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Abstract
We report experimental characterization of DC electro-optic coefficients r13, r23 and r33 in thin film single crystalline BaTiO3 on DyScO3. The epitaxial BaTiO3 thin film is sandwiched between a SrRuO3 bottom electrode and an indium tin oxide (ITO) top electrode. We characterize the DC electro-optic coefficients r13, r23, and r33 by the prism coupling method at 636.6 nm for the BaTiO3 thin film. The results show the DC coefficients r13 = 4.2 pm/V, r23 = 4.6 pm/V and r33 = 9.0 pm/V.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Barium titanate (BaTiO3, or BTO) has excellent electro-optic properties, with its largest r-parameter (unclamped (stress-free) r42 = 1300 pm/V, clamped (strain-free) r42 = 730 pm/V) [1] more than an order of magnitude larger than that of traditional lithium niobate (LiNbO3, r33 = 30.9 pm/V) [2–4], and the other terms of its Pockels matrix also have decent strength (unclamped r13 = 8 pm/V, r33 = 105 pm/V, clamped r13 = 10.2 pm/V, r33 = 40.6 pm/V) [1]. Thin film BaTiO3 grown on a substrate of low refractive index has advantages over bulk BaTiO3 in several aspects, such as better vertical optical confinement, structural stability, higher phase transition temperature, etc. [5–9]. Thin film BaTiO3 on an MgO substrate has been explored in quite a few studies and has shown, though weaker than that of its bulk, as strong or even stronger electro-optic effects compared to lithium niobate [10–19]. Even though r42 or r51 are the largest parameters in the Pockels matrix and are more widely studied, the r values along the c-axis (or z-axis) of BaTiO3 thin film are yet to be studied [20–22]. Despite r42 (or r51) being large, there is a key utility difference between r42 (or r51) and r13 (or r23, r33). The former are off-diagonal Pockels terms such that an applied voltage will induce off-diagonal terms of refractive index causing polarization rotation of any mode within the influence of the applied field, while the latter only induce changes in the diagonal terms of the permittivity matrix and thus maintain polarization, causing only phase slip [2]. To the best of our knowledge this is the first report of the r13 (or r23, r33) values in BaTiO3 thin film. There has been an investigation of the vertical electro-optic effect in BaTiO3 polycrystalline thin film on MgO [23], but due to the random distribution of the polarization (or c-axis direction) in each domain, the effect probed is actually an effective r-value in the vertical direction instead of the actual r13, r23, r33 values, whereas in our single crystalline BaTiO3 thin film, these values can be disentangled. In this study we characterize the r13, r23, r33 parameters by measuring the effect of variable applied vertical DC electric fields on the refractive indices of propagating optical slab modes. Although the resulting values we found are much smaller than those of the off-diagonal terms typically reported, the utility value of a having polarization-maintaining controllable phase shift in device design is important which is why these terms should not be overlooked, as this ability is absent when using r42 or r51.
We grow BaTiO3 on a DyScO3 (DSO) substrate with SrRuO3 (SRO) and indium tin oxide (ITO) as the bottom and top electrodes, respectively, to characterize the vertical electro-optic coefficient (r13, r23, r33) of the BaTiO3 layer. DyScO3 (110) has been used as the substrate for BaTiO3 epitaxial growth due to the small lattice mismatch [24].
