Asymmetric alloy formation at the Fe-on-Ti and Ti-on-Fe interfaces

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Journal of Physics: Condensed Matter

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Asymmetric alloy formation at the Fe-on-Ti and Ti-on-Fe interfaces

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1. Introduction

The special magnetic properties of surfaces and interfaces induce a variety of new magnetic phenomena [1] in nanoscale magnetic-nonmagnetic bilayers or multilayer heterostructures.

Understanding such phenomena and their technological appli- cation alike requires the knowledge of atomic structure and element distribution across the interfaces. Most nano-devices are hetero-structures of different layers of various elements and alloys. Concentration distribution of the magnetic elements along the growth direction generally implies a distribution of the local magnetic moments and may affect the overall magnetization directly, as well as through the variation of the

anisotropies and interactions between the magnetic moments.

The knowledge of the relevant interface asymmetries may help in designing the proper deposition sequence of the layers in order to achieve the desired magnetic behaviour.

Fe–Ti multilayers have been extensively studied in the past and, mainly as a consequence of interface formation, the magn etic properties depend on the thickness of both the magnetic Fe and the nonmagnetic Ti layers [2–4] in the few nm thickness range. Sequential deposition of Fe and Ti by sputtering [2–4] results in chemical mixing at the interface of body centered cubic (bcc) Fe and hexagonal close packed (hcp) Ti layers. The interface regions may contain crystalline bcc-Fe_100−xTi_x (for x < 10), Fe2Ti, FeTi, hcp-Ti_100−yFe_y

Journal of Physics: Condensed Matter

Asymmetric alloy formation at the Fe-on-Ti and Ti-on-Fe interfaces

J Balogh¹, P Süle², L Bujdosó¹, Z E Horváth², D Kaptás¹ , A Kovács³, D G Merkel¹ , A Nakanishi⁴, Sz Sajti¹ and L Bottyán¹

1 Wigner Research Centre for Physics, Hungarian Academy of Sciences, H-1525 Budapest 114, PO Box 49, Hungary

2 Centre for Energy Research, Hungarian Academy of Sciences, H-1525 Budapest 114, PO Box 49, Hungary

3 Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich 52425, Germany

4 Department of Physics, Shiga University of Medical Science, Shiga 520-2192, Japan E-mail: balogh.judit@wigner.mta.hu

Received 26 January 2018, revised 6 September 2018 Accepted for publication 28 September 2018 Published 22 October 2018

Abstract

The Fe-on-Ti and Ti-on-Fe interfaces were studied experimentally by Mössbauer spectroscopy (MS), transmission electron microscopy (TEM) and x-ray reflectometry (XRR) on Ti/Fe/Ti trilayers grown on Si(1 1 1) substrates by vacuum evaporation. The nanoscale structure and composition were explored in cross sections using TEM, the layer structure and the interface widths by specular x-ray reflectometry. MS was applied to identify the interface alloy phases and to determine the pure and alloyed Fe layer fractions. The experimental results were compared with molecular dynamics (MD) simulations of layer growth on Fe or Ti underlayers of different orientations. The concentration distributions provided by MD simulations show an asymmetry at the interfaces in the layer growth direction. The transition is atomically sharp at the Ti-on-Fe interface for the (0 0 1) and (1 1 0) crystallographic orientations of the Fe underlayer, while it spreads over a few atomic layers for Fe(1 1 1) underlayer and for all studied Ti underlayer orientations at the Fe-on-Ti interface. MS and XRR data on Ti/Fe/Ti trilayers confirm the asymmetry between the bottom and top Fe interface, but the inferred interface widths considerable exceed those deduced from the MD simulations.

Keywords: interfaces, Mössbauer spectroscopy, x-ray reflectivity, molecular dynamics (Some figures may appear in colour only in the online journal)

J Balogh et al

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J. Phys.: Condens. Matter

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10.1088/1361-648X/aae508

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Journal of Physics: Condensed Matter IOP

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https://doi.org/10.1088/1361-648X/aae508 J. Phys.: Condens. Matter 30 (2018) 455001 (9pp)

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(for y < 1) alloys. Moreover the presence of amorphous compounds similar to those obtained by co-sputtering were also reported [5, 6]. The phase formation under ion-irradiation [7]

or heat treatment [8, 9] of multilayers has also been investigated, but the Ti-on-Fe and the Fe-on-Ti interfaces were assumed equivalent in all these multilayer studies. Trilayers or single interfaces have rarely been investigated [10, 11].

An elaborate high-resolution transmission electron microscopy (TEM) study of multilayer samples [12] claimed non- equivalent Fe-on-Ti and Ti-on-Fe interfaces, but later TEM investigations [3, 9, 13, 14] gave no evidence for any interface asymmetry and the results on the phase formation were also controversial. Namely, references [9, 14] find no evidence of crystalline or amorphous alloys at the interfaces, while reference [12] identifies amorphous-like interface regions for small repetition periods (7.2 nm) and crystalline regions with chemical gradient along the layer-growth direction for large repetition periods (40 nm). The presence of amorphous and crystalline interface alloys is also observed by [3, 13].

Note, that bcc-Ti is only reported by [12] (for small multilayer periods). Beyond the exper imental studies molecular dynamics (MD) simulations were performed for Ti deposited onto Fe(0 0 1) substrates [15]. The results indicated an almost atomically sharp Ti-on-Fe interface under room temperature (RT) growth. These controversial results necessitate a more elaborate experimental and theoretical work in order to reveal the interface properties of polycrystalline Fe–Ti multilayers.

