Lead-Free Perovskite Thin Films with Tailored Pockels-Kerr Effects for Photonics

Pockels and Kerr effects are linear and nonlinear electro-optical effects, respectively, used in many applications. The modulation of the refractive index is employed in different photonic circuits. However, the greatest challenge is in photonic elements for quantum computing at room temperature. For this aim, materials with strong Pockels/Kerr effects and χ(2)/χ(3) nonlinear susceptibilities are necessary. Here, we demonstrate composition-modulated strong electro-optical response in epitaxial films of (Ba,Ca)(Ti,Zr)O3 perovskite titanate. These films are grown by pulsed laser deposition on SrTiO3. Depending on the ratios of Ca/Ba and Ti/Zr, films show high Pockels or Kerr optical nonlinearities. We relate the variable electro-optic response to the occurrence of nanopolar domains with different symmetries in a selected composition range. These findings open the route to easily implement nonlinear optical elements in integrated photonic circuits.


Supplementary Note 1 -Lattice parameters from X-ray diffraction
The XRD patterns of the three (1−x)Ba(Zr 0.2 Ti 0.8 )O 3 − x(Ba 0.7 Ca 0.3 )TiO 3 (x=0.45; 0.50; 0.55) (BCTZ 100x) targets are presented in Figure S1 (a). All the patterns are indexed as a pseudo-cubic lattice (S.G.  for the sake of simplicity and comparative evaluation. As discussed in the main text, the BCTZ solid solution exhibits a "tilted" morphotropic phase boundary (MPB) separating the rhombohedral (R) and tetragonal (T) phases by an intermediate orthorhombic (O) phase near x=0.5 at room temperature [Refs. [1][2][3]. The evolution from a rhombohedral (for x=0.45) to a tetragonal (for x=0.55) symmetry is evident for the (200) pc peak, showing the splitting of the singlet rhombohedral (202) peak to the tetragonal doublet (002)/(200) (Figure S1 (b)). Thus, the BCTZ45 target pattern was refined in a rhombohedral symmetry (S.G. R3m) and the BCTZ55 target pattern in a tetragonal symmetry (S.G. P4mm). The resulting crystallographic parameters were transformed into the equivalent pseudo-cubic parameters. The pseudo-cubic lattice constant (a pc ) represents the cube root of unit cell volume for ABO 3 [Ref. 4] . The obtained data are listed in Table S1. The BCTZ50 pattern displays very broad and ill-defined reflections as it can be observed in Figure S1 (a-c). For example the (200) pc peak transforms from the singlet rhombohedral (202) peak for BCTZ45 to a very large (402) orthorhombic peak for BCTZ50 or, in the case of (310) pc reflection, the double rhombohedral peak (214)/(312) of BCTZ45 merged in an extremely large orthorhombic peak for BCTZ50 (Figure S1 (c)).
The intermediate orthorhombic phase has actually multiple close diffractions peaks or might coexist with a rhombohedral phase or a tetragonal phase [Ref. 2]. Consequently, due to its limited accuracy, the BCTZ50 target profile was refined in a cubic symmetry (S.G. Pm-3m) in order to obtain the pseudocubic lattice constant. As expected, the pseudocubic lattice parameters exhibit a linear increase with increasing Ba/Ca ratios as a result of the larger ionic radius of Ba 2+ (1.61 Å) with respect to Ca 2+ (1.34 Å) ( inset in Figure S1 (a)).   The out-of-plane (op) and in-plane (ip) lattice parameters (a op and a ip ) for the deposited films were calculated from the symmetric and asymmetric XRD scans, respectively [Refs. [5][6][7][8][9].
The axial ratio (or tetragonal distortion) was calculated as the ratio a op /a ip . The out-of-plane and in-plane strains due to the misfit with respect to the substrate were calculated as follows: where a sto =3.905 Å.

Supplementary Note 2 -Transmission electron microscopy data
High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) was carried out on BCTZ films. The STEM images have been drift-corrected for geometric phase analysis.
In Figure S3, we show a low-resolution HAADF-STEM image (Figure S3   Low-resolution HAADF-STEM images taken on BCTZ45 film (Figure S7 (b)) evidence a similar columnar aspect with BCTZ55 film (Figure S7 (a)) although, apparently, the density of columns seems higher in BCTZ55 than in BCTZ45. This can be related to a higher effective in-plane strain in BCTZ55, although the values listed in Table 1 (manuscript file) for the in-plane strain are rather similar. However, at a second look, one can notice that near the substrate interface the columnar density seems equally higher in both films, and that it is the behavior at some distance from the substrate which is different. This is correlated with in the in-plane coherence length values, extracted from XRD ( Table 1-  The upper layer -AZO; b) idem for the BCTZ45 film.

Supplementary Note 3 -Compositional analysis and elemental mapping
Information about chemical composition on the nanoscale is important for the understanding of BCTZ film structure and physical properties. Eventual chemical inhomogeneities can bias phase structure and bring strong consequences on the physical properties. In order to verify film composition, extended maps of the elements have been obtained by Super-X energy-dispersive X-ray spectroscopy (EDX), which allows to acquire large area elemental maps with high spatial resolution and also light element sensitivity.   The mapping of the elements have been also measured at atomic level. Figure S10 shows   The complex capacitance of the Au/BCZT/STO thin film capacitors with IDE configuration has been obtained by dielectric spectroscopy measurements carried out at ambient temperature between 1 kHz and 10 MHz yield.
The in-plane dielectric constants of the BCTZ45, BCTZ50 and BCTZ55 films have been calculated by using the analytical model proposed in Refs. [10][11], which gives for the dielectric constant of the thin film  the following formula where  s is the dielectric constant of the substrate, h is the film thickness, C n is the measured capacitance of the IDE structure normalized to the finger length (L) and to the number of fingers (2N-1), while C K is a constant depending on IDE geometry. In the case of IDE patterns with equal finger width and spacing, C K = 4.53 pF/m (Refs. [10][11]). The dielectric constant of the STO substrate is 300, as reported in the datasheet.
However we have also measured this value, by depositing IDE structures on the surface of the STO substrates and applying the same model to extract the dielectric permittivity from the measured capacitance.

Supplementary Note 5 -Evaluation of electrooptic coefficients from spectroscopic ellipsometry
The change or refraction index due to electric field n (E) is related to the voltage-induced wavelength shift Then the wavelength shift can be expressed as: Thus the relationship between the refraction index shift and the phase shift is obtained as: The spectroscopic ellipsometry measurements under applied electric field for revealing the electro-optic effects have been performed at wavelength 500 nm and an angle of incidence 60 0 , as described in Methods.
The measured phase shift values have been used to calculate the birefringence shift n, according to the equation (7). Furthermore we obtained the electro-optic coefficients by fitting significant parts of the graphs of birefringence shift n(E) with polynomials of first degree (for BCTZ 45 and BCTZ 55) and of third degree (for BCTZ 50). The coefficients of the polynomials have been used to calculate the electro-optic coefficients as further described.
For the Pockels effect the refractive index change under an applied electric field is given by [Lines-Glass]: For the BCTZ50 thin film the best fitting has been achieved with a polynomial of third degree. From the fitting parameters the Pockels and Kerr effective coefficients have been extracted.