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Strain engineering of perovskite thin films using a single substrate
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 292201 (http://iopscience.iop.org/0953-8984/26/29/292201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.210.236.20 This content was downloaded on 26/06/2014 at 06:53
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 292201 (11pp)
doi:10.1088/0953-8984/26/29/292201
Fast Track Communication
Strain engineering of perovskite thin films using a single substrate P-E Janolin1, A S Anokhin2,3, Z Gui4, V M Mukhortov2, Yu I Golovko2, N Guiblin1, S Ravy5, M El Marssi6, Yu I Yuzyuk3, L Bellaiche4 and B Dkhil1 1
Laboratoire Structures, Propriétés et Modélisation des Solides, UMR CNRS-École Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry Cedex, France 2 Southern Scientific Center Russian Academy of Sciences, Rostov-on-Don, 344006, Russia 3 Faculty of Physics, Southern Federal University, Rostov-on-Don, 344006, Russia 4 Institute for Nanoscience and Engineering and Physics Department, University of Arkansas, Fayetteville, Arkansas 72701, USA 5 Synchrotron SOLEIL, L'Orme des Merisiers, Saint Aubin-B.P. 48, F-91192 Gif-sur-Yvette, France 6 Laboratoire de Physique de la Matière Condensée, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France E-mail: [email protected] Received 23 April 2014 Accepted for publication 23 May 2014 Published 25 June 2014 Abstract
Combining temperature-dependent x-ray diffraction, Raman spectroscopy and firstprinciples-based effective Hamiltonian calculations, we show that varying the thickness of (Ba0.8Sr0.2)TiO3 (BST) thin films deposited on the same single substrate (namely, MgO) enables us to change not only the magnitude but also the sign of the misfit strain. Such previously overlooked control of the strain allows several properties of these films (e.g. Curie temperature, symmetry of ferroelectric phases, dielectric response) to be tuned and even optimized. Surprisingly, such desired control of the strain (and of the resulting properties) originates from an effect that is commonly believed to be detrimental to functionalities of films, namely the existence of misfit dislocations. The present study therefore provides a novel route to strain engineering, as well as leading us to revisit common beliefs. Keywords: strain engineering, ferroelectrics, BST (Some figures may appear in colour only in the online journal)
Strain engineering has recently emerged as a powerful way to tune the remarkable physical properties of ABO3 perovskite thin films. For instance, it enables us to enhance the magnitude of the polarization in ferroelectrics [1] or multiferroics [2], to strongly shift the maximum (Curie) temperature for which ferroelectricity exists [1, 3], to induce ferroelectricity in incipient ferroelectric [4] or paraelectric [5] materials or to generate superior electromechanical properties through phase coexistence [6]. Strain engineering of perovskite thin films is typically realized through the choice of a substrate which imposes its lattice parameter onto the film through coherent epitaxy, implying that any desired strain requires its 0953-8984/14/292201+11$33.00
own specific substrate. Unfortunately, the limited number of substrates compatible with the perovskite structure (not mentioning their cost) imposes a drastic limitation to such strain engineering and therefore may prevent the optimization of several physical properties, since some regions of strains cannot be practically reached in some materials. Here, we use a combination of several experimental and theoretical techniques to demonstrate that an alternative and efficient method exists to allow a continuous variation of the misfit strain (including change of its sign), which thus results in the tuning and even optimization of several important physical properties. Examples of such properties are the direction 1
© 2014 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 292201
table 1 and figure 2). Dislocations tend to reduce the deposition strain originating from the mismatch in lattice parameters between the film and the substrate. Once the film is deposited, the dislocations form a fixed network that does not prevent the substrate from imposing its thermal evolution on the in-plane lattice parameter of the films. Because the thermal expansion coefficient of MgO is larger than that of BST, a thermal compressive stress arises when the film is cooled to room temperature. For thin films the low density of dislocations causes the (large) negative deposition strain to be partially compensated by the (positive) thermal strain, resulting in thin film under tension, whereas for thicker films the high density of dislocations causes the (small) negative deposition strain to be overcompensated by the (positive) thermal strain, resulting in an overall compression. Figure 3 illustrates this mechanism. A strain gradient developing throughout the thickness of the film would cause the in-plane lattice parameter of the films to be somewhere between the substrate and bulk lattice parameters, which is not the case for all investigated films. The proposed mechanism explains why all films are subjected to substrateinduced strains (negative for the deposition strain and positive for the thermal strain), but that various final misfit strain values (from positive to negative) can be obtained, on the same substrate, depending on the thickness deposited. Coherent epitaxy is the necessary condition for a substrate to impose its lattice parameter onto a film. In this regard, dislocations are considered as detrimental, as they prevent the substrate from imposing the targeted strain state on the film. In contrast, here, the absence of coherent epitaxy is at the very heart of strain engineering via thickness. Indeed, the misfit strain ( ηm ) is a