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Tetragonal-tetragonal-monoclinic-rhombohedral transition: Strain relaxation of heavily
compressed BiFeO3 epitaxial thin films
Z. Fu, Z. G. Yin, N. F. Chen, X. W. Zhang, Y. J. Zhao, Y. M. Bai, Y. Chen, H.-H. Wang, X. L. Zhang, and J. L. Wu
Citation: Applied Physics Letters 104, 052908 (2014); doi: 10.1063/1.4864077
View online: http://dx.doi.org/10.1063/1.4864077
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APPLIED PHYSICS LETTERS 104, 052908 (2014)
Tetragonal-tetragonal-monoclinic-rhombohedral transition: Strain relaxation
of heavily compressed BiFeO3 epitaxial thin films
Z. Fu,1 Z. G. Yin,1,a) N. F. Chen,2 X. W. Zhang,1 Y. J. Zhao,1 Y. M. Bai,2 Y. Chen,3
H.-H. Wang,3 X. L. Zhang,1 and J. L. Wu1
1
Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors,
Chinese Academy of Sciences, Beijing 100083, China
2
School of Renewable Energy Engineering, North China Electric Power University, Beijing 102206, China
3
Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing 100039, China
(Received 30 October 2013; accepted 21 January 2014; published online 4 February 2014)
BiFeO3 films with in-plane compressive strain of 3.5% were deposited on oxygen-deficient
La0.3Sr0.7MnO3-d buffered SrTiO3(001) substrates. This highly strained BiFeO3 does not relax
directly into its rhombohedral parent phase upon increasing the film thickness. Instead, a multi-step
path involving structural transitions is observed. The misfit stress is first accommodated by the
occurrence of true tetragonal BiFeO3 with c/a ratio of 1.23, then reduced by the transformation to
the MC-type monoclinic structure, and finally alleviated through the MC-rhombohedral transition.
Moreover, this process enables the formation of strain-driven morphotropic phase boundaries at a
C 2014 AIP Publishing LLC.
stress level much lower than the reported threshold of 4.5%. V
[http://dx.doi.org/10.1063/1.4864077]
BiFeO3 (BFO) has attracted considerable attention in
recent years, since the coexistence of ferroelectric and antiferromagnetic orders is of great interest to fundamental
physics and to potential applications such as actuators, sensors, and nonvolatile memories.1 For these applications BFO
is preferred in thin film form. However, the substrate-induced
epitaxial stress not only modifies the structure but also influences the physical behaviors of BFO films.2 For instance,
under moderate compressive biaxial strain the crystal symmetry of BFO changes from rhombohedral (R) R3c in its bulk
form, to tetragonal (T) or monoclinic distorted MA structures,3,4 depending on thickness and growth conditions.
Concomitantly, the ferroelectric Curie temperature is
reduced, contrary to what was observed in traditional ferroelectrics like BaTiO3.5 The compressive strain also leads to a
polarization rotation in the (110) plane, yielding a notable
polarization enhancement along the [001] direction.2 More
interestingly, giant compressive strain stabilizes a supertetragonal phase with c/a ratio of 1.23,6,7 implying a greatly
enhanced spontaneous polarization.8 This phase has a monoclinic MC structure,9 i.e., with the polarization vector constrained in the (010) plane, and is commonly referred to as
T-like BFO in literatures.
One of the most fundamental issues in heteroepitaxy is
the evolution of lattice strain. For classical metal and semiconductor epilayers, the misfit strain is relaxed through interfacial dislocations, once the stored elastic energy
overwhelms the dislocation formation energy at a critical
thickness. However, both the R-like and T-like BFO films exhibit quite different stress relaxation paths. Under moderate
compressive strain, the R-like BFO(001) film releases its
strain by domain tilt upon increasing the thickness,10,11 in
analogy to what was observed in rhombohedral
a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected].
0003-6951/2014/104(5)/052908/5/$30.00
La0.3Sr0.7MnO3-d (LSMO) epilayers.12 By contrast, tilted
R-like and T-like phases, namely, MI and MII,tilt, start to
appear to alleviate the elastic energy when the thickness of
the MC-BFO exceeds a threshold value.13,14 They form periodic stripe-like patches and are dispersed in the MC matrix.6
These bridging phases provide an avenue for the MC phase to
transform into the thermally stable rhombohedral phase.13,14
Despite these findings, the exact interrelationships between
the misfit strain and the thickness-dependent structural evolution of BFO still remain elusive. Typically, the lattice
relaxation process of the R-like BFO thin films grown on
large misfit substrates is not yet fully understood. In this
study, BFO thin films with in-plane compressive strain of
3.5% were deposited on oxygen-deficient LSMO buffered
SrTiO3 (STO) substrates. A multi-step, thickness-dependent
T-T-MC-R relaxation path is demonstrated.
