
Acknowledgement
This work was supported by the National Science Foundation through grant DMR-91-15987.
361
References
111Z.-L.
Han, S. Hardcastle, G.R. Harp, H. Li, X.-D. Wang, J. Zhang and B.P. Tonner, Surf. Sci. 258 (1991) 313. 121C.S. Fadley, in: Synchrotron Radiation Research: Advances in Surface Science, Ed. R.Z. Bachrach (Plenum, New York, 1990). Rev. Sci. t31 B.P. Tonner, Y.C. Chou and M.J. Robrecht, Instrum. 58 (1987) 1164. [41 B.P. Tonner, J. Zhang, X. Chen, Z.-L. Han, G.R. Harp and D.K. Saldin, J. Vat. Sci. Technol. B 10 (1992) 2082. b-1 S.A. Chambers, H.W. Chen, I.M. Vitomirov, S.B. Anderson and J.H. Weaver, Phys. Rev. B 33 (1986) 8810. [61 H. Li and B.P. Tonner, Phys. Rev. B 37 (1988) 3959. 171 G.R. Harp, D.K. Saldin and B.P. Tonner, Phys. Rev. Lett. 65 (1990) 1012. ml D.K. Saldin, G.R. Harp and B.P. Tonner, Phys. Rev. B 45 (1992) 9629. [91 B.P. Tonner, J. Zhang and Z.-L. Han, Appl. Surf. Sci. 70/71 (1993) 378. [lOI B.P. Tonner, Z.-L. Han and J. Zhang, Phys. Rev. B 47 (19931 9723. [Ill V.L. Moruzzi and P.M. Marcus, Phys. Rev. B 34 (1986) 1784; P.M. Marcus and V.L. Moruzzi, Solid State Commun. 55 (1985) 971. [12] H. Li and B.P. Tonner, Phys. Rev. B 40 (1989) 10241. [13] W.F. Egelhoff, Jr., I. Jacob, J.M. Rudd, J.R. Cochran and B. Heinrich, J. Vat. Sci. Technol. A 8 (1990) 1582. [14] D.T. Jiang, E.D. Crozier and B. Heinrich, Phys. Rev. B 44 (1991) 6401. [15] H. Li and B.P. Tonner, Surf. Sci. 237 (1990) 141. [16] J.J. Rehr and R.C. Albers, Phys. Rev. B 41 (1990) 8139. [17] A.P. Kaduwela, D.J. Friedmen and C.S. Fadley, J. Electron Spectrosc. Relat. Phenom. 57 (1991) 223. 1181 B.P. Tanner, Z.-L. Han, G.R. Harp and D.K. Saldin, Phys. Rev. B 43 (1991) 14423. [19] Z.-L. Han, PhD Thesis, University of WisconsinMilwaukee, unpublished (available from the authors). [20] M.-L. Xu and M.A. Van Hove, Surf. Sci. 207 (1989) 215. [21] J. Zhang and B.P. Tonner, to be published.
Surface Science North-Holland
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Epitaxy of fee and bee Co, Ni, and Cu studied by X-ray photoelectron diffraction J. Zhang, Z.-L. Han, S. Varma Department of Physics, University of Wisconsin-Milwaukee, 1900 East Kenwood Bhld., Milwaukee, WI 53211, USA
and B.P. Tonner Synchrotron Radiation Center, University of Wisconsin-Madison, Stoughton, WI 53589, USA Received
16 March
1993, accepted
for publication
20 March
1993
The structures of epitaxial transition-metal films with thicknesses of only a few monolayers were determined by X-ray photoemission diffraction (XPD) techniques. Ni ultrathin films were studied on two Cu single-crystal surfaces, and Cu/Ni multilayers (or “sandwich” structures) were also grown. On Cu(lOO), the initial Ni epitaxy is found to result in expansion of the Ni lattice constant to achieve lateral coherence with the substrate, along with a reduction in the Ni interplanar spacing perpendicular to the substrate, approximately maintaining a fixed Ni-Ni nearest-neighbor distance. This structure is a body-centered tetragonal distortion of the normal fcc(100) lattice. The behavior on Cu(l11) is different, in that the epitaxial Ni films retain the c/a axis relationship of bulk Ni(ll1). Films of Co, Ni, and Cu, which are normally fee or hcp crystals at room temperature, were grown on single-crystal Fe(100) substrates to induce bee ordering. Both Co and Ni grow as bcc(100) films on iron, but the Cu films are disordered. This is in contrast to epitaxy of Cu on strained layer Fe(100) films, which do support the growth of bee Cu(100). Modelling of ultrathin film XPD using multiple-scattering calculations was used for bond-length determinations with high accuracy, and for a determination of growth modes.
