1. Introduction

Ferroelectric domain engineering is a powerful tool to develop new photonic and optoelectronic devices. For instance, by using ferroelectric domain inverted structures with two dimensional geometries, photonic and phononic band-gap properties, optical deflection or broadly tunable conical frequency conversion processes have been demonstrated [1–4]. Moreover, the usefulness of such ferroelectric structures on optically active materials has shown to be of interest in the development of multifunctional solid state lasers [6], ordered arrays of multicolour emitters [6,7] or plasmon assisted photoluminescence enhancement in periodically poled ferroelectric structures [8,9]. The performance of these devices is directly connected to the size and shape of the inverted ferroelectric domains and so to the precise control of the fabricated structures. Indeed, due to the increasing demand of compact and versatile nonlinear photonic structures with a reliable multifunctional optical character, two dimensional ordered arrays of alternate domain structures with sub-micrometer sizes and periods are desired in optically active ferroelectric crystals.

Due to its excellent optical properties, LiNbO₃ is one of the most widely employed material for integrated optics, and the implementation of a millimeter size fully dense 2D ferroelectric domain structure has attracted large interest. Concerning to its optical activation, laser action and self-frequency conversion processes has been reported in both, single domain and periodically poled structures [5,10,11], thus increasing its already impressive multifunctional character. Recently, by using the versatile direct electron beam writing technique (DEBW), we have shown the successful fabrication of two dimensional (2D) square lattices of inverted domains with diameters and separation distances as low as 1 μm in Yb³⁺ doped LiNbO₃ laser crystal. To the best of our knowledge this represents the shortest period achieved in a 2D optically active bulk LiNbO3 crystal [12]. Further, simultaneous second to fifth conical harmonic generation has been reported in this type of ferroelectric patterns [13], pointing out the outstanding opportunities offered by fully dense nonlinear photonic structures with short lattice periods.

In this work, we demonstrate that stable inverted ferroelectric domains with diameters in the sub-micrometer scale are accessible in Yb³⁺ doped LiNbO₃ bulk crystals, a system in which diode pumped efficient laser action, self-frequency doubling processes and laser tunability have been demonstrated [5]. After the fabrication procedure, the effect of electron bombardment within the domain inversion process is analyzed at the micrometer scale by combining spatially resolved confocal Raman, Fluorescence and Second Harmonic Generation (SHG). SHG and Raman spectroscopy are known to be a powerful nondestructive tool to investigate lattice variations and so they can provide important information about the crystal structure after the poling process. In this context, recent works have systematically analyzed the frequency shift of the active Raman modes in LiNbO₃ due to an applied external electric field and domain inversion process [14], which provide a valuable source for comparison. Additionally, the role of extrinsic defects within the domain inversion process namely, Yb³⁺ luminescence, is employed as a complementary optical probe. The strong electron-phonon coupling, typical of Yb³⁺ ions, along with the possible presence of non-equivalent emitting centers due to the presence of charge compensation mechanism, make this ion a fine microscopic optical probe to provide information on the rearrangement of optically active ions associated with the polarization inversion process.

The manuscript is structured as follows: first we describe the DEBW process to fabricate large areas of regular alternate ferroelectric domain structures with 2D geometries, as desired for photonic applications. The size and shape of the inverted domains is analyzed across the whole sample thickness and the possibility to obtain sub-micrometer inverted domains in Yb³⁺ doped bulk LiNbO₃ crystal is discussed. Then, the linear and nonlinear spectroscopic signatures of the inverted domains are studied with micrometer spatial resolution to investigate possible structural changes associated with the polarization inversion. Note that while in the conventional domain inversion setup using planar switching electrodes, the electric field E is homogeneous throughout the sample, in the case of the electron beam, the electric field shows the inhomogeneity associated with that of a point source, so that the switching process differs significantly. The interaction between intrinsic defects and ferroelectric domain reversal structures (domains and domain walls) is also analyzed to evaluate the effect of the electronic irradiation on the optical properties of Yb³⁺ doped LiNbO₃ laser crystal.

2. Experimental

2.1 Two dimensional Ferroelectric patterning via DEBW

Prior to the irradiation process, a 0.5 mm thick plate from a congruent single domain ([Li]/[Nb] = 0.945) Yb³⁺:LiNbO₃ crystal was cut and polished with its main faces oriented parallel to the ferroelectric c-axis single domain. The Yb³⁺ concentration in the crystal was 0.5 wt%. Then, a 100 nm film of Al was deposited on the + z face prior to the irradiation process, which acted as a ground electrode during the electron irradiation. In the next step, the electron beam provided by a Philips XL30 Schottky field emission gun electron microscope was focused on the -z face of the crystal. During the irradiation process, the acceleration voltage and the current beam were fixed at 15 kV and 0.3 nA, respectively. The applied density charge was varied between 600 and 3000 µC/cm², depending on the desired domain size. Finally, an Elphy Raith nanolithography software was employed to run the e-beam across the designed 2D pattern. By this procedure, large areas of regular alternate ferroelectric domains with different size and distances can be obtained in 2D geometries without any previous lithographic step. To illustrate the scalability of the technique, Fig. 1 shows three different SEM pictures of two dimensional square lattices of hexagonal shaped inverted domains with different size and filling factor parameters. The total written area was as large as 0.5x0.5 mm². The fabricated domain structures were revealed by selective chemical etching in a 2:1 solution of HNO₃:HF and analyzed by using both, SEM and optical microscopy.

