Introduction

Ferroelectric materials, possessing excellent ferroelectric and electro-optical (EO) properties, have fostered the development of electronic and optoelectronic devices, e.g., sensors, actuesators, nonvolatile memories, and optical communication systems.1,2,3,4,5,6,7,8,9,10 In those applications, it is critical to understand ferroelectric domain orientations and domain switching through external stimulation, where the domain orientations have an intense influence on ferroelectric properties and the fluctuation of domain volume fractions due to domain switching or backswitching dominates the efficiency and stability of ferroelectric devices.11,12,13,14,15,16,17,18,19,20,21,22,23 Therefore, the precise determination of ferroelectric domain orientations and their volume fractions is required not only in view of ferroelectric device engineering but also in the corresponding physics mechanism, such as fatigue and retention.

A lot of efforts have been invested to evaluate domain structures of ferroelectrics. The typical methods including piezoresponse force microscopy (PFM) and transmission electron microscopy (TEM) provide high spatial resolution to visualize the local domain structures.24,25,26,27,28,29 However, they still have some drawbacks in accurately measuring domain volume fractions, especially for the in-plane domains in the disordered multi-domain system, where the PFM is only able to sense the domain structures near the material surface rather than the domains underneath, and the TEM is a ‘destructive’ characterization technique with a complicate process of specimen preparation, which usually presents the domain structures at a local region far from the whole picture of the domains in the sample.30,31,32,33,34 The precise determination of the domain distributions in ferroelectrics with complex domain structures in a non-destructive manner has not been achieved. Recent advances have pointed out that the second harmonic generation (SHG) is a promising all-optical approach for probing domain structures in ferroelectrics, as the symmetrical-dependent SHG signals present a unique response to the domain structures, and the adjustable probe size could adapt to the scale of the semiconductor devices.35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 Moreover, this optical approach can readily access the domain structures in the heterostructures that the ferroelectric layer is covered by non-ferroelectric materials.

Since the SHG response is highly sensitive to the polarization angle of the incident light with respect to ferroelectric domain orientations, the polarization-dependent SHG signals are usually used to study domain structures.50,51,52,53 However, in a ferroelectric with many possible domain variants, the quantitative analysis becomes very complex, which makes it difficult to achieve a completed picture for domain structures through the polarization-dependent SHG response only along the fixed domain directions of a ferroelectric sample.37,42,54,55 To solve this problem, an azimuth-dependent SHG is introduced to distinguish the predominant domain orientation from many random variants, because a rotation of a sample around z-axis can change the ferroelectric polarization directions of individual domains relative to the incident beam without external electric field, where different oriented domains lead to different SHG responses. Therefore, in this work, we have developed an improved ferroelectric domain characterization technique by collecting azimuth-polarization-dependent SHG signals with varying both the polarization angle of the incident beam and the azimuth angle of sample relative to the beam. By fitting the SHG signals to an established theoretical model, it is possible to correlate the SHG signals to the domain distributions in the measured area. Using this method, we give examples on the rhombohedral BiFeO3 (BFO) thin films with 71° and 109° domain walls, where the domain orientations and their volume factions are determined based on the collected SHG signals. Moreover, we also apply this SHG method to many other ferroelectric systems for domain structure characterization, such as, tetragonal BFO, Pb(Zr0.2Ti0.8)O3 (PZT), and BaTiO3 (BTO) thin films.