The atomistic simulation of the interface formation during the atomic deposition process is a feasible theoretical approach up to about 100 nm² surfaces. The most frequent characterization methods of multilayer interfaces, viz. grazing incidence x-ray or neutron reflectivity, Rutherford backscattering or Auger electron spectroscopy, use samples of macroscopic size and they are unable to distinguish between the topological roughness/waviness of the interface and chemical mixing of the layers. The various TEM methods may give atomic scale information about both the topological features and the chemical mixing, but they sample only a nanoscale section of a macroscopic sample and sample preparation might acciden- tally change the structure. Consequently, a quantitative comparison of the experimental results and the MD simulation is not unambiguous. Mössbauer spectroscopy (MS), being sen- sitive to the atomic scale neighbourhood of a specific isotope, can give unique information on the extent of the chemical mixing and on the nature of the compound phases formed at the interface. However, additional information on the morph- ology of the sample is inevitable for a sound identification of the different Mössbauer spectral components. For example,

57Fe probe nuclei surrounded exclusively by Fe atoms in the first and second coordination shell in a body centered cubic structure experience a hyperfine field similar to that in pure bcc-Fe, no matter if they sit at the interface of an iron layer, inside a small iron cluster or in a random dilute alloy.

In this work we study the alloy formation at the Ti-on-Fe and Fe-on-Ti interfaces in Ti/Fe/Ti trilayers by applying Mössbauer spectroscopy complemented by cross-sectional TEM and x-ray reflectometry (XRR). To attain the best Mössbauer signal to noise ratio conversion electron Mössbauer

spectroscopy (CEMS) was applied. Samples were prepared using iron metal highly enriched in the ⁵⁷Fe Mössbauer reso- nant isotope. In order to determine the phase fractions within the top (Ti-on-Fe) and bottom (Fe-on-Ti) Fe interface Ti/⁵⁷Fe/

Ti and Ag/⁵⁷Fe/Ti sample pairs were compared exploiting the non-mixing property [16, 17] of Fe and Ag. Analysing the spectra of Ag/⁵⁷Fe/Ti samples provides information on the Fe-on-Ti interface, since the Ag/Fe interface is indeed chemically sharp and the Ag layer causes only a small and well documented change [18] in the hyperfine parameters of

57Fe within the atomic layers nearest and next-nearest to the Fe–Ag interface. Additional spectral components appearing in the Mössbauer spectra of Ti/⁵⁷Fe/Ti samples reveal the specific properties of the Ti-on-Fe interface. The experimental results are compared with MD simulations of the layer growth performed for all basic crystal orientations of the respective underlayer, Ti or Fe. The samples were prepared by evaporation in high vacuum, which, to our knowledge, has not yet been used in the interface studies of this system.

2. Experimental methods

The metallic layers were prepared by vacuum evaporation onto Si(1 1 1) substrates in an evaporation chamber which per- forms 10⁻⁷ Pa base vacuum and is equipped with two substrate holders. Ti and Ag were e-beam evaporated, while the iron (95 per cent enriched in the ⁵⁷Fe isotope) was evaporated by resistive heating from a tungsten crucible onto RT substrates.

The evaporation rates were about 0.1 nm s⁻¹. Three sample pairs with 1.5, 2.5 and 3.5 nm ⁵⁷Fe layer thickness were prepared, as given in table 1.

The equal thickness of the ⁵⁷Fe layers within one sample pair was ensured by the simultaneous deposition of ⁵⁷Fe from a crucible placed at equal distances from two identical Si(1 1 1) substrates of 2″ diameter. Similarly, the respective Ti layers of the sample pairs were deposited simultaneously, but the distance to the substrates was somewhat different, which may result in some (below 1 nm) difference in the Ti layer thicknesses within the pair. The (Ti) capping layers in (Ti)/Ag/

Fe/Ti/Si samples are meant to prevent oxidation of the ⁵⁷Fe layer. The thin Ag layers on Fe are insufficient for the purpose, since they were found to get easily fractured [16].

Structural characterization was performed on sample Ti/3.5 Fe/Ti by TEM and XRR. Specimens for cross-sectional TEM studies were prepared in a dual-beam scanning electron microscopy and Ga⁺ focused ion beam (FIB) system (FEI Helios 440), which allowed to keep the sample temperature

Table 1. Layer sequence of the studied samples.

Sample

identifier Sample structure

Ti/1.5Fe/Ti 20 nm Ti/1.5 nm ⁵⁷Fe/10 nm Ti/Si(1 1 1)

Ag/1.5Fe/Ti 10 nm Ti/10 nm Ag/1.5 nm ⁵⁷Fe/10 nm Ti/Si(1 1 1) Ti/2.5Fe/Ti 20 nm Ti/2.5 nm ⁵⁷Fe/10 nm Ti/Si(1 1 1)

Ag/2.5Fe/Ti 10 nm Ti/10 nm Ag/2.5 nm ⁵⁷Fe/10 nm Ti/Si(1 1 1) Ti/3.5Fe/Ti 20 nm Ti/3.5 nm ⁵⁷Fe/20 nm Ti/Si(1 1 1)

Ag/3.5Fe/Ti 10 nm Ti/10 nm Ag/3.5 nm ⁵⁷Fe/20 nm Ti/Si(1 1 1)

J. Phys.: Condens. Matter 30 (2018) 455001

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unaltered during the preparation. Pure carbon was deposited on the surface as a protective layer. The surface damage induced by the high-energy Ga beam was reduced by low- energy Ar⁺ ion beam milling using Fischione NanoMill 1040 system at energies below 1 keV. The structure and chemical composition of the trilayer was studied using a conventional TEM (FEI Tecnai G2) and a probe-aberration-corrected scanning TEM (FEI Titan G2 80-200) equipped with in-column energy-dispersive x-ray spectroscopy (EDXS) detectors [19].