BFO/LSMO/STO(001) thin films were fabricated by
radio-frequency magnetron sputtering. The LSMO target was
made by traditional solid-state reaction technique, while the
BFO target was prepared by compressing the grinded Bi2O3
and Fe2O3 powder mixture (with molar ratio of 1.05:1) into a
80-mm-diameter copper cup without any high-temperature
sintering. Prior to deposition, the sputtering chamber was
evacuated to a base pressure of 5 105 Pa, and then filled
with the work gas (Ar and O2) to a total pressure of 0.8 Pa.
During the LSMO growth, the oxygen partial pressure was set
to 0.6 Pa and the substrate temperature to 750 C. For the subsequent BFO deposition, the conditions were adjusted to
0.2 Pa and 650 C. For all samples, the LSMO buffer layer
thickness was fixed at 160 nm. X-ray diffraction (XRD) 2h-h
scans were analyzed by a Rigaku RINT-TTR diffractometer
using Cu Ka radiation as the light source. Surface morphologies were characterized by a NT-MDT solver P47 atomic
force microscopy (AFM). Reciprocal space maps (RSMs)
were collected at beamline 1W1A at Beijing Synchrotron
Radiation Facility (BSRF) with an x-ray wavelength of
104, 052908-1
C 2014 AIP Publishing LLC
V
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Fu et al.
FIG. 1. RSMs around (a) (103) and (b) (113) reflections of the oxygendeficient LSMO epilayer on STO(001) substrate; (c) (001) to (003) qx-scans
of the LSMO layer.
˚ , and were shown in the plots of intensity with
1.5488 A
respect to q in the reciprocal lattice unit (rlu), where q ¼ k/2 d.
To reveal the detailed structure of the LSMO buffer
layer, RSMs around the (103) and (113) reflections were collected and the results are shown in Figs. 1(a) and 1(b). Note
that the pseudocubic notation is used throughout this paper.
Splitting was clearly observed for both the (103) and (113)
reflections, possibly due to domain tilt or the formation of
periodic domain modulation structure.12 The qx-scans shown
in Fig. 1(c) disclose that domain tilt dominates our LSMO
epilayer.12 In general, domain tilt results in increasing splitting from (001) to (003) qx-scans, while constant splitting is
expected in the periodic domain case.12 The derived lattice
˚ , b ¼ 3.79 A
˚ , and c ¼ 3.96 A
˚ . The
parameters are a ¼ 3.85 A
elongation of the out-of-plane lattice constant confirms the
oxygen-deficient nature of the LSMO layer,15 in good accordance with the oxygen-poor growth condition in this
work.
The feasibility of tuning the lattice parameters of LSMO
buffer by oxygen stoichiometry provides an efficient way to
manipulate the in-plane stress, and consequently, the structure of the following grown BFO thin films. Fig. 2 shows the
XRD 2h-h scans of the BFO films with various thicknesses
grown on oxygen-deficient LSMO buffered STO(001).
These BFO films are exclusively characterized by the [001]
growth without any evidence of impurity phases. Below
12 nm, the BFO film exhibits a single phase structure. The
reflection position of this structure is close to the mid-point
between those of T-like and R phases, and is almost independent of the film thickness. RSMs characterizations [(Figs.
3(a) and 3(b)] reveal that both the (103) and (113) peaks are
not split, indicating a tetragonal rather than monoclinic MA
structure, possibly due to the decoupling of lattice and polar
symmetry.16 Moreover, these reflections are quite elongated
along the qz direction, accounting well for the very broad
(00l) peaks observed in Fig. 2. The average lattice parame˚ and
ters extracted from these patterns are a ¼ b ¼ 3.82 A
Appl. Phys. Lett. 104, 052908 (2014)
FIG. 2. h-2h XRD patterns of BFO films with various thicknesses deposited
on oxygen-deficient LSMO buffered STO(001) substrates. Solid squares
(䊏), stars ($), circles (•), and triangles (䉱) denote the reflection positions
of LSMO, TR-BFO, T-like BFO, and R-BFO.
˚ , with c/a ratio of 1.12. The derived unit-cell
c ¼ 4.28 A
˚ 3, very close to that of the bulk R
volume (Vuc) is 62.45 A
1
phase. Here, for convenience we assign this heavily strained
BFO as TR, in which the subscript R stands for a
stress-distorted version of the R phase. The TR-BFO is
semi-coherently strained on the LSMO buffer layer, as
revealed by their similar average in-plane lattice constants.