thermodynamic quantity defined as the relative difference between the in-plane lattice parameter of the film (a∥) and the pseudo-cubic bulk lattice parameter (a0): ηm = ( a∥− a 0 ) / a 0. a0 is the lattice parameter the bulk material would have if it remained paraelectric for any temperature. Coherent epitaxy fixes a∥ to the substrate's lattice parameter, thereby imposing ηm. In contrast, misfit dislocations enable a∥ and then ηm, to vary. In this regard a large mismatch with the substrate (5% for BST on MgO at room temperature) appears as a prerequisite and eliminates the need to determine a critical thickness for relaxation (in contrast to SrTiO3 on DyScO3 [18]) or to investigate whether the growth mode provides such a relaxation as, e.g., in some aluminates [19]. We have calculated the linear density of dislocation, ρ, from ρ ( t ) = ( a∥( t ) − as ) / ( a∥( t ) as ), where as is the substrate lattice parameter. The calculated values of ρ (see appendix) are similar to those of Pb(Zr0.2Ti0.8)O3 thin films deposited on MgO [20] or BST thin films deposited on LaAlO3 [21–27]; that is, there is typically one dislocation every 15–20 unit cells. The in-plane lattice parameters and therefore the value of the misfit strain change depending on the thickness of the film (see figure 2), giving rise to a linear relation between ρ and ηm illustrated in figure 2 . This demonstrates that it is possible to change the misfit strain value continuously with thickness from positive to negative values, on a single substrate. Such continuous control is not possible when using the available substrates. In order to assess the possibilities of a thickness-driven continuous change of strain, we have investigated
of the polarization, the Curie temperature or the dielectric response. Surprisingly, this overlooked method ‘simply’ consists of varying the thickness of ferroelectric films (such as those made of (Ba0.8Sr0.2)TiO3 (BST), as done here) grown on the same substrate (namely, MgO, here). Even more surprisingly, it is an effect that is commonly believed to yield a degradation of properties that is at the heart of this desired continuous strain variation! This effect is the existence of dislocations at the film–substrate interface. More precisely, continuously changing the thickness of ferroelectric films grown on the same substrate leads to a systematic variation of the density of these dislocations, which then results in a controllable strain. The present study therefore also revisits commonly held beliefs, in addition to providing a novel, efficient and practical route to optimize physical properties via strain engineering. A series of BST thin films from 6 to 980 nm thick was sputtered on (0 0 1)-MgO substrate [7]. High-resolution x-ray diffraction (XRD) showed that all the films are mono-oriented along the growth direction (i.e. pseudo-cubic [0 0 1]) and free of secondary or parasitic phases, as illustrated in figure 1 and in the appendix. The in- and out-of-plane lattice parameters are determined from (h0l) peaks (see fi gure 1) and are reported in table 1. Interestingly, the lattice parameters of the film do not tend toward their bulk counterparts when thickness increases, indicating that, independent of the thickness, the films are strained by the substrate, contrary to some reports on e.g. manganites [8, 9] or aluminates [10]. Oxygen vacancies are a common defect in oxide thin films and are known to increase the unit-cell volume of ferroelectrics [11, 12]. The minute increase of the unit cell volume for the thickest film ( + 0.05%) compared to the bulk indicates that oxygen vacancies may be present in the films, although not in significant amounts (see appendix) and rules them out from being responsible for the observed behavior. It is worth underlining that this is not the first study reporting the changes of properties induced by varying the thickness of films of a given material on a single substrate. For example, Ba0.5Sr0.5TiO3 films with thickness over the same wide range of thicknesses have been deposited on MgO [13], using SrRuO3 as the bottom electrode. The coherent growth achieved thanks the choice of this electrode enabled an exponential strain gradient of the form reported by Kim et al [14] to develop within the thickness of the film. Using Landau–Ginzburg–Devonshire expansion Sinnamon et al provided a rationale for the observed stabilization of ferroelectricity [15]. Other studies of the effect of strain gradient on properties, such as on the dielectric constant of Ba0.5Sr0.5TiO3 films [16, 17] have also been carried out and provide a detailed framework for the analysis of such coherent films. In contrast, none of the films studied here are in coherent epitaxy with the substrate, which does not prevent them however from being strongly clamped and therefore strained by the underlying substrate. Indeed, as a consequence of the increasing density of dislocations created when thickness increases, the in-plane lattice parameter of thinner films is closer to the in-plane lattice parameter of the substrate and evolves away continuously when thickness increases (see 2
J. Phys.: Condens. Matter 26 (2014) 292201
Substrate 4
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Figure 1. Top: (004) (left) and (204) (center) reciprocal space maps and θ/2θ scan (right) illustrating the mono-oriented nature of the BST films. Bottom, from left to right: reciprocal space maps around the (204) peak for 12, 56, 150 and 980 nm films, illustrating the evolution of the lattice parameters as a function of thickness. Table 1. Lattice parameters at room temperature for the investigated
Misfit strain (10−3)
thin films (out-of-plane c∥[0 0 1] and in-plane (a∥[1 0 0], b∥[0 1 0] and mean a∥)), for bulk BST (tetragonal a and c and pseudo-cubic a0) and for the MgO substrate (cubic, as ). The misfit strain is ηm =(a∥-a0)/a0.