1. Introduction
Magnetic structures built up from epitaxial ultrathin films of transition metals are currently of great interest, due to the potential for applications in devices such as magnetic random-access memories, and magneto-resistive thin-film readwrite heads. In addition, there are still many open questions regarding fundamental magnetic properties of very thin films and multilayers of transition metals with local magnetic moments. The interplay between ferromagnetic ordering and crystallographic structure involves transitions between different lattice symmetries (such as fee to bee), and generally requires distinguishing be0039-6028/93/$06.00
0 1993 - Elsevier
Science
Publishers
tween lattice constants with accuracy better than 0.05 A. The techniques generally called X-ray photoemission (or photoelectron) diffraction (XPD), which includes X-ray-excited Auger electron diffraction, are particularly well suited to the study of the structure of very thin transition-metal films. There are at least two strong reasons for this. First, an XPD diffraction pattern or angular profile is collected from each chemical species in the sample independently. This can be very useful, say, for very thin layers of Ni on Cu which have nearly identical scattering power above about 100 eV. Secondly, the XPD pattern is a diffuse diffraction pattern, arising primarily from
B.V. All rights reserved
352
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
the local structure of a few atomic shells surrounding the emitting atom, so that long-range order is not necessary. The physical origin of this feature is the localized nature of the electron emission process. A close similarity exists between XPD, electron-excited Auger electron diffraction (AED), and medium-energy electron diffraction (MEED) [l], but XPD and AED are chemical-state or atomic-species selective. Reviews of the experimental techniques used in X-ray photoemission diffraction (including Xray-excited Auger diffraction) are readily available [21. In our work, we use a multi-chamber ultra-high vacuum system, which includes a loadlocked growth chamber for epitaxial film growth, a digital-LEED system for complimentary structural studies of long-range order, and the dedicated XPD system, equipped with a twin-anode Mg/Al X-ray source [l]. In the present studies of metal-on-metal epitaxy, energy resolution of the electron detector is not a significant limitation, since only elemental separation of emission lines is needed to distinguish the overlayer from the substrate. However, angular resolution is of great importance, as the small, sharp interference effects that directly carry information about bond lengths can be easily smeared out in conventional XPS systems. Due to the Helmholtz-Lagrange law, the angular resolution of our electron lens improves along with the energy resolution, as the energy analyzer pass energy is decreased. The calculated angular resolution for 100 eV pass energy, as typically used, is f2” for the CuLVV Auger electron line at 914 eV [3]. This compares favorably with the measured fine-structure from Si(lOO), for example, where peaks with a full-width half-maximum of only 3” were seen at 1337 eV [41. In this paper we report on a series of related XPD determinations of structures of epitaxial first-row transition-metal ultrathin films. These include a study of Ni epitaxy on Cu(100) and Cu(ll1) surfaces, and a (Ill)-oriented Cu/Ni/Cu multilayer sandwich structure. We next discuss a comparative study of attempts to grow metastable bee films of Co, Ni, and Cu on different substrates, including strained-layer epitaxial films of Fe(lOO). Finally, we give an example of a quanti-
tative growth-mode study, as applied taxial growth of Co on Cu(ll1).
2. Tetragonal
to the epi-
Ni(100)
The bulk lattice constants of Cu (3.61 A) and Ni (3.52 A) differ by 2.5%, which is large enough to result in the formation of misfit dislocations in epitaxial films of Cu on Ni(lOO) after a critical layer thickness of only 15 A [5]. Chambers et al. [5] studied the Cu/Ni(lOO) system using angle-resolved Auger diffraction, and concluded that the copper overlayers adopted the lateral lattice constant of the substrate, and an expanded interlayer spacing that was a function vf film thickness up to a thickness of about 30 A. In the growth of multilayer “sandwiches” or superlattices of nickel and copper, the free surface is alternately a low free-energy (Cu) or high free-energy (Ni) surface, which may result in different growth modes at the two types of interface. Here we report results of a study of Ni epitaxy on Cu(lOO), using the XPD technique. As our reference structure, we use the XPD pattern from the single-crystal Cu(100) substrate. Fig. 1 shows the experimental Auger diffraction
Fig. 1. X-ray-excited LW Auger electron diffraction pattern from Cu(100) at high angular resolution (914 eV).