Results

The experimental setup of SHG is schematically shown in Fig. 1a. A laser beam is incident on a ferroelectric sample with an incident angle γ (γ = 45°) and the generated SHG signals are collected in the reflection configuration. The linearly polarized fundamental electric-field \(E^{\mathrm{\omega}} (\varphi )\) of the incident light can be rotated through adjusting the angle φ in the range of 0° to 360°, where φ = 0° and φ = 180° correspond to p-polarized light field of \(p_{\mathrm{in}}^ +\) and \(p_{\mathrm{in}}^ -\), and, φ = 90° and φ = 270° correspond to s-polarized light field of \(s_{\mathrm{in}}^ +\) and \(s_{\mathrm{in}}^ -\) (\(p_{\mathrm{in}}^ +\) and \(s_{\mathrm{in}}^ +\) are abbreviated as pin and sin). The lab frame (s, k, z) is defined with s axis parallel to the direction of sin light field, and the sample coordinate (X, Y, Z) is defined to describe the direction of sample edges with respect to the optics. The sample can be rotated by a variable angle θ in the s–k plane, where θ = 0° is defined as the initial position when the X axis coincides with the direction of sin light field. The generated p or s polarized (pout and sout) SHG signals are selected to detect by an analyzer, and the localized SHG polarimetry system is performed. The nonlinear polarization of SHG can be expressed as \(P_{\mathrm{i}}^{\mathrm{2\omega} } = d_{\mathrm{{ijk}}}E_{\mathrm{j}}E_{\mathrm{k}}\), where \(d_{\mathrm{{ijk}}}\) is the nonlinear optical tensor, and the crystallography coordinate (X1, X2, X3) is established to denote the orientation of nonlinear optical tensor (\(d_{\mathrm{{ijk}}}\)) coordinates of each individual domain variants (the direction of each individual domain variants is along the X3 axis). An assumed arbitrarily oriented domain variant u is defined by three Euler angles (η, β, δ) in the sample coordinate (X, Y, Z) as shown in Fig. 1b, and the sample coordinate (X, Y, Z) is defined in the lab coordinate (s, k, z) by angle θ as shown in Fig. 1c. The nonlinear polarizations for a domain u are calculated by transforming the nonlinear tensor to the lab frame (s, k, z) with the rule \(T_{\mathrm{ijk}}^{\mathrm{new}} = a_{\mathrm{{il}}}a_{\mathrm{jm}}a_{\mathrm{kn}}T_{\mathrm{lmn}}^{\mathrm{old}}\), where T is the third rank property tensor, and \(a_{\mathrm{il}}{\mathrm{ = \hat e}}_{\mathrm{i}}^{\mathrm{{new}}} \cdot {\hat{\mathrm e}}_{\mathrm{i}}^{\mathrm{{old}}}\) (i, l = 1, 2, 3) is the corresponding coordinate transformation matrix. The calculated nonlinear polarization components \(P_{\mathrm{i}}^{2{\mathrm{\omega}} ,{\mathrm{u}}}\) (along i direction) are determined by the angle η, δ, φ, β, γ, and θ, where the details of the above calculations are shown in the Supplementary Materials. Moreover, the signals generated by domain wall are mostly negligible in the analysis due to its much smaller relative area fraction compared with domains. Therefore, the pout and sout SHG electric fields \(E_{{\mathrm{(p,s)}}}^{2{\mathrm{\omega}} ,{\mathrm{u}}}\) generated by a domain variant u can be defined as following:56

$$E_{\mathrm{p}}^{2{\mathrm{\omega}} ,{\mathrm{u}}} = \left| {S_{\mathrm{p}}\left( {F_{\mathrm{s}}P_{\mathrm{z}}^{2{\mathrm{\omega}} ,{\mathrm{u}}} - F_{\mathrm{c}}P_{\mathrm{k}}^{2{\mathrm{\omega}} ,{\mathrm{u}}}} \right)} \right|,$$
(1)
$$E_{\mathrm{s}}^{2{\mathrm{\omega}} ,{\mathrm{u}}} = \left| {S_{\mathrm{s}}P_{\mathrm{s}}^{2{\mathrm{\omega}} ,{\mathrm{u}}}} \right|.$$
(2)
Fig. 1
figure 1

a Schematic diagram of SHG experimental system, where lab frame (s, k, z) is defined with s axis parallel to the sin incident beam. b Schematic sketch of arbitrarily oriented domain variant u in sample coordinate (X, Y, Z). The β is the angle between X1 axis and the intersection line (\(\tilde XL\)) of X–Y and X1–X2 plane. The η is the angle between X axis and line \(\tilde XL\). The δ is the angle between X3 axis and Z axis. c Schematic sketch of the defined sample coordinate (X, Y, Z) in the lab coordinate (s, k, z), where the θ is the angle between s and X axes, or, k and Y axes

