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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 11 — May. 26, 2008
  • pp: 8219–8228
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Size-dependent optical properties of BaTiO3 - SrTiO3 superlattices

J. Hiltunen, J. Lappalainen, J. Puustinen, V. Lantto, and H. L. Tuller  »View Author Affiliations


Optics Express, Vol. 16, Issue 11, pp. 8219-8228 (2008)
http://dx.doi.org/10.1364/OE.16.008219


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Abstract

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

1. Introduction

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

1. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Oxford University Press Inc., New York, 1977).

,2

2. B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric ceramics (Academic Press Inc., New York, 1971).

]. 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 [3

3. Z. Yuan, Y. Lin, J. Weaver, X. Chen, C. L. Chen, G. Subramanyam, J. C. Jiang, and E. I. Meletis, “Large dielectric tunability and microwave properties of Mn-doped (Ba,Sr)TiO3 thin films,” Appl. Phys. Lett. 87, 152901 (2005). [CrossRef]

] and multilayer [4

4. S. Gevorgian, P. K. Petrov, Z. Ivanov, and E. Wikborg, “Tailoring the temperature coefficient of capacitance in ferroelectric varactors,” Appl. Phys. Lett. 79, 1861–1863 (2001). [CrossRef]

,5

5. S. Zhong, S. P. Alpay, and J. V. Mantese, “High dielectric tunability in ferroelectric-paraelectric bilayers and multilayer superlattices,” Appl. Phys. Lett. 88, 132904 (2006). [CrossRef]

] 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) [6

6. D. G. Schlom, J. H. Haeni, J. Lettieri, C. D. Theis, W. Tian, J. C. Jiang, and X. Q. Pan, “Oxide nano-engineering using MBE,” Mater. Sci. Eng. B 87, 282–291 (2001). [CrossRef]

] and pulsed-laser-deposition (PLD) [7

7. H. Tabata, H. Tanaka, and T. Kawai, “Formation of artificial BaTiO3/SrTiO3 superlattices using pulsed laser deposition and their dielectric properties,” Appl. Phys. Lett. 65, 1970–1972 (1994). [CrossRef]

,8

8. J. Kim, Y. Kim, Y. S. Kim, J. Lee, L. Kim, and D. Jung, “Large nonlinear dielectric properties of artificial BaTiO3/SrTiO3 superlattices,” Appl. Phys. Lett. 80, 3581–3583 (2002). [CrossRef]

]. 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 [8

8. J. Kim, Y. Kim, Y. S. Kim, J. Lee, L. Kim, and D. Jung, “Large nonlinear dielectric properties of artificial BaTiO3/SrTiO3 superlattices,” Appl. Phys. Lett. 80, 3581–3583 (2002). [CrossRef]

].

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 [9

9. Powder Diffraction File, Card No 00-035-0734, International Centre for Diffraction Data, Newton Square, PA, USA.

], while BTO is tetragonally distorted with lattice constants of a=3.994 Å and c=4.038 Å [10

10. Powder Diffraction File, Card No 00-005-0626, International Centre for Diffraction Data, Newton Square, PA, USA.

]. 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 [1

1. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Oxford University Press Inc., New York, 1977).

]. 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).

Fig. 1. (a) Perovskite unit cells of BaTiO3 and SrTiO3. The arrow points in the direction of the spontaneous polarization Ps in ferroelectric BaTiO3. (b) Illustration of the formation of a super cell. The arrows show the interface induced compressive and tensile stress in BaTiO3 and SrTiO3 cells, respectively.

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 [11

11. K. Johnston, X. Huang, J. B. Neaton, and K. Rabe, “First-principles study of symmetry lowering and polarization in BaTiO3/SrTiO3 superlattices with in-plane expansion,” Phys. Rev. B 71, 100103 (2005). [CrossRef]

]. 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

12. K. J. Choi, M. Biegalski, Y. L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche, Y. B. Chen, X. Q. Pan, V. Gopalan, L.-Q. Schlom, D. G. Chen, and C. B. Eom, “Enhancement of Ferroelectricity in Strained BaTiO3 Thin Films,” Science 306, 1005–1009 (2004). [CrossRef] [PubMed]

]. These issues have also been recently considered theoretically in the case of superlattices [15

15. S. Lisenkov and L. Bellaiche, “Phase diagrams of BaTiO3/SrTiO3 superlattices from first principles,” Phys. Rev. B 76, 020102 (2007). [CrossRef]

,16

16. L. Kim, J. Kim, U. V. Waghmare, D. Jung, and J. Lee, “Structural transition and dielectric response of an epitaxially strained BaTiO3/SrTiO3 superlattice: A first-principles study,” Phys. Rev. B 72, 214121 (2005). [CrossRef]

]. 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) [17

17. A. Q. Jiang, J. F. Scott, H. Lu, and Z. Chen, “Phase transition and polarizations in epitaxial BaTiO3/SrTiO3 superlattices studied by second-harmonic generation,” J. Appl. Phys. 93, 1180–1185 (2003). [CrossRef]

