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# Enhancement of Ferroelectricity in Strained BaTiO3 Thin Films

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Science  05 Nov 2004:
Vol. 306, Issue 5698, pp. 1005-1009
DOI: 10.1126/science.1103218

## Abstract

Biaxial compressive strain has been used to markedly enhance the ferroelectric properties of BaTiO3 thin films. This strain, imposed by coherent epitaxy, can result in a ferroelectric transition temperature nearly 500°C higher and a remanent polarization at least 250% higher than bulk BaTiO3 single crystals. This work demonstrates a route to a lead-free ferroelectric for nonvolatile memories and electro-optic devices.

Enormous strains can exist in thin films when one material is deposited on another (1), resulting from differences in crystal lattice parameters and thermal expansion behavior between the film and the underlying substrate or arising from defects formed during film deposition (2, 3). As a result, the properties of thin films can be markedly different than the intrinsic properties of the corresponding unstrained bulk materials (49). Although such strain often leads to degraded film properties, if judicious use is made of substrates and growth parameters, strain offers the opportunity to enhance particular properties of a chosen material in thin film form, namely strain engineering.

Strain engineering could facilitate the introduction of more environmentally benign ferroelectric random-access memories (FeRAM). Large shifts in the paraelectric-to-ferroelectric transition temperature (Tc) and remanent polarization (Pr) are expected (1014) and have been observed (1517) in ferroelectrics, signaling the viability of a strain-engineered advance for FeRAM. The major disadvantages of the two materials most widely being pursued for FeRAM (18), Pb(Zr,Ti)O3 and SrBi2Ta2O9, are (i) the volatility of the lead and bismuth constituents of these materials, which complicates their introduction into semiconductor fabrication facilities, and (ii) environmental issues associated with the toxicity of lead. We demonstrate that the ferroelectric properties of BaTiO3 can be enhanced with the use of strain to make them viable for ferroelectric memory applications. The widespread use of (Ba,Sr)TiO3 in semiconductor fabrication facilities for dynamic random-access memories (DRAM) greatly simplifies the introduction of this related material into silicon-based devices.

To predict the Tc enhancement and the temperature dependence of the lattice parameters of BaTiO3 thin films under large biaxial strains with the use of Landau thermodynamic theories (10), we determined a new set of phenomenological coefficients, because existing ones are only applicable to small compressive strains (<∼0.4%) (11). Figure 1 shows the Tc enhancement predicted from thermodynamic analysis for a BaTiO3 thin film under biaxial strain ϵs = (aa0)/a0, where a0 is the lattice parameter of free-standing cubic BaTiO3 and a is the inplane lattice parameter of a biaxially strained (001) BaTiO3 film. The green region shows the range in predicted Tc resulting from the range of reported property coefficients for BaTiO3 that enter into the thermodynamic analysis (1921). Figure 1 implies that a biaxial compressive strain of only ∼1% should be sufficient to produce strained (001) BaTiO3 films with a Tc comparable to or higher than unstrained Pb(Zr,Ti)O3 films.

Although Fig. 1 might seem to imply that Tc can be enhanced without bound, there are limits to strain engineering. The driving force for film relaxation increases with strain and film thickness. When films are grown to thicknesses greatly exceeding their critical values, relaxation toward a zero-strain state by the introduction of dislocations begins. Thus, for strain engineering to be effective, it is important to grow films below, or at least close to, their critical thickness for relaxation. Because the critical thickness at which dislocations begin to form varies approximately inversely with lattice mismatch (1), lower mismatch is desired to allow the growth of strained BaTiO3 films that are thick enough to allow their ferroelectric properties to be conveniently probed or used in devices. Notably, Fig. 1 only applies to thick strained ferroelectrics; as ferroelectrics get thin (<∼100 Å), their ferroelectric properties can be substantially diminished by finite-size effects (17, 2224). Optimizing the trade-off between strain and film thickness depends on the particular application. For FeRAM, films several hundred angstroms in thickness are needed (25). Based on the equilibrium critical thickness (1, 26) for BaTiO3, this would constrain ϵs to be less than about 0.5%; however, we experimentally found that it is possible to grow coherent BaTiO3 films at ϵs = –1.7% that are 500 Å thick.