The high-resolution images and elemental maps were pro- cessed using the FEI Velox software.

XRR measurements were performed by a Bruker AXS D8 Discover diffractometer equipped with a Göbel-mirror and a scintillation detector using Cu K_α radiation. The XRR probes the refractive index depth profile in flat samples perpend- icular to the surface. Interpretation of the reflectivity involves modelling the depth profile by an approximate multilayer structure of constant scattering length densities of the layers and interface regions (or the respective indices of refraction determined by the composition and density). Specular reflectivity does not distinguish the interface roughness and the lat- erally homogeneous intermixing e.g. due to inter-diffusion.

The collected reflectivity data were evaluated by using the FitSuite code, a free multipurpose software [20]. FitSuite uses a transfer matrix method described in [21] for calculation of x-ray reflectograms. It treats the interface roughness as described in [22, 23] assuming a Gaussian height distribution and a corresponding error function-type interface depth profile characterized by the standard deviation of the Gaussian, the (rms) roughness, σ. The Gaussian’s full width at half maximum FWHM = 2·√

2·ln2·σ ≈ 2.355 σ covers the central region of the error function profile between 4.8%

and 95.2%. Independent of the shape, we will characterize the interface width by W5-95, the distance between the 5% and 95% quanti les of the profile.

The CEMS measurements were carried out by a conventional constant acceleration Mössbauer spectrometer. For the detection of the conversion electrons a low background gas filled proportional counter was used with pure H2 gas at low temperatures [24], and 96%He–4%CH4 gas mixture at RT. The spectra were measured by a 50 mCi ⁵⁷Co(Rh) single line Mössbauer source. The hyperfine field (HF) distributions were evaluated according to the Hesse–Rübartsch method [25], by fitting the amplitudes of a number of sextets with HFs increasing with equal step values. The isomer shift (IS) values are given relative to that of α-Fe at room temperature.

3. Atomistic simulation methods

Classical molecular dynamics calculations were used in parallel environment using GPU nodes reaching a significant speedup, as implemented in the LAMMPS code (Large-scale Atomic/Molecular Massively Parallel Simulator) [26] The applied MD scheme is as follows:

–determination of the decomposed spatial regions within the periodic simulation box to be used for the message interface passing (MPI) parallel calculations on supercomputers

–the code first builds a neighbour list within the predefined cut-off distance (3–4 Angstrom) and stores this list throughout the full simulation time

–initial guess: the atoms’ initial positions and initial velocities according to the initial temperature with Boltzmann distribution

–analytical calculation of the forces within the cut-off distance and moving the atoms according to the forces acting on them–dynamical time stepping via numerically adjustable time step which roughly inversely depends on the forces acting on the atoms (Close to the equilibrium state the time stepping becomes faster.)

–integrating the equations of motion using Verlet algorithm to find the new atomic positions and velocities

–introducing temperature effects via the NPT (Nose– Hoover prestostat and thermostat) algorithm

–the above scheme is continued until the predefined time limit is reached.

The isobaric-isothermal (NPT ensemble) simulations were carried out at 300 K, allowing for the variation of the supercell size and shape, which ensured further flexibility in absorbing pressure waves and/or in relaxing the occasional strain in the system. Periodic boundary conditions were ensured along the lateral directions (x,y) and vacuum regions were inserted above and below the slab of the film/substrate system. The size of the vacuum region was chosen a few nanometers in order to keep sufficient space between the evaporated particles and the forming surface of the deposit. The temperature of the substrate was kept at 300 K exploiting the variable time step algorithm. The atomic and nanoscale structures were displayed using the OVITO code [27]. The specific (fix deposit) algorithm of the LAMMPS was applied for the simulation of the thin film growth. The flux of the deposited atoms was kept at 2.25 · 10²⁵ atoms s⁻¹ cm⁻² (one particle per 10 k simulation steps). In total, at least 15–20 monolayers (ML) of adatoms were deposited on the substrate in which each ML corre- sponded to nearly 200 adatoms for the Fe and Ti layers on the 4 × 4 nm² substrate surface. The EAM potentials were used for both Fe and Ti as generated by the EAM database tool [28]

provided by the LAMMPS code. The FeTi cross-interaction was taken into account by the Johnson mixing rule [29] which provides reasonable alloy properties. Further details of the simulated thin film growth can be found in [17].