353
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
pattern from Cu(1001, taken with a higher angular resolution than in our previously published work [6]. This Auger pattern shows the rich and subtle structures that are present in the diffuse diffraction of photoelectrons. Many of the characteristics of these high-energy Auger diffraction patterns are also seen in quasi-elastic electron backscattering diffraction patterns (or “Kikuchi” patterns) [7], since the strongest features are dominated by final-state scattering and interference, and the influence of final-state angular momentum is small [S]. Diffraction patterns like those of fig. 1 are built up from individual polar-angle intensity plots at discrete azimuths spanning a segment of the hemisphere of possible emission angles. To reduce the effort of data collection, only those azimuths corresponding to unique directions are acquired, as shown in fig. 2 for a 10 ML film of Ni on Cu(lOO), and the complete diffraction pattern is then created by appropriate rotation and reflection operations. As shown in the example of Ni/Cu(lOO) (fig. 21, the locations of the high-symmetry azimuths ([loo] and [llO] in this case) are determined experimentally by taking additional polar plots surrounding each emission mirrorplane. This process also helps to eliminate possi-
Ni(lOML)
on
Cu(100)
A: n
Cu(100) I
B: Ni film A
+ <211>,
+ 410>
Fig. 3. Auger electron XPD intensity contour maps from a Cu(100) substrate reference crystal and from the 10 ML tetragonal Ni film. The symbols are located at angular positions corresponding to low-index crystallographic directions. The Ni-film intensity maxima are shifted towards higher angles (away from normal emission).
ble systematic errors from the symmetry operations. In the future, automated sample goniometers will facilitate full-hemisphere data collection and eliminate the need for symmetrizing the data. Iso-intensity contours created from the polar intensity profiles for the Cu(100) substrate and the Ni(100) 10 ML ultrathin film are found in fig. 3. The symbols locate the angular positions of low-index crystallographic directions of a bulk fee crystal, uncorrected for refraction effects (which are small on the scale of the symbols). It is characteristic of high kinetic energy XPD patterns that there is a close correspondence between intensity maxima and low-index crystallographic directions in real-space, as borne out by the Cu(100) data in fig. 3A [l]. This is a result of strong forward scattering at high energy, and is present in metals, semiconductors, and insulators
Dl.
Fig. 2. Polar-angle
intensity profiles of Ni Auger 10 ML Ni film on CutlOO).
XPD from a
The diffraction pattern from bulk Ni(100) would look very similar to bulk Cu(100) in fig. 3A (also see the NKllll case below). The ultrathin film of Ni(lOO), however, has a different diffraction pattern from that of the substrate, as shown in fig. 3B. The symbols on the Ni-film contour plot mark the same low-index directions as for the bulk Cu(100) contour (noting that forwardscattering peaks in all fee structures occur at the same angles). However, the location of the intensity maxima in the 10 ML Ni film data are uni-
_I.Zhang et al. / Epitaqv of fee and bee Co, Ni, and Cu studied by XPD
354 I
’
I 18.4”
0
’
I
’
I
45.0”
20 40 Polar Angie jdeg)
’ [loo]*
60
80
Fig. 4. XPD from the 10 ML Ni film, compared to a reference curve from single-crystal CuUOO), along the mirror-plane azimuths. Polar angle 4.5” on azimuth [loo] (top curves) corresponds to [llO] direction; polar angle 35.3” on azimuth [110] (bottom curves) corresponds to 11123direction.
