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Thickness dependence of (001) texture evolution in FePt thin films on an amorphous substrate
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Thin Solid Films 516 (2008) 1147 – 1154 www.elsevier.com/locate/tsf
Thickness dependence of (001) texture evolution in FePt thin films on an amorphous substrate Jae-Song Kim ⁎, Yang-Mo Koo Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea Received 19 July 2006; received in revised form 6 April 2007; accepted 8 June 2007 Available online 15 June 2007
Abstract Thickness dependency of (001) texture evolution in Fe54Pt46 thin films on an amorphous substrate was investigated using in-house X-ray diffraction or a synchrotron source. The (001) texture was well developed in Fe54Pt46 thin films, especially when its thickness was equivalent to the grain height. The findings show that strain relaxation anisotropy along the film axis, which leads to a (001) crystal (a crystal with a (001) plane parallel to the film plane) that is more stable than others, was large for a low thickness film. In addition, abnormal grain growth was used to explain the abrupt development of a (001) texture. The advantage of multilayered as-deposited structure is also discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: FePt; Texture; Transformation into ordered phase; Strain by phase transformation; Vook–Witt condition
1. Introduction The L10 FePt alloy is an attractive candidate for use in ultra high density media such as perpendicular recording media (PRM), in that it has a high uniaxial anisotropy energy and is highly resistant to corrosion which confers thermal stability even at the nano grain size [1–3]. To apply a FePt alloy to PRM, the (001) crystallographic fiber texture must be normal to the film plane because the L10 FePt alloy has a magnetic easy axis in the [001] (c-axis) direction. Epitaxial growth methods have been widely used, in attempts to produce a (001) texture, and a MgO substrate or MgO, Cr, CrRu intermediate layers have been used [4–8]. C.P. Luo and H. Zeng recently succeeded in obtaining a (001) texture through the postannealing of (FePt/B2O3)n or (Fe/Pt)n multilayered films on an amorphous substrate [9,10]. Similarly, we found that a co-sputtered Fe55Pt45 thin film has a (001) texture after postannealing if the film is of an appropriate thickness [11]. FePt thin films having a non-epitaxial (001) texture show a similar tendency in which as-deposited films have no (001) texture that develops through phase transformation and grain growth during postannealing. ⁎ Corresponding author. Tel./fax: +82 54 279 5130(2399). E-mail address: [email protected] (J.-S. Kim). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.06.071
Traditional theories have mainly considered surface energy or biaxial strain energy for the postannealing texture in thin films [12]. However, in the case of a FePt thin film, the (111) surface has the lowest surface energy, and the (100) crystal (crystal with a (100) plane parallel to the film plane) has the lowest strain energy under biaxial strain conditions [13]. Therefore, the traditional theories cannot be applied to this case. In a previous paper, we proposed that phase transformation (fcc → L10) strain is able to stabilize the (001) crystal more than others and to induce a (001) texture under appropriate conditions such as tensile in-plane strain or Vook–Witt conditions (plane stress condition) [13,14]. A FePt thin film generally remains in a metastable fcc phase after deposition. The fcc FePt alloy cannot be used for recording media due to its soft magnetic property. Therefore, FePt thin films require a postannealing process accompanied by a transformation into ordered phase (fcc →L10) which induces anisotropic strains, especially up to 3% along c-axis. In-plane tensile strain is an isotropic strain parallel to the film plane, which can be attributed to volume shrinkage caused by the elimination of defects and grain growth during postannealing. In the case of the (001) crystal, inplane tensile strain and phase transformation (fcc →L10) strain are in a diametrically opposite directions, so strain energy induced by transformation into ordered phase (fcc→ L10) can be cancelled out by the in-plane tensile strain [13] and a (001) crystal is more stable than other crystals. The Vook–Witt condition is an anisotropic grain
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interaction model along the specimen axis since the strain parallel to the film plane is equal for all crystallites (as in Voigt conditions) and the stress perpendicular to the film plane is zero for all crystallites (as in Reuss conditions) [14,15]. Therefore, the Vook–Witt condition can be described by a strain and stress tensor in the film coordinate system as follows [14] 2 3 2 3 e 0 e13 r11 r12 0 e¼4 0 e e23 5; r ¼ 4 r12 r22 0 5: ð1Þ 0 0 0 e13 e23 e33 The “3” direction is the direction perpendicular to the film plane, and the orientation of the orthogonal “1” and “2” axes is the direction parallel to the film plane. “e” is the value of a given in-plane strain, and six unknowns (ε13, ε23, ε33, σ11, σ12, σ22) can be calculated by solving Hook's law [16]. Under the Vook– Witt condition, the (001) crystal has free stress in the c-axis. Consequently, phase transformation strain which exists mainly along the c-axis is easily relaxed in the case of a (001) crystal. On the other hand, the phase transformation strain of (100) crystals, the orientation of which is a perpendicular to the (001) crystal is difficult to relax because its c-axis is tightly constrained by the substrate. As both of the (100) and (001) crystal seem to be an extreme case for the relaxation of phase transformation strain, assuming anisotropic interactions (Vook–Witt assumption) along the in-plane or out-of-plane, it can be inferred that the Vook–Witt condition can increase the relative stability of a (001) crystal over others by the additional relaxation of the phase transformation strain of a (001) crystal [13]. We experimentally verified that phase transformation strain and tensile in-plane strain co-exist in a FePt thin film, and that such a strain state can stabilize the (001) crystal [11]. However, phase transformation strain and tensile in-plane strain are limited in their ability to explain the thickness dependence of the (001) texture [9,17,18]. Changes in in-plane tensile strain are mainly induced by lateral volume shrinkage, caused by grain growth parallel to the film plane. However, as in-plane tensile strain would be expected to be large for high thickness film (a thick film has little stagnation of grain growth by film thickness compared to a thin film), the inverse relation between film thickness and (001) texture, which will be shown in the present study, is difficult to describe using only in-plane tensile strain. Instead, the Vook–Witt condition, which is generally considered to be one of the important origins of (001) texture in previous studies [13], seems to offer an alternative factor for explaining thickness dependence because the Vook–Witt condition is related to the entire microstructure of a thin film. Thin films having a low thickness have the opportunity to be under the Vook–Witt condition because grains in such films get little interference from other grains in the direction perpendicular to the film plane (ensuring minimal stress normal to the film plane), and the aspect ratio – width/height – of grains tends to be large, ensuring the Vook–Witt condition [19]. Based on a previous theoretical prediction [13], the Vook–Witt condition contributes to the stability of a (001) crystal, even under compressive inplane strain. In other words, the Vook–Witt condition can facilitate the development of a (001) texture, even under an
unfavorable macroscopic strain condition. These relationships suggest that the Vook–Witt condition is a dominant factor in explaining the thickness dependence of (001) texture. The purpose of this study was to examine the relation between film thickness and (001) texture by confirming that the (001) crystal can be relatively stabilized over others by effectively relaxing its phase transformation strain when an appropriate microstructure (for example, thin thickness film) which satisfies the Vook–Witt condition is present. The texture, ordering parameter, lattice parameter, and grain size of Fe54Pt46 thin films were analyzed for various film thicknesses as a function of annealing time, using X-ray diffraction (XRD) in our laboratories or a synchrotron source. The relation of film thickness and (001) texture was examined by conducting a semi-quantitative texture analysis. Next, we show that strain relaxation enables the (001) crystal in a thinner film to be relatively stabilized, based on investigating the variation of lattice parameter and grain size because they have a good microstructure that satisfies the Vook– Witt condition. In Section 2, the procedures for specimen preparation and the X-ray experiments are described. In Section 3, the origins of thickness dependence of the (001) texture are discussed on the basis of the experimental results obtained. Finally, our conclusions are presented in Section 4. 