2. Experiments, results, and discussion
2.1 Prism coupling measurement and birefringent refractive indices of DyScO3
To obtain refractive indices of BaTiO3, we need to first characterize the refractive indices of the DyScO3 substrate. DyScO3 has an orthorhombic crystal structure (a$\ne $b$\ne $c), and is thus expected to be birefringent [24,25]. We measured the refractive indices of two samples – the DyScO3 (001) and DyScO3 (110) substrates (CrysTec GmbH) – by the prism coupling method (Metricon), as shown in Fig. 1(a). The crystal orientation of DyScO3 (001) and DyScO3 (110) are shown in Fig. 1(b), where during measurement of refractive indices, the prism (TiO2 rutile, prism index = 2.8654) was rotated to specific angles to align with the desired axis, and the resultant measurements with different configurations and at different wavelengths are labeled A-F. Figure 1(c) illustrates the polarization of incident light during measurement of the samples. For the measurement of the DyScO3 (001) substrate, the laser’s transverse electric (TE) polarization was aligned with the crystal’s x-axis (A, D) and y-axis (B, E) with the transverse magnetic (TM) polarization corresponding to the z direction. For the measurement of the DyScO3 (110) substrate, the laser’s TE polarization was aligned with the z-axis (C, F), with the TM mode naturally aligning with the xy plane near an angle of 45° to the x-axis (nearly 43.555° because a$\ne $b). Both samples were measured at a wavelength of 636.6 nm and 1548.4 nm. The results are shown in Table 1. Clear birefringence can be observed, where at 636.6 nm, nx = 2.0851${\pm} 0.0002$, ny = 2.0802${\pm} 0.0002$, and nz = 2.0370${\pm} 0.0002$ [23]; nxy can be calculated from measurements A, B by
Fig. 1. (a) Schematic drawing of the prism coupling measurement setup. (b) Crystal structure and (c) refractive indices of DyScO3 (001) and DyScO3 (110). The crystal orientations are labeled in black, and the refractive indices are labeled in colors which correspond to the polarization directions in the prism coupling measurements.
Table 1. Refractive indices of (a) DyScO3 (001) and (b) DyScO3 (110) substrate by the prism coupling method. The polarization of the incident light is denoted after the sample label.
The small birefringence may play a role in the polarization of the propagating light modes. When considering the construction of a phase modulator, such as a Mach-Zehnder modulator, this effect may be ignored as the amplitude change induced by the change of polarization is minor; on the other hand, for the design of a polarization modulator, it would possibly make a small difference. Therefore, in optical device design, a thick enough BaTiO3 layer should be used to keep the confined optical field from overlapping the DyScO3 substrate as much as possible, unless for some reason passive polarization rotation would be desirable. The results can be useful for further studies based on BaTiO3 on DyScO3.
2.2 Electro-optic effect along the c-axis
We then fabricated c-axis BaTiO3 on a 100 mm2 DyScO3 (110) substrate with top and bottom electrodes, i.e., a structure of ITO/BaTiO3/SrRuO3/DyScO3 device (labeled as IBSD) by pulsed laser deposition (KrF laser, 248 nm wavelength), where SrRuO3 (SRO) is used as the bottom electrode in the stack while ITO acts as top electrode. First, SRO was grown at 600°C under 100 mTorr oxygen gas pressure with a laser pulse energy density of 2 J cm-2. Then, a corner was covered by a shadow mask after the deposition of the bottom electrode, for the convenience of exposing the SRO surface for subsequent electrode connection. Following this, the BTO layer was grown at 650°C under 10 mTorr with a laser pulse energy density of 1.5 J cm-2, followed by cooling at 100 Torr oxygen gas pressure. The ITO top electrode was then deposited at room temperature under 10 mTorr oxygen gas pressure with a laser pulse energy density of 2 J cm-2. Silver paste (SP) was used to attach electrical leads to the top and bottom electrodes of each sample, at different corners. The device configuration is shown in Fig. 2. For this device (IBSD), the thicknesses of the ITO, BTO and SRO layers were 60 nm, 860 nm, 10 nm, respectively. The growth rate of each material is first measured and the thicknesses of the various layers are subsequently monitored by growth time. The growth rates for SRO and BTO are measured by reflection high-energy electron diffraction (RHEED), while the growth rate for ITO is determined by growing ITO with a shadow mask covering the substrate followed by measuring the step profile in atomic force microscopy (AFM).
Fig. 2. (a) Schematic of the device structure and (b) picture of the actual device ITO/BaTiO3/SrRuO3/DyScO3 (IBSD). SP refers to silver paste.