formly shifted toward the perimeter of the diffraction pattern (see particularly the [l lo] and Ill21 maxima). This shift towards higher polar-angle (away from the sample normal) is emphasized in the polar plots for the two mirror-plane azimuths, found in fig. 4. The polar plot data is shown here (fig. 4) without correction for refraction, so we will consider primarily relative comparisons between the Cu and Ni diffraction profiles. The overall shape, number of intensity maxima, and relative peak intensities are similar between the single-crystal Cu(100) and the Ni epitaxial film data. The high intensity of the XPD features shows that the Ni film is well ordered, and the similarity in peak positions and shapes shows that the structure of the Ni film can be viewed as a distortion of the fee lattice structure of the substrate. There is a consistent displacement of the diffraction features from the Ni towards higher polar angle, along the [loo] azimuth near 45” ((110) direction), and near 35.3” and 54.7” in the (1101 azimuth. This is a direct result of lattice matching of the Ni film to the Cu substrate, in
the interface plane. This requires an expansion of the Ni lattice constant for the film, relative to bulk Ni. In response to this expansion, the Ni film interlayer spacing contracts, causing a shift of the peak positions towards higher polar angle. We can identify the internuclear axes that are primarily responsible for the intensity maxima at 45” along [loo], and at 35.3” and 54.7” along [llO]. We measure the angular displacement of the peaks in the Ni film, relative to that of bulk Cu, and use this displacement to determine the interlayer spacing and nearest-neighbor distance in the Ni film directly from geometric arguments. The polar-angle plots were collected with 0.5” step sizes, and with angular resolution below -&2”. Peak shifts can be determined easily to within a precision of 0.3” from the polar plots, and with higher precision by model calculations 191.A precision of 0.3” in the present case corresponds to an interlayer spacing accuracy of 0.02 A. The experimentally determined interlayer spacing d perp for 10 Mb Ni/Cu(lOO) is found to, be dperp = 1.73 + 0.01 A, as compared to 1.76 A in bulk Ni, and 1.805 A in bulk Cu. Since the lattice constant of Ni parallel to the surface is that of bulk Cu, the reduction in Ni interlayer spacing relative to Cu produces a distorted fee structure which is referred to as body-centered tetragonal (bet). We can determine the nearest-neighbor distance in bet Ni/Cu(OOl) from the same geometrical procedure, and get a value cf rNN = 2.50 A, which is to be compared to 2.49 A in bulk fee Ni. The bet distortion can therefore be interpreted as Ni atoms behaving like hard-spheres maintaining a constant interatomic distance. As the spacing parallel to the interface is increased, the interlayer spacing decreases. The same hardsphere model expiains the bet distortion of Cu on Nif 100) [S].
3. Epitaxial Ni(ll1)
and Cu/Ni
multilayers
The cases of Cu/Ni(lOO) and Ni/Cu(lOOI film growth were both found to exhibit lateral coherence (at the interface), with a corresponding expansion or contraction of the interlayer spacing to maintain an approximately constant nearest-
355
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
neighbor spacing. In both cases a distorted fee lattice results with two inequivalent lattice parameters. This pattern did not continue for epitaxy along the (111) direction, however, as we found in a study of Ni/Cu(lll) films, and Cu/Ni/Cu(lll) multilayer structures. As before, a reference study of the diffraction pattern from a Ni(ll1) substrate was done, and is shown in fig. 5. This diffraction pattern is very similar to that of Cu(1 ll), which can be found in ref. [l]. The structure of epitaxial Ni(ll1) films on Cu(ll1) for film thicknesses of 5, 10, and 15 ML is summarized in the polar-angle XPD profiles shown in fig. 6. These polar plots are for the two azimuths that comprise the mirror-plane of the fee (111) surface, and the XPD profiles from substrate Cm11 1) and Ni(l11) are shown for reference. The major forward-scattering peaks are marked with vertical lines. Note that normal emission (0”) does not correspond to a forwardscattering maximum in fee (111) structures. The most obvious result evident from fig. 6 is the close similarity, even for small details such as the region around normal emission, between the diffraction patterns from these materials. It can immediately be concluded that epitaxial Ni on
Fig. 5. LW
Auger
electron XPD substrate.
pattern
from
a Ni(ll1)
I
I
I
I
I
I
I
o;Bo Polar
Angle
B (deg)
Fig. 6. Auger electron polar-angle intensity profiles for Ni films of varying thickness on Cu(1 ll), along with reference curves from Cu(ll1) and NKlll) substrates. The profiles are taken in an azimuth corresponding to the surface mirror-plane.