2. Experimental details Magnetic thin films with composition Fe54Pt46 were dc magnetron sputtered on an oxidized silicon substrate with a 100nm thickness silicon oxide layer, where a FePt alloy target was used. The base pressure of the chamber was less than 7 × 10− 5 Pa, and a working pressure of 0.27 Pa Ar was used during the sputtering. The deposition rate was ∼ 0.1 nm/s, and the substrate was mounted on a water-cooled rotating table. Fe54Pt46 thin films were prepared in five different thicknesses — 9, 22, 44, 66, and 88 nm at room temperature. The film thickness and composition were confirmed by X-ray reflectivity and Rutherford Backscattering Spectroscopy (RBS). As-deposited films were rapid thermal annealed at 550 °C in ∼0.4 bar of N2 gas for 3, 10, 30, 100 and 300 s, where the heating rate was 100– 150 °C/s. X-ray diffraction experiments were performed with an inhouse (Huber goniometer with Rigaku 18 kW) or synchrotron XRD (10C1 at the Pohang Light Source). The former was mainly used to analyze the texture, and its experimental conditions were a symmetric θ–2θ scan method, Cu Kα source, 15–105° 2θ range, 0.02° step size, and 10 s data collection time for each data point, respectively. A synchrotron experiment was conducted for a more exact calculation of the lattice parameter and grain size. Experimental conditions in the Synchrotron experiment were similar to the conditions of the in-house X-ray experiments except that the diffraction 2θ ranges are narrowly set only to investigate the (001) and (002) peaks, and in-plane diffraction was additionally performed to obtain information on the direction parallel to the film plane. For in-plane diffraction, the films were rotated by as much as ∼88° about the χ axis. The position, integral intensity of the diffraction peaks and the calculation of grain size using the diffraction peaks were performed with WinFit
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30, and 300 s). The as-deposited film had only a weak (111) or no texture, and the rapid grain growth of the (001) crystal was observed after 30 s. To analyze the variation in (001) texture quantitatively, the orientation distribution function must be calculated based on the measured pole figures. However, this is a difficult and timeconsuming process for thin film, with a thickness of a few tens of nanometers because of its weak diffraction peaks. Instead, a semi-quantitative method such as the Lotgering orientation factor (LOF) is used [21]. The LOF represents the degree of specific texture and has values from 0 to 1, where ‘0’ and ‘1’ indicate a random distribution and a perfect oriented distribution for specific crystal orientation, respectively, and is defined as follows when the specific orientation is {00l} [21], p p0 ; 1 pP 0 P ð00lÞsample ð00lÞpowder where p ¼ P ; p0 ¼ P : all ðhklÞsample all ðhklÞpowder
LOF ¼
Fig. 1. XRD patterns of Fe54Pt46 films after postannealing for 300 s, for various film thicknesses.
[20], where the peak model used was the Pearson VII function, and the grain size was calculated using the integral breadth method. 3. Results and discussion XRD patterns of Fe54Pt46 thin films, with various thicknesses of 9, 22, 44, 66, and 88 nm, annealed at 550 °C for 300 s are shown in Fig. 1. By observing the variations in the intensity of the (001) and (002) diffraction peaks, we were able to conclude that the (001) texture was more developed in the case of a low thickness film. Fig. 2 shows XRD patterns of 22 nm Fe54Pt46 thin films prepared for various annealing times (0, 3,
ð2Þ
For the calculation of the LOF, the sum of the intensities of the {00l} reflections and the sum of the intensities of all (hkl) reflections which occur in a certain range of 2θ (in the present study, 15–105°) were calculated for an oriented sample (value p) and for a non-oriented sample (value p0), respectively. Therefore, X-ray diffraction data of the non-oriented sample are required, and a powder sample is often used for this purpose. However, powder X-ray diffraction data for a nonstoichiometric Fe54Pt46 alloy are not available. Since it is very difficult to prepare a free textured Fe54Pt46 powder sample, X-ray diffraction data of nonoriented Fe54Pt46 alloy were obtained by simulation of the diffraction pattern with the FullProf program [Leon Brillouin Laboratory, DRECAM, Commission de l'énergie atomique — CEA, France] instead of using experimental data. The assumptions for the simulation and the intensities of resultant diffraction peaks are shown in Tables 1 and 2. p0, p, and the LOF were calculated from the simulated (non-oriented) and measured (oriented) XRD patterns. Before the calculation of LOF, the XRD data of thin films were corrected for the background spectrum, beam-size, and absorption. Fig. 3 shows LOF values of 22, 44, and 88 nm Fe54Pt46 films as a function of annealing time. The (001) texture did not appear at all in as-deposited films and developed differently as the annealing time passed. The 22-nm film showed an abrupt (001)
Table 1 Assumptions used for the simulation of the Fe54Pt46 L10 diffraction pattern Condition Lattice parameter a a = 0.38423 nm, c = 0.37072 nm Structure L10 Fe site; fully occupied by Fe atoms Pt site; random occupied by Fe and Pt atoms (Fe:Pt = 8:92) X-ray source Cu Kα average (0.15418 nm) Monochromator Graphite Geometry Bragg–Brenntano Polarization No Fig. 2. XRD patterns of 22 nm Fe54Pt46 films for various annealing times.
a
Ref. [22].
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Table 2 Calculated intensity of each diffraction peak in the case of the L10 Fe54Pt46 alloy hkl
2θ (Degree)
Intensity (arb. units)
hkl
2θ (Degree)
Intensity (arb. units)
001 110 111 200 002 201 112 220 202 221 003 310 311 113 222
24.00 32.97 41.19 47.32 49.15 53.74 60.46 69.15 70.61 74.37 77.19 78.76 83.78 86.52 89.43
257 235 999 331 147 122 87 101 189 48 11 41 231 107 99
203 312 400 401 004 223 330 331 114 313 420 402 421 204 332
95.76 98.69 106.75 112.00 112.57 114.99 116.69 122.39 123.01 125.69 127.60 129.35 134.16 134.89 142.66
28 54 38 25 19 25 13 76 26 157 80 81 60 88 35
Phase transformation strain is basically required for the stability of the (001) crystal irrespective of what the dominant factor is – tensile in-plane strain or the Vook–Witt condition – according to a previous study [13]. Therefore, it must be confirmed that Fe54Pt46 films are transformed into ordered phase before grain growth and so phase transformation strain can affect subsequent grain growth. The long-range ordering parameter (LRO), S, is considered to be a measure of the degree of long-range ordering and is defined as [23], S¼
ra xFe rb xPt ¼ ; yb ya
ð3Þ
where yα and yβ are, respectively, the fractions of α-sites (Fe site in L10 structure) and β-sites (Pt site in L10 structure), so both have ‘0.5’, in the case of Fe54Pt46 L10 alloy. xFe, xPt are atomic fractions (xFe + xPt = 1), and rα, rβ are the fractions of α- and β-sites occupied by the right atoms so their values become ‘0.54’, ‘0.46’, ‘1’ and ‘0.92’ because of its nonstoichiometric composition. Therefore, LRO, S becomes ‘0.92’ when the crystal is perfectly transformed into ordered phase. LRO can be experimentally measured from the ratio of the superlattice and fundamental peaks such as the (001) and (002) peaks of Fe54Pt46 alloy as follows, !1=2 Ið001Þs S ¼ kd ; ð4Þ Ið002Þf
texture development and was close to being in a perfectly oriented state within about 30 s. As the thickness increased, however, the abrupt growth of the (001) crystal in the 22-nm film was no longer evident, although the 44-nm film showed a faster texture development compared to an 88-nm film which showed little (001) texture development up to 300 s. These results support a few conclusions. First, the (001) texture does not originate from a specific crystallographic relationship with pre-existing textures, but from the preferable grain growth of the (001) crystal during postannealing. Second, the preferable growth of the (001) crystal is enhanced with decreasing thickness, especially, below a specific value. The preferable growth of the (001) crystal is induced by its relative lower energy, compared to others. As mentioned in the Introduction, the inverse relation between film thickness and (001) texture is difficult to explain by the cooperation of phase transformation strain and biaxial in-plane strain because the thicker film can have a large tensile in-plane strain. Therefore, the thickness dependence of the (001) texture in a FePt thin film must be rationalized by another thickness-dependent factor such as an anisotropic interaction model, like the Vook–Witt condition, which was considered to be one of the important origins for the (001) texture in our previous study [13].
where k value can be determined from powder or simulated XRD patterns. In this study, the k value obtained from simulated data was used, which considered the polarization of synchrotron Xrays and the thickness-dependent absorption factor (1 − exp (−2μlayertlayer / sinθinc) [24]). The k values obtained were 0.583, 0.588, and 0.597 for 22, 44, and 88 nm Fe54Pt46 films, respectively. Fig. 4 shows the variation in LRO parameters calculated from synchrotron XRD data for various thicknesses as a function of annealing time. Films – 22, 44, and 88 nm – were transformed into ordered phase before 30 s, and their LRO parameters approached the maximum value of 0.92 after 100 s. This result proves that phase transformation strain can exist before grain growth and can affect the subsequent grain growth.
