Barium titanate ( BaTiO 3 ) RF characterization for application in electro-optic modulators

Barium titanate (BaTiO3 or BTO) is currently one of the most promising ferroelectric materials for enabling Pockels modulation that is compatible with silicon photonic circuits. The relative permittivity of BTO has been characterized in thin films deposited on a silicon-on-insulator (SOI) substrate. High values between 800 and 1600 have been estimated at 20 GHz. Furthermore, no substantial difference has been obtained by using BTO grown by molecular beam epitaxy and sputtering. The obtained permittivity has been used to properly design the RF electrodes for high-speed modulation in hybrid BTO/Si devices. Electrodes have been fabricated and the possibility of achieving modulation bandwidths up to 40 GHz has been demonstrated. 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Introduction
Ferroelectric materials with high permittivity have been largely investigated for ceramic applications [1,2]. However, these materials have also found application in other fields such as phased array antennas [3] or planar microwave integrated phase shifter [4]. In this context, barium titanate (BaTiO 3 or BTO) is one of the most representative ferroelectric materials. For photonic applications, BTO is one of the best candidates to develop high performance electrooptical modulators thanks to its large Pockels coefficients [5]. The Pockels coefficients in bulk BTO crystals is several orders of magnitude higher than lithium niobate (LiNbO 3 ), which has motivated the development of BTO-based photonic devices. Nowadays the most common modulation mechanism used in silicon devices is the plasma dispersion effect [6]. However, the modulation speed is limited by the carrier lifetime and optical losses are also induced. The Pockels effect is intrinsically lossless and ultra-fast. In this way, high modulation efficiencies and the potential for achieving modulation bandwidths above 40 GHz have been demonstrated by using BTO deposited on top of magnesium oxide (MgO) substrates [7][8][9][10][11]. However, in the last years, the successful growth of high quality BTO films on silicon has opened a new path for providing electro-optic functionalities to the silicon photonic platform [12][13][14][15][16]. The possibility of an integration process compatible with large size silicon wafers makes BTO more attractive than other materials such as lithium niobate in which the integration is based on bonding processes [17]. The electro-optical performance of hybrid BTO/Si modulators has been mostly analyzed under static conditions and simulated modulation efficiencies as low as 0.27 V·cm have been reported [18][19][20][21]. However, high speed modulation cannot be achieved unless RF electrodes are properly designed. Hence, an accurate measurement of the relative permittivity of the BTO layer is a prerequisite to accomplish such design task.
The BTO permittivity depends on the crystallographic axes of the material. A value of about 56 for the direction parallel to the optical axis and of about 2200 for the direction perpendicular to the optical axis have been taken as a gauge of good quality of clamped, single-domain crystals [5]. However, the permittivity may show a huge variability depending on the fabrication conditions. Low values between 83 and 120 have been reported for films deposited at room temperature by RF sputtering [22]. Conversely, high values up to 6000 have also been measured and correlated with the grain size and microstructural characteristics of the material [3]. The permittivity may also depend on the thickness of the BTO layer and the frequency of the applied electric field. Values between 230 and 1000 have been measured for BTO films with thicknesses ranging from 30 to 580 nm at a low frequency of 1 KHz [23]. At higher frequencies, a decrease of permittivity from 2200 to 500 has been estimated for RF frequencies among 1 and 40 GHz [24].
In this work, the relative permittivity of thin BTO films deposited on silicon-on-insulator (SOI) substrates is first analyzed. A multiline method is proposed to estimate the effective permittivity at wafer level and then electromagnetic simulations are carried out to extract the BTO permittivity. Therefore, the BTO can be characterized in the same growth conditions as the ones used to fabricate the devices. Once the BTO permittivity is obtained, RF electrodes have been designed for high speed modulation in hybrid BTO/Si devices. Finally, the designed electrodes have been fabricated and characterized.

BTO fabrication process
BTO layers have been grown on a SOI substrate with a device silicon layer thickness of 100 nm and a buried oxide thickness of 2 µm. A thin (3-4 nm thick) SrTiO 3 buffer is required to accommodate the crystallographic and chemical heterogeneity between BTO and Si and ensure single crystallinity and high crystal quality of the BTO layer. Molecular beam epitaxial (MBE) was used to grow the SrTiO 3 template, as described in [12] and [25]. Then, two different approaches, MBE and RF sputtering, were employed to grow the BTO layer with a thickness of about 50 nm.
RF-sputtering was used to grow 50 nm-thick BTO film on the SrTiO 3 /SOI template. A BTO stoichiometric target was sputtered under Ar and O 2 mixing atmosphere and using a RF generator at a substrate temperature of 650°C. After growth, the BTO layer was submitted to rapid thermal annealing to improve its structural quality and ensure good oxidation of the thin layer. On the other hand, using a similar SrTiO 3 /Si template, a 50 nm thick BTO was grown by MBE using Ba and Ti co-deposited at 600°C under an oxygen partial pressure of about 10-5 Torr. More details can be found in [12].

