Introduction

Silicon photonics (SiPh) has had a recent surge in interest due to its possibility for combining photonics and electronics in the same package for highly efficient optical transducers in the field of optical communications and data centers1,2, and as a potential successor to certain aspects of computing such as quantum and neuromorphic computing along with high-performance coherent optical modulators3,4,5,6,7,8. It is also a key enabling technology for making chip-to-chip optical interconnects on the same printed circuit board9,10,11. Currently, SiPh devices have been utilizing the plasma dispersion effect8, modulating both the real and imaginary part of the refractive index, which means modulating absorption, and the thermo-optic effect8,11, which consumes a lot of power and has now reached its limit in terms of modulation speed. Additionally, both of these methods provide a relatively weak modulation8,11, especially when compared to the linear electro-optic (EO) effect, otherwise known as the Pockels effect. The Pockels effect is the first order change in the real part of the index of refraction with respect to an applied electric field. However, it requires a non-centrosymmetric crystal, while Si is centrosymmetric. Straining Si does remove inversion symmetry, but produces only a very weak Pockels response8,12. Thus, several materials exhibiting the Pockels effect intrinsically are being investigated for integration onto Si in order to provide a substantial EO response for silicon photonics devices. The two most attractive materials for Pockels-based devices thus far have been BaTiO3 (BTO) and LiNbO3 (LNO). LNO is the more established of the two and has been shown to have very low propagation losses in integrated structures, but is limited by its modest electro-optic response of about 32 pm/V and complicated processing required for integration with Si13,14,15,16. Most importantly, Li is a major contaminant in CMOS technology making combined fabrication with electronics problematic. On the other hand, BTO is a burgeoning material, which is attractive due to its exceptionally large EO response and compatibility with CMOS fabrication infrastructure17. Recent work has shown a tensor component response of ~923 pm/V on Si18. The fabrication of BTO-based waveguides and optical modulators is relatively new and with further development, it can likely reach propagation losses similar to LNO. Mach–Zehnder modulators based on BTO have already shown low VπL values (the voltage-length product required to produce a phase shift of 180°) relative to LNO18,19,20. This provides a strong prospect for reducing the size and/or power consumption of Si-integrated BTO-based photonic structures. A recent comparison of LN and BTO modulators can be found in refs. 21,22.

Thick BTO films grown by molecular beam epitaxy (MBE) have been extensively studied for their EO properties18,23. Different growth methods, which yield different film microstructures, have been compared in the literature to study its effect on the measured Pockels coefficient of BTO integrated on Si24. Microstructural and crystallographic analysis25 and the corresponding relationship of the two have also been recently reported20. The measured effective EO coefficient depends on the direction of the ferroelectric polarization (c-axis) of the film relative to the modulating external field and the optical electric field. The film orientation convention is that a film is “c-axis oriented” if the long axis of the tetragonal BTO crystal is perpendicular to the surface of the substrate, and it is “a-axis oriented” if the long axis is parallel to it, i.e. in-plane. For standard BTO films grown on Si, a buffer layer of SrTiO3 (STO) is required for the film to grow epitaxially26. Vaithyanathan et al.27 provided a qualitative argument on how to control the crystallographic orientation, but this was for relatively thin films of up to about 25 nm thickness. The traditional explanation for films grown on STO-buffered Si typically begin c-axis oriented and eventually relax to a-axis oriented due to the thermal expansion mismatch between Si and BTO27. Some of the parameters to control this have been investigated25,28,29,30. Currently, however, there have not been any thorough studies relating the heating and cooling rates during the growth of these films to the crystallographic and EO properties of the films. Cooling rates have been shown to be tied to residual strain that affects various materials properties such as crystallographic orientation, dielectric constant, ferroelectric and ferroelastic domain structure31,32,33,34,35,36. This leads to a necessity to study it for EO applications, as BTO film’s EO properties are tied to the crystallographic and ferroelectric properties37. It could also have an effect on film’s modulation capabilities due to the overlap integral for photonic waveguide design20 and waveguide loss parameters due to scattering at domain walls22,38.