Fig. 3. Lotgering orientation factors in the b00lN orientation for various film thicknesses as a function of annealing time.
Fig. 4. LRO (long-range ordering) parameters for various film thicknesses as a function of annealing time.
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The phase transformation strain mainly exists in the c-axis ([001] direction) because phase transformation into L10 phase induces the contraction of the c-axis by as much as 3% with respect to the disordered FCC matrix. Therefore, the existence of phase transformation strain in a crystal having a certain orientation can be predicted from the variation in (001) plane spacing in its crystal. Fig. 5 shows the variation in (001) plane spacing for (100) and (001) crystals, and Fig. 5 also includes d0 values. The (001) and (100) crystals were mainly investigated because they are extreme orientations for the relaxation of phase transformation strain since crystals in a thin film undergo, respectively, the weakest and the strongest constraint in the direction perpendicular and parallel to the film plane. From the strain difference for (001) and (100) crystals (strain relaxation anisotropy), the quantity of relative relaxation of phase transformation strain in a (001) crystal can be inferred over other crystals. To estimate the (001) plane spacing, the (002) diffraction peak from the synchrotron source was used. The strain state at the annealing temperature needs to be considered because grain growth and texture evolution from it occur at the annealing temperature. Therefore, the d0 value means an unstressed (001) plane spacing when the temperature increases from R.T. (ex situ X-ray experiment temperature) to 550 °C (annealing temperature). In the case of Fe54Pt46 thin films on an oxidized silicon substrate, the temperature difference induces compressive inplane strain because of the difference in thermal expansion of Silicon and the FePt alloy [13]. Thus, the c-axis of the (100) crystal receives a compressive thermal strain by the substrate of as much as 0.41%, regardless of the interaction model. However, contrary to the fixed in-plane strain, various perpendicular strains to the film plane are possible, based on grain interaction models
Fig. 5. (001) Plane spacing of (a) (001) and (b) (100) crystals for various film thicknesses as a function of annealing time.
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such as the Voigt assumption or the Vook–Witt assumption. Therefore, the d0 value for (001) plane spacing in a (001) crystal is presented differently according to the interaction models as in Fig. 5. When a 0.41% in-plane strain was applied for the (001) plane spacing in a (001) crystal, the calculated thermal strain and corrected d0 values were about 0.48%, 0.3725 nm (for the Voigt assumption) and 0.67%, 0.3689 nm (for the Vook–Witt assumption), respectively. Details of the calculation procedure are presented in the Appendix. As the Voigt and Vook–Witt assumptions are extreme grain interaction models in the direction perpendicular to the film plane, the real d0 is probably located in the hatched region between the two values. In Fig. 5, the (001) plane spacing (lattice parameter c) of (001) crystal in the 22-nm film approached d0 values rapidly compared to other films, indicating that the phase transformation strain energy of (001) crystals in a 22-nm film is smaller than that in the other films. On the other hand, the (001) plane spacing of the (100) crystal in 22-nm thin films was quite different from the d0 value compared to the other films, indicating that the phase transformation strain energy of (100) crystals in a 22-nm film is larger than that in the other films. In other words, the (001) crystal is relatively stable in the case of a 22-nm film because of the relaxation anisotropy of phase transformation strain along the film axis. Moreover, such relaxation anisotropy has a tendency to decrease as the film thickness increases, up to a thickness of 88 nm. These findings suggested that the inverse relation between film thickness and (001) texture may be caused by the variations in phase transformation strain relaxation anisotropy as a function of film thickness. The relaxation anisotropy along the film axis is an expected phenomenon in films having the Vook–Witt condition. The Vook–Witt condition has a different grain interaction depending on the film axis in that the strain parallel to the film plane is fixed for all grains and the stress perpendicular to the film plane is free for all grains. Thus, the relaxation of phase transformation strain can occur differently depending on the film axis if Vook–Witt condition is given. Moreover, if the relation between film thickness and Vook–Witt condition is known, the relation between film thickness and (001) texture is expected to be also understood by the medium of the Vook–Witt condition and related relaxation anisotropy. Generally, as film thickness decreases, the film has an opportunity to satisfy the Vook–Witt condition because grains in a low thickness film have little interaction with other grains in the direction perpendicular to the film plane, and they are constrained by the substrate in the direction parallel to the film plane. However, in order to confirm that a thin film has a more appropriate structure for the Vook–Witt condition as the film thickness decreases, the microstructure such as grain height must be investigated for various film thicknesses. Fig. 6 shows (001) reflections for 22 nm Fe54Pt46 films for various annealing times. Fringes developed near the (001) peak after a few tens of seconds. This indicates that the grain growth in the direction perpendicular to the film plane was completed by the limited film thickness, and the grain height became uniform over the film within a few tens of seconds. The grain heights were calculated from the period of the fringes [25], and
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Fig. 6. (001) Reflections of 22 nm Fe54Pt46 film for various annealing times.
their values were the same as the film thickness. This suggests that the film was composed of one grain in the direction perpendicular to the film plane, and, as a result, is a suitable microstructure for anisotropic grain interactions because grains in such films interact negligibly with other grains in the direction perpendicular to the film plane because of its free surface, and are strongly constrained by the substrate owing to their direct attachment to the substrate. The grain height for various film thicknesses was calculated using the WinFit program [20] using the (001) reflection in the Fe54Pt46 X-ray pattern obtained using the synchrotron. Instrument correction was performed with silicon powder before calculation of the grain size. The program offers two different methods for calculating the grain size: the integral breadth method and a Fourier coefficient analysis. In this study, the integral breadth method was used because it agreed more precisely with the value estimated from the Bragg-peak fringe [25]. Fig. 7 shows the ratio of grain height to film thickness for various film thicknesses as a function of annealing time. If the ratio approaches ‘1’, film is composed of one grain in the direction perpendicular to the film plane. This, therefore, assumes that the relaxation anisotropy would increase if the ratio is close to ‘1’. In Fig. 7, the ratio for the 22-nm film was already close to ‘1’ within 30 s, and the ratio for the 44-nm films remained below the ratio for the 22-nm film during postannealing. In the case of 88-nm films, the ratio was small compared to others and consistently remained below ‘0.3’ during the postannealing. These results support the expectation that a low thickness may play the role of a suitable microstructure for relaxation anisotropy in a film. However, the abrupt (001) texture development in 22-nm films near 30 s seems to be related to other kinematic reasons, such as abnormal grain growth, because the relative relaxation anisotropy of the 22-nm films is not large enough to induce an abrupt (001) texture evolution only in the 22-nm films. The distinct feature of the 22-nm film is that it is composed of one grain in the direction normal to the film plane during postannealing, which can be an important source for relatively
rapid growth of the (001) crystal. Abnormal grain growth generally occurs when grain growth stagnation and grain orientation driving forces for grain growth coexist [26,27]. In the case of the 22-nm film, it appears that the completion of grain growth to the surface normal within 30 s causes growth stagnation by groove formation, and the relatively high stability of the (001) crystal induces the abnormal grain growth of the (001) crystal. Consequently, a strong (001) texture resulted. Finally, these results explain the origins of the (001) texture evolution in Fe54Pt46 thin films, and also why the specific (001) texture is rapidly generated below a specific value. Phase transformation (fcc → L10) strain is the basic origin of (001) texture evolution, and in order to maximize its effect, other conditions such as in-plane strain conditions and an appropriate microstructure for Vook–Witt grain interactions are required. Especially, if the thin film has one grain in the direction normal to the film plane, it satisfies not only the Vook–Witt interaction but also the abnormal grain growth condition, and their cooperation results in an abrupt (001) texture evolution. However, the Vook–Witt interaction is not always satisfied for thin film having one grain in the normal direction. If the aspect ratio – the ratio of width to height – of grains in the film is very small, such as for grains in columnar structure frequently found in Co alloy media structures [28], the relaxation of phase transformation strain in the direction perpendicular to the film plane can be interrupted by lateral grains owing to the large contact area with them. Our analysis of the (200) reflection from in-plane X-ray experiments revealed that the width of the grains in 22-nm films in this study was consistently ∼ 20 nm after a few tens of seconds. Therefore, the aspect ratio of the 22 nm Fe54Pt46 film is maintained at about ‘1’ during the postannealing, and it seems to positively affect relaxation anisotropy by maintaining the Vook–Witt condition. However, for engineering applications, such a thin thickness is not appropriate because of its low Ms value. In addition, because non-epitaxial (001) texture evolution accompanies active lateral grain growth, the magnetic domain tends to be large, which obstructs high density media. Therefore, the nanocomposite film obtained from the multilayered structure with FePt and non-magnetic materials seems to be an alternative method for obtaining a (001) texture
Fig. 7. Ratios of grain height to film thickness for various film thicknesses as a function of annealing time.