−8−6−4−2 0 2 4 6 8
(a)
t (nm)
c (Å)
a (Å)
b (Å)
a∥ (Å)
ηm (10 )
6 12 38 56 80 150 240 980 Bulk
3.995 3.993 3.995 4.012 4.007 4.041 4.036 4.039
4.003 3.993 3.997
3.996 3.992 3.992 3.972 3.974 3.955 3.959 3.955 a (Å) 3.991
3.999 3.992 3.995 3.972 3.974 3.957 3.959 3.956 a0 (Å) 3.982 as (Å) 4.211
4.4 2.6 3.2 − 2.4 − 1.9 − 6.2 − 5.7 − 6.6
Substrate (MgO)
3.975 3.959 3.960 3.956 c (Å) 3.978
Thickness (nm)
(Ba0.8Sr0.2)TiO3 thin films − 3
100
10 3.95
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−8−6−4−2 0 2 4 6 8
(b)
1.5 1.45 1.4 1.35 1.3 1.25 1.2 1.15 1.1
−8−6−4−2 0 2 4 6 8
Misfit strain (10−3)
Figure 2. Left, misfit strain and a∥ versus thickness, illustrating the large change in misfit strain, including its sign, when thickness is increased. Right, linearly decreasing dislocation density with increasing misfit strain.
one of the prominent implications of strain engineering in perovskite thin films: the possibility to tune critical temperatures (e.g., to significantly increase the Curie temperature, TC , in classical ferroelectrics such as BST). We have therefore first carried out temperature-dependent XRD. Figure 4 shows the dependence of the film's tetragonality (defined as c/a∥ − 1) on temperature for thicknesses ranging from 6 to 980 nm. For each thickness the high temperature linear variation is followed by an abrupt change of slope, which signals the onset of ferroelectricity. Interestingly, the corresponding temperature, TC, does not exhibit a monotonic evolution but rather a ‘V’ shape, with an increase for thicknesses above 38 nm and below 12 nm. Similar to the behavior of the lattice parameters, TC does not tend toward its bulk value of 330 K when thickness increases. This rules out the hypothesis that the system is mainly influenced by a strain gradient that would develop throughout the thickness of the film, since the relaxed portion of the film would then increase with increasing thickness and the overall behavior would tend toward the bulk one. This is unambiguously not the case here.
In order to definitely ascertain that the change of slope in the evolution of tetragonality with temperature does correspond to the paraelectric to ferroelectric phase transition (i.e. to TC ), we have studied polarized Raman spectra as a function of temperature (see appendix). For the 980 nm film, above 560 K, no Raman mode is active and the spectrum does not exhibit any peak. This temperature corresponds to the change of slope in figure 4 observed by XRD. Such a lack of Raman mode is consistent with a paraelectric phase. On the other hand, below 560 K, modes appear and correspond to those observed in bulk BST in its ferroelectric phase except the soft mode, which is shifted due to strain imposed by the substrate [29]. There is therefore a paraelectric-to-ferroelectric transition in the film at the temperature at which structural anomalies were detected in the 980 nm thick film. Similarly, the TC values determined by Raman spectroscopy and XRD are in good agreement for all investigated thicknesses.
3
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J. Phys.: Condens. Matter 26 (2014) 292201
2.1
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Figure 5. Tetragonality (c/a − 1) at low temperature and wavenumber at low temperature for the 980 nm film.
980 240
600
56
12 38 6 t(nm)
Temperature (K)
paraeletric phase
Figure 3. Schematic representation of the thermal evolution of
the in-plane lattice parameter (a∥) for the thin and thick films investigated compared to the ones of the substrate and bulk material. For thin films the density of dislocations at the deposition temperature is low and a∥ is closer to the substrate than for thick films, where the density of dislocations is larger. From these values at the deposition temperature, the thermal evolution of the substrate dictates the variation of a∥ and brings its value either above the pseudo-cubic lattice parameter of the bulk (a0), implying a positive misfit strain ( ηm ), or below, causing the misfit strain to be negative.