In this paper, we report Si-integrated BTO films with effective Pockels coefficients exceeding 550 pm/V. Using MBE, we grow 150-nm thick single crystal BTO films on Si (001) using different heating and cooling rates and perform extensive structural and EO analysis. X-ray diffraction (XRD) provides insight into the crystallographic evolution of the films as they grow thicker. Plan-view scanning transmission electron microscopy (STEM) combined with precession electron diffraction (PED) elucidates the crystallographic orientation and domain sizes of the film’s top region. Transmission EO measurements are performed to compare the performance of each film to determine if the variation in microstructure has a noticeable effect on the response. We find that, in general, the traditional explanation of the microstructure evolution of BTO films grown on Si does not appear to hold for thicker films, and that while the raw EO modulation of each film is not identical, the fitted Pockels coefficients accounting for crystallographic orientation distribution are very similar. Also, we find that for thick BTO films that are undergoing strain relaxation from c- to a-axis oriented as films grow thicker, the EO response does not appear to depend on the size of the crystallographic domains, nor does the relaxation of the lattice constants.

Results and discussion

Crystallographic analysis

The process by which BTO relaxes on STO buffered Si has been examined extensively in the literature20,25,27,30. When grown on STO-buffered Si, BTO will first assume the c-axis orientation (long axis perpendicular to the substrate) before gradually transitioning into the a-axis orientation (long axis parallel to the substrate). The commonly accepted explanation for such reorientation is that there are two main contributions to strain in the BTO film, namely the thermal expansion mismatch between the different layers, along with the lattice constant difference between the layers27. The large thermal expansion coefficient mismatch forces the film to be a-axis oriented, while the lattice constant differences prefer a c-axis orientation. The recent study by Li et al. suggests a more complicated picture39. They have investigated the BTO on Si morphology as function of the cooling rate using phase field simulations, and found that c-oriented BTO is quite stable under fully strained conditions and slow cooling, while the a-oriented film is preferred under the condition that BTO is fully relaxed at the growth temperature and contracts at a rate corresponding to the Si thermal expansion coefficient during fast cooling. As discussed below, we observe the opposite trend in our films (more c-oriented with fast cooling), which leads us to believe that there is some other effect that should considered for thick BTO films grown on Si.

Both out-of-plane (OOP) and in-plane (IP) fine scans of the 004 region were performed on all three films to investigate the effects of varying the cooling rate on the crystallographic structure of the film. The 004 region is used due to the larger separation between (004) and (400) peaks, making quantification easier. OOP scans of each film are shown in Fig. 1a–c and IP of the 5 °C/min film is shown in Fig. 1d, with the extracted lattice constants and equivalent a-axis thickness shown in Table 1. Details of the classification scheme used for this analysis can be found in ref. 20, the details of which can be found in Supplementary Note 2; here we only provide a brief overview. The equivalent thickness is calculated by taking the sum of the area of each of the fitted peaks, and then finding fractions of each peak relative to the entire sum. When comparing the orientational equivalent thicknesses, we find an unexpected result. As stated previously, the conventional thought for BTO on Si is that by cooling faster, the film will be forced into the a-axis orientation because of thermal expansion mismatch27. However, our films show the opposite result. The film cooled at 50 °C/min has the largest thickness of c-axis oriented BTO, and the a-axis oriented region’s OOP lattice constant is not fully relaxed to bulk lattice constants. However, the films cooled at 10 °C/min and 5 °C/min show a smaller region of c-axis oriented BTO, while their a-axis oriented region shows the most relaxed OOP lattice constant, which is getting close to the bulk value40. The 5 °C/min sample shows even more resolved splitting than the other two films, which we think may be related to even greater relaxation. For equivalent thickness fitting, the a-axis portion of the film for the films grown with 50 and 10 °C/min rates was taken to be half of the mixed c/a region plus the a-axis region, while the 5 °C/min film was taken to be the “a” region along with the fully relaxed a-axis region. The general trend for the OOP lattice constant of the a-oriented region is that by cooling slower, the film relaxes more. The IP scans for each film show the expected result for a two-domain structure, with the split peaks consistent with crystallographic regions that are 90° rotated from one another. The extracted lattice constants for OOP and IP scans, along with equivalent thickness of the a-oriented region for each film and the tetragonality based on the IP lattice constants, are shown in Table 1. The results shown by OOP XRD are opposite to what has been expected in prior studies20,27. Because these films are sufficiently thicker than traditional BTO films grown by MBE20,27,30, one possible explanation is that the electromechanical boundary conditions begin to have a stronger effect on the cubic-to-tetragonal transition when BTO films surpass a certain thickness. This would mean that instead of thermal expansion mismatch and initial compressive strain on the BTO being the primary cause for strain relaxation for films cooled slowly, the electrostatic energy build-up causes a preference for the film to be polarized in-plane near the surface versus out-of-plane, which causes the film to fall in-plane more easily39,41. While we have not determined the exact thickness at which this effect becomes the dominating factor, in our prior work we have seen that BTO films grown by MBE with ~110 nm thickness cooled at 50 °C/min show an almost c-axis oriented OOP lattice constant, while still showing a large electro-optic response20.

