1. Introduction

Lithium Niobate is a key material for integrated optical and non-linear photonics devices [1–4]. A critical step in exploiting the optical properties of lithium Niobate is to engineer its ferroelectric domains at micrometric scales [5–7]. Many efforts have been made to achieve good control of the domain reversal process and, in this regard, attention has been focused on the presence of the internal field (IF) that influences the required coercive fields [8,9]. The first question is: which property of the crystal lattice determines the IF? Several studies suggest that it originates from the non-stoichiometric defects associated with crystal growth from a congruent melt [10–13]. Here we show the defect dependence of the IF using a full-field interferometric method. The IF is measured directly on some clusters of defects embedded in a stoichiometric matrix. Indeed, the IF value is found to grow near defects and vanish far from them.

In the last ten years, many radio-spectroscopic methods, as nuclear magnetic resonance (NMR)[14], electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) [15] have been applied to study the crystal lattice and defect structure of Lithium Niobate (LN). Moreover, synchrotron X-ray diffraction has been used to image domains by topography [16] and phase contrast [17,18] and to measure the strain field around a ferroelectric domain [19].

On these bases, a defect model was developed according to which a defect complex present in a non-stoichiometric LN crystal includes a Niobium antisite (Nb_Li ) ⁴⁺, i.e. a Niobium atom in a lithium site, and four lithium vacancies (V_Li )- [20]. Other indirect evidence supporting this defect model come from an analysis of the chemical and physical properties of MgO doped LN [21 and refs. therein], because of a strong correlation existing between the intrinsic and extrinsic defect subsystems [22].

This defect model explains well the IF existence as well as domain switching features like backswitching and domain stabilization times (ref. 12 and refs therein). In fact, the defect complex is associated with an electrical dipole moment that has two contributions: one comes from the (Nb_Li ) ⁴⁺ antisite defect whereas the other contribution arises from the relative arrangement of Lithium vacancies (V_Li )^- around a Niobium antisite defect (Nb_Li ) ⁴⁺. Before any external field is applied, defect generated dipoles are aligned, thus stabilizing the polarization state of the virgin crystal. After an electrical domain reversal, the two components of the defect polarization present a different behaviour. The inversion time scale of one component is observed to be faster than the other one, which requires a thermal annealing to occur [12]. The stabilization time of ferroelectric inverted domains is related to the fast-switching defect generated dipole while the slow-switching one causes the asymmetry in the polarization-electric field hysteresis loop, i.e. the IF. Its magnitude is defined as half the difference between the field required for forward poling E_f and that required for reverse poling E_r (E_int=(E_f-E_r)/2). A first proof of defect dependence of IF was given by Gopalan et al. [11]. They compared the electric fields (E) required for ferroelectric domain reversal between the conventional congruent LN crystal and the stoichiometric (SLN) one. It was found that the electric field required for spontaneous polarization (Ps) switching in a stoichiometric crystal was about one fifth of that necessary in a congruent one. The IF calculated from the Ps asymmetry versus E hysteresis disappears in a SLN crystal.

However, it is remarkable that SLN samples grown with different techniques, like double Czochralski crucible from Li rich melt [23] or potassium enriched melts [24], have different intrinsic defect concentrations and, above all, the Li/Nb ratio is often not constant throughout the boule. Therefore, classical IF measurements [see ref. 11] performed on two wafers with the same nominal stoichiometry can give different results and thus an ambiguous response on stoichiometric defect dependence of IF. Recently, we have performed an interferometric quantitative analysis of IF in congruent LN samples of uniform composition by measuring the optical phase retardation in opposite ferroelectric domains [25].

2. Methods and experimental results

By using a Mach-Zehnder interferometer [25] in a microscope configuration and a reflective grating interferometer (RGI), both employing a digital holography (DH) technique [26], we studied an off-congruent z-cut single domain crystal. The sample measures (25×25×10) mm3 and was grown by a Czochralski method.

As mentioned before, in order to obtain SLN composition, it is necessary to grow crystals starting from a lithium rich melt, or by adding K2O during the growth process. The growth of defect-free SLN crystals from the melt is quite difficult. Both mechanical twinning [27] and lithium excess micro-clusters are possible due to compositional variation on the melt-crystal interface during the growth of off-congruent bulk LN crystals. There are not enough experimental observations that give a thorough understanding of such defects, however. Lithium excess micro-clusters are generated during the crystallization process. They are commonly present in a limited area close to the interface and come from the bottom of the crucible from which they are transported by the natural convection currents. The clusters force the formation of lithium aggregates in the crystal lattice, generating a micro-region with a different structure with typical dimensions of 30–50µm (Fig. 1). Only half of the tested off-congruent sample area was domain reversed [28]. During electric poling, however, defects in the virgin sector act as domain seeds. As a consequence, an inverted hexagonally shaped area appears around each defect (Fig 1(a)), and, therefore, several inverted ferroelectric domains are obtained. Some of their domain walls are close to the clusters of defects while others are far from them (Fig 1(b)).