Cu(ll1) is also in an fee (111) stacking sequence, with the same orientation as the substrate (not a twinned interface). This is substantively different from Co epitaxy on Cu(lll), which instead shows a complex stacking sequence which is fee only for the first two layers [lo]. Unlike the Ni/Cu(lOO) case, however, there are no peak position shifts in Ni(l11) films relative to the Cu(ll1) substrate. Furthermore, the Ni ultrathin films have peak positions and peak shapes that are nearly indistinguishable from bulk Ni(ll1). There are significant changes in the peak intensities from the films as compared to the substrate, which is due to a progressive roughening of the film surface with thickness. Relying on the data of fig. 6 alone, with no additional information, it is only possible to determine that the ratio of the lattice constant normal to the surface (c axis) and parallel to the surface (a axis) is identical in the films to that of ideal fcc(ll1). Therefore, epitaxy of Ni on Cu(l11) does not produce a distorted fee structure. This differs not only from Ni on the Cu(100) surface, but also from other fee (111) systems such as Cu/Ir(lll) [91, which produces a distorted fcc(ll1) Cu film. We suggest that the Ni/Cu(lll) interfaces in these films are not coherent, lattice-matched interfaces, and that films from 5 ML thickness on are fully relaxed bulk Ni(ll1) structures.
.I. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
4. Metastable
epitaxial
bee Co(lOO), Ni(lOO), and
Cu(100)
-80
-60
-40
-20
0
20
40
60
80
Polar Angle (deg) Fig. 7. Comparison of XPD from a Cu overlayer in a Cu/Ni/Cu(lll) multilayer structure (0, and the XPD from the Ni middle layer in this structure (B). The curve for a 15 ML Ni/Cu(lll) film is also shown for reference (A).
We further investigated the structure of 3 ML Cu/15 ML Ni/Cu(lll) multilayers using XPD. One interesting aspect of the XPD technique is that both the outer Cu layers and the middle Ni film structure can be simultaneously and independently measured. This is illustrated in fig. 7, which shows the XPD results for a 15 ML NKlll) film on Cu(lll), in comparison to the Ni underlayer and Cu overlayer XPD curves for the multilayer “sandwich” structure. When the 15 ML Ni film is coated with 3 ML of Cu (curve B), the only change to the XPD profiles is a general reduction in peak intensity, which is a result of scattering through Cu layers which have less order than the Ni middle layer. The reduction in intensity is not due to simply inelastic attenuation, since this effect is explicitly removed by the data normalization procedure. The 15 ML Ni film completely attenuates the substrate Cu emission, so that all of the copper signal that is seen when the 3 ML overlayer is deposited comes from the overlayer itself. This overlayer also shows an fee (111) structure (see curve 0, but with reduced order compared to either the Cu(ll1) substrate (fig. 6) or the 15 ML Ni film on Cu(ll1) (compare also the 5 ML Ni film in fig. 6). From this data, it can be concluded that the entire structure, Cu/Ni/ Cu(1 11) is in an ideal abcabc . . . fee (111) stacking sequence.
Epitaxial growth is a powerful method for producing thin films of metals with non-equilibrium crystal structures. Of particular importance in magnetism are the bee metastable phases of the first-row transition elements, which have been the subject of several theoretical investigations using local-density functional methods [ll]. Consider an fcc(100) thin film. To transform this structure into a bee lattice, it can be uniaxially compressed along the surface normal (100) direction. Alternatively, the (100) axes parallel to the surface can be expanded, while simultaneously contracting the interlayer spacing along the surface normal. This is the approach used in attempts to grow bee metastable films of Co, Ni, and Cu. We have previously studied the epitaxy of Co and Fe on Ag(lOO), and Co on strained bee Fe(100) grown epitaxially on Ag(100) [12]. With a 45” rotation in orientation of the surface (100) directions, there is a close lattice match between the silver substrate bond lengths and bulk Fe(100). Using XPD, Fe was shown to be bcc(100) on AdlOO), but Co formed a body-centered tetragonal (bet) structure with lattice constants intermediate between fee and bee. Co did form bcc(100) films on strained Fe/Ag(lOO) templates. In this work, we attempted to grow bee metastable films directly on Fe(100) substrates, which have a slightly smaller lattice constant than the strained bee films of Fe/Ag(lOO). We performed XPD structure measurements on clean Fe(100) single crystals, and on Co, Ni, and Cu films grown on this substrate. All depositions were done at room temperature, and the substrate temperature was at all times kept below 400°C to avoid the bee to fee phase transition of bulk Fe(100). A range of film thicknesses were investigated ranging up to about 15 ML. The specific data reported here are for films of approximately 20 A thickness, corresponding to 1416 layers. The experimental results are shown in fig. 8, which has the XPD polar plots for the [loo] and [llO] bee azimuths. At the top of the figure is the
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD 80 R
60
40
20
Azimuth:bcc[lOO]
0
80
60
40
20
0
Azimuth:bcc[llO]
Fig. 8. XPD polar-angle profiles for epitaxy of Co, Ni, and Cu on Fe(100) substrates. Co and Ni exhibit high-quality XPD intensities, consistent with the formation of metastable bee epitaxial films for these materials. Cu, in contrast, shows little evidence of ordering.