P4/mmm
500 400 c phase
300
aa phase
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−0.6
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−0.2
0
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0.6
Misfit strain (%) bulk 2.5 Tc
c/a−1 (%)
2
Figure 6. Calculated (linked triangles) and experimental (squares, XRD; bullets, Raman spectroscopy) temperature-misfit strain phase diagram.
980 nm 240 nm 56 nm 38 nm
1.5 1
At low temperature, the evolution of the film's tetragonality exhibits a second change of slope at the temperature where the soft mode hardens (see figure 5). The low-temperature phase may adopt the monoclinic symmetry expected from calculations (see figure 6 and [26]). From the experimental transition temperatures obtained on thin films of various thicknesses, we can draw in figure 6 an experimental temperature–misfit strain phase diagram, over which we have superimposed the phase diagram calculated from the first-principles-based effective Hamiltonian. These results are in agreement with the corresponding phenomenological phase diagram [26]. It is worth noting that, here, the calculations are done by imposing various in-plane lattice parameters on bulk BST, in order to mimic coherent epitaxy on different substrates, according to the classical strain-engineering paradigm, whereas the experimental points are obtained from the currently investigated 6–980 nm thick films that are all grown on identical substrates (namely, MgO). Note that the discrepancy in the slopes of the phase transition lines can be minimized by adjusting the parameters that characterize the interaction between strain and local mode in our
0.5 0 −0.5
−(c/a−1) (%)
−1 12 nm 6 nm
0.2 0.1 0 −0.1 −0.2 300 400 500 600 700 800 Temperature (K)
Figure 4. Tetragonalities (c/a − 1) for films of various thicknesses. The vertical axis (scale and sign) is different in the two panels. The arrows underline the evolution of TC as a function of thickness. 4
J. Phys.: Condens. Matter 26 (2014) 292201
10000
ε||
parameters induce misfit strain values that differ by more than 0.15%, with the exception of EuScO3 and TbScO3, where the values of misfit strain along the two in-plane directions differ by less than 0.05% . These three substrates would induce three fixed misfit strain values of − 0.09% (EuScO3), + 0.20% (KTaO3) and − 0.60% (TbScO3), obviously restricting the possible exploration of the phase diagram. In conclusion, our results demonstrate that the increase in dislocation density when thicker films are deposited on a mismatched substrate can be used to tune precisely the thermodynamic quantity governing the property of ferroelectric films, i.e. the misfit strain. Such a control was so far mostly envisioned through the imposition onto the film of the substrate's lattice parameter through coherent epitaxy. Despite the great achievements, both experimental and theoretical, of this method and the valuable possibility to exploit the flexoelectric effect, such an avenue suffers from the limited number of available substrates, which drastically limits the number of attainable misfit strains. As a consequence, the systematic experimental investigation of the temperature-misfit strain phase diagram is at best cumbersome and imposes determination of many deposition conditions to deposit coherent films on as many substrates. We show that, using one single substrate, it is possible to continuously change the density of dislocation by varying the thickness of the film. As a consequence of the quasi-linear relation between the dislocation density and misfit strain, this method enables a continuous tuning of the misfit strain. The physical properties of ferroelectric thin films being governed by this thermodynamic quantity, we show that physical properties of ferroelectric films can be tuned by thickness. In contrast to thickness effects such as metal to insulator transitions [31], here the thicknesses considered are too large to directly induce any change in the ferroelectric properties. This allows the strainengineering via thickness avenue presented here not to be thwarted by dimensionality-related issues and reinforces its usefulness and practicality.