4. Experimental results

4.1. Electron microscopy

The structure of the deposited layers of the Ti/3.5 Fe/Ti was studied in cross-section using various TEM methods, as shown in figure 1. Figure 1(a) displays a bright-field (BF) scanning TEM (STEM) image of the Ti and Fe layers deposited on Si substrate. The Fe layer thickness on the STEM images was measured to be 4.2 nm, about 20% above the nominal thickness. The ~1 nm thick native SiO2 layer is also visible on the surface of the Si substrate. Both Ti layers show polycrystalline structure with grain sizes ranging from 5 to 15 nm. The light

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contrast of ~3.5–4 nm thickness on the top of the upper Ti layer is due to surface oxidation. Figure 1(b) shows the colour coded chemical composition map of the Ti and Fe layers extracted from EDXS measurement. The standard background removal and the Cliff–Lorimer method were applied to calcu- late the atomic fraction of the elements. Figure 1(c) shows the corresponding variation across the Fe interfaces measured in the map of figure 1(b). The Fe concentration peaks at approxi- mately 0.94 in the middle of the Fe layer. EDXS does not reveal differences between the Fe-on-Ti and the Ti-on-Fe transition zones, both appear around 3 nm thick. Figure 1(d) displays the high-resolution BF STEM image. In figure 1(e) the digital diffractogram of the high-resolution image shows the Ti and Fe lattice arrangements relative to each other. The analysis of the pattern suggests [0 1 0] orientation of the analysed Ti grain and [1 0 0] orientation of the Fe grain.

4.2. X-ray reflectivity

Results of the XRR measurements performed on the Ti/3.5 Fe/Ti sample using the Cu Kα line (0.154 nm) are shown in figure 2 and table 2. The layer thicknesses were found to be

21.5 nm, 3.63 nm, 20.4 and 4 nm for the bottom Ti, Fe, top Ti, and TiO_x layers, respectively. The native SiO₂ layer of 1 nm thickness on the Si substrate and the surface TiO_x layer were included in the layer model in accordance with the TEM results. Significant intermixing occurs only at the bottom of the Fe layer, i.e. at the Fe-on-Ti interface, as the roughness of the bottom Ti layer is 0.86 nm while that of the Fe layer is found quite sharp, 0.23 nm.

4.3. Mössbauer spectroscopy

The CEMS spectra of the three as-received sample pairs measured at RT and 15 K are shown in figures 3(a) and (b), respectively. All spectra (except for sample Ti/1.5Fe/Ti at RT) were fitted by a set of sextets with hyperfine fields allowed in the 5–40 T range and a broadened doublet with a single quadrupole splitting (QS). The evaluated normalized HF distributions are shown as insets to each spectrum in figure 3. In the spectrum fitting the line-width of the sextet components of the HF distribution was fixed to 0.24 mm s⁻¹, the HF step value was an iteration parameter in the 0.7–0.8 T range. The isomer shifts were assumed proportional to the HFs, the lower the HF the larger negative value to have. The intensities of the second and fifth lines relative to that of line three and four of the sextets were close to 4 in each case, indicating an in-plane orientation of the Fe magnetic moments.

The most important parameters of the spectra are summa- rized in table 3. The magnetic component is divided into two subgroups for each spectrum. The one indicated as bcc-Fe, is a sum of the sextets in the 0.5 T vicinity of 33 and 33.8 T, the literature HF values of bcc-Fe at RT and 15 K, respectively. This component can be attributed to Fe atoms without Ti or Ag as first neighbours. The component stemming from the sextet intensities below 32.5 and 33.3 T at RT and 15 K, respectively is labelled as magnetic alloy and belongs to Fe atoms with Ti (or Ag) neighbours in the first and/or second

Figure 1. Structure of the Ti/3.5 Fe/Ti sample studied in cross- section using various TEM methods; bright-field STEM image of the Ti and Fe layers deposited on Si substrate (a), colour coded chemical composition map of the Ti and Fe layers extracted from EDXS recordings (b), atomic fraction of the elements across the interfaces calculated from the composition map (c), high resolution bright-field STEM image (d), digital diffractogram of the area marked in the high resolution image (e).

Figure 2. Measured and fitted x-ray reflectivity curve for the Ti/3.5 nm Fe/Ti sample. The inset shows the concentration profiles of the different materials corresponding to the fitted parameters.

Red (dark) and green (light) thick lines indicate Ti and Fe. The components appearing around 0 and 50 nm depth and above— indicated by thin black lines—belong to TiOx, SiO2, and Si, respectively. The asymmetry of the Fe–Ti interface is salient.

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neighbour shells [31]. The average HF of this component is largely different for samples Ti/1.5Fe/Ti and Ag/1.5Fe/Ti, but remains constant within the ~0.5 T experimental error for Fe thicknesses of 2.5 and 3.5 nm. The spectral fraction of the different components (bcc-Fe, paramagnetic alloy, magnetic alloy) was transformed into Fe equivalent layer thicknesses

by multiplying it with the nominal thickness of the Fe layer.

(The Mössbauer-Lamb factors were assumed equal for all components.) The Fe equivalent layer thicknesses will be labelled as d_bcc, d_para, and d_mag for the bcc-Fe, for the paramagnetic alloy and for the magnetic alloy components, respectively.

Table 2. The parameters obtained from the fit of x-ray reflectivity measurements. The roughness values refer to the top interface of the respective layer. The complex refractive indices (n=1−δ+iβ), see [30], were kept constant in the fit. The densities of the TiOx and SiO₂ were assumed to be 3.78 and 2.2 g·cm⁻³, respectively. These densities correspond to TiO₂ in the anatase and SiO₂ in the amorphous phase, respectively. The errors indicated are statistical errors. Based on various model simulations we estimate the overall uncertainty of the layer thickness and the interface roughness below ±5% and ±20%, respectively.