We used the single-crystal substrates GdScO3 and DyScO3, because they are structurally (27), chemically (27), and thermally (28) compatible with BaTiO3, and they have appropriate lattice constants to impart ϵs of about –1.0 and –1.7%, respectively, on coherent (001) BaTiO3 films (21). Epitaxial BaTiO3 thin films were grown on (110) GdScO3 and (110) DyScO3 substrates by reactive molecular beam epitaxy (MBE) and by pulsed-laser deposition (PLD) with in situ high-pressure reflection high-energy electron diffraction (21).

The lattice parameters of the strained (001) BaTiO3 thin films are summarized in Table 1. These films are epitaxial, purely c-axis oriented (the c axis of all BaTiO3 domains is perpendicular to the wafer surface), and, with the exception of the BaTiO3 film on DyScO3 that is 2000 Å thick, are fully coherent with the substrates, without any resolvable lattice relaxation.

Table 1.

Results from high-resolution x-ray diffraction measurements on the films. The in-plane (a) and out-of-plane (c) lattice constants and full width at half maximum (FWHM) of rocking curves of various peaks (002 of BaTiO3, 200pseudo-cubic of SrRuO3, and 200pseudo-cubic of GdScO3 and DyScO3) at room temperature are given. The a- and c-lattice parameters of single-crystalline BaTiO3 are 3.992 and 4.036 Å, respectively (20).

a (±0.002) (Å) c (±0.0005) (Å) FWHM (°)
Molecular beam epitaxy
BaTiO3 (1000 Å) on GdScO3
BaTiO3 3.964 4.0693 0.080
GdScO3 3.965 3.9638 0.009
BaTiO3 (500 Å) on DyScO3
BaTiO3 3.940 4.0953 0.120
DyScO3 3.943 3.9396 0.009
Pulsed-laser deposition
BaTiO3 (2000 Å) on SrRuO3 (1000 Å) on GdScO3
BaTiO3 3.965 4.0692 0.042
SrRuO3 3.968 3.9052 0.036
GdScO3 3.964 3.9646 0.008
BaTiO3 (500 Å) on SrRuO3 (2000 Å) on DyScO3
BaTiO3 3.939 4.0989 0.045
SrRuO3 3.943 3.9110 0.022
DyScO3 3.944 3.9396 0.009
BaTiO3 (2000 Å) on SrRuO3 (1000 Å) on DyScO3
BaTiO3 3.958 4.0819 0.135
SrRuO3 3.947 3.9187 0.047
DyScO3 3.944 3.9398 0.009

To identify the ferroelectric phase transition, the temperature dependence of the in-plane and out-of-plane lattice parameters of the films and substrates was measured with a variable-temperature four-circle x-ray diffractometer equipped with a two-dimensional (2D) area detector with an angular resolution of ∼0.02°. Unstrained BaTiO3 undergoes a ferroelectric transition at about 130°C from the high-temperature cubic phase ($Math$) to the low-temperature tetragonal phase (P4mm) (20). Figure 2A shows 2D images of the 002 and 202 diffraction peaks at selected temperatures from a BaTiO3 single crystal as well as from coherent BaTiO3 thin films grown on (110) GdScO3 and (110) DyScO3 substrates. There is no substantial change in the diffraction peaks of the BaTiO3 thin films that are at or above Tc ∼ 130°C. As expected, the single diffraction spot of the BaTiO3 single crystal splits into two below 130°C, corresponding to a and c domains of the tetragonal (P4mm) ferroelectric phase.