Calculations
8000 6000 4000 2000 0
5000
ε||
4000
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-0.6
-0.4
-0.2 0 Misfit strain (%)
0.2
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Experiments ηm>0
ηm
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Strain engineering of perovskite thin films using a single substrate
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 292201 (http://iopscience.iop.org/0953-8984/26/29/292201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.210.236.20 This content was downloaded on 26/06/2014 at 06:53
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 292201 (11pp)
doi:10.1088/0953-8984/26/29/292201
Fast Track Communication
Strain engineering of perovskite thin films using a single substrate P-E Janolin1, A S Anokhin2,3, Z Gui4, V M Mukhortov2, Yu I Golovko2, N Guiblin1, S Ravy5, M El Marssi6, Yu I Yuzyuk3, L Bellaiche4 and B Dkhil1 1
Laboratoire Structures, Propriétés et Modélisation des Solides, UMR CNRS-École Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry Cedex, France 2 Southern Scientific Center Russian Academy of Sciences, Rostov-on-Don, 344006, Russia 3 Faculty of Physics, Southern Federal University, Rostov-on-Don, 344006, Russia 4 Institute for Nanoscience and Engineering and Physics Department, University of Arkansas, Fayetteville, Arkansas 72701, USA 5 Synchrotron SOLEIL, L'Orme des Merisiers, Saint Aubin-B.P. 48, F-91192 Gif-sur-Yvette, France 6 Laboratoire de Physique de la Matière Condensée, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France E-mail: [email protected] Received 23 April 2014 Accepted for publication 23 May 2014 Published 25 June 2014 Abstract
Combining temperature-dependent x-ray diffraction, Raman spectroscopy and firstprinciples-based effective Hamiltonian calculations, we show that varying the thickness of (Ba0.8Sr0.2)TiO3 (BST) thin films deposited on the same single substrate (namely, MgO) enables us to change not only the magnitude but also the sign of the misfit strain. Such previously overlooked control of the strain allows several properties of these films (e.g. Curie temperature, symmetry of ferroelectric phases, dielectric response) to be tuned and even optimized. Surprisingly, such desired control of the strain (and of the resulting properties) originates from an effect that is commonly believed to be detrimental to functionalities of films, namely the existence of misfit dislocations. The present study therefore provides a novel route to strain engineering, as well as leading us to revisit common beliefs. Keywords: strain engineering, ferroelectrics, BST (Some figures may appear in colour only in the online journal)
Strain engineering has recently emerged as a powerful way to tune the remarkable physical properties of ABO3 perovskite thin films. For instance, it enables us to enhance the magnitude of the polarization in ferroelectrics [1] or multiferroics [2], to strongly shift the maximum (Curie) temperature for which ferroelectricity exists [1, 3], to induce ferroelectricity in incipient ferroelectric [4] or paraelectric [5] materials or to generate superior electromechanical properties through phase coexistence [6]. Strain engineering of perovskite thin films is typically realized through the choice of a substrate which imposes its lattice parameter onto the film through coherent epitaxy, implying that any desired strain requires its 0953-8984/14/292201+11$33.00
own specific substrate. Unfortunately, the limited number of substrates compatible with the perovskite structure (not mentioning their cost) imposes a drastic limitation to such strain engineering and therefore may prevent the optimization of several physical properties, since some regions of strains cannot be practically reached in some materials. Here, we use a combination of several experimental and theoretical techniques to demonstrate that an alternative and efficient method exists to allow a continuous variation of the misfit strain (including change of its sign), which thus results in the tuning and even optimization of several important physical properties. Examples of such properties are the direction 1
© 2014 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 292201
table 1 and figure 2). Dislocations tend to reduce the deposition strain originating from the mismatch in lattice parameters between the film and the substrate. Once the film is deposited, the dislocations form a fixed network that does not prevent the substrate from imposing its thermal evolution on the in-plane lattice parameter of the films. Because the thermal expansion coefficient of MgO is larger than that of BST, a thermal compressive stress arises when the film is cooled to room temperature. For thin films the low density of dislocations causes the (large) negative deposition strain to be partially compensated by the (positive) thermal strain, resulting in thin film under tension, whereas for thicker films the high density of dislocations causes the (small) negative deposition strain to be overcompensated by the (positive) thermal strain, resulting in an overall compression. Figure 3 illustrates this mechanism. A strain gradient developing throughout the thickness of the film would cause the in-plane lattice parameter of the films to be somewhere between the substrate and bulk lattice parameters, which is not the case for all investigated films. The proposed mechanism explains why all films are subjected to substrateinduced strains (negative for the deposition strain and positive for the thermal strain), but that various final misfit strain values (from positive to negative) can be obtained, on the same substrate, depending on the thickness deposited. Coherent epitaxy is the necessary condition for a substrate to impose