] and Raman spectroscopy [18

18. D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukissan, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing Nanoscale Ferroelectricity by Ultraviolet Raman Spectroscopy,” Science 313, 1614–1616 (2006). [CrossRef] [PubMed]

] 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 [19

19. J. Hiltunen, D. Seneviratne, R. Sun, M. Stolfi, H. L. Tuller, J. Lappalainen, and V. Lantto, “BaTiO3 - SrTiO3 multilayer thin film electro-optic waveguide modulator,” Appl. Phys. Lett. 89, 242904 (2006). [CrossRef]

]. 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 [20

20. Ch. Buchal, L. Beckers, A. Eckau, J. Schubert, and W. Zander, “Epitaxial BaTiO3 thin films on MgO,” Mater. Sci. Eng. B 56, 234–238 (1998). [CrossRef]

]. 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.

2. Experimental

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 [21

21. H. Adachi and K. Wasa, “Sputtering Preparation of Ferroelectric PLZT Thin Films and Their Optical Applications,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 38, 645–655 (1991). [CrossRef]

], 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.

Fig. 2. (a) Superlattice induced polarization state shift from linear to elliptical when light is transmitted through the test structure and (b) measurement setup used to characterize the shift of in-plane birefringence due to electro-optic effect.

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 [22

22. B. D. Cullity, Elements of X-ray Diffraction (Addison-Wesley Publishing Company, Reading, MA, 1967).

]. 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.

Fig. 3. Simulated and measured X-ray diffraction θ-2θ patterns of BTO-STO thin film stacks with varying stacking periodicity. (a) The measured and simulated patterns of the structures with 3 & 4, 6 and 13 unit cell periodicity. The numbers on the peaks represent the multiples of the superlattice satellite reflections. In the lowest simulation pattern, the 3 and 4 unit cell plots are superimposed. (b) The measured scans of the stacks with periodicity of 314 and 1670 Å.

Fig. 4. (a) In-plane and out-of-plane refractive indices of BTO-STO superlattices at 633 nm wavelength as a function of stacking periodicity and (b) corresponding birefringence behavior. The dashed line represents the trend line of the birefringence with increasing stacking periodicity.

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

28. J. Hiltunen, D. Seneviratne, R. Sun, M. Stolfi, H. L. Tuller, J. Lappalainen, and V. Lantto, “Optical properties of BaTiO3 thin films: Influence of oxygen pressure utilized during pulsed laser deposition,” J. Electrocer. (published online, DOI 10.1007/s10832-008-9463-9).

]. 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 [21

21. H. Adachi and K. Wasa, “Sputtering Preparation of Ferroelectric PLZT Thin Films and Their Optical Applications,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 38, 645–655 (1991). [CrossRef]

]

δΔn=12n3rE,
(1)

where n is the in-plane refractive index obtained from prism coupling measurements and E the applied electric field.

Fig. 5. (a) Field induced birefringence shift at 633 nm wavelength for BTO-STO superlattices with stacking periodicities ranging from 27-1670 Å and (b) corresponding electro-optic coefficient behavior.

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 [31

31. X. Y. Meng, Z. Z. Wang, and C. Chen, “Mechanism of the electro-optic effect in BaTiO3,” Chem. Phys. Lett. 411, 357–360 (2005). [CrossRef]

], 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 [32

32. T. Harigai, D. Tanaka, H. Kakemoto, S. Wada, and T. Tsurumi, “Dielectric properties of BaTiO3/SrTiO3 superlattices measured with interdigital electrodes and electromagnetic field analysis,” J. Appl. Phys. 94, 7923–7925 (2003). [CrossRef]

]. 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 [7

7. H. Tabata, H. Tanaka, and T. Kawai, “Formation of artificial BaTiO3/SrTiO3 superlattices using pulsed laser deposition and their dielectric properties,” Appl. Phys. Lett. 65, 1970–1972 (1994). [CrossRef]

]. 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% [34

34. Y. Lu and R. J. Knize, “Enhanced dielectric and electro-optic effects in relaxor oxide heterostructured superlattices,” J. Phys. D: Appl. Phys. 37, 2432–2436 (2004). [CrossRef]

].

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 [11

11. K. Johnston, X. Huang, J. B. Neaton, and K. Rabe, “First-principles study of symmetry lowering and polarization in BaTiO3/SrTiO3 superlattices with in-plane expansion,” Phys. Rev. B 71, 100103 (2005). [CrossRef]

]. 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 [15

15. S. Lisenkov and L. Bellaiche, “Phase diagrams of BaTiO3/SrTiO3 superlattices from first principles,” Phys. Rev. B 76, 020102 (2007). [CrossRef]

]. 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 [16

16. L. Kim, J. Kim, U. V. Waghmare, D. Jung, and J. Lee, “Structural transition and dielectric response of an epitaxially strained BaTiO3/SrTiO3 superlattice: A first-principles study,” Phys. Rev. B 72, 214121 (2005). [CrossRef]

]. 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 [35

35. A. Petraru, J. Schubert, M. Schmid, and Ch. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002). [CrossRef]

]. When the polarization vector and external electric field are aligned, the reversal of the domains can produce non-linear net response [36

36. K. Uchino, Ferroelectric Devices (Marcel Dekker, Inc., New York - Basel, 2000), Chap. 8.

].