As the film thickness approaches 12 nm T-like BFO
appears, and its XRD reflection intensity sharply increases
with the thickness (Fig. 2). Further increase of the film thickness to 220 nm leads to the formation of fully relaxed R
phase. Notably, the appeared T-like BFO has an exact tetragonal but not the expected monoclinic MC symmetry at low
thickness (20 nm), as demonstrated by the fact that no measurable splitting of (103) RSM was found in Fig. 3(c). This
tetragonal phase (T-BFO) has a c/a ratio of 1.23. For the
FIG. 3. RSMs around (a) (103) and (b) (113) reflections of the heavily
strained TR-BFO; (c) and (d) (103)-RSMs of T-like BFO collected from the
20- and 60-nm-thick films. The dashed circles are guides for the eyes.
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Fu et al.
Appl. Phys. Lett. 104, 052908 (2014)
FIG. 4. Morphologies collected from (a) the 20-nm-thick and (b) the 60-nmthick BFO films. Stripe-like patches composed of MI and MII,tilt appear on
the 60-nm-thick film surface.
60-nm-thick film, a three-fold splitting of (103) reflection of
T-like BFO appears [Fig. 3(d)], indicative of the monoclinic
MC symmetry.9 Tilted phases including MI and MII,tilt, which
are structural bridges between the MC and R phases,13,14 also
occur in this film. Further evidence of the presence of MI
and MII,tilt comes from the stripe-like structures on the
60-nm-thick film surface, as revealed in Fig. 4. Such structures are fingerprints of the formation of strain-driven morphotropic phase boundaries (MPBs).6,17
On basis of these observations, the entire stress relaxation process of the heavily strained TR-BFO film is established as follows: (i) An exact tetragonal phase (T-BFO)
appears to alleviate the stress as the film thickness of TRBFO is beyond the critical value of 6 nm; (ii) with further
increasing the film thickness T-BFO transforms into the
monoclinic distorted MC-BFO, along with the appearance of
tilted phases (MI and MII,tilt); and (iii) MC-BFO eventually
evolves into the thermally stable R phase through MI and
MII,tilt. This multi-step stress relaxation path is schematically
shown in Fig. 5. Note that T-BFO is the high-temperature
form of MC-BFO, and is not stable at ambient conditions.18
However, the above results show that it can serve as a structural bridge between TR- and MC-BFO and exist at room
temperature.
We now turn to the question why the heavily strained
TR-BFO alleviates its epitaxial stress through such a multistep route. Fig. 6(a) shows the out-of-plane lattice strain ezz,
as a function of the in-plane strain exx of the strained R-like
BFO films. The epitaxial growth of fully strained BFO films
on (001)-oriented STO and (LaAlO3)0.3(Sr2AlTaO6)0.7
(LSAT) yields out-of-plane lattice parameters of 4.08 and
˚ (data not shown), respectively. With increasing the
4.16 A
in-plane misfit from 0 to 3.5%, the out-of-plane strain linearly rises, suggesting a pure elastic deformation of our highly
strained TR-BFO. The extracted Poisson’s ratio by a linear
fit of the data in Fig. 6(a), using ¼ 1/(1 2exx/ezz), is 0.5,
in good accordance with the value obtained by Chen et al.9
Following the equation19
Eelas ¼ 2G
1þv 2
e ;
1 v xx
(1)
where G (56 GPa) is the shear modulus,20 we can easily
derive the elastic energy Eelas of the strained R-like BFO
films, as illustrated in Fig. 6(b). Note that the elastic energy
FIG. 5. Schematic illustration of the thickness-dependent structural evolution of BFO deposited on oxygen-deficient LSMO buffered STO(001). Red,
pink, blue, and green arrows represent the polarization directions of TR-, T-,
MC-, and R-BFO, and black arrows denote the structural phase transition
path.
stored in the lattice is composed of two parts: shear strain
energy and normal strain energy.19 For simplicity, the shear
strain energy is neglected, since it is one order of magnitude
lower than the normal strain term in the region near exx
¼ 3.5%. For comparison, we also show the calculated elastic energy of T-BFO in Fig. 6(b) as a function of in-plane lattice constant according to Eq. (1), given G ¼ 59 GPa and
¼ 0.21.21 The crossover of the two curves at in-plane lat˚ implies two possible lattice relaxation paths
tice of 3.86 A
of the heavily strained R-like BFO: from TR to T or from TR
to R.