Fig. 1: Fine scan XRD of films.
Fig. 1: Fine scan XRD of films.The alternative text for this image may have been generated using AI.
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a–c OOP 004 scans of each film, showing the effect of the heating and cooling rates on the crystallographic structure of each film. d Exemplary scan of IP 004 region of the film using 5 °C/min, showing the expected splitting of the peaks that is standard for in-plane oriented BTO. Bulk lattice constants from ref. 40 are labeled with dashed lines.

Table 1 Extracted lattice constants and a-axis equivalent thicknesses for each film
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The conventional model for BTO growth evolution is based on two limiting cases of strain-temperature path during cooling: (1) “fully constrained” and (2) “fully relaxed” but “glued to Si.”39. It appears that our films may follow what Li et al. have called Scenario III. The films start out moderately compressed at the growth temperature, undergoes the paraelectric-to-ferroelectric transition at temperature much higher than bulk stress-free BTO (~125 °C), and maintains a large in-plane polarized region close to the surface. Two 90° domains are present in the top region. Close to the interface the film is c-oriented, with 180° domains. This is shown in Fig. 2. From the XRD results, we think this is the mechanism occurring during the growth of our films. What is different, however, is that the cooling rate effects the thickness at which the relaxation occurs for sufficiently thick films. The relaxation occurs at a lower thickness for slow cooled films, while at a larger thickness for fast cooled films.

Fig. 2: Phase field simulation of domain morphology.
Fig. 2: Phase field simulation of domain morphology.The alternative text for this image may have been generated using AI.
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a BTO domain morphology at 300 °C and under biaxial −0.88% compressive strain, which is the first ferroelectric phase in the discrete simulation path. White arrows indicate the direction of polarization. Red and blue regions are c axis oriented BTO phase while the green area is a-axis oriented. b Details of BTO phases on the top surface of Fig. 2a. Red and blue corresponds to (P00) and (0P0) domains. (from Ref. 39).

To visualize the effect of cooling rate on the films’ microstructure, plan-view STEM was conducted on the samples (Fig. 3a). Films cooled at rates of 50 °C/min and 5 °C/min both exhibit a high concentration of defects, as evidenced by the bright field images shown in Fig. 3b, c, respectively. These defects manifest as dark regions in the BF-STEM images due to the high-angle scattering of electrons from the defects and diffraction contrast. The concentration of defects appears comparable in both films based on images acquired from various regions. High-magnification HAADF images confirm these defects as straight and threading dislocations, as depicted in Fig. 3d, e, respectively, appearing parallel to the film growth direction (Fig. 3f). A shear strain map obtained from geometric phase analysis (GPA), presented in Fig. 4g, reveals the spatial distribution of dislocations in a region ~130 nm × 130 nm. Interestingly, the dislocations appear as pairs, forming an angle of around 45° with each other. It should be noted that the mechanical boundary conditions in a plan-view lamella may not be the same as in the original film on substrate and it is likely that the quantitative strain observed may be different.

Fig. 3: Plan-view STEM.
Fig. 3: Plan-view STEM.The alternative text for this image may have been generated using AI.
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a Schematic of the BTO thin film on Si. Low magnification BF images of the thin film plan-view cooled at b 50 °C/min and c 5 °C/min. Atomic-scale HAADF images showing d a straight dislocation and e a threading dislocation growing perpendicular to the film plane as schematically shown in (f). g A shear strain map obtained from GPA analysis with the inset showing the HAADF image. The dotted ellipses highlight the ordered dislocation pairs.