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non-epitaxially during postannealing, as suggested by the Sellmyer group [9,29]. A nanocomposite film has a domain size as small as a few nanometers, which is preferable for practical applications. In addition, the as-deposited multilayered structure has positive kinematical factors for (001) texture evolution, in that it has grains with a large aspect ratio and a driving force for recrystallization. In the early stage of postannealing, FePt grains have the potential of becoming a thin plate owing to their multilayered structure, and such a grain shape has a large aspect ratio, which ensures Vook–Witt interactions [19] that stabilize the (001) crystal. Moreover, the impurities and low crystallinity of the multilayered structure can offer a chance for the FePt grains to reorientate through fast transformation into ordered phase, recrystallization and grain growth. However, the proposed method may require much additional effort for engineering applications because tailoring the microstructure to obtain the desired property is not an easy task because of the strong dependency between microstructure and (001) texture. 4. Conclusion The thickness dependence of (001) texture evolution in FePt thin films was experimentally shown to be related to the relaxation anisotropy of phase transformation strain for various thicknesses. In particular, films composed of flat single grains perpendicular to the plane have good environments for a (001) texture in terms of relative stability and the grain growth of (001) crystals. For engineering applications of non-epitaxial growth of a (001) texture, the nanocomposite film obtained by postannealing of a multilayered film can be a good alternative because nanometer-sized grains are maintained, and the grains have very large aspect ratio that ensures Vook–Witt interactions. Acknowledgments This work was supported by the Nanocomposites & E-Beam Technology Center, a National Research Laboratory sponsored by the Ministry of Science and Technology of Korea. Appendix A. Procedure used for calculation of the strain in the c-axis of a (001) crystal under in-plane strain In the Voigt assumption, all grains are subjected to the same strain as the entire specimen. Therefore, the strain in the c-axis of a (001) crystal is the same as the normal strain of the entire polycrystal specimen. Thus, it can be calculated, by using the following formula, if the polycrystal specimen is assumed to have an isotropic elastic property [30], ¯v 2V eSout ¼ eCout ¼ d eSin ¼ eCin : ¯v 1 V
ð5Þ
S C εout and εout are the perpendicular strain of (001) crystal and the S C whole film. And, εin and εin are the in-plane strain on (001) crystal applied and the whole film by thermal expansion difference. Voigt averaged Poisson's ratio, v¯v, can be calculated from the single
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crystal constant (stiffness) [31], using a few formula for Voigt averaging in tetragonal structure as follows [30,32], 1 ¯ v ¼ d ð2ðC11 þ C12 Þ þ C33 þ 4C13 Þ K 9 1 ¯ G v ¼ d ð2C11 þ C33 C12 2C13 þ 6C44 þ 3C66 Þ 15 ¯ v =3K ¯v 1 2G ; m¯v ¼ ¯ v =3K ¯v 2 þ 2G
ð6Þ
where K¯v and G¯v are bulk and shear modulus, respectively. C Therefore, εout under the in-plane strain condition can be easily derived based on the calculated bulk properties using Eq. (5). C εout under the Vook–Witt assumption can be calculated by solving Hook's law in the short notations as follows, ei ¼ Sij rj :
ð7Þ
Vook–Witt assumption and compliance, Sij, of (001) crystal in the tetragonal structure can be described as the following matrices in the short notation [16], 1 0 1 1 0 C 1 0 0 r1 r11 e ein Br C Br C B e C B eC C C B in C B 22 C B 1 C B C B C C C B B B B 0 C B0C B e33 C B eCout C C B C C;r ¼ B C¼B e¼B B 0 C ¼ B 0 C; B 2e C B e C C B C B B 23 C B 4 C C B C C C B B B @ 0 A @0A @ 2e31 A @ e5 A 0
0 s11
Bs B 12 B B s13 S¼B B 0 B B @ 0 0
s12
0 s13 0
0
s11 s13
s13 s33
0 0
0 0
0
0
s44
0
0 0
0 0
0 0
s44 0
r12 1 0 0 C C C 0 C C: 0 C C C 0 A
r6
ð8Þ
s66
C Therefore, εout can be calculated by using the following equation, which is reconstructed from Eqs. (7) and (8),
eCout ¼
2S13 d eC : S11 þ S12 in
ð9Þ
References [1] K. Ouchi, IEEE Trans. Magn. 37 (2001) 1217. [2] D. Weller, A. Moser, L. Folks, M.E. Best, W. Lee, M.F. Toney, M. Schwickert, J.-U. Thiele, M.F. Doerner, IEEE Trans. Magn. 36 (2000) 10. [3] E.Y.L. Yiua, D.T.S. Fangb, F.C.S. Chub, T.W. Chowb, J. Dent. 32 (2004) 423. [4] T. Suzuki, N. Honda, K. Ouchi, IEEE Trans. Magn. 35 (1999) 2748. [5] S.-K. Jeong, M.E. McHenry, D.E. Laughlim, IEEE Trans. Magn. 37 (2001) 1309. [6] Y. Xu, J.S. Chen, J.P. Wang, Appl. Phys. Lett. 80 (2002) 3325. [7] Z.G. Zhang, K. Kang, T. Suzuki, Appl. Phys. Lett. 83 (2003) 1785. [8] H. Kim, S. Lee, J. Appl. Phys. 97 (2005) 10H304-1. [9] C.P. Luo, S.H. Liou, L. Gao, Y. Liu, D.J. Sellmyer, Appl. Phys. Lett. 77 (2000) 2225. [10] H. Zeng, M.L. Yan, N. Powers, D.J. Sellmyer, Appl. Phys. Lett. 80 (2002) 2350. [11] J.-S. Kim, N.-S. Shin, Y.-M. Koo, J. Appl. Phys. 100 (2006) 093909. [12] C.V. Thompson, R. Carel, Mater. Sci. Eng., B, Solid-State Mater. Adv. Technol. 32 (1995) 211.
