Epitaxial growth and stress relaxation of vapor-deposited Fe–Pd magnetic shape memory films

To achieve maximum performance in microscale magnetic shape memory actuation devices epitaxial films several hundred nanometers thick are needed. Epitaxial films were grown on hot MgO substrates (500 °C and above) by e-beam evaporation. Structural properties and stress relaxation mechanisms were investigated by high-resolution transmission electron microscopy, in situ substrate curvature measurements and classical molecular dynamics (MD) simulations. The high misfit stress incorporated during Vollmer–Weber growth at the beginning was relaxed by partial or perfect dislocations depending on the substrate temperature. This relaxation allowed the avoidance of a stress-induced breakdown of epitaxy and no thickness limit for epitaxy was found. For substrate temperatures of 690 °C or above, the films grew in the fcc austenite phase. Below this temperature, iron precipitates were formed. MD simulations showed how these precipitates influence the movements of partial dislocations, and can thereby explain the higher stress level observed in the experiments in the initial stage of growth for these films.


Introduction
The magnetic shape memory (MSM) effect is a promising candidate for realizing actuation in microsystems as well as in smart sensor concepts as required, e.g. in micro-electromechanical systems, and has attracted significant interest in recent years [1]- [6]. Even though higher strains have been reported for Ni-Mn-Ga [7], the Fe-Pd system in the proximity of the composition Fe 70 Pd 30 [1] has several advantages for practical applications, including its high ductility and the orientation of its easy axis of magnetization along the long c-axis of the martensite, allowing the use of an out-of-plane magnetic field in a thin-film-actuator.
While Fe-Pd bulk properties have been studied thoroughly already [8], little is known about Fe-Pd thin films around the composition Fe 70 Pd 30 . Recently, the growth of very thin epitaxial films on MgO substrates produced by pulsed laser deposition (PLD) has been reported [9]. However, in these films epitaxy breaks down at a thickness of 10-20 nm because of massive (111)-twinning induced by strong tensile stress [10]. While Sugimura et al [2] and Inoue et al [11] reported on MSM Fe-Pd thin films grown by sputtering, little research has been conducted on thin films grown by thermal vapor deposition. The latter provides growth conditions closer to thermal equilibrium compared to sputtering and PLD, where the kinetic energies of the deposited atoms are considerably higher, and therefore have a major influence on film properties. Polycrystalline thin films have already been prepared [12], but epitaxial (i.e. single crystalline) films are necessary to achieve maximum strain and performance in applications.
For investigations of basic atomic scale processes that determine the macroscopic properties of epitaxial Fe-Pd thin films, transmission electron microscopy (TEM) investigations provide information on the atomic structure, whereas in situ mechanical stress measurements reveal valuable information about microscopic processes during and after film growth. In order to gain insight into the mechanisms and kinetics of the stress relaxation processes, molecular dynamics (MD) simulations based on the results of TEM investigations as well as the results of the stress measurements were run to directly observe the atomic processes. 3 The films discussed here were grown with a total rate of about 0.15 nm s −1 on highly polished MgO (100) single crystal substrates, which were heated to temperatures between 400 and 750 • C by a radiation heater from the back side. A calibration was conducted between the temperatures of an additional thermocouple attached directly to a substrate and the setpoint of the heating system. In order to ensure thermal homogeneity and to desorb a possible layer of hydroxide from the surface, the substrate temperature was kept constant for at least 90 min before deposition. For comparison, one film grown on amorphous SiO 2 at a temperature of 770 • C was also investigated.