TiOx Top Ti ⁵⁷Fe Bottom Ti SiO2

δ · 10⁶ 11.62 13.52 22.45 13.52 7.12

β · 10⁶ 0.58 1.13 2.90 1.13 0.09

Thickness (nm) 4.0 ± 0.02 20.4 ± 0.02 3.63 ± 0.02 21.5 ± 0.04 1 ± 0.03

Roughness (nm) 0.87 ± 0.02 1.36 ± 0.01 0.23 ± 0.05 0.86 ± 0.03 0.53 ± 0.01

Figure 3. Mössbauer spectra of the as received samples measured at RT (a) and at 15 K (b). The sub-spectra belonging to the doublet component and to the HF distributions (shown in the insets) are indicated by blue (light) and red (dark) lines, respectively. In the insets the horizontal (HF) scales are the same for all HF distributions and are labelled in the topmost insets in tesla units. The vertical intensity scales of the insets, however, are normalized to unit area and vary from graph to graph one tick belonging to p(B) = 0.1 T^–1 in each inset.

Table 3. Mössbauer parameters of the spectra measured at RT and 15 K; isomer shift (IS), quadrupole splitting (QS) and line width (W) of the doublet, average hyperfine field of the magnetic alloy component (HF_mag) and the iron content of the different components expressed in Fe equivalent layer thicknesses, as calculated from the spectral fractions and the nominal thickness of the deposited Fe layer. Typical errors are given in the second row.

IS (mm s⁻¹) QS (mm s⁻¹) W (mm s⁻¹) HF_mag (T) d_bcc (nm) d_para (nm) d_mag (nm)

Typical error ±0.02 ±0.02 ±0.05 ±0.5 ±0.05 ±0.05 ±0.05

Temperature RT/15 K RT/15 K RT/15 K RT/15 K RT/15 K RT/15 K RT/15 K

Ti/1.5 Fe/Ti −0.17/− 0.10 0.29/0.52 0.40/0.62 0/16.4 0/0 1.50/0.66 0.00/0.84

Ag/1.5 Fe/Ti −0.18/− 0.10 0.38/0.51 0.61/0.57 25.0/25.2 0.04/0.25 0.46/0.24 1.00/1.01 Ti/2.5 Fe/Ti −0.21/− 0.07 0.47/0.50 0.56/0.69 26.3/27.5 0.61/0.66 0.33/0.39 1.56/1.45 Ag/2.5 Fe/Ti −0.22/− 0.09 0.42/0.46 0.51/0.43 27.1/27.0 0.54/0.91 0.21/0.19 1.75/1.40 Ti/3.5 Fe/Ti −0.21/− 0.08 0.45/0.50 0.65/0.56 27.1/27.5 1.53/1.46 0.35/0.33 1.62/1.71 Ag/3.5 Fe/Ti −0.19/− 0.11 0.46/0.54 0.47/0.61 27.0/28.3 1.73/1.80 0.21/0.26 1.56/1.44

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5. Atomistic simulations

The classical MD simulations of the thin film growth of Fe–Ti bilayers were carried out with different orientations of either the Fe or the Ti underlayer. The cross-sectional view of the grown interfaces is shown in figures 4(a) and (b) and the calculated concentration depth profiles for different substrate orientations are displayed in figure 5. The Fe-on-Ti interfaces are slightly intermixed and the interface broadening depends on the orientation of the substrate, although the variation is small.

W5-95, the distance between the 5 and 95 at% intersection points of the interface profile is around 1 nm for Fe/Ti(1 1 0 1) and 0.8 nm for Fe/Ti(0 0 0 1). In the Ti-on-Fe case no atomic mixing can be seen for the Fe(0 0 1) substrate orientation, but the interface is slightly wavy, as shown in figure 4(b), which results in a W5-95 = 0.3 nm width of the concentration depth profile. For the Fe(1 1 0) orientation a modest intermixing also takes place and the intermixed region is slightly wider, W5-95 = 0.5 nm. The largest intermixing takes place in case of the Fe(1 1 1) substrate orientation, but W5-95 = 0.7 nm still remains below the Fe-on-Ti values. In summary, the simulations give evidence of a somewhat orientation dependent intermixing which is asymmetric with respect to the interchange of the constituents of the growing film and the underlayer.

6. Discussion

The most direct experimental information on the range of the chemical mixing is obtained from Mössbauer spectroscopy therefore we discuss those results first. The room temperature spectra shown in figure 3(a) are in line with previous Fe/

Ti multilayer studies [2, 4]. The observed room temperature IS and QS values of the Ti/1.5Fe/Ti sample, −0.18 mm s⁻¹ and 0.38 mm s⁻¹, respectively, suggest that below 2 nm thickness of the Fe layer, all Fe atoms are alloyed with Ti in an amorphous structure. Although the paramagnetic component may contain minor contributions from crystalline Fe2Ti, FeTi and FeTi2 [5, 6], it will be referred as amorphous component.

Further on the low temperature CEMS spectra in figure 3(b) reveal that the amorphous component is not homogeneous.

Indeed, the Ti/1.5Fe/Ti spectrum reveals 40% paramagnetic

Fe atoms at 15 K, while the remaining Fe exhibits a broad HF distribution in the 5 to 30 T range. The well resolved magnetic component that can be observed in the spectrum of Ag/1.5 Fe/Ti at RT, is not present in the spectrum of Ti/1.5 Fe/Ti, which demonstrates that the Fe-on-Ti and the Ti-on-Fe interfaces overlap in Ti/1.5 Fe/Ti. The single Fe-on-Ti interface of the Ag/1.5 Fe/Ti sample, in addition to amorphous alloys, certainly contains crystalline bcc-Fe_100−xTix alloy phase, since it is the only magnetic Fe–Ti phase at RT. All other crystalline or amorphous alloys are known to exhibit Curie temperatures below RT in the entire concentration range.