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[13] J.-S. Kim, Y.-M. Koo, S.-R. Lee, B.-J. Lee, J. Appl. Phys. 99 (2006) 053906. [14] M. van Leeuwen, J.-D. Kamminga, E.J. Mittemeijer, J. Appl. Phys. 86 (1999) 1904. [15] F. Witt, R.W. Vook, J. Appl. Phys. 39 (1968) 2773. [16] J.F. Nye, Physical Properties of Crystals, Oxford University Press, 1985, p. 131. [17] C.P. Luo, D.J. Sellmyer, Appl. Phys. Lett. 75 (1999) 3162. [18] M.L. Yan, H. Zeng, N. Powers, D.J. Sellmyer, J. Appl. Phys. 91 (2002) 8471. [19] U. Welzel, S. Fréour, E.J. Mittemeijer, Philos. Mag. 85 (2005) 2391. [20] S. Krumm, Mater. Sci. Forum 228–231 (1996) 183 (part 1). [21] F.K. Lotgering, J. Inorg. Nucl. Chem. 9 (1959) 113. [22] H. Okamoto, Phase Diagrams of Binary Iron Alloys, 1st ed., Monograph Series on Alloy Phase Diagram, vol. 9, ASM International, USA, 1993, p. 330.
[23] B.E. Warren, X-ray Diffraction, Dover Publications, New-York, 1990, p. 208. [24] P.F. Fewster, Rep. Prog. Phys. 59 (1996) 1339. [25] V. Holy, U. Pietsch, T. Baumbach, High-Resolution X-ray Scattering from Thin Films and Multilayers, Springer-Verlag, Berlin, 1999, p. 134. [26] C.V. Thompson, R. Carel, J. Mech. Phys. Solids 44 (1996) 657. [27] H.J. Frost, C.V. Thompson, D.T. Walton, Acta Mater. 40 (1992) 779. [28] D.E. Lauglin, S. Kumar, Y. Peng, A.G. Roy, IEEE Trans. Magn. 41 (2005) 719. [29] D.J. Sellmyer, M. Yan, Y. Xu, R. Skomski, IEEE Trans. Magn. 41 (2005) 560. [30] G.E. Dieter, Mechanical Metallurgy, McGraw-Hill Book Company, Singapore, 1988, p. 47. [31] J.-S. Kim, J. Mater. Res. 21 (2006) 199. [32] J.P. Watt, J. Appl. Phys. 60 (1986) 3120.
Thin Solid Films 516 (2008) 1147 – 1154 www.elsevier.com/locate/tsf
Thickness dependence of (001) texture evolution in FePt thin films on an amorphous substrate Jae-Song Kim ⁎, Yang-Mo Koo Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea Received 19 July 2006; received in revised form 6 April 2007; accepted 8 June 2007 Available online 15 June 2007
Abstract Thickness dependency of (001) texture evolution in Fe54Pt46 thin films on an amorphous substrate was investigated using in-house X-ray diffraction or a synchrotron source. The (001) texture was well developed in Fe54Pt46 thin films, especially when its thickness was equivalent to the grain height. The findings show that strain relaxation anisotropy along the film axis, which leads to a (001) crystal (a crystal with a (001) plane parallel to the film plane) that is more stable than others, was large for a low thickness film. In addition, abnormal grain growth was used to explain the abrupt development of a (001) texture. The advantage of multilayered as-deposited structure is also discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: FePt; Texture; Transformation into ordered phase; Strain by phase transformation; Vook–Witt condition
1. Introduction The L10 FePt alloy is an attractive candidate for use in ultra high density media such as perpendicular recording media (PRM), in that it has a high uniaxial anisotropy energy and is highly resistant to corrosion which confers thermal stability even at the nano grain size [1–3]. To apply a FePt alloy to PRM, the (001) crystallographic fiber texture must be normal to the film plane because the L10 FePt alloy has a magnetic easy axis in the [001] (c-axis) direction. Epitaxial growth methods have been widely used, in attempts to produce a (001) texture, and a MgO substrate or MgO, Cr, CrRu intermediate layers have been used [4–8]. C.P. Luo and H. Zeng recently succeeded in obtaining a (001) texture through the postannealing of (FePt/B2O3)n or (Fe/Pt)n multilayered films on an amorphous substrate [9,10]. Similarly, we found that a co-sputtered Fe55Pt45 thin film has a (001) texture after postannealing if the film is of an appropriate thickness [11]. FePt thin films having a non-epitaxial (001) texture show a similar tendency in which as-deposited films have no (001) texture that develops through phase transformation and grain growth during postannealing. ⁎ Corresponding author. Tel./fax: +82 54 279 5130(2399). E-mail address: [email protected] (J.-S. Kim). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.06.071
Traditional theories have mainly considered surface energy or biaxial strain energy for the postannealing texture in thin films [12]. However, in the case of a FePt thin film, the (111) surface has the lowest surface energy, and the (100) crystal (crystal with a (100) plane parallel to the film plane) has the lowest strain energy under biaxial strain conditions [13]. Therefore, the traditional theories cannot be applied to this case. In a previous paper, we proposed that phase transformation (fcc → L10) strain is able to stabilize the (001) crystal more than others and to induce a (001) texture under appropriate conditions such as tensile in-plane strain or Vook–Witt conditions (plane stress condition) [13,14]. A FePt thin film generally remains in a metastable fcc phase after deposition. The fcc FePt alloy cannot be used for recording media due to its soft magnetic property. Therefore, FePt thin films require a postannealing process accompanied by a transformation into ordered phase (fcc →L10) which induces anisotropic strains, especially up to 3% along c-axis. In-plane tensile strain is an isotropic strain parallel to the film plane, which can be attributed to volume shrinkage caused by the elimination of defects and grain growth during postannealing. In the case of the (001) crystal, inplane tensile strain and phase transformation (fcc →L10) strain are in a diametrically opposite directions, so strain energy induced by transformation into ordered phase (fcc→ L10) can be cancelled out by the in-plane tensile strain [13] and a (001) crystal is more stable than other crystals. The Vook–Witt condition is an anisotropic grain
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interaction model along the specimen axis since the strain parallel to the film plane is equal for all crystallites (as in Voigt conditions) and the stress perpendicular to the film plane is zero for all crystallites (as in Reuss conditions) [14,15]. Therefore, the Vook–Witt condition can be described by a strain and stress tensor in the film coordinate system as follows [14] 2 3 2 3 e 0 e13 r11 r12 0 e¼4 0 e e23 5; r ¼ 4 r12 r22 0 5: ð1Þ 0 0 0 e13 e23 e33 The “3” direction is the direction perpendicular to the film plane, and the orientation of the orthogonal “1” and “2” axes is the direction parallel to the film plane. “e” is the value of a given in-plane strain, and six unknowns (ε13, ε23, ε33, σ11, σ12, σ22) can be calculated by solving Hook's law [16]. Under the Vook– Witt condition, the (001) crystal has free stress in the c-axis. Consequently, phase transformation strain which exists mainly along the c-axis is easily relaxed in the case of a (001) crystal. On the other hand, the phase transformation strain of (100) crystals, the orientation of which is a perpendicular to the (001) crystal is difficult to relax because its c-axis is tightly constrained by the substrate. As both of the (100) and (001) crystal seem to be an extreme case for the relaxation of phase transformation strain, assuming anisotropic interactions (Vook–Witt assumption) along the in-plane or out-of-plane, it can be inferred that the Vook–Witt condition can increase the relative stability of a (001) crystal over others by the additional relaxation of the phase transformation strain of a (001) crystal [13]. We experimentally verified that phase transformation strain and tensile in-plane strain co-exist in a FePt thin film, and that such a strain state can stabilize the (001) crystal [11]. However, phase transformation strain and tensile in-plane strain are limited in their ability to explain the thickness dependence of the (001) texture [9,17,18]. Changes in in-plane tensile strain are mainly induced by lateral volume shrinkage, caused by grain growth parallel to the film plane. However, as in-plane tensile strain would be expected to be large for high thickness film (a thick film has little stagnation of grain growth by film thickness compared to a thin film), the inverse relation between film thickness and (001) texture, which will be shown in the present study, is difficult to describe using only in-plane tensile strain. Instead, the Vook–Witt condition, which is generally considered to be one of the important origins of (001) texture in previous studies [13], seems to offer an alternative factor for explaining thickness dependence because the Vook–Witt condition is related to the entire microstructure of a thin film. Thin films having a low thickness have the opportunity to be under the Vook–Witt condition because grains in such films get little interference from other grains in the direction perpendicular to the film plane (ensuring minimal stress normal to the film plane), and the aspect ratio – width/height – of grains tends to be large, ensuring the Vook–Witt condition [19]. Based on a previous theoretical prediction [13], the Vook–Witt condition contributes to the stability of a (001) crystal, even under compressive inplane strain. In other words, the Vook–Witt condition can facilitate the development of a (001) texture, even under an