Stress measurements were performed using a single laser beam deflection dilatometer, as described previously [14], while the rectangular substrate (dimensions 25 mm × 10 mm × 0.22 mm) was clamped to the holder with one short side. For this geometry, the average film stress σ times film thickness t f can be calculated from the substrate curvature using the modified Stoney equation [15]: with B s being the biaxial modulus of the substrate, taken as B s = 3.19 × 10 11 Pa from [16], and t s and 1/r being the substrate thickness and the substrate curvature, respectively. Owing to the limited dynamics range of the lock-in-amplifier used, a neutral gray filter was inserted into the laser beam path at a film thickness 22 nm during the growth of the film prepared at 630 • C. This change in the optical setup leads to the observed deviations from a linear slope at this thickness. Films with total thicknesses between 30 and 500 nm were studied, which is to be taken as mass equivalent thicknesses. Within the limitations of energy dispersive x-ray spectroscopy (EDX) measurements on thin films, a Pd content of about 30 at.% was confirmed with a system manufactured by the Thermo Electron Corporation attached to an LEO supra 35 scanning electron microscope that was also used for imaging. The surface morphology was confirmed with atomic force microscopy (AFM) topographs, taken with a Veeco Nanoscope IV system in tapping mode, which are not shown here. The crystal structure of the films was characterized by x-ray θ -2θ scans performed with a Bruker AXS D8 advance ™x-ray diffractometer and Cu K α radiation as well as by texture measurements on the [113]-pole with a Philips X'pert system and Co K α radiation to prove epitaxy. Thin lamellae were cut from the samples with an FEI Nova Nanolab 200 focused ion beam (FIB) system using Ga + ions after application of a Pt protection layer, and then studied in a Philips CM200-UT-FEG TEM operated at 200 kV.

Experimental results
The three films that will be discussed in more detail here were prepared at different substrate temperatures, while all other growth parameters (esp. the evaporation rates) were kept constant in order to ensure the comparability of these samples. Characterizations with respect to basic growth mode show a Volmer-Weber growth for all films investigated. A continuous film is formed at a critical thickness, which increases with increasing substrate temperature. For a substrate temperature of 630 • C SEM images (see figure 1) and AFM topographs confirm that the islands have coalesced at about 50 nm thickness, while for films grown at a substrate temperature of 690 • C the films are not completely closed at a thickness of 100 nm.
The phases, structures and lattice parameters of the films were investigated for different deposition temperatures, summarized in table 1. For films grown at 690 • C or above TEM diffraction patterns confirm the phase to be the fcc austenite with a cube-on-cube relationship The islands have almost completely coalesced to a smooth, closed film. The remaining holes (shown either as dark or bright rectangles, depending on whether they reach down to the substrate or not) and the terraces show a rectangular shape, with a preferred orientation along the substrate (100) direction. between film and substrate, as was also observed in the initial stage of films prepared by PLD [9]. The lattice parameter as calculated from the TEM diffraction patterns as well as the (200) peak in the x-ray diffraction (XRD) spectra is a = 3.76 × 10 −10 m, being consistent with the results obtained by Cui et al [8] for bulk Fe 70 Pd 30 . Growth at temperatures below 690 • C leads to partial demixing of the films. In addition to the Fe 70 Pd 30 fcc peak mentioned above, the XRD-spectra of these films show a bcc Fe (200) peak (lattice parameter a = 2.87 × 10 −10 m) as well as a (200) and an additional superstructure peak from the ordered Fe 50 Pd 50 L1 0 phase leading to an out-of-plane lattice parameter of c = 3.67 × 10 −10 m. The microstructure of the Fe-Pd films was investigated by high-resolution TEM (HRTEM). Epitaxial growth was observed for all films grown at substrate temperatures of 500 • C and above (i.e. all films mentioned here); see the HRTEM image in figure 2. It needs to be pointed out that no thickness limit was found for epitaxial growth, either by HRTEM for film thicknesses up to 100 nm, or by texture measurements on the {113}-pole for film thicknesses up to 500 nm, the latter showing the expected fourfold symmetry with no additional peaks. Careful inspection of the images shows that if Fe precipitates are present they are favorably placed flat on the substrate with a thickness range of 5-10 nm from the substrate, but there are also some Fe precipitates throughout the whole volume of the film. Dislocations could be found at the substrate-film interface for both films with and without Fe precipitates.
Microtwins are observed in all investigated lamellae of films grown at or below 630 • C, whether they are continuous or not; see figures 3 and 4. The angle of 55 • between the twinning planes and the film surface in the projection onto the [110] plane of the TEM lamella is as expected for {111} twinning planes. Microtwins were not found in a non-demixing film deposited at 690 • C.