RF characterization of the BTO layer
The relative permittivity of the BTO has been characterized on the same multilayer stack, shown in Fig. 1, used to develop the optimum travelling-wave electrodes for high speed modulation. In this case, the BTO permittivity cannot be measured as in a conventional capacitor by extracting the capacitance between its plates [1]. Therefore, a multi-line method [26,27] can be used to estimate the effective permittivity of the complete multilayer stack. The proposed method is part of the well-known Thru-Reflect-Line (TRL) algorithm and has the advantage of allowing on-wafer characterization [28, 29]. Transmission lines with different lengths were used to apply the multiline method. A length of 1 mm was chosen for the thru (reference) line while lengths of 2 mm, 2.5 mm and 3 mm were used for the other lines. The difference in length between the thru and the rest of the lines is acceptable for minimizing the inaccuracy caused by the manual alignment of RF probes on the metal pads. The scattering parameters of the CPW were measured and then used to extract the effective permittivity by applying the multi-line method described below. The BTO relative permittivity was obtained by matching the simulated effective relative permittivity with the one obtained by measurements.

Characterization of the effective permittivity
The multi-line method allows to obtain the complex propagation constant (γ) and the effective permittivity of the multilayer stack through the following equation [30]: where c is the speed of light and f is the RF frequency. One of the main advantages of this method is that it does not require vector network analyzer (VNA) calibration to measure the scattering parameters (S 11 , S 12 , S 21 and S 22 ). Figure 2 shows the fabricated CPWs with different lengths. To apply the method, the scattering parameters matrix are first converted into transmission parameters with S S S S Δ = − (3) The use of transmission matrices instead of scattering parameters has the advantage of exploiting the cascade multiplying property. Let the transmission matrices of the thru (reference line with shortest length) and of the longer delay lines to be denoted as T t and T d respectively. T 1 and T 2 represent the error matrices introduced in each port of the uncalibrated VNA. Thereby, the measured transmission matrices can be expressed as where T l represents the delay line without the error and Δl represents the length difference between thru and the respective delay line. The following matrix elements can be calculated from the measured matrices by such that the propagation constant can be calculated as where the influence of the error matrices, T 1 and T 2 , has been suppressed [28]. The sign assignment in Eq. (8) should be such that |e 2γl |<1. Finally, the real part of the effective permittivity is obtained from Eq. (1).   Figure 3(b) shows the real part of the effective permittivity as a function of the RF frequency by using the transmission matrix of the 2 mm long delay line in Eq. (5). Similar results are obtained when considering the other delays lines. The effective permittivity is also very similar for the samples with BTO fabricated by MBE or RF sputtering.

Estimation of the BTO relative permittivity
Simulations by COMSOL Multiphysics have been carried out to obtain the microwave index of the quasi-TEM mode that propagates in the CPW. Figure 4(a) shows the electric field distribution of the quasi-TEM mode at the frequency of 20 GHz. The microwave index n m is directly related to the effective permittivity. The relative permittivity of the BTO layer has been modified in the simulations to match the real part of the effective permittivity with the measured values. Figure 4(b) shows the obtained simulation results for 20 GHz and the measured values extracted from the different delay lines for both BTO fabrication processes. The BTO layer has a relatively small influence on the effective permittivity due to its low thickness. Simulation and experimental values are matched for a BTO permittivity between 800 and 1600. Hence, an average value of 1200 has been chosen to design the optimum electrodes for high speed modulation. The high value obtained for the BTO is in agreement with BTO grown mostly with c-axis ferroelectric domain orientation [5,24], which was confirmed by X-ray diffraction (XRD) measurements