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The meanings of Sp, Ss, Fs, and Fc are shown in the Supplementary Materials. The total SHG intensity \(I_{{\mathrm{(p,s)}}}^{2{\mathrm{\omega}} }\) contributed from all the individual domains can be expressed as:

$$I_{{\mathrm{(p,s)}}}^{2{\mathrm{\omega}} } = \left| {E_{{\mathrm{(p,s)}}}^{2{\mathrm{\omega}} }} \right| = \left| {{\sum} {F_{\mathrm{u}}} E_{{\mathrm{(p,s)}}}^{2{\mathrm{\omega}} ,{\mathrm{u}}}} \right|^2 + b_{{\mathrm{(p,s)}}}.$$
(3)

\(F_{\mathrm{u}}\) is the fraction ratio of the domain variant u and the \(b_{{\mathrm{(p,s)}}}^{}\) is artificially added to simulate the background. Based on the Eq. (3), we can know that the SHG intensity increases with the increasing of volume fraction \(F_{\mathrm{u}}\), and the total SHG electric field \(E_{{\mathrm{(p,s)}}}^{2{\mathrm{\omega}} }\) originates from the superposition of fields from all individual domains, where the “+” and “−” fields are compensated. Here, the positive oriented of in-plane (IP) and out-of-plane (OP) domain components are defined: along s and -k, and, -z axes, respectively. According to the above model, some criterions can be established. Firstly, the IP domain components can be distinguished by analyzing the azimuth-polarization-dependent SHG patterns, because the changes of SHG patterns caused by sample rotation are attributed to the IP domain components. Secondly, the OP domain components can be verified by comparing with the SHG patterns at θ = 0° and 180°, because the IP domain components give an opposite sign of SHG fields with same magnitude after a sample rotation by 180°, if the sample has no OP domain components, the SHG patterns should be same when the θ equals 0° and 180°. Thirdly, the vertical relationship between IP domain components and sin light filed can be distinguished by observing the sin–sout SHG signals, since the domain components do not contribute to sin–sout SHG signals when they are perpendicular to the direction of sin light filed (the OP domain components always do not generate sin–sout signals, and the details are shown in Supplementary Materials). In our experiments, only the sout SHG signals are selected as an output, and the domain distributions can be figured out by fitting the measured sout SHG intensity.

Discussion

The BFO thin films are chosen as a model system in our work. This films have four structural variants lied along <111>directions with eight distinct polarization variants on the (001)C perovskite surface (Fig. 2a). The r1, r2, r3, and r4 correspond to \(P_1^{ + / - }\), \(P_2^{ + / - }\), \(P_3^{ + / - }\), and \(P_4^{ + / - }\), respectively, where the “+” and “−” stand for “up” and “down” polarization directions.57,58,59,60 The allowed polarization configurations can form domain boundaries along either {101}C or {100}C, so called 71° or 109° domain walls, respectively. Firstly, the BFO film with 71° domain wall is studied by SHG. The IP-PFM image of this thin film is shown in Fig. 2b, which exhibits the ordered 71° domain arrays.59 The possible variant patterns of BFO film with 71° domain wall are (011)-r1/r2, \(\left( {\bar 10\bar 1} \right)\)-r2/r3, \(\left( {0\bar 1\bar 1} \right)\)-r3/r4 and (101)-r4/r1.58 The projected polarizations of \(P_1^ -\), \(P_2^ -\), \(P_3^ -\), and \(P_4^ -\) are shown by the sense of arrows in Fig. 2c (the sample coordinate axes are defined as X = [100]p, Y = [010]p, and Z = [001]p directions of the BFO film, respectively). The polarization-dependent SHG patterns with θ = 0°, 90°, and 180° of BFO film with 71° domain wall are shown in Fig. 2d-f, respectively. All the SHG patterns present a shape of two double lobes, and the pattern shape changes with the rotation of angle θ. Therefore, the BFO film with 71° domain wall has IP domain components. After a sample rotation by 180°, one can see that the SHG pattern in Fig. 2f is different from that in Fig. 2d, which indicates the existence of OP domain components in BFO film with 71° domain wall. Moreover, strong sin–sout SHG signals can be found in Fig. 2d when the θ equals to 0°, while the sin–sout signals disappear in Fig. 2e when the θ equals to 90°. In fact, the sin–sout SHG signals at the θ = 0° are only generated by the IP domain components of \(\left[ {100} \right]_{\mathrm{p}}^{ + / - }\) (\(\left[ {100} \right]_{\mathrm{p}}\) or \(\left[ {\bar 100} \right]_{\mathrm{p}}\)), since the domain components of \(\left[ {010} \right]_{\mathrm{p}}^{ + / - }\)are perpendicular to the sin light field in this case. Therefore, the IP domain components could be only reasonably existed along \(\left[ {100} \right]_{\mathrm{p}}^{ + / - }\). Accordingly, the possible domain variants in the BFO film with 71° domain wall are r2/r3 and r4/r1.