its lattice parameter onto a film. In this regard, dislocations are considered as detrimental, as they prevent the substrate from imposing the targeted strain state on the film. In contrast, here, the absence of coherent epitaxy is at the very heart of strain engineering via thickness. Indeed, the misfit strain ( ηm ) is a thermodynamic quantity defined as the relative difference between the in-plane lattice parameter of the film (a∥) and the pseudo-cubic bulk lattice parameter (a0): ηm = ( a∥− a 0 ) / a 0. a0 is the lattice parameter the bulk material would have if it remained paraelectric for any temperature. Coherent epitaxy fixes a∥ to the substrate's lattice parameter, thereby imposing ηm. In contrast, misfit dislocations enable a∥ and then ηm, to vary. In this regard a large mismatch with the substrate (5% for BST on MgO at room temperature) appears as a prerequisite and eliminates the need to determine a critical thickness for relaxation (in contrast to SrTiO3 on DyScO3 [18]) or to investigate whether the growth mode provides such a relaxation as, e.g., in some aluminates [19]. We have calculated the linear density of dislocation, ρ, from ρ ( t ) = ( a∥( t ) − as ) / ( a∥( t ) as ), where as is the substrate lattice parameter. The calculated values of ρ (see appendix) are similar to those of Pb(Zr0.2Ti0.8)O3 thin films deposited on MgO [20] or BST thin films deposited on LaAlO3 [21–27]; that is, there is typically one dislocation every 15–20 unit cells. The in-plane lattice parameters and therefore the value of the misfit strain change depending on the thickness of the film (see figure 2), giving rise to a linear relation between ρ and ηm illustrated in figure 2 . This demonstrates that it is possible to change the misfit strain value continuously with thickness from positive to negative values, on a single substrate. Such continuous control is not possible when using the available substrates. In order to assess the possibilities of a thickness-driven continuous change of strain, we have investigated
of the polarization, the Curie temperature or the dielectric response. Surprisingly, this overlooked method ‘simply’ consists of varying the thickness of ferroelectric films (such as those made of (Ba0.8Sr0.2)TiO3 (BST), as done here) grown on the same substrate (namely, MgO, here). Even more surprisingly, it is an effect that is commonly believed to yield a degradation of properties that is at the heart of this desired continuous strain variation! This effect is the existence of dislocations at the film–substrate interface. More precisely, continuously changing the thickness of ferroelectric films grown on the same substrate leads to a systematic variation of the density of these dislocations, which then results in a controllable strain. The present study therefore also revisits commonly held beliefs, in addition to providing a novel, efficient and practical route to optimize physical properties via strain engineering. A series of BST thin films from 6 to 980 nm thick was sputtered on (0 0 1)-MgO substrate [7]. High-resolution x-ray diffraction (XRD) showed that all the films are mono-oriented along the growth direction (i.e. pseudo-cubic [0 0 1]) and free of secondary or parasitic phases, as illustrated in figure 1 and in the appendix. The in- and out-of-plane lattice parameters are determined from (h0l) peaks (see fi gure 1) and are reported in table 1. Interestingly, the lattice parameters of the film do not tend toward their bulk counterparts when thickness increases, indicating that, independent of the thickness, the films are strained by the substrate, contrary to some reports on e.g. manganites [8, 9] or aluminates [10]. Oxygen vacancies are a common defect in oxide thin films and are known to increase the unit-cell volume of ferroelectrics [11, 12]. The minute increase of the unit cell volume for the thickest film ( + 0.05%) compared to the bulk indicates that oxygen vacancies may be present in the films, although not in significant amounts (see appendix) and rules them out from being responsible for the observed behavior. It is worth underlining that this is not the first study reporting the changes of properties induced by varying the thickness of films of a given material on a single substrate. For example, Ba0.5Sr0.5TiO3 films with thickness over the same wide range of thicknesses have been deposited on MgO [13], using SrRuO3 as the bottom electrode. The coherent growth achieved thanks the choice of this electrode enabled an exponential strain gradient of the form reported by Kim et al [14] to develop within the thickness of the film. Using Landau–Ginzburg–Devonshire expansion Sinnamon et al provided a rationale for the observed stabilization of ferroelectricity [15]. Other studies of the effect of strain gradient on properties, such as on the dielectric constant of Ba0.5Sr0.5TiO3 films [16, 17] have also been carried out and provide a detailed framework for the analysis of such coherent films. In contrast, none of the films studied here are in coherent epitaxy with the substrate, which does not prevent them however from being strongly clamped and therefore strained by the underlying substrate. Indeed, as a consequence of the increasing density of dislocations created when thickness increases, the in-plane lattice parameter of thinner films is closer to the in-plane lattice parameter of the substrate and evolves away continuously when thickness increases (see 2
J. Phys.: Condens. Matter 26 (2014) 292201
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4
2
2.25 2.3 2.15 2.2 H 2.05 2.1
500 450 400 350 300 250 200 150 100 50 0 4.25 4.2 4.15 L 4.1 4.05
500 450 400 350 300 250 200 150 100 50 0
4
2
10
Substrate
Film
2.4
1 (bulk)
0.1 38.5
39
39.5
40
40.5 2θ /deg.