Epitaxial growth as it is observed for our films is only possible if the initial lattice misfit is reduced by relaxation. To gain further insights into the processes that occur during film growth, in situ substrate curvature measurements were performed during film growth. Such in situ mechanical stress measurements for films grown at 630 • C, 690 • C and 750 • C, respectively, are shown in figure 5. A positive slope of σ t f corresponds to tensile stress by convention. For all films, no data points could be recorded while the substrate shutter was closed (prior to deposition while the evaporators were heated, and immediately after deposition, until the sources had cooled down). A characteristic change in substrate curvature immediately after opening the substrate shutter and during the first 120 s occurs, regardless whether a film is deposited on the substrate or not. This change in substrate curvature is a temperature effect of the deposition system. Opening of the shutter in front of the substrate at the beginning of the deposition run leads to a short drop in temperature and thus a tilting of  the substrate. Temperature measurements with a thermocouple attached to the substrate show that after about 2 min (corresponding roughly to the deposition of 15 nm) thermal equilibrium is reached again. Therefore, all data from these periods has been excluded from all graphs and evaluations. In situ substrate curvature measurement during and after film growth. Deposition periods and thickness of film are both marked with a bar in the corresponding color. In both cases, tensile stress is developed in the early stages of film growth. In the later stage, the film grown at 700 • C shows almost stressfree growth, while the film grown at 630 • C shows a decrease in substrate curvature, and a much higher overall stress. The smallest stress is observed at the highest substrate temperature of 750 • C, where the signal-to-noise-ratio (SNR) is dramatically decreased.
For the film grown at 630 • C, we observe a tensile stress of 1.00(15) GPa up to a film thickness of 50 nm, where the substrate curvature has a maximum. After this thickness, the slope is negative (−0.21(15) GPa), which corresponds either to compressive stress in the newly grown layers, or to a relaxation of the tensile stress in the deeper layers of the film. After deposition, the film stress decreases approximately exponentially as a function of time. The film prepared at 690 • C was grown in two steps. In the first step, a film with a thickness of 138 nm was deposited. Then, a shutter underneath the substrate was closed, as the material in the evaporators had to be remelted in order to ensure stable rates and evaporation characteristics over the long deposition run. Subsequently, another 69 nm were deposited on top of the film. For this film, a tensile stress of 0.38(5) GPa is observed during the first 40 nm of film growth. A maximal curvature of the substrate is reached at a thickness of 60 nm. However, this maximum is not as pronounced as for the film grown at 630 • C. The second deposition run shows a rise in curvature for the first 20 nm deposited, after which the curvature of the substrate is constant and almost identical to the level before the interruption, so the newly grown layers of the film are not stressed. After the end of the deposition, a decrease in curvature can be observed, which is of a very similar magnitude and duration as at the beginning of the second deposition run.
The film grown at 750 • C shows a dramatically decreased SNR, because the light emitted from the radiation heater is much more intense at this temperature. Nevertheless, an initial slope of about 0.2 GPa can be determined, which seems to decrease towards the end of the film growth.

Simulation details
The lattice constant of bcc-Fe is between the values for MgO and Fe 70 Pd 30 , so for the demixing film one could expect an iron buffer layer between the substrate and the film, and a relatively low 8 stress in the film. However, this film reaches the highest substrate curvature, much higher than with the non-demixing films. Precipitates not only form at the substrate-film interface, but also in the whole film volume. In order to understand the influence of these precipitates on stress relaxation, classical MD simulations were performed using a group-maintained code also used in [17]. For these simulations, FePt was chosen as a model system because of the availability of the well tested analytic bond-order potential derived in [18]. This choice can be justified by the great chemical and structural similarities between Pt and Pd, and especially the phase diagrams for Fe-Pd and Fe-Pt in the region of the 50 : 50 composition. This potential reproduces the overall properties of equiatomic alloys well, even though it is known to overestimate the twinning energy [18], so only qualitative conclusions can be drawn from the simulations. Upon straining, the simulations show a stress relaxation via microtwins, which has also been found in ordered L1 0 FePd-films experimentally [19].