unfavorable macroscopic strain condition. These relationships suggest that the Vook–Witt condition is a dominant factor in explaining the thickness dependence of (001) texture. The purpose of this study was to examine the relation between film thickness and (001) texture by confirming that the (001) crystal can be relatively stabilized over others by effectively relaxing its phase transformation strain when an appropriate microstructure (for example, thin thickness film) which satisfies the Vook–Witt condition is present. The texture, ordering parameter, lattice parameter, and grain size of Fe54Pt46 thin films were analyzed for various film thicknesses as a function of annealing time, using X-ray diffraction (XRD) in our laboratories or a synchrotron source. The relation of film thickness and (001) texture was examined by conducting a semi-quantitative texture analysis. Next, we show that strain relaxation enables the (001) crystal in a thinner film to be relatively stabilized, based on investigating the variation of lattice parameter and grain size because they have a good microstructure that satisfies the Vook– Witt condition. In Section 2, the procedures for specimen preparation and the X-ray experiments are described. In Section 3, the origins of thickness dependence of the (001) texture are discussed on the basis of the experimental results obtained. Finally, our conclusions are presented in Section 4. 2. Experimental details Magnetic thin films with composition Fe54Pt46 were dc magnetron sputtered on an oxidized silicon substrate with a 100nm thickness silicon oxide layer, where a FePt alloy target was used. The base pressure of the chamber was less than 7 × 10− 5 Pa, and a working pressure of 0.27 Pa Ar was used during the sputtering. The deposition rate was ∼ 0.1 nm/s, and the substrate was mounted on a water-cooled rotating table. Fe54Pt46 thin films were prepared in five different thicknesses — 9, 22, 44, 66, and 88 nm at room temperature. The film thickness and composition were confirmed by X-ray reflectivity and Rutherford Backscattering Spectroscopy (RBS). As-deposited films were rapid thermal annealed at 550 °C in ∼0.4 bar of N2 gas for 3, 10, 30, 100 and 300 s, where the heating rate was 100– 150 °C/s. X-ray diffraction experiments were performed with an inhouse (Huber goniometer with Rigaku 18 kW) or synchrotron XRD (10C1 at the Pohang Light Source). The former was mainly used to analyze the texture, and its experimental conditions were a symmetric θ–2θ scan method, Cu Kα source, 15–105° 2θ range, 0.02° step size, and 10 s data collection time for each data point, respectively. A synchrotron experiment was conducted for a more exact calculation of the lattice parameter and grain size. Experimental conditions in the Synchrotron experiment were similar to the conditions of the in-house X-ray experiments except that the diffraction 2θ ranges are narrowly set only to investigate the (001) and (002) peaks, and in-plane diffraction was additionally performed to obtain information on the direction parallel to the film plane. For in-plane diffraction, the films were rotated by as much as ∼88° about the χ axis. The position, integral intensity of the diffraction peaks and the calculation of grain size using the diffraction peaks were performed with WinFit
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30, and 300 s). The as-deposited film had only a weak (111) or no texture, and the rapid grain growth of the (001) crystal was observed after 30 s. To analyze the variation in (001) texture quantitatively, the orientation distribution function must be calculated based on the measured pole figures. However, this is a difficult and timeconsuming process for thin film, with a thickness of a few tens of nanometers because of its weak diffraction peaks. Instead, a semi-quantitative method such as the Lotgering orientation factor (LOF) is used [21]. The LOF represents the degree of specific texture and has values from 0 to 1, where ‘0’ and ‘1’ indicate a random distribution and a perfect oriented distribution for specific crystal orientation, respectively, and is defined as follows when the specific orientation is {00l} [21], p p0 ; 1 pP 0 P ð00lÞsample ð00lÞpowder where p ¼ P ; p0 ¼ P : all ðhklÞsample all ðhklÞpowder
LOF ¼
Fig. 1. XRD patterns of Fe54Pt46 films after postannealing for 300 s, for various film thicknesses.
[20], where the peak model used was the Pearson VII function, and the grain size was calculated using the integral breadth method. 3. Results and discussion XRD patterns of Fe54Pt46 thin films, with various thicknesses of 9, 22, 44, 66, and 88 nm, annealed at 550 °C for 300 s are shown in Fig. 1. By observing the variations in the intensity of the (001) and (002) diffraction peaks, we were able to conclude that the (001) texture was more developed in the case of a low thickness film. Fig. 2 shows XRD patterns of 22 nm Fe54Pt46 thin films prepared for various annealing times (0, 3,
ð2Þ
For the calculation of the LOF, the sum of the intensities of the {00l} reflections and the sum of the intensities of all (hkl) reflections which occur in a certain range of 2θ (in the present study, 15–105°) were calculated for an oriented sample (value p) and for a non-oriented sample (value p0), respectively. Therefore, X-ray diffraction data of the non-oriented sample are required, and a powder sample is often used for this purpose. However, powder X-ray diffraction data for a nonstoichiometric Fe54Pt46 alloy are not available. Since it is very difficult to prepare a free textured Fe54Pt46 powder sample, X-ray diffraction data of nonoriented Fe54Pt46 alloy were obtained by simulation of the diffraction pattern with the FullProf program [Leon Brillouin Laboratory, DRECAM, Commission de l'énergie atomique — CEA, France] instead of using experimental data. The assumptions for the simulation and the intensities of resultant diffraction peaks are shown in Tables 1 and 2. p0, p, and the LOF were calculated from the simulated (non-oriented) and measured (oriented) XRD patterns. Before the calculation of LOF, the XRD data of thin films were corrected for the background spectrum, beam-size, and absorption. Fig. 3 shows LOF values of 22, 44, and 88 nm Fe54Pt46 films as a function of annealing time. The (001) texture did not appear at all in as-deposited films and developed differently as the annealing time passed. The 22-nm film showed an abrupt (001)
Table 1 Assumptions used for the simulation of the Fe54Pt46 L10 diffraction pattern Condition Lattice parameter a a = 0.38423 nm, c = 0.37072 nm Structure L10 Fe site; fully occupied by Fe atoms Pt site; random occupied by Fe and Pt atoms (Fe:Pt = 8:92) X-ray source Cu Kα average (0.15418 nm) Monochromator Graphite Geometry Bragg–Brenntano Polarization No Fig. 2. XRD patterns of 22 nm Fe54Pt46 films for various annealing times.
a
Ref. [22].