We then performed structural characterization. The sample showed a smooth surface with a sub-nanometer root mean square (RMS) roughness, as shown in the atomic force microscopy image in Fig. 3(a). The crystallinity of IBSD was characterized by X-ray diffraction (XRD), as presented in Fig. 3(b) and 3(c) in comparison with a reference BaTiO3 thin film directly grown on DyScO3. In Fig. 3(b) the XRD 2θ-ω scan shows that the BaTiO3 layer in both has only (001) and (002) peaks, indicating single crystallinity oriented with the c-axis out-of-plane. In Fig. 3(c) compares the rocking curve of both at the BaTiO3 (002) peak, where the full width at half maximum (FWHM) in IBSD is much larger than that of the reference BaTiO3 thin film. This indicates that although the BaTiO3 in the former is c-axis oriented, the c-axis alignment is not as good as with the latter. This degradation in crystal quality is due to the existence of the SRO buffer layer which affects subsequent BaTiO3 growth.
Fig. 3. Structural characterization of IBSD. (a) AFM surface topography of IBSD, with RMS roughness of 0.279 nm. (b) XRD 2θ-ω scan of IBSD (colored in red) showing a single crystalline c-axis oriented BaTiO3 (BTO) thin film, in comparison with BaTiO3 on DyScO3 (colored in blue). (c) XRD rocking curve at the BaTiO3 (002) peak of IBSD (colored in red), with the FWHM of 0.41°, in comparison with 0.07° for BaTiO3 on DyScO3 (colored in blue).
XRD reciprocal space mapping (RSM) is performed to investigate the strain state of the BaTiO3 thin film in IBSD, as shown in Fig. 4. BaTiO3 is strained and clamped to the substrate. The RSM is done near BaTiO3 (002), (-103) and (013). In the RSM plots, H, K, L represent the reciprocal lattice indices constructed in reference to the reciprocal lattice constants of DyScO3, where the horizontal axes H and K represent the in-plane reciprocal lattice, while vertical axis L represents the out-of-plane reciprocal lattice. (H and K represent the two orthogonal in-plane directions.) Fig. 4(a, b) show the RSM near BaTiO3 (002) in the H and K directions, respectively, with the distribution in L illustrating the spreading in the out-of-plane reciprocal lattice, which corresponds to the lattice relaxation as shown in Fig. 4(c, d). Figure 4(c, d) shows the in-plane reciprocal lattices. The SRO (-103) and (013) peaks are aligned with those of the DyScO3 substrates with the same H and K values, indicating that the thin layer of SRO is fully strained to the substrate. On the other hand, we can observe the BaTiO3 (-103) and (013) peaks shifting from the substrate H and K values to smaller absolute H and K values, indicating in-plane strain relaxations in the two directions as the BaTiO3 layer gets thicker.
Fig. 4. XRD reciprocal space mapping (RSM) on IBSD near BaTiO3 (002) (a, b), (-103) (c) and (013) (d). Horizontal axes H and K represent the in-plane reciprocal lattice, while vertical axis L represents the out-of-plane reciprocal lattice. H, K, L values are labeled in reference to the reciprocal lattice constants of DyScO3. Pseudo cubic (PC) lattice index notations are used for DyScO3 and SrRuO3, respectively, in the figures for convenience of comparison. A bluer color corresponds to a higher intensity. The dashed lines in (c, d) represent the H and K values of the substrate as a guide to the eye.