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.

4. Conclusions

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.

Acknowledgments

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.

References and links

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M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Oxford University Press Inc., New York, 1977).

2.

B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric ceramics (Academic Press Inc., New York, 1971).

3.

Z. Yuan, Y. Lin, J. Weaver, X. Chen, C. L. Chen, G. Subramanyam, J. C. Jiang, and E. I. Meletis, “Large dielectric tunability and microwave properties of Mn-doped (Ba,Sr)TiO3 thin films,” Appl. Phys. Lett. 87, 152901 (2005). [CrossRef]

4.

S. Gevorgian, P. K. Petrov, Z. Ivanov, and E. Wikborg, “Tailoring the temperature coefficient of capacitance in ferroelectric varactors,” Appl. Phys. Lett. 79, 1861–1863 (2001). [CrossRef]

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S. Zhong, S. P. Alpay, and J. V. Mantese, “High dielectric tunability in ferroelectric-paraelectric bilayers and multilayer superlattices,” Appl. Phys. Lett. 88, 132904 (2006). [CrossRef]

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D. G. Schlom, J. H. Haeni, J. Lettieri, C. D. Theis, W. Tian, J. C. Jiang, and X. Q. Pan, “Oxide nano-engineering using MBE,” Mater. Sci. Eng. B 87, 282–291 (2001). [CrossRef]

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J. Kim, Y. Kim, Y. S. Kim, J. Lee, L. Kim, and D. Jung, “Large nonlinear dielectric properties of artificial BaTiO3/SrTiO3 superlattices,” Appl. Phys. Lett. 80, 3581–3583 (2002). [CrossRef]

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P. Tang, D. J. Towner, A. L. Meier, and B. W. Wessels, “Low-Loss Electrooptic BaTiO3 Thin Film Waveguide Modulator,” IEEE Photon. Technol. Lett. 16, 1837–1839 (2004). [CrossRef]

30.

P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “BaTiO3 thin-film waveguide modulator with a low voltage-length product at near-infrared wavelengths of 0.98 and 1.55µm,” Opt. Lett. 30, 254–256 (2005). [CrossRef] [PubMed]

31.

X. Y. Meng, Z. Z. Wang, and C. Chen, “Mechanism of the electro-optic effect in BaTiO3,” Chem. Phys. Lett. 411, 357–360 (2005). [CrossRef]

32.

T. Harigai, D. Tanaka, H. Kakemoto, S. Wada, and T. Tsurumi, “Dielectric properties of BaTiO3/SrTiO3 superlattices measured with interdigital electrodes and electromagnetic field analysis,” J. Appl. Phys. 94, 7923–7925 (2003). [CrossRef]

33.

A. Sarkar and S. B. Krupanidhi, “Ferroelectric interaction and polarization studies in BaTiO3/SrTiO3 superlattice,” J. Appl. Phys. 101, 104113 (2007). [CrossRef]

34.

Y. Lu and R. J. Knize, “Enhanced dielectric and electro-optic effects in relaxor oxide heterostructured superlattices,” J. Phys. D: Appl. Phys. 37, 2432–2436 (2004). [CrossRef]

35.

A. Petraru, J. Schubert, M. Schmid, and Ch. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002). [CrossRef]

36.

K. Uchino, Ferroelectric Devices (Marcel Dekker, Inc., New York - Basel, 2000), Chap. 8.

37.

T. Zhao, Z.-H. Chen, F. Chen, W.-S. Lu, H.-B. Shi, and G.-Z. Yang, “Enhancement of second-harmonic generation in BaTiO3/SrTiO3 superlattices,” Phys. Rev. B 60, 1697–1700 (1999). [CrossRef]

OCIS Codes
(160.2100) Materials : Electro-optical materials
(160.2260) Materials : Ferroelectrics
(260.1440) Physical optics : Birefringence
(310.6860) Thin films : Thin films, optical properties

ToC Category:
Materials

History
Original Manuscript: March 10, 2008
Revised Manuscript: May 9, 2008
Manuscript Accepted: May 9, 2008
Published: May 21, 2008

Citation
J. Hiltunen, J. Lappalainen, J. Puustinen, V. Lantto, and H. Tuller, "Size-dependent optical properties of BaTiO3 - SrTiO3 superlattices," Opt. Express 16, 8219-8228 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-8219


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  32. T. Harigai, D. Tanaka, H. Kakemoto, S. Wada, and T. Tsurumi, "Dielectric properties of BaTiO3/SrTiO3 superlattices measured with interdigital electrodes and electromagnetic field analysis," J. Appl. Phys. 94, 7923-7925 (2003). [CrossRef]
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