Fig. 4: Large-area domain analysis by precession 4D-STEM.
Fig. 4: Large-area domain analysis by precession 4D-STEM.The alternative text for this image may have been generated using AI.
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Strain maps obtained from the plan-view of thin films cooled at a 50 °C/min and b 5 °C/min. Ratio of x- and y- strain for films cooled at c 50 °C/min and d 5 °C/min calculated from a and b, respectively.

We conducted further investigation into the crystallographic domain structure and size distribution in the films cooled at different rates using precession electron diffraction. In precession 4D-STEM, an electron beam with very small spot size is scanned over a 2D region in the sample, while diffraction patterns are recorded at every beam position with precession. Using these diffraction patterns, we calculated the ratio of in-plane horizontal (x) and vertical (y) lattice parameters for the samples cooled at 50 °C/min and 5 °C/min, as shown in Fig. 4a, b, respectively. The ratio of x-spacing to y-spacing can be used to map the orientation of the orthogonal a-domains, as confirmed by our atomic-scale polarization analysis (Supplementary Note 3, Supplementary Fig. S1) as well as nano-scale GPA analysis (Supplementary Note 3, Supplementary Fig. S2). A ratio larger than 1 indicates the long axis of the crystal in the x direction (red regions), i.e., an x-oriented a-domain (ax), whereas a ratio smaller than 1 indicates the longer axis along the y direction (blue regions), i.e., a y-oriented a-domain (ay). Similarly, a ratio close to 1 represents domain walls or c-domains. Interestingly, the domain morphology appears similar in both samples cooled at 50 °C/min and 5 °C/min. The domains manifest as patches, with some being continuous and others around 50–100 nm in size. On the other hand, there is an obvious difference in the distribution of the x/y ratio for the samples cooled at 50 °C/min and 5 °C/min (Fig. 4c, d). Slow cooled sample shows more relaxed in-plane lattice constants compared to the fast cooled sample. This corresponds well with the XRD results.

Regardless of the crystallographic structural parameters, the domain structure and domain size appear comparable in fast-cooled and slow-cooled films. The dislocations observed in the films may provide favorable elastic and electrostatic conditions for the stabilization of a-domains by relaxing the strain associated with the orthogonal a-domains (Supplementary Note 3, Supplementary Fig. S2). This could be the reason why the domain morphology seems similar in both the films cooled at 50 °C/min and 5 °C/min.

Electro-optic measurements

Along with extensive crystalline and domain characterization, electro-optic (EO) measurements are performed on each of the thin films to confirm that they are EO active, and to investigate whether the differences in the crystal structure yield differences in the electro-optic response. The first order EO or Pockels effect is the change in the index of refraction with respect to a linear applied electric field. It is written as37,

$${n}_{{ij}}\left(E\right){=n}_{{ij}}\left(0\right)-\frac{1}{2}{{n}_{{ij}}}^{3}\left(0\right) {\sum}_{k}{{r}_{{ijk}}E}_{k}$$
(1)

where the electric field is indexed by k and the electro-optic tensor is represented by rijk; its magnitude indicates how much the applied field can vary the index of refraction.

For 4 mm or BTO, the electro-optic tensor can be written in contracted Voigt notation as

$${r}_{{ijk}}=\left(\begin{array}{c}\begin{array}{ccc}0 & 0 & {r}_{13}\\ 0 & 0 & {r}_{23}\\ 0 & 0 & {r}_{33}\end{array}\\ \begin{array}{ccc}0 & {r}_{42} & 0\\ {r}_{51} & 0 & 0\\ 0 & 0 & 0\end{array}\end{array}\right)$$
(2)

However, r13 = r23 and r51 = r42 due to crystalline symmetry for 4 mm BTO37. For this research, we use the optical axis method, where the polarization axis of the crystal is kept aligned with axis 3.