The prism coupling method is used to characterize the refractive index, with a TE and TM polarized laser at a wavelength of 636.6 nm, as illustrated in Fig. 1(a). This wavelength is chosen because ITO is highly transparent at 636.6 nm and lossy at 1548.4 nm. The slab mode indices are first measured without an applied voltage, and then with applied voltages. The relationship between refractive index changes and applied electric field is
where $\varDelta {\varepsilon _{ij}}$ is the square of the element (i, j) in the refractive index change matrix, ${n_i}$ or ${n_j}$ are the ith or jth respective elements of the diagonal terms of the refractive index tensor, ${r_{lk}}$ the electro-optic coefficient in compressed index form and ${V_k}$ the electric field in the k direction. Index changes induced by r13, r23, r33 are along the diagonal of the index tensor and hence do not alter polarization states if the propagating optical mode is aligned with one of the crystal’s principal axes, which is the ordinary situation [2].To distinguish the crystal orientation from that of DyScO3, we use the BaTiO3 crystal lattice axes a, b, c to describe the sample orientation. The IBSD sample was first positioned where the TE polarization was along the a direction, and then TE slab modes were measured, with results shown in Fig. 5(a); then the sample was rotated in-plane by 90 degrees to align the TE polarization with the b direction and the measurement was repeated with results shown in Fig. 5(b). The measured data are linearly fitted and electro-optic coefficients are calculated using Eq. (2) with the fitted slope. The results show that r13 and r23 values are not equal, due to the small in-plane anisotropy in BaTiO3 mediated from DyScO3 substrate, yet they show only a very small birefringence because of the partially relaxed state of BaTiO3. Note that the measured coercive field is 496 kV/cm in the BaTiO3 thin film, while the range of electric field applied in the r measurements (< 233 kV/cm) is smaller than the coercive field. In the experiment, we verified through repeated DC scans (i.e., when this procedure is altered) that no hysteresis in the refractive index vs. applied field was observed, consistent with there being little domain switching at these applied fields.
Fig. 5. DC electro-optic effect in ITO/BTO/SRO/DSO (IBSD) measured at 636.6 nm wavelength with the TE polarization aligned with the sample a-axis (a) and b-axis (b) direction. The slope of the linear fit for the measured data is used to calculate the electro-optic coefficients, where r13 = 4.2 ± 1.7 pm/V and r23 = 4.6 ± 1.5 pm/V. The error bars for each measurement of the square of the refractive index in the diagrams are inferred from known error of table position (i.e., angle error during prism coupling), and provide an evaluation of a maximum and minimum linear fitting slope (dashed lines) within the error bars. The slopes of the dotted lines are subsequently used to calculate the upper and lower bound errors for the r values. The larger error of the two is chosen to represent the error for the r values.
Then, incident laser light is set to TM, and TM slab modes are measured. Figure 6 shows the results and r33 is measured to be 9.0 ± 2.1 pm/V. The observed reduction of these r values as compared with the bulk values can be due to the degraded crystallinity, as compared above in Fig. 3. Despite the fact that the measured coefficients are smaller than what would be expected in a bulk crystal, it is known that bulk BaTiO3 is comparatively limited in utility for device fabrication (the phase transition at 120 ℃ being severely limiting in terms of cleanroom processes, for instance) while this thin film BaTiO3 grown on DSO more amenable to device fabrication due to excellent optical confinement, good thermal stability and a much higher phase transition temperature [9]. Therefore, potential device applications are still possible utilizing these somewhat lower coefficients. At this point, we have characterized all three ri3 values under an applied DC electric field.
Fig. 6. DC electro-optic effect in ITO/BTO/SRO/DSO (IBSD) measured at 636.6 nm wavelength with TM polarization. The slope of the linear fit for the measured data is used to calculate the electro-optic coefficient r33 = 9.0 ± 2.1 pm/V. Dashed lines represent the maximum and minimum slope for linear fitting within error bars, as described in the caption of Fig. 5.
To further understand the reduced r values and their relationship with crystallinity, we replace the SRO bottom electrode layer with another conducting layer La0.67Sr0.33MnO3 (LSMO), which has a different lattice constant. LSMO has a larger lattice mismatch with the DyScO3 substrate (1.96%), in comparison with that of SRO (0.7%). For such a device ITO/BaTiO3/LSMO/DyScO3 (labeled as IBLD), the thickness of the ITO, BaTiO3 and LSMO layers were 60 nm, 700 nm, 6 nm, respectively. The LSMO layer is grown at 600°C under 100 mTorr oxygen gas pressure with a laser pulse energy density of 2 J cm-2, while growth for the other layers is the same. Like IBSD, the resulting device has a similar smooth surface, as shown in Fig. 7(a). But due to larger lattice mismatch, the BTO layer has a degraded crystal quality, presenting a major BTO (001) orientation with an impurity BTO (110) orientation, as shown in Fig. 7(b).