Fig. 2
figure 2

a Schematic of four different structural variants and eight domain variants in (001) rhombohedral BFO film. b IP-PFM image of the BFO thin film with 71° domain wall. c Possible domain patterns for BFO film with 71° domain wall. The projected polarizations of the \(P_1^ -\), \(P_2^ -\), \(P_3^ -\), and \(P_4^ -\) are shown by the sense of arrows. d–f Polar plots of measured s-polarized SHG intensity as a function of polarization angle φ with θ = 0°, 90°, and 180°, respectively. g Contour pattern of monitored s-polarized SHG intensity vs. sample rotation angle θ and polarization angle φ. h The s-polarized SHG intensity as a function of angle θ under the fixed pin and sin incident light fields. i Fractions of domain variants in the BFO thin film with 71° domain wall. The symbols present the experimental data, and the lines indicate the theoretical fits. Comparison of the polarization-dependent SHG patterns with θ = 0° and 90° are as insets in d, where the green is the SHG pattern at θ = 90°. The schematic illustrations of the domain variants at angle θ = 0°, 90°, and 180° relative to incident beam are as insets

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To further investigate the domain variants of BFO film with 71° domain wall, the azimuth-polarization-dependent SHG signals are collected at intervals of 10° in the range of 0° to 360°. The SHG intensity vs. the angle φ and θ are presented in the contour pattern in Fig. 2g. The maximum of SHG intensity at different polarization angles φ under a certain azimuth angle θ are defined as “SHGM-P”, where the intensity of “SHGM-P” changes with the azimuth angle θ. It can be found that the maxima intensity of “SHGM-P” is present at θ = 180°, and the minima value is located at θ = 90° (the comparison of the polarization-dependent SHG patterns with θ = 90° and θ = 270° is shown in the Supplementary Materials, Fig. S1). The intensity of “SHGM-P” is broadly larger at θ = θ0 + 180° (θ0 = 0°~180°) than that at θ = θ0, where the comparison of the intensity of “SHGM-P” at θ = θ0 and θ = θ0 + 180° are presented in the Supplementary Materials (Fig. S2). As a matter of the fact, the intensity of “SHGM-P” would be enlarged after a rotation of sample by 180°, when the signs of the SHG fields from net IP and OP domain components are opposite at initial states, otherwise, the SHG intensity would be decreased. Hence, we can infer that the signs of the SHG fields from net IP and OP domain components of BFO film with 71° domain wall is opposite at θ = θ0, which exhibits as: “+” and “−”, or, “−” and “+”. Therefore, the orientations of net IP and OP polarizations are along \(\left[ {100} \right]_{\mathrm{p}}\) and \(\left[ {001} \right]_{\mathrm{p}}\), or, \(\left[ {\bar 100} \right]_{\mathrm{p}}\) and \(\left[ {00\bar 1} \right]_{\mathrm{p}}\). Summing up, the possible domain variants in the BFO film with 71° domain wall are r4/r1. Then, we extract the SHG signals as a function of angle θ under the fixed pin and sin incident light fields, and the results of pin–sout and sin–sout are shown in Fig. 2i. The line profiles have the same varying tendency and the intensity peaks are located at θ = n*180° (n = 0, 1, 2), while the valley positions are located at θ = 90° + n*180° (n = 0, 1). We know that the SHG intensity from the OP domain components is fixed under the pin–sout geometry, and it is not existed under the sin–sout geometry, thus the peak signals are mostly attributed to IP domain components of \(\left[ {100} \right]_p^{ + / - }\) at θ = n*180° (n = 0, 1, 2). Therefore, those azimuth-dependent SHG intensity features further illustrate that the net IP domain components are only along \(\left[ {100} \right]_{\mathrm{p}}^{ + / - }\) directions. Moreover, the volume fractions of the net polarization vectors are analyzed by fitting the measured azimuth-polarization-dependent SHG signals by using Eqs. (2) and (3) (the results are shown in Fig. 2i), where the volume fractions of net polarization vector (Pi) is defined as: the differences of the fractions of the positive (\(P_{\mathrm{i}}^ +\)) and negative (\(P_{\mathrm{i}}^ -\)) domains. The BFO film with 71° domain wall possesses the net polarization vectors of P4 and P1 with both volume fractions of 50%. In addition, an estimation of domain fraction was made by contrast statistics based on vector PFM (Supplementary Fig. S6 and Fig. S7), which is agreement with our SHG results.