data from the clean Fe(100) substrate. There are three major XPD peaks identified, which are due to the major low-index direction of the bee lattice. These are at normal emission (bee [OOl]), 45” along the [loo] azimuth, and 54.7” along the [llOl azimuth. There is no mistaking an fee structure for a bee one, as the peaks for fee would be at 54.7” instead of 45”, and 45” instead of 54.7” in the respective azimuths. From the figure, we immediately conclude that the Co and Ni films both adopt the bee (1001 structure. There is a great deal of similarity between the XPD curves for the Fe substrate, and the Co and Ni films, both along the low-index directions and for the additional secondary peak structures. For both the Co and Ni films, the magnitude of the XPD intensities are comparable to those from the single-crystal substrate, indicating a high degree of long-range order in these metastable films. The relative peak heights of the XPD structures in the epitaxial films are similar to those for the substrate. This implies that the films do not grossly deviate from flat overlayers. The situation for the Cu/Fe(lOO) is very different. As displayed, the Cu XPD pattern is nearly isotropic (no peak structures), indicating that there is no epitaxial relationship between the film and the substrate. This Cu film is either polycrystalline or highly disordered. For the Co and Ni
351
experiments, all depositions produced bee XPD patterns, independent of film thickness (up to the maximum studied). In the case of Cu, however, there were noticeable variations between depositions, indicating a sensitive dependence on growth conditions. In some cases, deposition at slightly elevated substrate temperatures (loo-200°C) produced XPD patterns with weak features due to a bee structure. In other cases, weak evidence for fee XPD peaks were seen. This suggests that further study of growth rates and substrate temperatures might uncover conditions under which Cu could be reliably grown as a bee structure on Fe(100). From earlier work using Ag(100) substrates, it is known that bee Cu can be reproducibly grown on strained-layer bee Fe/Ag(lOO) films [13]. A bet distortion from bee was found for Cu grown directly on the Ag(100) surface [141. However, the slight difference in lattice constant between Fe/Ag(lOO) and bulk Fe0001 surfaces is enough to prevent room-temperature bee growth of Cu/Fe(lOO). A very similar relationship was found in the prior study of bee metastable film growth of Co [12]. The bee Co structure formed for Co(100) grown on strained Fe/Ag(lOO) films, but bee Co could not be grown directly on AdlOO). The difference in lattice constant between Fe/Ag(lOO) and bulk Fe(100) is less than 2%, which highlights the importance of quantitative lattice constant measurements with high precision.
