Artificial BaTiO3 - SrTiO3 superlattices with stacking periodicity varying between 27 and 1670 Å in separate films were grown on MgO substrates by pulsed laser deposition. Both the static and active optical properties were found to be sensitive on the stacking periodicity. Birefringence decreased with increasing individual layer thickness due to relaxation of the interface originated stress. The electro-optic response also showed a layer thickness dependence, reaching a maximum at an individual layer thickness of 13 unit cells.
©2008 Optical Society of America
Oxide ferroelectric materials have attracted both scientific and technological interest due to functional properties, such as, relatively high and nonlinear permittivity, piezoelectricity, photorefractivity and electro-optic activity [1,2]. BaTiO3 (BTO) commonly serves as a model perovskite ferroelectric and has been intensively studied in both bulk and thin film forms. Research efforts have been focused on attempts to improve the properties of BTO by the formation of solid solutions  and multilayer [4,5] structures with paraelectric SrTiO3 (STO). Advances in thin film growth techniques have offered means for fabricating artificial BTO-STO superlattice structures with highly accurate control of stacking periodicity, down to the length scale of about a unit cell. These methods have included e.g. molecular-beam-epitaxy (MBE)  and pulsed-laser-deposition (PLD) [7,8]. Nanostructured superlattices, consisting of two or more materials, often exhibit distinctly different physical properties from compositionally equivalent solid solutions. For example, the stacking structure of symmetrical BTO - STO superlattices has been shown to be an important parameter for engineering permittivity and its nonlinearity with up to 94% tunability, a value considerably higher than that exhibited by single layer BTO, STO or Ba0.5Sr0.5TiO3 thin films .
The formation of a BTO-STO superlattice structure is illustrated in Fig. 1. Bulk, non-polar STO has cubic symmetry with lattice constant of 3.905 Å , while BTO is tetragonally distorted with lattice constants of a=3.994 Å and c=4.038 Å . The spontaneous polarization Ps in BTO is along the elongated lattice direction <001> (see arrow in Fig. 1(a)) due to a slight displacement of Ti4+ and O2- ions relative to Ba2+ in their cubic positions . Since the lattice constant of STO is smaller than the a- or c-constants of BTO, the coherent interface introduces <100>/<010> in-plane compressive stress into the BTO layer and tensile stress into the STO layer as shown by arrows in Fig. 1(b).
Theoretical studies addressing interfacial strain-polarization coupling issues suggest that the compressive stress state in the BTO layer tends to maintain the polarization component along the <001> (out-of-plane) direction, and in ultrashort superlattice stacks (about three unit cells), this induces aligned dipoles in the STO layers as well . Increase of stacking periodicity by about the factor of two results in the development of a dipole component along the <100>/<010> (in-plane) direction in the STO layers. Furthermore, the examination of substrate effects in modifying ferroelectricity originated properties in thin films has received much attention [12–14]. These issues have also been recently considered theoretically in the case of superlattices [15,16]. Although the situation is more complicated in superlattices, with stacking periodicity dependence and possibly spatially non-uniform dipole distributions, generally, substrate originated compressive stress enhances polarization along the out-of-plane direction, while tensile stress favors the polarization along the in-plane direction.
While the majority of the experimental research on BTO-STO superlattices has been focused on x-ray crystallography and electrical permittivity studies, optical methods have also been utilized to study their structural properties. Second harmonic generation (SHG)  and Raman spectroscopy  techniques have been utilized to obtain information on the temperature-dependent internal dipole distribution in BTO-STO superlattices. From the application point of view, an electro-optical waveguide modulator, based on a BTO-STO multilayer thin film, has recently been demonstrated . Thin film technology is considered attractive in both electronics and photonics applications, given its ability to a) utilize a wide variety of materials not processable in the bulk as it is the case for superlattices, and b) achieve high levels of component integration . In this work on the optical properties of PLD grown BTO-STO superlattices, the influence of stacking structure on refractive index, birefringence and electro-optic response is studied.