 

Fig. 1. (a) Optical microscope image of a defect surrounded by an inverted hexagonally shaped domain, visualized by crossed polarizers. (b) Hexagonally poled zone (z+) clearly visible around a defect, after etching.

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In the experimental diagnostic set-up, a frequency doubled Nd:Yag (532 nm wavelength) provided the laser radiation for the interferometer, and the crystal wafer was inserted in one arm of the interferometer. The plane reference wave and the object wave, which passed through the sample, interfere at a CCD camera. A digital hologram was electronically recorded and its wave front reconstruction obtained through a Fresnel–Kirchoff integral [26].

The sample was mounted in a Plexiglas holder and electrical contact on the sample surface was obtained by liquid electrodes. This configuration insured both the homogeneity of the external electric field within the sample, due to the uniform adhesion of the electrolyte to the crystal surface and transparency along the z direction, which allows illumination of the sample through the quartz windows during the poling process and the following measurements. Domain inversion was achieved by applying one positive high voltage pulse, slightly exceeding the coercive field of the material (<21kV/mm for LN), to the z+ face of the crystal sample. A Signal Generator drove an High Voltage Amplifier (2000×) to deliver +12kV and a series resistor Rs=100 MΩ was used to limit the current flowing in the circuit. During the poling, a displacement current I_pol flows in the external circuit due to the charge redistribution within the crystal structure. This current was measured by acquiring the voltage drop across the resistor R_m through the oscilloscope, while a high voltage probe was used to measure the voltage across the sample, and consequently the coercive field [28].

Just after electric field poling, was possible to measure the “static” IF, i.e., with no external voltage applied to the sample, by the reconstructed phase maps. To this aim, optical phase retardation was obtained by double exposure holographic interferometry [25].

Figure 2(a) shows the numerically reconstructed phase-map of the off-congruent sample [26]. It is clearly shown that a residual phase-step was localized at the wall boundaries, close to the defects. By contrast, the phase-difference appears to be almost zero across the domain wall far from the defect, at the image center (Fig. 2(a)). The phase-profile along a row of the data matrix (Fig. 2(b), top) allows us to compare quantitatively the phase difference across the two kinds of boundaries (Fig. 2(b), bottom). Null phase results across the domain wall far from defect, while a phase difference of ~0.9 rad was measured between opposite ferroelectric domains across the inverted hexagon. By evaluating this phase step, (indicated by the arrow in Fig. 2(b) down) across the hexagonal boundary, it was possible to measure the internal field through the formula Δϕ=(2π/λ)(dΔn₀+Δd(n₀-1)=(2π/λ)(-r₁₃${\mathrm{n}}_0^3$+2d₃₃(n_0-1)) d*E_int, where d was the crystal thickness, Δd was the piezoelectric thickness change generated by the electric field E_int, which depends on the component d₃₃ of the piezoelectric strain tensor (d₃₃=7.57×10^-12 m/V), while r₁₃ and n₀ are the electro-optic coefficient and the ordinary refractive index, respectively. An IF equal to ~735 V/mm was measured close to the defect, and, therefore, these measurements unequivocally demonstrate that the IF was caused by defects.

Beyond the phase step across the domain wall of hexagonally poled area, we can note an high variation of phase across the defect in the phase profile shown in Fig. 2(b). It was surely due to the different lattice structure of the defect with respect to stoichiometric matrix in which it was embedded. We were not directly interested in this, however, since our aim was only to demonstrate that the presence of the defect affects the properties of the crystal in that neighbourhood.

 

Fig. 2. (a) In the optical phase retardation map, a null phase step is noticeable across the domain boundary (black line) between the reversed (B) and un-reversed (A) regions whereas a phase step is visible in proximity of defects. (b) (Upper portion) Close-up of the phase map in which a hexagonally shaped reversed area is evident around a defect. (Lower portion) Plot showing the phase profile along the dashed line.

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Afterwards, we compared the results obtained by our interferometric technique, with its micrometric resolution, to those collected by the electric poling method [11]. We measured on the same sample the magnitude of IF as obtained by taking the difference between the field required for forward poling, E_f and that required for reverse poling, E_r . By means of this technique, the IF was measured to be ~675 V/mm, in good agreement with the value measured by the interferometric method. A difference between the two values exists because the latter technique was able to provide a spatially resolved map of IF, while the former can only measure an IF value averaged throughout the whole sample (including both stoichiometric areas and defects).