The in-plane and out-of-plane lattice parameters of the strained BaTiO3 films grown by MBE were determined from the 202 and 002 diffraction peaks and are plotted as a function of temperature in Fig. 2B. The inplane lattice parameters of the BaTiO3 are coherent to the underlying substrates over the entire temperature range (25° to 700°C). There are marked differences in the evolution of the lattice parameters with temperature between the unstrained BaTiO3 single crystal and the strained BaTiO3 thin films. Notably, the BaTiO3 thin films never become cubic; they remain tetragonal as a result of the biaxial substrate constraint. The predicted dependence of the c-lattice parameter of biaxially strained BaTiO3, with and without a ferroelectric phase transition, was calculated from thermodynamic analysis (10) and is shown by the green solid and dashed curves in Fig. 2B, respectively. Because the BaTiO3 film is clamped inplane, all structural changes resulting from the phase transition and thermal expansion are accommodated through changes in the out-of-plane lattice parameter only. The agreement between the solid green prediction and the measured c-axis lattice parameters in Fig. 2B is strong evidence that the change in slope in the c-axis lattice parameter at high temperature corresponds to a ferroelectric phase transition. Analogous lattice constant behavior has been observed in other constrained ferroelectric films (15, 17), is consistent with theory (13, 17), and has been used to determine Tc. The Tc of the coherent BaTiO3 thin films shown in Fig. 2B is ∼400°ConGdScO3 and ∼540°C on DyScO3.

To confirm the huge shifts in Tc, we attempted to measure polarization hysteresis loops on a 2000-Å-thick coherent BaTiO3 film grown by PLD on a coherent SrRuO3 bottom electrode on (110) GdScO3. At temperatures up to about 200°C, hysteresis loops were clearly seen, but at higher temperatures the dielectric losses in the films became too high for reliable measurements. We made second harmonic generation (SHG) measurements as a function of temperature on this PLD-grown BaTiO3/SrRuO3/GdScO3 sample as well as the MBE-grown BaTiO3/GdScO3 sample, whose lattice constants versus temperature behavior is shown in Fig. 2B (21). An SHG signal is only exhibited by materials that lack inversion symmetry. All ferroelectrics must lack inversion symmetry, but there are many materials that lack inversion symmetry and are not ferroelectric. This makes SHG a necessary but insufficient probe for ferroelectricity. Nonetheless, SHG (Fig. 2C) shows that the phase we know from hysteresis loops to be ferroelectric at room temperature remains noncentrosymmetric to the same high temperature (29, 30) at which x-ray diffraction indicates a phase transition. The interpretation consistent with all our analyses—x-ray diffraction, SHG, and hysteresis measurements—is that biaxial compressive strain increases the Tc of BaTiO3.

Hysteresis measurements were made on 200-μm-diameter capacitors of strained BaTiO3 thin films sandwiched between epitaxial top and bottom electrodes of the conducting perovskite oxide SrRuO3 (31). High-resolution x-ray diffraction measurements (summarized in Table 1) revealed the BaTiO3 ferroelectric layers as well as the 1000-Å-thick SrRuO3 bottom electrodes to be fully coherent with the underlying substrates. No relaxation was observed even for BaTiO3 films as thick as 500 Å on DyScO3 and 2000 Å on GdScO3. The critical thicknesses of BaTiO3 thin films grown on coherent SrRuO3 bottom electrodes on GdScO3 and DyScO3 are higher than those of BaTiO3 films grown directly on GdScO3 and DyScO3. This observation is consistent with critical thickness theory, in which the difference arises from strain partitioning between the layers as well as the altered geometry of misfit dislocations in a single layer versus a bilayer (26). Because the leakage in the coherent stack containing a 500-Å-thick BaTiO3 layer on DyScO3 was too high for good ferroelectric hysteresis measurements, a SrRuO3/BaTiO3/SrRuO3/DyScO3 stack was grown with a 2000-Å-thick BaTiO3 layer. This latter stack had low leakage; however, it was partially relaxed.