The BFO film with 109° domain wall is also studied by SHG. The IP-PFM image exhibits the ordered 109° domain arrays (Fig. 3a).60 The possible variants for BFO film with 109° domain wall are (100)-r1/r2, (010)-r2/r3, (100)-r3/r4, and (010)-r4/r1,58 and the projected polarizations of the \(P_1^ +\), \(P_2^ -\), \(P_3^{\mathrm{ + }}\) and \(P_4^ -\) are shown by the sense of arrows in Fig. 3b. Figure 3c-e shows the polarization-dependent SHG patterns with θ = 0°, 90°, and 180°, respectively. The SHG pattern shape and signal intensity are in greatly differences, which implies the existence of both IP and OP domain components. Meanwhile, we can see that strong sin–sout SHG signals both present in Fig. 3c, d, which suggests the existence of net IP domain components along \(\left[ {100} \right]_{\mathrm{p}}^{ + / - }\) and \(\left[ {010} \right]_{\mathrm{p}}^{ + / - }\). Moreover, the intensity of sin-sout signals in Fig. 3d is significantly higher than that in Fig. 3c, which means that the net IP domain population of \(\left[ {010} \right]_p^{ + / - }\) should be more than that of \(\left[ {100} \right]_p^{ + / - }\). Therefore, the possible variant patterns of BFO film with 109° domain wall are r2/r3 and r4/r1. The SHG intensity vs. the angle φ and θ is shown in Fig. 3f. One can see that the maximal intensity of “SHGM-P” is located at θ = 270°, and the intensity of “SHGM-P” at θ = θ0 + 180° is obviously stronger than that at θ = θ0 (the change process of the intensity of “SHGM-P” at θ = θ0 and θ = θ0 + 180° are shown in the Supplementary Materials, Fig. S2), which suggest that the signs of SHG fields from the largest population of net IP and OP domain components are opposite at initial states. To further determine the signs of fields from the two IP domain components, the azimuth-dependent SHG response of pin–sout are analyzed. In Fig. 3g, the line profile presents two peaks at θ = 90° and 270°, and the maxima is located at 270°. We can know that the maximal SHG intensity of pin–sout occurs only when the sign of the fields from all IP and OP domain components are at same under pin light field. Thus, the sign of the fields from two IP domain components are in the same at θ = 270°, while they are opposite at θ = 0°. Therefore, the orientations of two net IP and one OP polarizations are along \(\left[ {\bar 100} \right]_p\), \(\left[ {0\bar 10} \right]_p\), and [001]p, or, [100]p, [010]p, and \(\left[ {00\bar 1} \right]_{\mathrm{p}}\), where the signs of the fields exhibit as: “−”, “+”, and “−”, or, “+”, “−”, and “+”. In this case, the possible domain variants of \(P_4^ - /P_1^ +\) and \(P_4^ + /P_1^ -\) can be excluded in the BFO film with 109° domain. This conclusion is further supported by the sin–sout SHG