With increasing the thickness of deposited Fe the formation of a bcc-Fe layer and two separated interfaces, Fe-on-Ti and Ti-on-Fe, are expected. The formation of two well separated interfaces is signalled by constant values of the HF parameters and of the interface width as a function of the deposited Fe thickness. In samples Ti/2.5 Fe/Ti and Ti/3.5 Fe/Ti the interface components give an Fe equivalent layer thickness of dpara + dmag ≈ 2 nm, in accordance with former publications [2, 4] and with our above conclusion on the overlapping interfaces below 2 nm Fe thickness. In these two samples the HF distributions (insets in figure 3) and the HFmag values in table 3

Figure 4. Typical cross-sectional view with 1 nm slab thickness of Fe/Ti(0 0 0 1) (a) and Ti/Fe(0 0 1) (b) interfaces as obtained from MD simulations. Blue (dark) and red (light) spheres are Fe and Ti atoms, respectively.

Figure 5. Concentration profiles across the Fe-on-Ti and Ti-on- Fe interfaces as calculated from MD simulations for different orientations of the substrate layer. The substrate orientations which belong to the different curves and the thickness (W_5-95) of the respective interface alloy are indicated in the inset.

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agree with each other within the experimental error and differ from those in Ti/1.5 Fe/Ti. The bcc-Fe component in Ti/2.5 Fe/Ti and Ti/3.5 Fe/Ti forms a layer of dbcc = 0.64 nm and 1.50 nm, respectively. Although the bcc-Fe component might as well be assigned to Fe atoms with no Ti neighbours in a dilute alloy, but the formation of a continuous bcc-Fe layer in Ti/3.5 Fe/Ti seems to be justified by the following observa- tions: (i) for a 1 nm increase of the nominal Fe thickness dbcc

was found to increase almost the same amount, 0.86 nm, (ii) the interface properties (dpara, dmag, QS, HFmag) do not depend on the deposited Fe thickness for the Ti/2.5 Fe/Ti and Ti/3.5 Fe/Ti samples and finally (iii) TEM and XRR (see figures 1 and 2) are indicative of a continuous Fe layer separating the Fe-on-Ti and Ti-on-Fe interfaces in the Ti/3.5 Fe/Ti sample.

The minor difference between the spectra of Ti/3.5 Fe/Ti and Ag/3.5 Fe/Ti samples (see figure 3) implies that the Ti-on-Fe interface is chemically rather sharp and the interface alloys are formed predominantly at the Fe-on-Ti interface.

The interface asymmetry will be analysed below by com- paring the Ti/3.5 Fe/Ti and Ag/3.5 Fe/Ti samples. Since the amorphous alloy and the crystalline bcc alloy phases can be clearly distinguished in the RT Mössbauer spectra, the interface widths will be calculated from the RT spectral fractions.

The properties of the Fe-on-Ti interface are directly mani- fested in the Ag/3.5 Fe/Ti spectra. The paramagnetic and the magnetic alloy component contains dpara (Fe-on-Ti) = 0.21 nm and dmag (Fe-on-Ti) = 1.56 nm Fe, respectively, however, this latter value in Ag/3.5 Fe/Ti contains two monolayers (~0.3 nm) Fe contribution of the Ag-on-Fe interface, therefore in further calcul ations we use a corrected value, d^c_mag (Fe-on-Ti) = 1.26 nm. To unravel details of the Ti-on-Fe interface, the Ti/3.5 Fe/Ti and Ag/3.5 Fe/Ti spectra will be compared. In Ti/3.5 Fe/Ti dpara and dmag are slightly larger than in Ag/3.5 Fe/Ti at the expense of dbcc, while the hyperfine parameters (IS, QS and HFmag) are practically the same in the two samples. This indicates the presence of similar phases in different thicknesses in the corresponding interface regions. The small difference in the intensity of the paramagnetic comp onent is clearly seen in the spectra of figure 3. For Ti/3.5 Fe/Ti dpara is larger than for Ag/3.5 Fe/Ti and this way dpara(Ti-on-Fe) = 0.14 nm. The slight difference in the HF distributions, with a 0.06 nm larger dmag for Ti/3.5 Fe/Ti than for Ag/3.5 Fe/Ti, results in d_mag^c (Ti-on-Fe) = 0.36 nm.

In the following, we attempt to estimate the relative phase volumes/thicknesses (Dpara, Dmag) from the Fe equivalent layer thicknesses (dpara, d_mag^c ) by considering the known concentration limits of the amorphous and crystalline alloys identified by MS. In lack of experimental data on the density of the different compounds, the alloyed thicknesses will be calculated using the bulk densities and the molar masses of the elements (ρFe, ρTi, MFe, and MTi, resp.), and the Fe concentration of the respective alloy (cFe) as follows:

D=d Å

1+ρ_FeM_Ti(1−c_Fe) ρ_TiMFecFe

ã .

(1) Determination of the alloy concentrations or the concentration distributions is impossible from the present Mössbauer spectra both for the amorphous and for the crystalline alloy.