RF electrodes design for modulator
The hybrid BTO/Si optical waveguide depicted in Fig. 5(a) has been proposed for enabling electro-optical modulation with high performance. A layer of amorphous silicon (a-Si) is deposited on top of the BTO/SOI structure and then etched down to form the optical waveguide. The influence of the waveguide parameters on the static electro-optical performance has been previously reported [20]. The electrodes are placed on top of the BTO layer after opening lateral windows in the SiO 2 cladding to enhance the modulation efficiency.
The high value of the BTO relative permittivity (ε r~1 200) will increase the capacitance of the electrodes and thus the impedance will be reduced with respect to materials with lower dielectric constants. A narrow gap between electrodes and the optical waveguide is desirable to improve the modulation efficiency though a too small value will give rise to optical losses due to interaction of the optical mode with the metal electrodes [20]. Coplanar strip-line (CPS) electrodes have been designed to achieve the best modulation performance in a travelling-wave configuration. The maximum thickness of the metal electrodes allowed by the fabrication process, which is around 750 nm as depicted in Fig. 5(a), has been initially fixed. The gap and width of the CPW electrode have then been designed taking into account their influence on the impedance and microwave index. Both impedance and microwave index decrease when the electrode width increases. However, they change in an opposite way when the gap is varied, as it is shown in Fig. 5(b). The microwave and optical group indices should be matched to maximize the bandwidth. The simulated optical group index of the hybrid BTO/Si optical waveguide is 3.66 for TE polarization (Fig. 5(c)) and 3.85 for TM polarization (Fig. 5(d)). Thereby, the optimum parameters of the CPS electrode have been found for a gap of 2.5 µm and an electrodes width of 2 µm. The resulting impedance and microwave index are 54 Ω and 4.52, respectively, as it can be observed in Fig. 5(b). An impedance close to 50Ω allows achieving maximum voltage transfer and avoids electrical reflections. In addition, the potential bandwidth by assuming negligible microwave propagation losses (α = 0) can be easily estimated by where c is the speed of light, L is the modulation length and n m and n o are the microwave and optical group indices [30]. Bandwidths higher than 40 GHz for modulation lengths up to 5.5 mm would be feasible based on Eq. (10). The designed CPS electrode has been fabricated and characterized. The experimental impedance was extracted from the reflection coefficient of the scattering parameters. Figure 6(a) shows the simulated and experimental impedance as a function of the RF frequency. It can be seen that the influence of the BTO fabrication process on the experimental impedance values is low. Furthermore, there is a rather good agreement between simulation and experimental results. The microwave propagation losses have also been extracted from the measured scattering parameters. Propagation losses are mainly originated due to conductor and dielectric losses [31]. Conductor losses have a square root dependence with frequency due to the skin effect. Besides, dielectric losses depend on the polarization and ohmic losses of the dielectric materials. At high frequencies, the heating associated with the polarization become the dominant source of losses. Figure 6(b) shows the experimental losses as a function of the RF frequency. Simulations considering conductor losses have also been carried out to compare with experimental results. The difference between experimental and simulation results increases for high RF frequencies. Such higher losses are attributed to dielectric losses of the materials but also from additional conductor losses due to surface roughness at the electrodes. However, it is interesting to notice that the sample with BTO fabricated by sputtering has higher losses than the sample with BTO growth by MBE. Therefore, the obtained results also suggest that BTO losses may play an important role and that lower losses are achieved by MBE. Furthermore, for a given microwave propagation losses and considering that the CPS electrode is terminated by its impedance, the small signal electro-optical modulation response can be calculated by 2 2 where L is the modulation length, α is the loss coefficient, Δf is given by Eq. (10) and f is the RF frequency [32].  Figure 7 shows the simulated frequency response for a modulation length of 1.5 mm, TM polarization and taking into account the simulated and measured microwave losses depicted in Fig. 6(b). The electro-optical response is practically the same for TE polarization (n o = 3.66). Therefore, for both light polarizations, the modulation bandwidth would be drastically reduced to around 5 GHz for the BTO grown by sputtering due to the high losses. However, a modulation bandwidth of 40 GHz would be achieved for the BTO grown by MBE. Furthermore, a half-wave voltage, V π , of around 5 V for TM polarization and 7.9 V for TE polarization has been obtained by simulation for c-axis oriented BTO and the modulation length of 1.5 mm.

Conclusions
A multi-line method combined with electromagnetic simulations has been proposed and demonstrated to obtain the relative permittivity of BTO thin films deposited on top of a SOI substrate. In such a way, the permittivity can be obtained at wafer level and at the same process conditions used for fabricating the devices. Similar values around 1200 at high RF frequencies have been obtained for BTO grown by two different techniques: MBE and sputtering. The high permittivity value is associated with the c-axis ferroelectric domain orientation of the BTO layer.
A coplanar strip-line electrode has also been designed and experimentally demonstrated for high speed modulation in a hybrid BTO/Si device. The modulation bandwidth is limited by the microwave propagation losses. Lower losses have been obtained by MBE compared to RF sputtering which suggest that process conditions could be optimized to minimize the dielectric losses of the BTO layer. Nevertheless, modulation bandwidths up to 40 GHz have been demonstrated to be feasible.