Pulsed laser deposition, using a XeCl laser (Lambda Physik Compex 200), operating at a wavelength of 308 nm, was utilized to grow BTO-STO multilayer structures on single crystal MgO substrates with (001) orientation. The thin film stacks were deposited by alternately focusing the laser beam on nominally stoichiometric BTO and STO targets. The thickness of each layer was controlled by tracking the number of laser pulses during deposition with known deposition rates. A substrate temperature of 800 °C and total oxygen working pressure of 5*10-3 mbar were maintained during deposition. At first, a BTO seed layer with thickness of 20 nm was grown on the substrate followed by periodic pairs of BTO-STO layers with a total film thickness of about 360 nm. The crystal structure of the multilayer BTO-STO stacks was analyzed by x-ray diffraction (XRD). θ-2θ scans were utilized to calculate the out-of-plane lattice parameters and to estimate the epitaxy quality. Refractive indices were measured with a prism coupler (Metricon 2010). The setup was equipped with a polarization state shifter allowing one to determine refractive indices along both in-plane and out-of-plane directions. In order to estimate the electro-optic response of the BTO-STO films, Cr electrodes were deposited on the top of the stack by e-beam evaporation with physical masking. Fig. 2(a) shows the measurement principle of the electro-optic response. In this arrangement, a He-Ne laser (633 nm) sourced beam was directed into the gap between the electrodes. The polarization state angle of the incoming beam was at 45° relative to the applied electric field direction and the electro-optic effect induced birefringence changing the polarization state of the light from linear to elliptic. The measurement setup is similar to one used e.g. by Adachi et al , and it is illustrated in Fig. 2(b). By using a quarter-wave plate the polarization state was returned back to linear but with a slightly different angle from 45°. This angle was measured by a polarization-splitting prism with two oppositely connected photodiodes to determine the phase retardation and to evaluate the strength of the electro-optic response. The setup was equipped with a phase lock amplifier frequency matched with a chopper modulating the laser light.
3. Results and discussion
Figure 3 shows the low angle regions of the XRD θ-2θ diffraction patterns of the BTO-STO multilayer structures. The characteristic reflections of BTO and STO were replaced by the bundle of superlattice satellite reflections in the case of short periodicity superlattices as shown in Fig. 3(a). Out-of-plane lattice parameters were estimated by a simulation method taking into account angle depended x-ray scattering factors of different ions in the perovskite structure and the Lorentz-polarization factor . The periodicity values of 27, 49 and 105 Å were obtained with the out-of-plane lattice parameters of 4.20–4.22 Å for BTO and 3.91 Å for STO. In terms of unit cells, this would lead to the stacking periodicity of [BTO]3–4 - [STO]3–4, [BTO]6 - [STO]6 and [BTO]13 - [STO]13 for the films with 27, 49 and 105 Å periodicities, respectively. This indicates mixing of 3 and 4 unit cells within the stacking structure of films with the shortest periodicity. Mixing was also suggested by the broadening of the measured -1 satellite reflection over the same simulated satellite reflections of the [BTO]3-[STO]3 and [BTO]4-[STO]4 structures.
The c-lattice parameter of BTO bulk is 4.038 Å vs 4.20–4.22 Å in the stacks, which implies a highly strained lattice in these superlattices . On the contrary, the STO lattice parameter was relatively close to the bulk value of 3.905 Å . A similar behavior composed of highly strained BTO out-of-plane lattice and more stable STO structure were also observed in previous studies [7,19]. In this work, the high strain could also be partly originated from the MgO substrate. The lattice constant of MgO is 4.21 Å . This would suggest that BTO and STO thin films experience tensile stress when deposited on MgO substrate. However, if the film growth occurs at elevated temperature, MgO substrate can induce compressive stress in BTO thin film due to higher thermal expansion coefficient of MgO than BTO . This has been reported to stabilize c-axis orientation in tetragonally distorted BTO films on MgO . In this study, the MgO substrate could thereby place the stack into compressive stress favoring c-axis orientation. Furthermore, the lattice parameter of BTO-STO alloy  and superlattice  thin films is also known to be sensitive to the oxygen working pressure used during deposition. Lattice parameter values, obtained from the simulation of diffraction patterns, were also supported by the measurement results of the films with 314 and 1670 Å periodicities, see Fig. 3(b). Only the characteristic BTO and STO reflections were observed and the periodicity was estimated by comparing the number of deposited layers with the measured total film thickness resulting in periodicities of 314 and 1670 Å. BTO peaks were broad in these patterns indicating a strong relaxation of the out-of-plane lattice parameter. In the film with 314 Å periodicity, the BTO (001) reflection showed a double peak form. This is attributed to the relaxation of the strained crystal from the lattice parameter of 4.21 Å to 4.08 Å supporting the results of highly shifted BTO out-of-plane lattice parameter in superlattices of short stacking periodicity due to interface induced stress. Similar strain relaxation was also observed in the BTO-STO stack of 1670 Å periodicity. In this structure, the maximum XRD peak intensity corresponds to the lattice parameter of about 4.08 Å, implying that most of the BTO lattice volume is partly relaxed. The lattice parameter of 4.08 Å correlates also with the results in previous study on pulsed laser deposited single layer BTO films, when the low background oxygen pressure (below 1.3*10-2 mbar) produced films with the out-of-plane lattice parameter between 4.07–4.09 Å .