For reference, a rectangular simulation cell of 2.5 × 10 5 Fe atoms and 2.5 × 10 5 Pt atoms was prepared in the L1 0 structure. In accordance with the experiments, this cell with periodic boundary conditions in all spatial directions was heated to a temperature of 900 K using a Berendsen thermostat and barostat [20] set to zero hydrostatic pressure. After a relaxation of 200 ps, the volume was kept constant, and the periodic boundary conditions were released in the z-direction. In addition to that, the last two atomic layers in the negative z-direction were fixed in order to mimic a rigid substrate, while in the positive z-direction a free surface was formed. This now resembled an infinite film in the x y-plane stuck epitaxially to a rigid substrate. The reference cell was relaxed in this geometry for an additional 40 ps. During this relaxation time, the total energy of the system reached a constant value.
Based on the results of TEM and XRD investigations, which show that the film grown at 630 • C has at least partially demixed into a L1 0 Fe 50 Pd 50 matrix and bcc iron precipitates, a second cell is created from the reference cell by cutting out 10 spherical holes at random positions and placing a bcc-Fe precipitate in each. As with the reference cell, the cell with precipitates is relaxed, but for 100 ps to ensure a full relaxation of the cell. After these preparation steps, both cells are being strained with a rate of 10 −7 per fs by rescaling the xand y-axes. In addition, tests with other straining rates are performed, and no dependence on the strain rate is observed. During this straining process, each snapshot corresponds to a film grown on a substrate with a lattice mismatch equivalent to the applied strain.
Snapshot images for all atomic positions are taken regularly, and the central-symmetry parameter c as defined in [21] for each atom is being calculated at each snapshot. For visualization, all atoms within a certain range of this parameter are rendered using the software AtomEye [22]. This parameter quantifies how much the surrounding of a given atom deviates from a point symmetric geometry. These deviations are either caused by thermal fluctuations, or by changes in the crystal structure. For a twin boundary, which can be seen as an intrinsic stacking fault in the fcc-crystal, a value of c = 0.042 can be expected, whereas thermal fluctuations are significantly smaller [22], so a range of 0.014 < c < 0.4 is chosen for all images.

Simulation results
The simulation cells, both with and without the iron precipitates, show a similar qualitative stress-strain behavior as shown in figure 6. Quantitatively, however, the elastic modulus and the critical strain required to trigger a stress relaxation differ. While the elastic modulus for the film without precipitates is 192.6 ± 0.5 GPa (see [18] and the discussion of elastic moduli therein), the film with precipitates shows a significantly higher modulus with 238.6 ± 0.4 GPa. After reaching a critical strain of 4.5%, the film without precipitates starts to deform plastically via partial dislocations, while the cell with precipitates does so after a strain of 4.7%.
In the simulation cell without precipitates in figure 7, partial dislocations nucleate after reaching the critical stress and move through the whole cell on {111}-planes. As the strain is increased further, additional partial dislocations move through the planes adjacent to the planes of the first stacking faults, thus increasing the width of the microtwin as shown in figure 7(d). This is in excellent agreement with the experimental results on L1 0 FePd films [19].
In the simulation cell with precipitates, pinning of a partial dislocation at a precipitate can be observed ( figure 7(a)). Shortly after, a new microtwin parallel to the blocked one intersecting the precipitate appears and moves through the sample ( figure 7(b)). This new microtwin increases its thickness by the gliding of additional partial dislocations on the twin boundary planes while the blocked twin starts to disappear ( figure 7(c)). This shows that the creation of a new microtwin at the cost of the energy of two stacking faults is more energetically favorable than the movement of the twin boundary through the precipitate. A direct comparison between the simulation cells for a given strain shows that the cell without precipitates has fewer but wider twins, whereas the cell with precipitates has more but thinner microtwins.