5. Growth-mode
simulations
In order to use XPD quantitatively for solving structures, it is necessary at some point to compare the experiment to a model calculation. This is true both to improve the accuracy of interpretation of the forward-scattering peaks, and to attempt to get direct information about bond lengths. The angular position of forward-scattering peaks are due to bond angles, and in themselves do not reveal the bond-length information needed for solving a structure. This information resides in the more subtle interference modulations in the XPD polar plots, which are directly
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
358
influenced by the final-state angular momentum and kinetic energy. An additional requirement for more advanced quantitative use of XPD data arises in studies of the growth modes of epitaxial films [El. In trying to distinguish between ideal layer-by-layer growth and more complex growth modes that involve the nucleation of three-dimensional islands, it is necessary to interpret the relative intensities of XPD features quantitatively, rather than simply locating the angular positions of peak maxima. A quantitative theory of XPD peak intensities must include multiple-scattering effects, which are very strong in the forward-scattering directions for epitaxial metal films. Multiple-scattering calculations using exact Green’s functions in a real-space cluster model have been very successful in accurately reproducing experimental XPD data from single-crystal substrates, for which many layers of atoms contribute to the diffraction pattern, and multiplescattering effects are large [8]. Although such exact calculations are highly successful in identifying the origin of XPD peak positions, shapes, and intensities, the calculations typically require substantial computation times that make it infeasible to engage in extensive searches of model structures with several varying parameters. We have therefore developed alternative, approximate scattering methods that retain the essential physical concepts necessary to correctly account for multiple scattering, but are considerably faster computationally since they use only approximate forms for the free-electron propagator. One of the methods is based on the separable Green’s function approximation using the formalism of Rehr and Albers [16,171. An effective, spherical-wave-corrected atomic scattering factor is constructed from the formula f&r,
r’>
=$(Zi+l)
eiSl sin 6,P,(i.?‘)c,(r)c,(r’),
I=0 (1)
where k is the electron wavenumber, atomic scattering phase-shift corrected
6, is the for finite
temperature, r and r’ are the vectors defining the scattering event at a particular atom, and the cI(r) are the spherical-wave correction factors [16,18]. In the forward direction (zero-scattering angle), this effective scattering factor is identical to the Rehr and Albers [3 X 31 matrix scattering factor method. At finite scattering angles, it is similar to the [l x 11 approximation, with the following modification. Separable approximations can have numerical instabilities at large kinetic energy, which is related to the approximation of the Bessel function that appears in the free-electron Green’s function where x = [Z(1+ l)/‘(/’ + l)/ ;;,,‘$$‘;hl’ en kr is small (nearest neighbors), and either 1 or I’ is large, the replacement of J,, with unity is invalid. To compensate for this problem, we place an upper bound (I,,,) on the angular momentum sum in fCfr, instead of relying on the decreasing size of t, = eiS/ sin S, to attenuate the high angular momentum terms. This “semi-empirical” approach to fefr is calibrated by performing calculations for small clusters of atoms using the f,rf method and exact calculations, adjusting the value of I,,, for best agreement (for detailed examples, see ref. [19]>. The scattering amplitude for a particular path, resulting in an electron travelling in the direction P, is given by eikrl
X $%A
t-27 t-3) eikrN
x
. . . -
rN
feff(rN,
rm>
epik.‘~~N,
(2)
where ri is the bond-length between the atom at the origin and the first scattering atom in the sequence, and rON is the vector from the origin to the terminal atom in the sequence. The final-state angular momentum appears in the spherical harmonic YL,,,where L = (I,m). IneIastic damping is included by introducing an imaginary component to the electron wavevector k. An additional approximation that is made for XPD at electron energies above a few hundred
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
eV is the “negligible back-scattering (NBS) approximation”, for which scattering paths with scattering angles above some maximum value are neglected. For cases such as the LVV Auger diffraction patterns of Co, Ni, Cu, and Fe, we find that a scattering angle of less than 90” is usually sufficient to reproduce all measurable features. If the atom cluster is visualized as being constructed from shells of atoms, this constraint is the same as only considering shell-to-shell multiple scattering in the forward direction, while neglecting intrashell multiple scattering. Finally, for Auger diffraction patterns, we use the s-wave final-state approximation to the angular momentum, since angular-momentum effects have been found to be small (though detectable) at high energy [Bl. Fig. 9 shows a comparison between the feff NBS calculation and a full multiple-scattering calculation by Xu and Van Hove [20], using the Taylor-series magnetic quantum number expansion method, for atomic clusters of nickel atoms and copper Auger electron emitters. The singlescattering calculations are identical, as expected, and the multiple-scattering calculations differ in only relatively minor details. The NBS path-formalism calculations have been found to work well for metal substrates and thin films [4,9,10], and for semiconductor substrates [21]. Some of the most important scattering effects that are used in determining a film growth mode by XPD can be seen in multiple-scattering calculations for chains of atoms, as shown in fig. 10 for a chain of copper atoms embedded in a uniform medium, simulating the [llO] forward-scattering direction in a Cu(100) single crystal. In a growthmode study, the intensity of forward-scattering peaks are compared as a function of film thickness, to determine the local coverage and geometry of (possible) islands in the film. As shown in fig. lOA, single-scattering calculations greatly overestimate the contribution of scattering from deep atoms, relative to those near the surface. Multiple-scattering effects limit the “visibility” of atoms along high-density chains to only a few layers (note, however, that some features in an XPD pattern from metals arise from as much as 10 layers deep).