Our results show that the direct relaxation route from
TR-BFO to its parent R phase is kinetically suppressed,
although it is thermodynamically favorable. To better understand this, it is useful to refer back to the stress relaxation
mechanism of BFO films under moderate compressive strain.
Fully strained BFO films can retain on STO(001) (misfit
1.4%) up to 90 nm,23 one order of magnitude larger than
the critical thickness estimated through elastic theory.
Similar phenomenon was observed on LSAT(001) (misfit
2.4%).24 Accordingly, the classical interfacial dislocationmediated mechanism is not responsible for the strain relaxation of these BFO(001) films. Very recently, Daumont et al.
have revealed a tetragonal-monoclinic (MA) symmetry
change in the BFO/STO(001) system below 100 nm.3 For
thicker (001)-oriented films, MA-BFO gradually transforms
to fully relaxed R phase through out-of-plane domain tilt.11
In these processes, the relaxation of the misfit stress is
extremely slow and energy costly. For a 720 nm-thick film,
the c/a ratio is merely relaxed from 1.04 in the fully coherent
case to 1.02.10 By sharp contrast, the BFO(111) films exhibit
a very fast stress relaxation,25 in good accordance with the
interfacial dislocation mechanism. It seems that the associated symmetry change may possibly result in the slow stress
relaxation of the (001)-oriented films in the moderate misfit
range, and contribute to the kinetic barrier of the TR to R
transition for the heavily strained case.
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052908-4
Fu et al.
Appl. Phys. Lett. 104, 052908 (2014)
study, and we demonstrate that it serves as a structural bridge
between MC-BFO and the strained R-like phase. Such a finding sheds light on the relationship between the epitaxial
stress and the possible polymorphs of BFO. Also worth
noting is that the relaxation mechanism illustrated here leads
to the formation of MPBs at in-plane compressive stress of
3.5%, much lower than the reported threshold value of
4.5%,6,13,17 providing avenues for future magnetoelectric,
piezoelectric, and piezomagnetic applications.
In conclusion, we show that the in-plane stress plays a
key role in determining the lattice relaxation route of BFO
thin epitaxial films. The use of oxygen-deficient LSMO buffer
layer enables us to fabricate heavily strained BFO films on
STO(001) substrates, and a multi-step TR-T-MC-R relaxation
route involving structural phase transitions was observed.
This finding enriches the knowledge on the thickness-strain
phase diagram of BFO, and benefits a deeper understanding
of the stress relaxation process of epitaxial thin films.
This work was financially supported by the National
Natural Science Foundation of China (Nos. 11274303,
51071145, and 61076051), the National Basic Research
Program of China (No. 2012CB934203), and the Knowledge
Innovation Program of the Chinese Academy of Sciences
under Grant No. ISCAS2009T03.
1
FIG. 6. (a) The out-of-plane lattice constant (open black) and strain ezz (solid
blue) as a function of the in-plane misfit strain exx; the solid line shows a linear fit of the data. (b) Calculated elastic energy per unit cell of both the Rlike and tetragonal BFO films with respect to the in-plane lattice constant;
an free energy difference of 0.04 eV per unit cell between the fully relaxed
R- and T-BFO is chosen.22
The occurrence of a small quantity of BFO with inplane lattice near 3.82 and c/a ratio higher than 1.12, as evidenced by the elongation of the (103) and (113) reflections
along qz [Figs. 3(a) and 3(b)] and the very broad (00l) peaks
(Fig. 2) of TR-BFO, makes the transition from TR- to T-BFO
more favorable. According to previous studies, the polarization vector of R-like BFO rotates from [111] towards [001]
with increasing compressive biaxial stress.2,16 BFO with tetragonal symmetry and c/a ratio exceeding 1.12 can bridge
the transition between TR- and T-BFO, allowing a continuous
polarization rotation to [001] direction. T-BFO is inherently
unstable and a transformation to MC-BFO occurs with
increasing the films thickness. At even larger thickness, the
MC-BFO transforms into R-BFO through tilted intermediate
phases, which was deeply investigated in literatures.17,26
Although the TR-T-MC-R path involves structural phase transitions, it divides the barrier of TR-R transition into three separate barriers and therefore is kinetically more feasible. Such
a stress relaxation route has a close correlation with the
intrinsic phase richness of BFO.
In a previous study, a compressive stress induced R-MAMC-T structural transition sequence was predicted.27 Our
results show that the strain-dependent phase diagram of BFO
may be more complex than expected. Highly elongated, true
tetragonal phase of BFO which has not been available previously without chemical alloying is clearly observed in this
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