In BTO thin films integrated on Si, the strongest EO coupling occurs when the electric field is applied 45° relative to the BTO crystalline axes18,23. Therefore, we will focus on devices in that geometry. This allows us to couple to the largest component in the EO tensor, the r42 component. Figure 5a, b shows schematics of the setup that was used to perform the measurements, along with the important physical quantities. This is described in more detail in our previous works20,42,43. Figure 5c shows an example fit of ΔP/P, by which one can extract the value of δ/2 and use this to find our effective Pockels coefficient. The equations used for ΔP and P are shown as an inset in Fig. 5c. The a-axis thickness of each film is summarized in Table 1.

Fig. 5: Electro-optic measurements setup considerations and example figures.
Fig. 5: Electro-optic measurements setup considerations and example figures.The alternative text for this image may have been generated using AI.
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a Physical considerations for sample in transmission geometry. b Schematic of setup showing individual components and the resultant phase shift. c Example ΔP/P showing electro-optic modulation on the film cooled at 50 °C/min. d θi versus reff performed on a pad on the film cooled at 5 °C/min.

To compare the EO properties of each film, we first measure each film setting the input angle of the light to θi = 0°. EO modulation has been shown to depend on the input angle, and this angle has been shown to be the angular input corresponding to maximum electro-optic modulation for 4 mm BTO barring any misalignments of the optical setup or sample mounting23,44. To perform the measurements, the BTO is first poled using a ±30 V DC (3 ×106 V/m) bias for 2 min, well beyond the coercive field seen for other thick BTO films23. Then, the measurement is performed using a ±20 V DC bias and 3 Vpp AC bias. A typical measurement is shown in Fig. 5c. Both positive and negative DC biases were measured to account for possible variations in the EO signal when applying the fields in opposite directions as a result of possible polarization pinning30. Finally, we measured the electro-optic response versus the input angle more carefully on a contact pad on the film cooled at 5 °C/min, and the resulting curve is shown in Fig. 5d. This solidifies evidence that the response we are seeing is indeed due to the Pockels effect. The resulting modulation and extracted Pockels response of each film within 10° of the input angles θi = 0° and 90° (sufficiently close to the peaks) are used for averaging and are shown in Table 2. Each data point is a result of at least 30 measurements. More details of the electro-optic measurements can be found in Supplementary Note 4.

Table 2 Experimental results from electro-optic measurements
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First of all, we note that the effective Pockels response for these films is very large and even higher than other recently reported effective coefficients which max out at ~525 pm/V4,23,45, which we think is due to extensive relaxation while maintaining a high level of epitaxy when compared to our previous work20]. Secondly, the raw modulation, which does not account for the a-axis equivalent thickness of the film, δ/2, shows noticeable variance between the 50 °C/min versus the 10 °C/min and 5 °C/min. When the raw modulation is converted to effective Pockels coefficients after accounting for a-axis equivalent thickness, the values are much closer. This implies the effective Pockels response of the films is almost the same even with differing lattice constants and thus relaxation, and that after sufficient a- to c- relaxation has occurred the films will give similar electro-optic responses. This indicates that the effective Pockels response is either not dependent or only weakly dependent on the relaxation of the BTO beyond a certain point for sufficiently thick films24. However, the raw modulation is different due to a difference in the equivalent thickness of a-axis oriented BTO in each of the films. The films cooled at 5 °C/min and 10 °C/min have almost the same thickness of a-axis BTO while the film cooled at 50 °C/min has noticeably less, and have comparable raw modulation even though their relaxation is different. This compares favorably with the 4D precession STEM, which showed that films cooled at different rates have similarly sized domains but different relaxation. This implies that the raw modulation is not dependent on the domain size, only on the thickness of a-axis oriented BTO.

Conclusions

BTO films of 150 nm thickness were grown via MBE using varying heating and cooling rates from 50 °C/min to 5 °C/min. The films showed noticeably varying XRD results, which indicate that films cooled slower have more a-axis oriented BTO versus fast cooled films, indicating more substantial relaxation. This result is opposite to the results in the literature for BTO. We think this may be due to the electro-static boundary conditions having a more noticeable effect in the strain relaxation dynamics. The film’s orientation was studied using 4D STEM precession diffraction, and we found that the crystallographic domain size does not vary strongly with different cooling rates, and is more dependent on defect density which is similar between the films. We found that the domains manifested as patches, with some being continuous and some being ~50–100 nm in size. The degree of relaxation does vary though, in a similar fashion to the XRD results. The electro-optic response of the films is very large, likely due to the sufficient relaxation of the films. The raw modulation of the films is similar with films that have similar a-thicknesses of BTO, while the effective response is similar between all of the films. This work provides valuable insight for Si-integrated photonics by providing a robust process for BTO growth and showing the Pockels response is either not dependent or not strongly dependent on the relaxation after a sufficient thickness and that cooling rates affect the thicknesses of a-axis oriented BTO. For BTO in Si-integrated photonics, it is preferable to have either a majority a- or c-axis oriented BTO depending on device geometry. Therefore, we have found that the equivalent thickness of a-axis BTO can be controlled by adjusting heating and cooling rates.