Discussion
In thin epitaxial Fe 70 Pd 30 films, a temperature of 690 • C is sufficient to avoid demixing, which is significantly lower than the 760 • C which is necessary to avoid demixing in bulk samples [23]. While bulk samples are entirely governed by volume properties, surface properties have a major influence on thin films. Often, a structure stabilized at the interface is also kept stable in the volume when the old surface layer has been overgrown. Comparisons to polycrystalline films grown on amorphous SiO 2 show that the fcc structure of Fe 70 Pd 30 is stabilized by the epitaxial relation to the substrate, as these films on SiO 2 show a complete demixing at temperatures as high as 770 • C, which is even slightly above the bulk value. In contrast to thin films grown by PLD, thermal evaporation of Fe-Pd shows no breakdown of epitaxy for thicknesses up to 500 nm. The kinetic energies of the incident atoms seem to be a key factor as they are much lower for thermal evaporation than for PLD, where generation of numerous interstitial atoms by shot-peening leads to the breakdown of epitaxy at about 10-20 nm of film thickness [10]. 11 We attribute the strong tensile stresses observed in all films at thicknesses of 10-50 nm to the large misfit of the Fe-Pd-on-MgO growth system. A rough estimation of the misfit stress σ yields with the strain = 0.105 corresponding to the substrate-film mismatch, E = 120 GPa (taken from [24]) being Young's modulus of Fe 70 Pd 30 at about 600 • C and ν = 1/3 being the Poisson ratio. This value is not observed in the experiment due to incomplete coverage of the substrate, and very likely due to compensation for a part of the strain by dislocations at the film-substrate interface.
Above a thickness of about 100 nm, the film grown at 690 • C shows an almost constant curvature (apart from a stage at the beginning of the second deposition run, which then leads to the same value as before the growth interruption). As the stress in the just-grown layer is the first derivative of the substrate curvature, further atomic layers grow stress free and epitaxial growth can be maintained to very high film thicknesses despite the large initial lattice mismatch of about 10%. Together with the fact that no microtwins were observed in the samples prepared above 690 • C, this suggests that during film growth edge dislocations are intrinsically incorporated into the film, until the misfit is compensated for and the equilibrium lattice constant of the Fe 70 Pd 30 film is reached at a film thickness of about 60 nm.
For the demixing films, it is favorable to create Fe precipitates between the substrate and the film, thus acting as a buffer between film and substrate as the misfit for 45 • rotated growth of α-Fe is only about 3.4%. Stress relaxation via partial dislocation motion has been observed for ordered Fe 50 Pd 50 before [25], and is also supported by our HRTEM investigation of the films grown below 690 • C. In fcc crystals, the favored glide system is {111} 110 ; see e.g. [26]. As these 1/2 110 perfect dislocations can split into 1/6 112 Shockley partial dislocations, there are two kinds of mechanism expected to relax misfit strains in fcc metallic thin films. A pile-up of partial dislocations leads to the formation of microtwins [25]. An estimation of the energy cost of these two mechanisms in ordered and disordered Fe 50 Pd 50 was carried out by Halley et al [19] and can easily be generalized to a broader composition range. The propagation of a perfect dislocation in a perfectly ordered Fe 50 Pd 50 L1 0 structure leaves an antiphase boundary (APB) in the {111} glide plane with an energy estimated to be γ APB 111 ≈ 0.2 J m −2 [19]. This contribution vanishes in the same degree as the ordering vanishes. On the other hand, the propagation of a partial dislocation always leaves a stacking fault in the glide plane that is linked to a stacking fault energy, while the total energy of the partial dislocation is independent of chemical order. We can thus estimate the energy of the partial dislocation from the stacking fault energies of pure iron [27] and pure palladium [28] 30 : for the ordered L1 0 structure partial dislocations and thus microtwins are the favored mechanism for mechanical stress relaxation, whereas for a decreasing degree of order perfect dislocations become favorable.