Figure 3A shows the ferroelectric hysteresis loops measured on the ferroelectric stacks grown on GdScO3 and DyScO3 substrates with 2000-Å-thick BaTiO3 layers, together with results from a BaTiO3 single crystal (32). The hysteresis loops are shifted in the positive voltage direction. This imprint effect is probably due to the asymmetric interfacial properties of the top and bottom electrodes to the BaTiO3 films. Even though we used SrRuO3 for both electrodes, the growth temperature (350°C) of the top electrode was much lower than that of the bottom electrode (680°C), which might lead to poor crystallinity of the top electrode and asymmetric interfaces. The Pr and coercive field (Er) were determined to be ∼50 μC/cm2 and 80 kV/cm for the fully coherent BaTiO3/GdScO3 sample and ∼70 μC/cm2 and 25 kV/cm for the partially relaxed BaTiO3/DyScO3 sample, respectively. This Pr value is almost 270% of the 26 μC/cm2 (32) of single crystal BaTiO3, 3.5 times higher than the maximum switching charge density (20 μC/cm2) assumed in the scaling analysis of FeRAM (18), and comparable to the Pr of unstrained Pb(Zr,Ti)O3 films (33). As this Pr of ∼70 μC/cm2 was observed in a partially relaxed sample with ϵs of –1.3%, a coherently strained BaTiO3/DyScO3 sample with ϵs of –1.7% could have an even higher Pr.

Another important issue for the application of ferroelectric capacitors to memory devices is the loss of switched polarization after repeated switching, i.e., fatigue. We performed fatigue measurements by applying 8.6-μs-wide pulses with a repetition frequency of 10 kHz to the top and bottom SrRuO3 electrodes of the SrRuO3/BaTiO3/SrRuO3/GdScO3 structure at Vmax = 4 V, where Vmax is the amplitude of the voltage pulse. Vmax = 4 V corresponds to 200 kV/cm of the electric field. The switched polarization decreased by 10% of its original value after 106 fatigue cycles, but recovered its original value after 1010 cycles. This is consistent with previous observations of fatigue-free behavior when conducting oxide electrodes are used (34, 35).

As a check that the enhancement of Tc observed in coherently strained BaTiO3 thin films grown by MBE (Fig. 2B) is inherent and applicable to a device structure with a conductive bottom electrode, we performed high-temperature x-ray diffraction measurements on the coherent BaTiO3 thin films with SrRuO3 bottom electrodes grown by PLD. Figure 3B shows the evolution of the inplane (a) and out-of-plane (c) lattice parameters of the BaTiO3 film and the GdScO3 and DyScO3 substrates as a function of temperature. The in-plane lattice parameters reveal that both the BaTiO3 and SrRuO3 layers are coherently strained to the underlying substrates over the entire temperature range. This is consistent with the absence of misfit dislocations along the interface between GdScO3 and SrRuO3 and along the interface between SrRuO3 and BaTiO3, as shown by the cross-sectional transmission electron microscope images in figs. S1 and S2 (21). As seen in the figure, the transition behavior of the PLD samples is quite similar to those grown by MBE. Tc was determined to be ∼420° and ∼680°C for samples grown on GdScO3 and DyScO3, respectively. The green solid and dashed lines in Fig. 3B are theoretical predictions of c-lattice parameters with and without the ferroelectric phase transition, which are fairly consistent with the experimentally measured values. The agreement in the results for films grown by MBE and PLD indicates that the observed shifts in ferroelectric properties with strain represent the intrinsic behavior of strained BaTiO3. This experimental dependence of Tc on ϵs is also consistent with the expectations shown in Fig. 1.

In summary, we have demonstrated that the ferroelectric properties of BaTiO3 can be markedly enhanced through strain engineering. These strain-engineered heteroepitaxial thin films provide a broad range of operating temperatures as well as higher remanent polarization for improved noise immunity and the ability to scale FeRAM to smaller cell sizes. Another application of strain-engineered BaTiO3 films is high-speed electro-optic modulators, in which the sizeable electro-optic coefficients of BaTiO3 can be enhanced by appropriate strain engineering. The ability to withstand huge strains gives thin films a degree of freedom absent from bulk. This can be exploited to enhance the ferroelectric properties of any ferroic system, including multiferroics (8, 22, 36), whose ferroic order parameter has a strong coupling to strain.

Supporting Online Material

Materials and Methods

Figs. S1 and S2

References

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