150 nm
Int. (arb.unit)
120 100 80 60 40 20 0 4.25 4.2 4.15 L 4.1 4.05
2.2
56 nm
Int. (arb.unit)
Int. (arb.unit)
12 nm
100
2
3.6
0 -0.4
4 3
3
3.9
5 Substrate
4
4
(002) t=980 nm
1000
6
Film
4.2
5
L
L
6 4.1
-0.6
7
7
4.2
10000
8
4.4
2.25 2.3 2.15 2.2 H 2.05 2.1
350 300 250 200 150 100 50 0 4.25 4.2 4.15 L 4.1 4.05
350 300 250 200 150 100 50 0
4
2
(a domains)
41
41.5
42
42.5
980 nm
2.25 2.3 2.15 2.2 H 2.05 2.1
Int. (arb.unit)
8
Film
9
4.6
9
Int. (log scale)
10 4.3
500 450 400 350 300 250 200 150 100 50 0 4.25 4.2 4.15 L 4.1 4.05
500 450 400 350 300 250 200 150 100 50 0
4
2
2.25 2.3 2.15 2.2 H 2.05 2.1
Figure 1. Top: (004) (left) and (204) (center) reciprocal space maps and θ/2θ scan (right) illustrating the mono-oriented nature of the BST films. Bottom, from left to right: reciprocal space maps around the (204) peak for 12, 56, 150 and 980 nm films, illustrating the evolution of the lattice parameters as a function of thickness. Table 1. Lattice parameters at room temperature for the investigated
Misfit strain (10−3)
thin films (out-of-plane c∥[0 0 1] and in-plane (a∥[1 0 0], b∥[0 1 0] and mean a∥)), for bulk BST (tetragonal a and c and pseudo-cubic a0) and for the MgO substrate (cubic, as ). The misfit strain is ηm =(a∥-a0)/a0.
−8−6−4−2 0 2 4 6 8
(a)
t (nm)
c (Å)
a (Å)
b (Å)
a∥ (Å)
ηm (10 )
6 12 38 56 80 150 240 980 Bulk
3.995 3.993 3.995 4.012 4.007 4.041 4.036 4.039
4.003 3.993 3.997
3.996 3.992 3.992 3.972 3.974 3.955 3.959 3.955 a (Å) 3.991
3.999 3.992 3.995 3.972 3.974 3.957 3.959 3.956 a0 (Å) 3.982 as (Å) 4.211
4.4 2.6 3.2 − 2.4 − 1.9 − 6.2 − 5.7 − 6.6
Substrate (MgO)
3.975 3.959 3.960 3.956 c (Å) 3.978
Thickness (nm)
(Ba0.8Sr0.2)TiO3 thin films − 3
100
10 3.95
3.97
3.99 a// (Å)
4.01
1.6
Dislocation density (106 cm−1)
1000
1.55
−8−6−4−2 0 2 4 6 8
(b)
1.5 1.45 1.4 1.35 1.3 1.25 1.2 1.15 1.1
−8−6−4−2 0 2 4 6 8
Misfit strain (10−3)
Figure 2. Left, misfit strain and a∥ versus thickness, illustrating the large change in misfit strain, including its sign, when thickness is increased. Right, linearly decreasing dislocation density with increasing misfit strain.
one of the prominent implications of strain engineering in perovskite thin films: the possibility to tune critical temperatures (e.g., to significantly increase the Curie temperature, TC , in classical ferroelectrics such as BST). We have therefore first carried out temperature-dependent XRD. Figure 4 shows the dependence of the film's tetragonality (defined as c/a∥ − 1) on temperature for thicknesses ranging from 6 to 980 nm. For each thickness the high temperature linear variation is followed by an abrupt change of slope, which signals the onset of ferroelectricity. Interestingly, the corresponding temperature, TC, does not exhibit a monotonic evolution but rather a ‘V’ shape, with an increase for thicknesses above 38 nm and below 12 nm. Similar to the behavior of the lattice parameters, TC does not tend toward its bulk value of 330 K when thickness increases. This rules out the hypothesis that the system is mainly influenced by a strain gradient that would develop throughout the thickness of the film, since the relaxed portion of the film would then increase with increasing thickness and the overall behavior would tend toward the bulk one. This is unambiguously not the case here.
In order to definitely ascertain that the change of slope in the evolution of tetragonality with temperature does correspond to the paraelectric to ferroelectric phase transition (i.e. to TC ), we have studied polarized Raman spectra as a function of temperature (see appendix). For the 980 nm film, above 560 K, no Raman mode is active and the spectrum does not exhibit any peak. This temperature corresponds to the change of slope in figure 4 observed by XRD. Such a lack of Raman mode is consistent with a paraelectric phase. On the other hand, below 560 K, modes appear and correspond to those observed in bulk BST in its ferroelectric phase except the soft mode, which is shifted due to strain imposed by the substrate [29]. There is therefore a paraelectric-to-ferroelectric transition in the film at the temperature at which structural anomalies were detected in the 980 nm thick film. Similarly, the TC values determined by Raman spectroscopy and XRD are in good agreement for all investigated thicknesses.