The evolution of the epitaxy breakdown in stacks with thin layers is also worth noting. In the films of long periodicity (314 Å and 1670 Å), only (001)-plane reflections were observed, while in films of short periodicity the intensity of (110)/(101) peak increased with decreasing stacking periodicity. This can be potentially related with the number of BTO-STO interfaces that might generate lattice defects and contribute to the breakdown of epitaxy. These crystal defects and polycrystalline media can act as a source for light scattering, which is an important factor especially in planar optical devices. The breakdown of epitaxy can also have an effect on the electo-optic response by suppressing the electric-field penetration in the substrate-aligned columns.
The influence of strain relaxation was observed in directional dependent refractive index measurements. The out-of-plane and in-plane refractive indices at 633 nm wavelength are shown as a function of stacking periodicity in Fig. 4(a). The static indices were measured without external electric field. Furthermore, both the in-plane and out-plane indices might have spatial variation due to stacking structure and, possibly, varying dipole distribution. The measured refractive index is thereby an average value of the film. In multilayers of short periodicity, the in-plane index is about 2.33 and the out-of-plane index about 2.30. Their difference, i.e. birefringence, is plotted in Fig. 4(b). It shows a slightly decreasing trend with increasing periodicity and a steeper decrease between the 314 and 1670 Å region. This can be explained by analysis of the XRD measurements. In the 1670 Å periodicity film, most of the BTO volume is at least partly relaxed resulting in a decrease in ion distances and thereby an increase in <001> out-of-plane refractive index. In previous work, birefringence value of 0.028 was measured for the strongly c-oriented BTO film with the out-of-plane lattice parameter of 4.07 Å . This indicates that the STO layers reduce the average level of birefringence. This is also supported by the XRD measurements suggesting that the STO lattice parameter was relatively close to the value in bulk with cubic symmetry.
Figure 5(a) shows the electro-optic response induced in-plane birefringence shift δΔn as a function of applied electric field. The curves are plotted with an offset value of 5*10-5 for clarity. The shift is non-linear with a weak dependence at low fields followed by a steeper increase at about 1V/µm. The measurement was carried out with an electric field sweep between -3 to 3 V/µm, but only one polarity is shown in Fig. 5(a) as the curves were centrosymmetric. Though the response is highly non-linear, the first order term is used to compare the strength of the electro-optic response with the reported linear values in single layer BTO films, e.g. Refs [28–30]. In this work, this is obtained by using the linearized part between 2.5 and 3 V/µm (region between the dashed lines in Fig. 5(a)). The linear electro-optic coefficient r is expressed as 
where n is the in-plane refractive index obtained from prism coupling measurements and E the applied electric field.
Calculated r values as a function of stacking periodicity are plotted in Fig. 5(b). As the stacking periodicity decreased from 1670 Å to 106 Å, the effective electro-optic response increased from 12 to 51 pm/V. After reaching a maximum point, the r value decreased again with decreasing periodicity. In previous work, the linear effective value of 20 pm/V at 1550 nm wavelength was determined for the strongly c-oriented BTO film grown by pulsed laser deposition. Correspondingly in films grown by metalorganic chemical-vapor deposition (MOCVD), the reported effective response varies between 38 pm/V and up to 360 pm/V at about 1550 nm wavelength [29,30].