Recently, we investigated the IF in a congruent LN sample by analyzing the linear electro-optic response [29]. In that work, a previously unknown IF component, which we defined as elastic, was measured using digital holography by evaluating the optical phase retardation as a function of the applied voltage in areas of the sample with opposite ferroelectric polarization states. We found that, just after poling, the phase retardation due to the linear electro-optic and piezoelectric effects has different values in opposite ferroelectric polarization domains [29 and refs therein]. As to the origin of the IF elastic component, we supposed that it arises from the elastic components of the electrical dipoles associated with defect complexes present in congruent crystals. In fact, according to the defect model, the presence of defect-complexes causes local distortions of the structure deforming the lattice cell. An analysis of structural distortions caused by the Niobium antisite defect, performed by X-rays, revealed the presence of a “contraction” of the nearest three oxygen ions and a displacement from the Z axis of the nearest ⁹³Nb nuclei. Defect-complexes also have an elastic dipole moment, therefore, that we think gives rise to elastic IF. The defect dependence of elastic internal field was supported by the evidence that the asymmetry in the EO response between two antiparallel domain areas came out only in samples that are not annealed so that the static IF was not zero. The asymmetry disappeared if the sample was thermally annealed so that the static IF value was equal to zero.

In this work we measured the elastic IF across the two different kinds of domain walls from the same phase map, i.e. one near the defect and the other one far from it. In this way we definitely demonstrate that elastic IF depends on defect presence as does static IF. To measure elastic IF we record a reference digital hologram h_r with the sample in the interferometer arm, with no applied voltage. Then, a sequence of digital holograms h_i are recorded while a linear voltage ramp ranging from 0 to 2.7 kV was applied across the sample, with a recording frame rate of 10 holograms per second. The optical phase retardation variation Δφ_i , occurring in the sample for each hologram h_i , was obtained by subtracting from the phase map φ_i of the current hologram the phase retardation φ_r of the reference hologram h_r [29]. The induced phase retardation distribution was generated simultaneously by linear electro-optic and piezoelectric effect along the z crystal axis.

Figure 3(a) shows a frame of the movie obtained collecting the two-dimensional map of the optical phase retardation, calculated for each hologram during application of an external voltage. In this case, all domain walls are clearly visible due to the opposite signs of the electro-optic and piezoelectric coefficients in the two domains. The inverted hexagon was not well defined because of the low spatial resolution of this map. The mean value of the phase maps in the two framed regions A and B, versus the applied voltage, is shown in Fig.3(b). No differences are noticed between the virgin (A) and the poled (B) area since they are far from defects, as happen for static IF, i.e., when no external voltage was applied. Indeed, optical phase retardation values have opposite signs but equal magnitude in the two anti-parallel domains areas (see movie 1).

 

Fig. 3. (a) Phase map of the sample at fixed applied voltage (2.7 kV). A phase step is visible across the domain boundary between the reversed (B) and un-reversed (A) areas and also across reversed areas in proximity of defect. (b) Plot of the averaged phase on virgin A(∘) and poled B(Δ) areas as function of the applied voltage. No differences are noticed between the electro-optic behaviour of the two areas. (c) Phase map with higher magnification showing the poled zone around the defect (d) Plot of the averaged phase on A(∘) and B(Δ) areas versus the applied voltage. The asymmetric behaviour exhibited by the two regions is clearly visible.

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Fig. 4. (560 KB Movie 1-Dynamic evolution of phase retardation in the off-congruent sample. (Upper image) Domain walls either between the two reversed regions and around the defects are visible due to the electro-optic phase retardation. (Lower image) Temporal evolution of both external voltage and electro-optic phase retardations in the two reversed adjacent regions.

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To measure the elastic IF close to the defect we have improved the spatial resolution to micrometric scale to resolve the hexagon (Fig. 3(c)). The mean value of the phase maps in virgin (A) and poled area (B) around the defect, versus the applied voltage, is shown in Fig. 3(d), where the asymmetric behavior exhibited by the two regions is clearly visible (see movie 2).

 

Fig. 5. (515 KB Movie 2-Dynamic evolution of phase retardation in correspondence of a defect.(Upper left) Phase map recorded at higher resolution, showing the reversed zone around a defect while an external electric voltage (Upper right) is applied.(Lower left) Plot of the phase profile across the hexagonal pole zone around the defect.(Lower right) Phase versus voltage inside (red) and outside (blue) hexagonal area, respectively.

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3. Conclusions

We can assert that the elastic IF exists only in the neighborhood of a defect, as in the case of static IF. This is crucial information for the optimization of LN properties by variation of extrinsic and intrinsic defect subsystems [29]. Such results can be extended to other ferroelectrics as well as to dielectric materials and pave the way to a better control of micron and sub-micron material domain engineering for the fabrication of novel non linear photonic crystals devices.