Fig. 7. Structural characterization of IBLD. (a) AFM surface topography of IBLD, with an RMS roughness of 0.389 nm. (b) XRD 2θ-ω scan of IBLD showing a major BTO (001) orientation with an impurity BTO (110) orientation.
Then, r13 and r33 are subsequently measured for IBLD using the same method described above for IBSD. Figure 8 shows the results. r13 and r33 were measured as 2.9 ± 1.5 pm/V and 5.8 ± 1.4 pm/V respectively, and these values are smaller than those of IBSD. This can be due to the existence of impurity phases in the BaTiO3 layer. Comparing r values for IBSD and IBLD, we observe that the BTO layer with better crystallinity has a stronger DC electro-optic effect.
Fig. 8. DC electro-optic effect r13 (a) and r33 (b) in IBLD at 636.6 nm wavelength with TE polarization in line with sample a-axis direction. The coefficients r13 and r33 are measured 2.9 ± 1.5 pm/V and 5.8 ± 1.4 pm/V. Dashed lines represent the maximum and minimum slope for linear fitting within error bars, as described in the caption of Fig. 5.
3. Conclusion
In summary, we characterized the DC electro-optic coefficients r13, r23 and r33 in single crystalline BaTiO3 thin film with ITO and SrRuO3 as top and bottom electrodes respectively by the prism coupling method. We first characterized the birefringent refractive indices of DyScO3, with nx = 2.085, ny = 2.080, nz = 2.037 at 636.6 nm wavelength and nx = 2.049, ny = 2.044, nz = 2.004 at 1548.4 nm. We then characterized the DC electro-optic coefficients at 636.6 nm. A small difference is observed in r13 (4.2 pm/V) and r23 (4.6 pm/V) due to the small in-plane anisotropy in BTO thin film mediated from DSO substrate, yet are nearly isotropic in-plane because of the relaxed nature of the BaTiO3 thin film. r33 is a bit larger (9.0 pm/V). These measured values are smaller than those of bulk values, and this can be attributed to the degraded crystallinity resulting from the insertion of the bottom electrode buffer layer during film growth. This is supported by a subsequent measurement of r values on another device IBLD where the BaTiO3 has an impurity phase. If this hypothesis is false, on the other hand, then other, perhaps interesting, physical effects may be behind the observed relationship between crystal structure and electro-optic coefficient magnitude. Despite the fact that they are small, as discussed before, r13, r23, r33 can provide a particular functionality to device designs making use of the electro-optic effect in BaTiO3 as they permit controllable polarization-maintaining phase shifts. Despite these values being small, they provide a clear demonstration of electro-optic modulation within thin film BaTiO3, especially considering the good optical confinement and thermal stability of the BaTiO3.
Funding
National Research Foundation Singapore (NRF-CRP24-2020-0003).
Acknowledgement
This work is supported by the Singapore National Research Foundation (NRF) under the Competitive Research Programs (CRP Grant No. NRF-CRP24-2020-0003). P.Y. is supported by SSLS via NUS Core Support C-380-003-003-001. The authors would also like to acknowledge the Singapore Synchrotron Light Source (SSLS) for providing the facilities necessary for conducting the research. The SSLS is a National Research Infrastructure under the National Research Foundation Singapore. This work is supported by the Université Polytechnique Hauts-de-France (UPHF) under the Competitive Research Programs (Grant no: AAP 15-2021). The authors would like to acknowledge the platform FUMAP at IEMN site Valenciennes for providing the facilities necessary for conducting the optical and electrooptical measurements.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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