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Table 2 Calculated intensity of each diffraction peak in the case of the L10 Fe54Pt46 alloy hkl
2θ (Degree)
Intensity (arb. units)
hkl
2θ (Degree)
Intensity (arb. units)
001 110 111 200 002 201 112 220 202 221 003 310 311 113 222
24.00 32.97 41.19 47.32 49.15 53.74 60.46 69.15 70.61 74.37 77.19 78.76 83.78 86.52 89.43
257 235 999 331 147 122 87 101 189 48 11 41 231 107 99
203 312 400 401 004 223 330 331 114 313 420 402 421 204 332
95.76 98.69 106.75 112.00 112.57 114.99 116.69 122.39 123.01 125.69 127.60 129.35 134.16 134.89 142.66
28 54 38 25 19 25 13 76 26 157 80 81 60 88 35
Phase transformation strain is basically required for the stability of the (001) crystal irrespective of what the dominant factor is – tensile in-plane strain or the Vook–Witt condition – according to a previous study [13]. Therefore, it must be confirmed that Fe54Pt46 films are transformed into ordered phase before grain growth and so phase transformation strain can affect subsequent grain growth. The long-range ordering parameter (LRO), S, is considered to be a measure of the degree of long-range ordering and is defined as [23], S¼
ra xFe rb xPt ¼ ; yb ya
ð3Þ
where yα and yβ are, respectively, the fractions of α-sites (Fe site in L10 structure) and β-sites (Pt site in L10 structure), so both have ‘0.5’, in the case of Fe54Pt46 L10 alloy. xFe, xPt are atomic fractions (xFe + xPt = 1), and rα, rβ are the fractions of α- and β-sites occupied by the right atoms so their values become ‘0.54’, ‘0.46’, ‘1’ and ‘0.92’ because of its nonstoichiometric composition. Therefore, LRO, S becomes ‘0.92’ when the crystal is perfectly transformed into ordered phase. LRO can be experimentally measured from the ratio of the superlattice and fundamental peaks such as the (001) and (002) peaks of Fe54Pt46 alloy as follows, !1=2 Ið001Þs S ¼ kd ; ð4Þ Ið002Þf
texture development and was close to being in a perfectly oriented state within about 30 s. As the thickness increased, however, the abrupt growth of the (001) crystal in the 22-nm film was no longer evident, although the 44-nm film showed a faster texture development compared to an 88-nm film which showed little (001) texture development up to 300 s. These results support a few conclusions. First, the (001) texture does not originate from a specific crystallographic relationship with pre-existing textures, but from the preferable grain growth of the (001) crystal during postannealing. Second, the preferable growth of the (001) crystal is enhanced with decreasing thickness, especially, below a specific value. The preferable growth of the (001) crystal is induced by its relative lower energy, compared to others. As mentioned in the Introduction, the inverse relation between film thickness and (001) texture is difficult to explain by the cooperation of phase transformation strain and biaxial in-plane strain because the thicker film can have a large tensile in-plane strain. Therefore, the thickness dependence of the (001) texture in a FePt thin film must be rationalized by another thickness-dependent factor such as an anisotropic interaction model, like the Vook–Witt condition, which was considered to be one of the important origins for the (001) texture in our previous study [13].
where k value can be determined from powder or simulated XRD patterns. In this study, the k value obtained from simulated data was used, which considered the polarization of synchrotron Xrays and the thickness-dependent absorption factor (1 − exp (−2μlayertlayer / sinθinc) [24]). The k values obtained were 0.583, 0.588, and 0.597 for 22, 44, and 88 nm Fe54Pt46 films, respectively. Fig. 4 shows the variation in LRO parameters calculated from synchrotron XRD data for various thicknesses as a function of annealing time. Films – 22, 44, and 88 nm – were transformed into ordered phase before 30 s, and their LRO parameters approached the maximum value of 0.92 after 100 s. This result proves that phase transformation strain can exist before grain growth and can affect the subsequent grain growth.
Fig. 3. Lotgering orientation factors in the b00lN orientation for various film thicknesses as a function of annealing time.
Fig. 4. LRO (long-range ordering) parameters for various film thicknesses as a function of annealing time.
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The phase transformation strain mainly exists in the c-axis ([001] direction) because phase transformation into L10 phase induces the contraction of the c-axis by as much as 3% with respect to the disordered FCC matrix. Therefore, the existence of phase transformation strain in a crystal having a certain orientation can be predicted from the variation in (001) plane spacing in its crystal. Fig. 5 shows the variation in (001) plane spacing for (100) and (001) crystals, and Fig. 5 also includes d0 values. The (001) and (100) crystals were mainly investigated because they are extreme orientations for the relaxation of phase transformation strain since crystals in a thin film undergo, respectively, the weakest and the strongest constraint in the direction perpendicular and parallel to the film plane. From the strain difference for (001) and (100) crystals (strain relaxation anisotropy), the quantity of relative relaxation of phase transformation strain in a (001) crystal can be inferred over other crystals. To estimate the (001) plane spacing, the (002) diffraction peak from the synchrotron source was used. The strain state at the annealing temperature needs to be considered because grain growth and texture evolution from it occur at the annealing temperature. Therefore, the d0 value means an unstressed (001) plane spacing when the temperature increases from R.T. (ex situ X-ray experiment temperature) to 550 °C (annealing temperature). In the case of Fe54Pt46 thin films on an oxidized silicon substrate, the temperature difference induces compressive inplane strain because of the difference in thermal expansion of Silicon and the FePt alloy [13]. Thus, the c-axis of the (100) crystal receives a compressive thermal strain by the substrate of as much as 0.41%, regardless of the interaction model. However, contrary to the fixed in-plane strain, various perpendicular strains to the film plane are possible, based on grain interaction models
Fig. 5. (001) Plane spacing of (a) (001) and (b) (100) crystals for various film thicknesses as a function of annealing time.
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such as the Voigt assumption or the Vook–Witt assumption. Therefore, the d0 value for (001) plane spacing in a (001) crystal is presented differently according to the interaction models as in Fig. 5. When a 0.41% in-plane strain was applied for the (001) plane spacing in a (001) crystal, the calculated thermal strain and corrected d0 values were about 0.48%, 0.3725 nm (for the Voigt assumption) and 0.67%, 0.3689 nm (for the Vook–Witt assumption), respectively. Details of the calculation procedure are presented in the Appendix. As the Voigt and Vook–Witt assumptions are extreme grain interaction models in the direction perpendicular to the film plane, the real d0 is probably located in the hatched region between the two values. In Fig. 5, the (001) plane spacing (lattice parameter c) of (001) crystal in the 22-nm film approached d0 values rapidly compared to other films, indicating that the phase transformation strain energy of (001) crystals in a 22-nm film is smaller than that in the other films. On the other hand, the (001) plane spacing of the (100) crystal in 22-nm thin films was quite different from the d0 value compared to the other films, indicating that the phase transformation strain energy of (100) crystals in a 22-nm film is larger than that in the other films. In other words, the (001) crystal is relatively stable in the case of a 22-nm film because of the relaxation anisotropy of phase transformation strain along the film axis. Moreover, such relaxation anisotropy has a tendency to decrease as the film thickness increases, up to a thickness of 88 nm. These findings suggested that the inverse relation between film thickness and (001) texture may be caused by the variations in phase transformation strain relaxation anisotropy as a function of film thickness. The relaxation anisotropy along the film axis is an expected phenomenon in films having the Vook–Witt condition. The Vook–Witt condition has a different grain interaction depending on the film axis in that the strain parallel to the film plane is fixed for all grains and the stress perpendicular to the film plane is free for all grains. Thus, the relaxation of phase transformation strain can occur differently depending on the film axis if Vook–Witt condition is given. Moreover, if the relation between film thickness and Vook–Witt condition is known, the relation between film thickness and (001) texture is expected to be also understood by the medium of the Vook–Witt condition and related relaxation anisotropy. Generally, as film thickness decreases, the film has an opportunity to satisfy the Vook–Witt condition because grains in a low thickness film have little interaction with other grains in the direction perpendicular to the film plane, and they are constrained by the substrate in the direction parallel to the film plane. However, in order to confirm that a thin film has a more appropriate structure for the Vook–Witt condition as the film thickness decreases, the microstructure such as grain height must be investigated for various film thicknesses. Fig. 6 shows (001) reflections for 22 nm Fe54Pt46 films for various annealing times. Fringes developed near the (001) peak after a few tens of seconds. This indicates that the grain growth in the direction perpendicular to the film plane was completed by the limited film thickness, and the grain height became uniform over the film within a few tens of seconds. The grain heights were calculated from the period of the fringes [25], and
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Fig. 6. (001) Reflections of 22 nm Fe54Pt46 film for various annealing times.