This explains why microtwins occur in all films except for the non-demixing ones grown at high temperatures, which do not exhibit the ordered L1 0 phase. One can instead observe edge dislocations at the film-substrate interface in regular intervals. From the MD Simulations, it can be seen that the bcc-Fe precipitates have a negative effect on the stress relaxation via twinning: as seen in figure 7, a twin boundary can be stopped at a precipitate, and a new twin boundary 12 that does not intersect the precipitate is formed. From these results, it can be understood that the film with precipitates shows the highest average stress in the experiments.
For a growth temperature of 630 • C microtwins are already observed in a thin film of 30 nm thickness, which is consistent with the results obtained by Liu et al [29], who calculated the critical thickness for misfit twinning during growth with a tensile mismatch strain of 0.10 to be about 0.8 nm. Nevertheless, the overall trend of the stress measurement suggests that the vast majority of the stress relaxation happens at a film thickness of 50 nm, which also coincides with the thickness at which the islands coalesce to a continuous film. Before the stress is fully relaxed, it is energetically unfavorable to increase the tensile stress in the film even further by island zipping, whereas once the lattice misfit has fully been compensated the tendency to reduce the film surface leads to the formation of a continuous, smooth film. This picture is supported by the fact that the intensity of the reflected laser beam reaches a maximum shortly after the curvature has reached its maximal value. Here, the derivative of the substrate curvature, and thus the stress in the newly grown layers, is zero. The intensity of the reflected laser beam is related to the surface roughness of the film [30], so this maximum intensity is the signature of a minimum in roughness.
However, there has to be a further mechanism that can account for the exponential decay of the stress after deposition. As pure surface effects like a surface reconstruction after the end of film growth only affect the stress state in a few monolayers, this pronounced relaxation can only be volume effects. One explanation could be a dynamic balance between defects being incorporated into the film, and such defects annealing out. After the deposition has stopped these defects still heal out, while no new defects are created. This leads to the relaxation observed after the end of deposition, and could also explain the feature observed at the beginning of the second deposition run of the sample prepared at 690 • C, which shows the same inverse behavior as after the deposition, with a very similar magnitude and time constant. A massive surface roughening like an Asaro-Tiller-Grinfeld instability [31] can be excluded from the intensity of the reflected laser beam. Such a mechanism would lead to a characteristic decrease in intensity caused by surface roughening after the end of deposition and a corresponding increase when the grown is continued, which is not observed.

Conclusion
Despite the large lattice mismatch of roughly 10%, epitaxial growth of thick single-crystalline Fe 70 Pd 30 films on MgO is possible by e-beam evaporation at suitable substrate temperatures. During early stages of film growth, a strong tensile stress caused by the misfit to the substrate is incorporated into the film. This stress is relaxed by different mechanisms that depend on the phase and microstructure, which are strongly influenced by the substrate temperature. For lower temperatures, a demixing into (partially L1 0 ordered) Fe 50 Pd 50 and bcc-Fe precipitates is observed as expected from the bulk phase diagram. Even though coherent bcc-Fe precipitates can act as a buffer layer at the substrate-film interface, MD simulations show that the presence of such precipitates in the film volume hinders twin boundary motion, and thus leads to a higher residual stress in the film, as also observed in the experiments.
On MgO substrates, no demixing during film growth was found for substrate temperatures of 690 • C and above. The crystal structure forced upon the film by the epitaxial relation to the substrate obviously stabilizes the fcc Fe 70 Pd 30 phase to lower temperatures than in bulk samples or in films on amorphous substrates. At the same time, bcc iron precipitates that mainly occur at small thicknesses can act as a buffer layer, and thereby reduce the misfit dramatically, thus further stabilizing the system against demixing in later stages of film growth. These films with precipitates relax the stress via a pile-up of partial dislocations, leading to the formation of microtwins. As also observed in the MD simulations, the Fe precipitates hinder this stress relaxation and lead to a higher number of smaller twins, instead of fewer but larger twins as for pure Fe 50 Pd 50 .
Films without Fe precipitates do not show microtwins, so the stress is most likely relaxed by the introduction of perfect misfit dislocations during epitaxial growth. Once the lattice mismatch has been compensated, the epitaxy is preserved even for very high thicknesses.