(A)
rr 0
0
,& s
I” (W
.G
a
2
B (Cl 63.4” 1 2MLNi 1 MLCU
0
20 40 60
0 20 40 60 80
Polar Angle
Polar Angie
Fig. 9. Comparison of a forward-multiple-scattering spherical-wave approximation calculation (left), with full multiple-scattering calculations, using from ref. [20] the TS-MQNE approximation (right). (A) Single scattering, 8 atoms; (B) multiple scattering, 8 atoms; (Cl multiple scattering, 3 layers.
In the usual situation, it is the integrated intensity from several atomic layers that is measured (as opposed to an isolated buried layer), a case which is simulated for a chain in fig. 10B. Again, significant differences are seen between the single- and multiple-scattering calculations. The total intensity in the forward-scattering peak reaches a saturation value for chain lengths of only 4 atoms, which shows that the forwardscattering component of XPD is primarily a probe of the outer-layer structure of a film. The angular peak-width of the forward-scattering feature decreases in the multiple-scattering simulation at a faster rate than found in single-scattering. The intensity of XPD peaks along low-index directions, for both a substrate and an overlayer film of varying thickness, can be used to determine growth modes. In the simplest examples,
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
360
certain forward-scattering peaks only appear at a particular local coverage (say three layers), so that a growth mode can be established when the average coverage can be accurately determined by other means. We have calculated the rate of rise in XPD intensity along three directions for a Cu(ll1) substrate, and for a Co(l11) fee film of varying thickness. The calculation, which used an atomic cluster assuming ideal layer-by-layer
Co !2 0
Coverage
(ML)
Fig. 11. A growth-mode determination using XPD for epitaxy of Co on Cu(ll1). The theoretical curves (open symbols) are for an assumed ideal layer-by-layer growth mode. Solid symbols are experimental data. Significant deviations are seen for the overlayer emission (right); smaller effects are visible from the substrate (left).
B c E4 h 2 i 2 (4 -70
0 0
Angle
off
70
Normal
ti =: .r( E W
-70
@I
0
Angle
0
off
70
Normal
Fig. 10. Single- and multiple-scattering calculations for a chain of copper atoms embedded in a uniform medium. The chain is oriented 45” off the surface normal; the inter-nuclear distance is 2.55 A, and the mean free path 10 A. (A) Intensity from individual emitter atoms at the end of a chain; (B) sum of intensity for all emitters.
growth, is shown in fig. 11. The substrate forward-scattering intensities for all three directions show rather similar behavior, noting that the trivial inelastic loss attenuation is removed from the data before comparison. There are noticeable differences between directions for the overlayer, however. The thresholding behavior, for which a forward-scattering peak only is observed above a specific layer thickness, can be seen in the [112] direction calculation (open symbols). Notice as well how the XPD anisotropy saturates after only 4-5 monolayers along the [loo] and [llO] directions, but continues to rise along [112] which has a different atomic density. The growth of Co on Cu(ll1) turns out to be more complex than, say, Co on Cu(100) [lo]. Growth begins initially in fee stacking sequence, but hcp stacking faults begin to occur as early as the third layer. This unfortunately complicates the interpretation of the growth-mode curves of fig. 11. The substrate XPD features appear to follow the theoretical curves for up to 5 ML along the [loo] and [112] directions, but this should
J. Zhang et al. / Epitaxy of fee and bee Co, Ni, and Cu studied by XPD
probably be interpreted as indicating that the substrate diffraction features are not as reliable for growth-mode studies as the overlayer peaks. It is clear from the Co overlayer experimental diffraction data (filled symbols) that ideal fee layer-by-layer growth does not continue beyond the third layer.
6. Conclusion Structural studies of epitaxial layers using XPD at high kinetic energy benefit from several factors intrinsic to the technique, such as elemental and chemical-state specificity, and no requirement for long-range order. In addition, computational methods are available that yield excellent agreement between experiment and theory, in terms of absolute peak positions, intensities and lineshapes. The trend toward quantitative XPD analysis of ultrathin film and interface structure continues to show that XPD is capable of tetermining structures with an accuracy of 0.02 A, limited at this time in part by experimental angular smearing of XPD fine-structure.
Acknowledgement
This work was supported by the National Science Foundation through grant DMR-91-15987.
361
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