their values were the same as the film thickness. This suggests that the film was composed of one grain in the direction perpendicular to the film plane, and, as a result, is a suitable microstructure for anisotropic grain interactions because grains in such films interact negligibly with other grains in the direction perpendicular to the film plane because of its free surface, and are strongly constrained by the substrate owing to their direct attachment to the substrate. The grain height for various film thicknesses was calculated using the WinFit program [20] using the (001) reflection in the Fe54Pt46 X-ray pattern obtained using the synchrotron. Instrument correction was performed with silicon powder before calculation of the grain size. The program offers two different methods for calculating the grain size: the integral breadth method and a Fourier coefficient analysis. In this study, the integral breadth method was used because it agreed more precisely with the value estimated from the Bragg-peak fringe [25]. Fig. 7 shows the ratio of grain height to film thickness for various film thicknesses as a function of annealing time. If the ratio approaches ‘1’, film is composed of one grain in the direction perpendicular to the film plane. This, therefore, assumes that the relaxation anisotropy would increase if the ratio is close to ‘1’. In Fig. 7, the ratio for the 22-nm film was already close to ‘1’ within 30 s, and the ratio for the 44-nm films remained below the ratio for the 22-nm film during postannealing. In the case of 88-nm films, the ratio was small compared to others and consistently remained below ‘0.3’ during the postannealing. These results support the expectation that a low thickness may play the role of a suitable microstructure for relaxation anisotropy in a film. However, the abrupt (001) texture development in 22-nm films near 30 s seems to be related to other kinematic reasons, such as abnormal grain growth, because the relative relaxation anisotropy of the 22-nm films is not large enough to induce an abrupt (001) texture evolution only in the 22-nm films. The distinct feature of the 22-nm film is that it is composed of one grain in the direction normal to the film plane during postannealing, which can be an important source for relatively
rapid growth of the (001) crystal. Abnormal grain growth generally occurs when grain growth stagnation and grain orientation driving forces for grain growth coexist [26,27]. In the case of the 22-nm film, it appears that the completion of grain growth to the surface normal within 30 s causes growth stagnation by groove formation, and the relatively high stability of the (001) crystal induces the abnormal grain growth of the (001) crystal. Consequently, a strong (001) texture resulted. Finally, these results explain the origins of the (001) texture evolution in Fe54Pt46 thin films, and also why the specific (001) texture is rapidly generated below a specific value. Phase transformation (fcc → L10) strain is the basic origin of (001) texture evolution, and in order to maximize its effect, other conditions such as in-plane strain conditions and an appropriate microstructure for Vook–Witt grain interactions are required. Especially, if the thin film has one grain in the direction normal to the film plane, it satisfies not only the Vook–Witt interaction but also the abnormal grain growth condition, and their cooperation results in an abrupt (001) texture evolution. However, the Vook–Witt interaction is not always satisfied for thin film having one grain in the normal direction. If the aspect ratio – the ratio of width to height – of grains in the film is very small, such as for grains in columnar structure frequently found in Co alloy media structures [28], the relaxation of phase transformation strain in the direction perpendicular to the film plane can be interrupted by lateral grains owing to the large contact area with them. Our analysis of the (200) reflection from in-plane X-ray experiments revealed that the width of the grains in 22-nm films in this study was consistently ∼ 20 nm after a few tens of seconds. Therefore, the aspect ratio of the 22 nm Fe54Pt46 film is maintained at about ‘1’ during the postannealing, and it seems to positively affect relaxation anisotropy by maintaining the Vook–Witt condition. However, for engineering applications, such a thin thickness is not appropriate because of its low Ms value. In addition, because non-epitaxial (001) texture evolution accompanies active lateral grain growth, the magnetic domain tends to be large, which obstructs high density media. Therefore, the nanocomposite film obtained from the multilayered structure with FePt and non-magnetic materials seems to be an alternative method for obtaining a (001) texture
Fig. 7. Ratios of grain height to film thickness for various film thicknesses as a function of annealing time.
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non-epitaxially during postannealing, as suggested by the Sellmyer group [9,29]. A nanocomposite film has a domain size as small as a few nanometers, which is preferable for practical applications. In addition, the as-deposited multilayered structure has positive kinematical factors for (001) texture evolution, in that it has grains with a large aspect ratio and a driving force for recrystallization. In the early stage of postannealing, FePt grains have the potential of becoming a thin plate owing to their multilayered structure, and such a grain shape has a large aspect ratio, which ensures Vook–Witt interactions [19] that stabilize the (001) crystal. Moreover, the impurities and low crystallinity of the multilayered structure can offer a chance for the FePt grains to reorientate through fast transformation into ordered phase, recrystallization and grain growth. However, the proposed method may require much additional effort for engineering applications because tailoring the microstructure to obtain the desired property is not an easy task because of the strong dependency between microstructure and (001) texture. 4. Conclusion The thickness dependence of (001) texture evolution in FePt thin films was experimentally shown to be related to the relaxation anisotropy of phase transformation strain for various thicknesses. In particular, films composed of flat single grains perpendicular to the plane have good environments for a (001) texture in terms of relative stability and the grain growth of (001) crystals. For engineering applications of non-epitaxial growth of a (001) texture, the nanocomposite film obtained by postannealing of a multilayered film can be a good alternative because nanometer-sized grains are maintained, and the grains have very large aspect ratio that ensures Vook–Witt interactions. Acknowledgments This work was supported by the Nanocomposites & E-Beam Technology Center, a National Research Laboratory sponsored by the Ministry of Science and Technology of Korea. Appendix A. Procedure used for calculation of the strain in the c-axis of a (001) crystal under in-plane strain In the Voigt assumption, all grains are subjected to the same strain as the entire specimen. Therefore, the strain in the c-axis of a (001) crystal is the same as the normal strain of the entire polycrystal specimen. Thus, it can be calculated, by using the following formula, if the polycrystal specimen is assumed to have an isotropic elastic property [30], ¯v 2V eSout ¼ eCout ¼ d eSin ¼ eCin : ¯v 1 V
ð5Þ
S C εout and εout are the perpendicular strain of (001) crystal and the S C whole film. And, εin and εin are the in-plane strain on (001) crystal applied and the whole film by thermal expansion difference. Voigt averaged Poisson's ratio, v¯v, can be calculated from the single
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crystal constant (stiffness) [31], using a few formula for Voigt averaging in tetragonal structure as follows [30,32], 1 ¯ v ¼ d ð2ðC11 þ C12 Þ þ C33 þ 4C13 Þ K 9 1 ¯ G v ¼ d ð2C11 þ C33 C12 2C13 þ 6C44 þ 3C66 Þ 15 ¯ v =3K ¯v 1 2G ; m¯v ¼ ¯ v =3K ¯v 2 þ 2G
ð6Þ
where K¯v and G¯v are bulk and shear modulus, respectively. C Therefore, εout under the in-plane strain condition can be easily derived based on the calculated bulk properties using Eq. (5). C εout under the Vook–Witt assumption can be calculated by solving Hook's law in the short notations as follows, ei ¼ Sij rj :
ð7Þ
Vook–Witt assumption and compliance, Sij, of (001) crystal in the tetragonal structure can be described as the following matrices in the short notation [16], 1 0 1 1 0 C 1 0 0 r1 r11 e ein Br C Br C B e C B eC C C B in C B 22 C B 1 C B C B C C C B B B B 0 C B0C B e33 C B eCout C C B C C;r ¼ B C¼B e¼B B 0 C ¼ B 0 C; B 2e C B e C C B C B B 23 C B 4 C C B C C C B B B @ 0 A @0A @ 2e31 A @ e5 A 0
0 s11
Bs B 12 B B s13 S¼B B 0 B B @ 0 0
s12
0 s13 0
0
s11 s13
s13 s33
0 0
0 0
0
0
s44
0
0 0
0 0
0 0
s44 0
r12 1 0 0 C C C 0 C C: 0 C C C 0 A
r6
ð8Þ
s66
C Therefore, εout can be calculated by using the following equation, which is reconstructed from Eqs. (7) and (8),
eCout ¼
2S13 d eC : S11 þ S12 in
ð9Þ
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