Trials to fit the HF distributions of the crystalline alloy as a random solution by binomial distribution remained unsuc- cessful even for the separated RT spectral fractions. The small variation of IS and QS with the concentration of the amorphous alloy also make the estimation futile, therefore we use average concentrations by considering the known concentration limits of the amorphous and crystalline alloys. Consequently, in our modelling the possible concentration ranges 20 to 80at%

Ti for the amorphous [5] and 0 to 20at% Ti for the crystalline [32] components will be replaced by their average, 10 and 50at% Ti. Applying equation (1) to dpara and d_mag^c provides Dpara(Ti-on-Fe) = 0.35 nm, Dpara(Fe-on-Ti) = 0.52 nm, Dmag(Ti-on-Fe) = 0.42 nm, Dmag(Fe-on-Ti) = 1.47 nm thickness for the amorphous (Fe50Ti50) and crystalline (Fe90Ti10) alloy phases, respectively. The total Fe-on-Ti and Ti-on-Fe interface widths are 1.99 nm and 0.77 nm, respectively. The asymmetry of the interface width is beyond dispute, although the concentrations and the distribution of the interface alloys are somewhat uncertain. Allowing for relative deviations of the average concentrations as large as 50% (viz. 5 or 15 at% and 25 or 75 at% Ti for the magnetic and the paramagnetic alloy, respectively) results in 2.74 nm and 1.23 nm total Fe-on-Ti and Ti-on-Fe interface widths for the high Ti content and 1.67 nm and 0.60 nm for the low Ti content case.

From the above discussion of the Mössbauer results we may conclude that the Fe-on-Ti and Ti-on-Fe interfaces show a large difference in the total width, as displayed in figure 6, and in the relative amount of the Ti-rich amorphous and the Fe-rich magnetic alloys of the interface. The Fe-on-Ti interface appears almost three times thicker than the Ti-on-Fe interface. The Fe-rich bcc alloy dominates over the Ti-rich amorphous alloy in the Fe-on-Ti interface in contrast to the thinner Ti-on-Fe interface in which the two are of similar thickness (~0.4 nm). Such thin layers are often discontinuous.

The XRR measurements (see figure 2 and table 2) also indicate an asymmetry of the Fe-on-Ti and Ti-on-Fe interfaces beyond the estimated uncertainty of the roughness. The interface width is defined as the full width at half maximum 2·√

2·ln2·σ ≈ 2.355σ of the corresponding normal distribution, where σ is the interface (rms) roughness. The Gaussian distribution comprises 90% of its integral intensity (from 5 to 95%) within the full width at half maximum, therefore σ is a special case of a W5-95 interface width for an error-function like interface profile. Roughness values of 0.86 nm and 0.23 nm result in W5-95 = 2.0 and 0.54 nm for (the bottom) Ti and the Fe layers, respectively, to be compared with histogramic width of 1.99 and 0.77 nm estimated from the Mössbauer data.

The thickness of the Ti, TiOx and SiO2 deduced from the XRR measurements are consistent with those appearing in the TEM picture in figure 1(a). The derived layer structure is displayed in figure 6 along with the MS and EDXS data. XRR indicates a continuous Fe layer in Ti/3.5 Fe/Ti. The scaling of the experimental interface width may be model dependent, but an asymmetry between the (thinner) Ti-on-Fe and the (thicker) Fe-on-Ti interface is undoubtedly revealed by both the XRR and MS data.

The TEM measurements sample a much smaller area than XRR or MS, but reveal some further details of the structure.

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J Balogh et al

8

The 4.0 nm–4.2 nm Fe layer thickness, estimated from the dark contrast region in figure 1(a), appears larger than the XRR value of 3.6 nm, and exceed the nominal thickness of 3.5 nm.

Figures 1(a) and (d) clearly reveal a surface roughness of the Fe layer on both sides. From the contrast of the Fe layer the roughness can be estimated to be around 1–2 nm. Somewhat surprisingly, no alloyed bcc-Fe fraction can be identified and amorphous or disordered regions cannot be seen at the Fe–Ti interfaces, although the EDXS results indicate mixing between the layers. The Fe concentration peaks only at 95 at% and the concentration change is not abrupt but extends over 2–3 nm in the elemental concentration depth profile of figure 1(c) derived from the EDXS measurement. Moreover, EDXS does not show noticeable asymmetry between the Fe-on-Ti and Ti-on-Fe interfaces, which contradicts to the MS and XRR results, as shown if figure 6. To understand the mes- sages of figure 1, one has to consider the specimen geometry used in the TEM experiments. The specimen was approxi- mately 40 nm thick (in the view direction) and the measurement shows the projected signal in the maps. The elemental distribution is a result of averaging the signal across the specimen thickness parallel with the substrate surface. Moreover, the grain size of Fe (and of Ti) is smaller than the thickness of the specimen, the signal at a given point stems from sev- eral grains. The contributions of the grain boundaries and of the interface roughness along the electron beam direction are averaged, resulting in a broadened elemental distribution. The small crystallite size might explain an Fe concentration profile peaking at 95 at%, since the Ti deposition on Fe may results in Ti diffusion along the grain boundaries, which appears as the presence of Ti in the middle of the Fe layer, as shown in figure 1(c). Diffusion along the grain boundaries might also explain that the experimentally observed interface thickness is about one order of magnitude larger than the one obtained by MD simulations assuming perfect single crystal substrate layers. One may conclude that the EDXS measurement across small-sized crystalline layers using TEM may not give clear view on the distribution of the elements. Here we note, that

the high-resolution BF STEM image of figure 1(d) also allow alloying up to a few atomic percent at the interfaces, since it may be characteristic only to the change of the structure.