 

Fig. 1 SEM images of large areas of regular alternate ferroelectric domains ordered in a two dimensional geometry (square lattice). The diameter of the inverted domains was (a) 10 μm, (b) 3 μm and (c) 1 μm. The separation between adjacent domains was 30μm, 3μm and 1μm, respectively.

Download Full Size | PDF

2.2 Optical characterization: confocal spectroscopy and ferroelectric domain imaging

Spatially resolved spectroscopic experiments were performed at room temperature in a laser scanning confocal microscope by focusing the excitation beam at the crystal surface. As excitation sources, an Ar⁺ laser tuned at 488 nm, a pulsed fs-Ti-Sapphire laser and a tunable cw-Ti-sapphire laser were employed for Raman, SHG and fluorescence imaging, respectively. In all the cases, the pump laser beam was focused onto the sample by a microscope objective. The optical response was collected in backscattering geometry with the same objective (50x magnification, numerical aperture, N.A = 0.75 in air) and focused into a multi-mode fiber. The end of the fiber was directly connected to the spectrometer and the signal detected with a Peltier-cooled charge coupled device camera. A beam splitter and notch filter were used to attenuate the pump laser line. The sample was placed on a 2-axis XY motorized stage with 0.2 μm spatial resolution. A large motif (diameter ~15 μm) was selected to avoid spatial resolution limitations. Note that the influence of mechanical stress at domain walls may extend several microns away, therefore masking possible spectroscopic variations at the inverted areas. Indeed, our spatial resolution was estimated to be close to 1 μm. For the imaging experiments all the samples were manually re-polished after the chemical etching down to 0.25 μm surface roughness.

3. Results and discussion

3.1 Ferroelectric domain patterning via DEBW

Figure 2(a) and 2(b) shows the SEM images of a chemically etched square lattice of inverted ferroelectric domains obtained at the non irradiated ( + z) and irradiated (-z) faces of the LiNbO₃ crystal, respectively. The diameter of the irradiated single motives was 3 μm with a separation distance between adjacent domains of 3 μm. As seen, the inverted ferroelectric domains are directed along the polar axis of the crystal (c axis) crossing the whole sample thickness. The size and shape of the irradiated areas is preserved at both faces, pointing out the capability of the technique to provide high quality photonic devices with reduced domain size in a bulk configuration. According to previous works, the switching process via DEBW can be explained in terms of the so called ferroelectric domain breakdown phenomenon, where the switching occurs upon the high inhomogeneous electric field induced by a point source as the one provided by the e-beam [12,15]. In the frame of this model, the driving force for the domain formation is the condition of minimum free energy, which results into string-like shaped domains i.e inverted domains with a radius, r, considerably smaller than their length, l, (r = l). More specifically, after nucleation, the inverted domain grows to its equilibrium shape, which exhibit a power law dependence on the applied charge equal to 2/3 [16]. Such radius dependence has direct implications on the required charge density values delivered by the e-beam since they must be varied according to the size of the irradiated area. That is, the smaller the inverted area, the largest applied charge density values required to reverse the spontaneous polarization. However, increasing the applied density charge above the threshold value allows domain reversal to grow spontaneously, leading to uncontrolled domain merging [12,15].

 

Fig. 2 SEM images of a square lattice of hexagonal shaped inverted ferroelectric domains after selective chemical etching. (a) Non irradiated + Z face. (b) irradiated –Z face. The period of the nonlinear structure is Λ = 6 μm; the average diameter of the irradiated zones equal to 3μm. The electronic charge density was fixed at 1000 μC/cm² (c) Square lattice of sub-micrometer inverted domains in Yb³⁺:LiNbO₃ crystal. The period is Λ = 2 μm with average diameter of the inverted domains equal to 700 nm. The corresponding charge density value was 1800 μC/cm² (d) Detailed view of two aligned sub-micrometer (~500 nm) inverted domains. (e) SEM image of an individual hexagonal shaped submicrometric domain (~200 nm).The orientation of the crystallographic axis is marked in the figure.