3
85
2.3
80
2.25
75
2.2
70
2.15
65
c/a-1(%)
-1
2.35
Wavenumber (cm )
J. Phys.: Condens. Matter 26 (2014) 292201
2.1
100
150
200 Temperature (K)
60 300
250
Figure 5. Tetragonality (c/a − 1) at low temperature and wavenumber at low temperature for the 980 nm film.
980 240
600
56
12 38 6 t(nm)
Temperature (K)
paraeletric phase
Figure 3. Schematic representation of the thermal evolution of
the in-plane lattice parameter (a∥) for the thin and thick films investigated compared to the ones of the substrate and bulk material. For thin films the density of dislocations at the deposition temperature is low and a∥ is closer to the substrate than for thick films, where the density of dislocations is larger. From these values at the deposition temperature, the thermal evolution of the substrate dictates the variation of a∥ and brings its value either above the pseudo-cubic lattice parameter of the bulk (a0), implying a positive misfit strain ( ηm ), or below, causing the misfit strain to be negative.
P4/mmm
500 400 c phase
300
aa phase
P4mm
Amm2
200 r phase − Cm 100 −0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
Misfit strain (%) bulk 2.5 Tc
c/a−1 (%)
2
Figure 6. Calculated (linked triangles) and experimental (squares, XRD; bullets, Raman spectroscopy) temperature-misfit strain phase diagram.
980 nm 240 nm 56 nm 38 nm
1.5 1
At low temperature, the evolution of the film's tetragonality exhibits a second change of slope at the temperature where the soft mode hardens (see figure 5). The low-temperature phase may adopt the monoclinic symmetry expected from calculations (see figure 6 and [26]). From the experimental transition temperatures obtained on thin films of various thicknesses, we can draw in figure 6 an experimental temperature–misfit strain phase diagram, over which we have superimposed the phase diagram calculated from the first-principles-based effective Hamiltonian. These results are in agreement with the corresponding phenomenological phase diagram [26]. It is worth noting that, here, the calculations are done by imposing various in-plane lattice parameters on bulk BST, in order to mimic coherent epitaxy on different substrates, according to the classical strain-engineering paradigm, whereas the experimental points are obtained from the currently investigated 6–980 nm thick films that are all grown on identical substrates (namely, MgO). Note that the discrepancy in the slopes of the phase transition lines can be minimized by adjusting the parameters that characterize the interaction between strain and local mode in our
0.5 0 −0.5
−(c/a−1) (%)
−1 12 nm 6 nm
0.2 0.1 0 −0.1 −0.2 300 400 500 600 700 800 Temperature (K)
Figure 4. Tetragonalities (c/a − 1) for films of various thicknesses. The vertical axis (scale and sign) is different in the two panels. The arrows underline the evolution of TC as a function of thickness. 4
J. Phys.: Condens. Matter 26 (2014) 292201
10000
ε||
parameters induce misfit strain values that differ by more than 0.15%, with the exception of EuScO3 and TbScO3, where the values of misfit strain along the two in-plane directions differ by less than 0.05% . These three substrates would induce three fixed misfit strain values of − 0.09% (EuScO3), + 0.20% (KTaO3) and − 0.60% (TbScO3), obviously restricting the possible exploration of the phase diagram. In conclusion, our results demonstrate that the increase in dislocation density when thicker films are deposited on a mismatched substrate can be used to tune precisely the thermodynamic quantity governing the property of ferroelectric films, i.e. the misfit strain. Such a control was so far mostly envisioned through the imposition onto the film of the substrate's lattice parameter through coherent epitaxy. Despite the great achievements, both experimental and theoretical, of this method and the valuable possibility to exploit the flexoelectric effect, such an avenue suffers from the limited number of available substrates, which drastically limits the number of attainable misfit strains. As a consequence, the systematic experimental investigation of the temperature-misfit strain phase diagram is at best cumbersome and imposes determination of many deposition conditions to deposit coherent films on as many substrates. We show that, using one single substrate, it is possible to continuously change the density of dislocation by varying the thickness of the film. As a consequence of the quasi-linear relation between the dislocation density and misfit strain, this method enables a continuous tuning of the misfit strain. The physical properties of ferroelectric thin films being governed by this thermodynamic quantity, we show that physical properties of ferroelectric films can be tuned by thickness. In contrast to thickness effects such as metal to insulator transitions [31], here the thicknesses considered are too large to directly induce any change in the ferroelectric properties. This allows the strainengineering via thickness avenue presented here not to be thwarted by dimensionality-related issues and reinforces its usefulness and practicality.
Calculations
8000 6000 4000 2000 0
5000
ε||
4000
-0.8
-0.6
-0.4
-0.2 0 Misfit strain (%)
0.2
0.4
0.6
Experiments ηm>0
ηm