The apparently larger thickness of the Fe layer as compared the nominal value or to the MS and XRR values, also support this notion. One can conclude that while TEM provides very important information on the structure of the layers, but the cross-sectional analysis of the current polycrystalline samples is not suitable to unambiguously reveal the structure and the chemical composition of the interface.

It is worth putting the present results into context with the adhesion and surface energies of the layers. According to a rule of thumb, the smaller the surface energy of the underlayer as compared to that of the over-layer, the larger the tendency for clustering and consequent interface roughening [33]. Since the layer growth occurs under highly non-equilibrium conditions the kinetics of the process and the adhesive energies of the layers gain importance [34, 35]. The lower the adhesive energy of the underlayer, the more often atomic exchanges between the ad-atoms and the surface atoms of the underlayer take place. The experimental values for the surface energies [36–38] range from 1.99 to 2.10 (J m⁻²) for Ti and from 2.42 to 2.48 (J m⁻²) for Fe, which predict a slight asymmetry of the interfaces, the Ti-on-Fe being sharper than the Fe-on-Ti.

Our MD simulation results on interface mixing are in good agreement with the above expectations. It is worth a mention that the MD simulations provided a much larger asymmetry for the Fe–Al system [17] in accordance with the surface energy values, being smaller for Al (1.14–1.16 (J m⁻²)) than for Ti. The cohesive energy is also smaller for Al than for Ti [39], thereby making Al-for-Fe exchanges easier at the Al surface than Ti-for-Fe exchanges at the Ti surface. The experimental values obtained by Mössbauer spectroscopy and by x-ray reflectometry also show the asymmetry of the Fe-on-Ti and Ti-on-Fe interfaces, but the estimated interface width is larger than those derived from MD simulations. The larger intermixing is most probably due to the large amount of grain boundaries seen in the TEM pictures. An enhanced diffusivity along the grain boundaries certainly increases the width of the intermixed region and it may play a role in the formation of amorphous regions.

Solid state amorphization at thin film interfaces may occur when the diffusion coefficients of the elements of the layers in touch are largely different [40]. Iron (similarly to Co and Ni) is well known to exhibit fast diffusion in hcp-Ti, the Fe impu- rity diffusivities being more than 10⁴ times larger than the Ti self-diffusivity [41], while the diffusivity of Ti in bcc-Fe is about the same magnitude as in Ti [42]. In view of the diffusivities, the amorphous alloy formation is expected predominantly at the Fe-on-Ti rather than at the Ti-on-Fe interface, but fast diffusion along the grain boundaries or defect sites may alter the picture and explain why the estimated average thickness of the amorphous layers at the Fe-on-Ti and the Ti-on-Fe interfaces are so little different, Dpara = 0.52 nm and 0.35 nm, respectively. The absence of amorphous or disordered regions in the atomic layer structure visible in figure 1(b) supports the notion that the component identified as amorphous by Mössbauer spectroscopy does not form a continuous layer.

Figure 6. Layer and interface profiles of Fe in Ti/3.5Fe/Ti as inferred from MS, XRR and EDXS data. The common depth zero is chosen arbitrarily for all methods as the abscissa of the half maximum Fe concentration point at the Ti-on-Fe interface.

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7. Conclusion

Conversion electron Mössbauer spectroscopy and x-ray reflectometry measurements on Ti/Fe/Ti trilayers grown on Si(1 1 1) substrates by vacuum evaporation are indicative of asymmetric Fe interfaces, with the Fe-on-Ti interface being a factor of 2–3 times wider than the Ti-on-Fe interface. The alloys formed at the interfaces are identified by Mössbauer spectroscopy; Fe-rich bcc alloy as the main component and Ti-rich amorphous alloy as the minor component. The Fe-rich bcc alloy dominates over the Ti-rich amorphous alloy in the Fe-on-Ti interface in contrast to the thinner Ti-on-Fe interface in which the two are of similar thickness Atomic resolution TEM shows domains with rather sharp lattice spacing transition at the interfaces, supporting the idea that the amorphous alloy does not form a continuous layer at the interface.

Molecular dynamics simulations of the layer growth also show asymmetric concentration distribution along the layer growth direction; it is atomically sharp at the Ti-on-Fe interface for the (0 0 1) and (1 1 0) crystallographic orientations of the Fe layer, while it varies over a few atomic layers for Fe(1 1 1) substrate and at the Fe-on-Ti interface for all basic crystallographic orientations of Ti. The larger experimental interface width as compared to the simulated values is probably due to the polycrystalline nature of the layers, the small size of the Fe crystallites and the grain boundary diffusion during deposition. Experiments on single crystal or perfect epitaxial layers could explore the role of crystal orientations, grain boundaries and interface roughness and would allow for a more direct comparison of the experiments and the MD calculations.

Acknowledgment

The authors acknowledge financial support of the Hungarian Scientific Research Fund (OTKA) Grant K112811.

ORCID iDs

D Kaptás https://orcid.org/0000-0002-2084-8928 D G Merkel https://orcid.org/0000-0001-9644-2521 Sz Sajti https://orcid.org/0000-0002-8748-8242

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