signals as shown in Fig. 3g, where the line profile presents four peaks at θ = 45° + n*180° (n = 0, 1) and θ = 135° + n*180°. In fact, when the θ = 45° + n*180°, the sin–sout SHG signals are only generated by IP projections of domain \(P_{\mathrm{{i}} + 2}^{{\mathrm{ + }}/ - }\) (i = 0, 2), because the IP projections of domain \(P_{i + 1}^{{\mathrm{ + }}/ - }\) are perpendicular to the sin light field in this case. In contrast, when the θ = 135° + n*180°, the sin-sout signals are only generated by IP projections of domain \(P_{i + 1}^{{\mathrm{ + }}/ - }\), since the IP projections of domain \(P_{i + 2}^{{\mathrm{ + }}/ - }\) are perpendicular to the sin light field in that case (the schematic illustrations of the domain variants at θ = 45° and θ = 135° with respect to incident light are shown as insets in Fig. 3g). Thus, the larger SHG intensity at θ = 135° + n*180° suggests that the population of the net IP polarizations from Pi+1 are more than that from Pi+2 in the BFO film with 109° domain wall. Accordingly, the possible domain variants of the BFO film with 109° domain wall are r2/r3, where the population of the net ferroelectric polarization from P3 are larger than that from P2. By fitting the measured SHG signals, the volume fractions of net P2 and P3 in the BFO film with 109° domain wall can be determined, i.e., 25.5% and −29.8%, respectively (Fig. 3h), and a further analysis of the domain variants in this BFO film are presented in the Supplementary Materials. Moreover, by correlating the BFO domain structures and contour patterns shown in Figs. 2g and 3f, we can draw the conclusions that the inclined stripes are attributed to the rhombohedral phase structures in the BFO films. The BFO film with 71° domain wall exhibits larger SHG intensity than that in the BFO with 109° domain wall, due to the larger population of net IP and OP polarizations in the BFO film with 71° domain wall. The stripes of the contour pattern in the BFO film with 71° domain wall are “discontinuous”, while they are “continuous” in the BFO film with 109° domain wall, this results are largely determined by the net IP domain components in the BFO films where the BFO film with 71° domain wall only has one direction of net IP domain components along \(\left[ {100} \right]_{\mathrm{p}}^{ + / - }\), but there are two directions of net IP domain components along \(\left[ {100} \right]_{\mathrm{p}}^{ + / - }\) and \(\left[ {010} \right]_{\mathrm{p}}^{ + / - }\) for BFO film with 109° domain wall in our experiments. The calculated contour pattern of s-polarized SHG intensity vs. angles θ and φ was calculated based on the established azimuth-polarization-dependent model (Supplementary Fig. S8), which further support the above conclusions.