The mechanism influencing the change in electro-optic response as a function of stacking periodicity is not well understood. Furthermore, it is not clear, whether BTO or STO layer enhances the electro-optic response. The electro-optic effect in BTO has been proposed to be due to displacement of ions leading to changes in the polarizability of electrons , and the trend line of the electro-optic response resembles the observations of the dependence of permittivity on stacking periodicity of BTO-STO superlattices measured by interdigital-electrode configuration . In Ref. 33, the BTO-STO superlattices with polycrystalline nature were sandwiched between metal electrodes with the permittivity reaching a maximum in stacks with individual layer thickness of 20 nm and decreasing with both increasing and decreasing layer thickness. On the other hand, increasing permittivity with decreasing stacking periodicity down to about two unit cells has been reported . In relaxor oxide superlattices sandwiched between electrodes, electro-optic response was found to increase more than one order of magnitude with increase in dielectric constant of more than 50% .
Though the trend line follows the observations of reported permittivity, the response can also be biased by the internal polarization. In this work, the electric field used to induce the electro-optic response was oriented along the in-plane direction. As described above, theory suggests that the internal dipole structure is sensitive to stacking periodicity. The superlattices with short periodicity behave as a fairly homogenous material with the main polarization component along the <001> (out-of-plane) direction in both BTO and STO layers . Instead, in superlattices of longer periodicity, the polarization enhancement of the <100>/<010> (in-plane) component occurs in the STO layer. Theoretical studies also indicate that reducing compressive strain induces the reorientation of the polarization from the <001> to <100>/<010> direction, first in STO layers, followed by reorientation in the BTO layers . Both the out-of-plane and in-plane permittivity can also increase significantly along with the strain shift having a maximum near these polarization reorientation points . In both cases of the polarization direction, it is possible that the observed net effect is non-linear. If the polarization vector is along the out-of-plane direction, then the electric field is perpendicular to the polarization. The situation resembles the case in single layer BTO films with c-orientation and the response is non-linear due to rotation of principal axes . When the polarization vector and external electric field are aligned, the reversal of the domains can produce non-linear net response .
The stress state relaxation with increasing stacking periodicity observed in this work can also contribute to the increase of the tuning properties. As mentioned above, also the breakdown of epitaxy might modify the electric field distribution inside the polycrystalline media and consequently alter the electro-optic response. Potentially, a certain stacking structure can thereby lead to an optimal response for a specific electric field direction and explain the maximum in electro-optic response at a certain stacking periodicity.
The observations in this work, together with the results of previous studies [19,37], suggest that ferroelectric-paraelectric superlattices offer potential advances in technology of relevance to photonic applications. Besides electrical properties, nearly all of the static and active optical properties of ferroelectric-paraelectric superlattices are experimentally shown to be sensitive to their structure, which can be artificially engineered on the nanoscale to produce enhanced response. These adjustable optical properties include e.g. refractive index and consequently birefringence, second-harmonic-generation  and electro-optic activity. Furthermore, optical waveguiding has been demonstrated in BTO-STO superlattices  offering options for their utilization in planar photonic devices.
In conclusion, BTO-STO multilayer thin films with stacking periodicity between 27 and 1670 Å were grown on single crystal MgO (001) substrates. XRD measurements suggested a highly strained out-of-plane lattice parameter of 4.20–4.22 Å in the BTO layers due to interface induced stress in the case of short stacking periodicity. On the contrary, STO lattice parameter values were observed to be relatively close to that of the bulk value. The stress in the BTO layers was relaxed as the layer thickness increased leading towards a lattice parameter characteristic of the bulk. The influence of strain relaxation in the BTO layer was also observed in optical birefringence measurements leading to a birefringence decrease paralleling the crystal strain relaxation. The electro-optic response was found to increase at first with decreasing stacking periodicity reaching a maximum value of 51 pm/V in the superlattice stack with 105 Å periodicity. Further reduction in stacking periodicity resulted in a decrease in the effective electro-optic coefficient. Opportunities for integration of BTO-STO multilayer thin films into thin film photonic devices were briefly discussed.
This work was funded by the Finnish Funding Agency for Technology and Innovation (TEKES). Tuller thanks the US National Science Foundation for his support under DMR-0243993.
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