Methods

The films investigated in this study are grown on double-side polished 2” Si wafers that were exposed to ozone to remove hydrocarbons before being loaded into an ultra-high-vacuum system that includes a custom DCA 600 oxide molecular beam epitaxy (MBE) growth chamber with a Staib reflection high energy electron diffraction (RHEED) apparatus and kSA 400 imaging system attached, along with an X-ray photoelectron spectroscopy (XPS) chamber that uses a VG Scienta R3000 hemispherical analyzer and monochromated Al Kα X-rays. More details of our vacuum system can be found in our previous work20,42.

Details of the growth of BTO and STO on Si can be found in Supplementary Note I. For our previous research20, the heating and cooling rates were kept at a constant 50 °C/min. In this project, we varied the heating and cooling rates for the BTO growth, using three different values, 50, 10 and 5 °C/min. To ensure that any results are due to varying the heating and cooling rate and not due to film quality, we closely monitored the RHEED images of the films to ensure that no phase segregation was seen due to the stoichiometry deviating away from a 1:1 Ba:Ti ratio and used XPS to confirm the stoichiometry at 50, 100 and 150 nm thicknesses for BTO. RHEED images and XPS results of the film confirming high quality stoichiometry and epitaxy can be found in Supplementary Note 1.

The crystal quality of the films is then investigated with X-ray diffraction using an Ultima IV diffractometer. For out-of-plane (OOP) measurements, a Ge monochromator was used to ensure high resolutions of about 0.01°, while for in-plane (IP) scans a 0.5° vertical soller slit was used, resulting in a maximum uncertainty of about 0.5°.

STEM experiments were conducted to investigate the microstructure of the films. Plan-view samples were prepared through conventional mechanical polishing followed by subsequent Ar ion milling. Plan-view STEM is more beneficial for understanding the lateral domain structure and domain size distribution, specifically for domains where the polar axis lies in the plane of the film, compared to conventional cross-section-view STEM. STEM imaging was performed using a JEOL JEM 300CF operated at 300 kV. High-angle annular dark-field (HAADF) STEM imaging was carried out with an inner collection angle of 70 mrad and a probe convergence semi-angle of 25.7 mrad. Large-area strain maps were obtained via precession diffraction using a JEOL 2800 microscope equipped with Nanomegas, operated at 200 kV.

Electrical contact pads made of chromium were deposited onto the film afterwards using a positive lithography method. The procedure is described extensively elsewhere46. This allows us to apply an electric field to the BTO thin films to perform transmission electro-optic measurements. The electro-optic setup used for these experiments has been reported previously42,44. Briefly, a New Focus TLB 6800 LN diode laser producing 1550 nm light that is linearly polarized by a Glan Taylor prism is focused onto 10 μm gaps between chromium contact pads that are oriented at various angles with respect to the BTO crystallographic axes (here, we use 0° and 45° pads). The contact pads have both an AC and DC voltage applied to them using the signal generator of a Ametek Signal Recovery Model 7270 DSP Lock-In Amplifier and Keithley B2902A Source/Measure Unit, respectively. Due to the electro-optic effect and BTO’s intrinsic birefringence, the transmitted light polarization acquires some amount of ellipticity, which is then re-linearized with a quarter-wave plate, but with a rotation. The light then passes through a Glan-Taylor prism which is rotated, and both the direct power and modulated power are measured with a Femto OE-200 photodetector. Due to the films being thin, the modulation due to just the DC voltage being applied (the direct power), is small and cannot be detected easily. This necessitates the use of the AC voltage whose modulation can be detected via the lock-in amplifier.