Fig. 3
figure 3

a IP-PFM image of the BFO thin film with 109° domain wall. b Possible domain patterns for BFO film with 109° domain wall. The projected polarizations of the \(P_1^ +\), \(P_2^ -\), \(P_3^ +\), and \(P_4^ -\) are shown by the sense of arrows. c–e Polarization-dependent s-polarized SHG patterns with θ = 0°, 90°, and 180°, respectively. f Contour pattern of monitored s-polarized SHG intensity vs. angles θ and φ. g Azimuth-dependent SHG intensity under the pin–sout and sin–sout geometry. h Fractions of domain variants in BFO thin film with 109° domain wall. The schematic illustrations of the domain variants at θ = 45° and θ = 135° with respect to incident light are as insets

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To further illustrate the relationship between azimuth-polarization-dependent SHG signals and domain variants, the typical tetragonal (001)-oriented BTO, PZT, and BFO are also investigated. The possible domain variants of (001)-oriented BTO, PZT, and T-BFO are shown in Fig. 4a, where those films have six polarization orientations of \(P_1^{{\mathrm{ + }}/ - }\), \(P_2^{{\mathrm{ + }}/ - }\), and \(P_3^{ + / - }\). Their SHG intensity as a function of angle φ and θ are presented in Fig. 4b–d, respectively. The domain orientations and their corresponding volume fractions are measured, and the results are shown in Fig. 4e. It can be seen that the BTO film only has OP domains, and the PZT and BFO films have majority OP domains and minority IP domains, while the BFO film shows more population of IP domains than that in the PZT film. By observing the SHG contour patterns in Fig. 4a–c, we can find that all the stripes in SHG pattern are horizontal, and the stripes are continuous and invariant from BTO film, while they are continuous but not uniform from PZT film and they are partial discontinuous from BFO film. Based on that, we can deduce that the tetragonal (001)-oriented ferroelectric system exhibits horizontal stripes, and the stripes change from continuity to discontinuity when the population of net IP domains are increasing gradually. We note that the SHG method has resolution limitation comparing with PFM techniques, and its resolution is in the order of hundreds of nanometers. However, the SHG also exhibits the advantages of the adjustable spot size, which can be used for the characterization of ferroelectric devices.

Fig. 4
figure 4

a Schematic of domain variants of (001)-oriented tetragonal BTO, PZT, and BFO thin films. Contour pattern of s-polarized monitored SHG intensity vs. the angles θ and φ, b BTO, c PZT, and d BFO films. e Fractions of domain variants in the BTO, PZT, and BFO thin films

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In summary, we report an optimized SHG technique for ferroelectric domain characterizing, in which the correlation between SHG response and domain distributions are established. Based on this all-optical SHG method, all the domain variants and its population in BFO ferroelectric films are determined. We also apply our method to many other perovskite ferroelectrics, i.e., T-PZT, T-BTO, and T-BFO. This work provides an effective and all-optical method to determine the domain distribution for ferroelectric thin films and devices including the field of multifunctional heterostructures which combine with functional metals and complex oxide thin films.

Methods

The (001)-oriented rhombohedral (R-phase) BiFeO3 (BFO) films of approximately 60 nm thick with 71° and 109° domain wall were grown on SrRuO3-buffered and no-buffered DyScO3 (110) substrates by pulsed laser deposition (PLD), respectively. The (001)-oriented tetragonal (T-phase) BaTiO3 (BTO, 20 nm, grown on SrRuO3-buffered SrTiO3 substrate), BFO (40 nm, grown on LaNiO3-buffered LaAlO3 substrate) and Pb(Zr0.2Ti0.8)O3 (PZT, 150 nm, grown on SrRuO3-buffered SrTiO3 substrate) were also prepared by PLD. The domain structures were characterized by commercially available AFM platform (Dimension Icon AFM, Bruker) and the crystalline structure were characterized via X-ray Diffraction (Rigaku-D/Max 2500) with the Cu Kα radiation.

The SHG measurements were performed by using 800 nm laser (150 fs, 10 nJ, 76 MHz) generated by a coherent Ti:sapphire pulsed laser as the fundamental laser beam. This fundamental laser beam was focused by a long-focus lens onto the sample with a focal spot diameter of ~100 μm and the incident peak intensity is ~10 MW/cm2 at the sample position. The generated SHG signals from the sample were detected by a photomultiplier tube (PMT) with a fixed incident angle of 45° (γ = 45°) in the reflection geometry. The long-pass filter was located in front of the sample to pass through the fundamental laser beam, and the bandpass interference filter was installed behind the sample to filter out the fundamental laser beam. The Glan polarizer was rotated to adjust and analyze the generated SHG signals from the sample at 0° and 90° configurations, which corresponds to p-polarized (p-out) and s-polarized (s-out) SHG signals, respectively.

Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.