Download Full Size | PDF

Figure 2(c) shows a square array of sub-micrometer inverted domains (~700 nm) with a separation distance close to 1μm obtained in Yb³⁺:LiNbO₃ when the applied density charge was fixed at 1800 μC/cm². As for larger domains, the inverted area crossed the whole thickness of the sample while maintaining similar size and shape in both crystal faces. Their stability was ensured at least during months. At this point we would like to note that even when we succeed on the fabrication of smaller individual domains with average size of 500 nm (Fig. 2(d)) and 200 nm (Fig. 2(e)), the production of large areas of regular nanodomain patterns is still challenging and requires further investigation. In this sense, to obtain a better understanding on the effect of the electronic irradiation on the crystal structure, possible cross talking between inverted domains or the impact of ferroelectric domain breakdown on the structural changes associated with the polarization reversal, spatially resolved confocal Raman, fluorescence and SHG experiments were performed.

3.2 Characterization of inverted domains: Raman spectroscopy

LiNbO₃ belongs to the C3v space group with two formula units per unit cell. According to group theory, the C3v group has 27 possible optical modes which can be classified according to the irreducible representation as: Γ = 4A1 + 5A2 + 9E. The A2 modes are inactive while both, the A1 and E modes, are infrared and Raman active with the E modes being double degenerate. On the basis of this symmetry, a maximum of 13 optical modes would be expected. However, the long-range fields inside the LiNbO₃ crystal lift the degeneracy between longitudinal (LO) and transverse (TO) optical modes, thereby doubling the number of observed modes [17]. Figure 3 shows the unpolarized Raman spectra collected at: i) the center of the irradiated area (domain inverted), ii) domain wall and iii) the original (non irradiated) region. The number of Raman modes as well as their relative intensities is in good agreement with those previously reported for Z-cut congruent LiNbO₃ crystals [14,18]. At first sight, no differences can be detected either in the position of the Raman modes or in their spectral widths.

 

Fig. 3 Unpolarized micro-Raman spectra obtained from a Z-cut Yb³⁺ doped LiNbO₃ when the excitation/collection beam was focused at domain wall (blue line), center of the inverted hexagonal domain (red line) and the original (non inverted) area (black line). The observed Raman modes are labeled on the spectra.

Download Full Size | PDF

However, a more careful inspection of the spectra reveals slight spectroscopic changes occurring at both inverted domains and domain walls. Those changes were found to be stable after several months and have been related to the strong lattice re-arrangement during polarization reversal. More specifically, the E(TO)₁, E(TO)₃, E(TO)₈ and A(LO)₄ Raman modes exhibit a red frequency shift of about 0.5 cm⁻¹ at the reversed areas, while the A(LO)₂ mode shows a blue shift close to 0.3 cm⁻¹. On the other hand, the relative intensities of the E(TO)_7, A(LO)₄ and E(TO)₉ Raman modes vary at domain walls. Further, tiny variations in the full width at half maximum (FWHM) are also detected for the E(TO)₁, E(TO)₇ and A(LO)₄ Raman modes after the fitting process. At this point we would like to mention that even when the overlapping between different Raman modes could introduce some errors into the curve fitting parameters, the systematic spectroscopic variations allowed to image not only the polarization reversed areas but also the domain walls. Figure 4 shows four different spatial Raman maps obtained when the intensity, frequency shift and spectral linewidth of the E(TO)₇, E(TO)₉ and A(LO)₂ phonon modes are analyzed for an individual hexagonal inverted domain in Yb³⁺:LiNbO₃. Here, it should be noted that every pixel in the images corresponds to an independent Raman spectrum. A clear distinction between domain walls (Fig. 4(a)) and inverted/non inverted areas (Fig. 4(b)) is observed across the whole scanned area. A detailed view for some of these spectra is displayed in Fig. 4(c) and 4(d) where the E(TO)₉ and E(TO)₁ modes has been selected.

 

Fig. 4 (a) Raman spatial maps showing the domain walls after analyzing the intensity of the E(TO)₇ and E(TO)₉ modes. (b) Raman spatial maps after analyzing the frequency shift of the A(LO)₂ and E(TO)₁ optical phonons. The corresponding scale bar for the frequency shift is shown below the images. (c) Detailed view of the E(TO)₉ Raman mode collected at domain walls and non inverted area. (d) Detailed view of the E(TO)₁ Raman mode collected at the hexagonal inverted and original (non inverted) areas.

Download Full Size | PDF

Previous works have established that the physical mechanism behind the observed spectroscopic contrast in the Raman response are due to the influence of mechanical stress in the vicinity of domain walls -which may extend the perturbation several microns away and to the presence of intrinsic defects in the crystal structure of LiNbO₃ due to its congruent (non-stoichiometric) composition. Those intrinsic defects exhibit a polar nature which, in turn, originates an internal electric field in the crystal structure. The strength of this internal field is reduced after polarization reversal as manifested in the different values between the forward and backward threshold coercive field in congruent LiNbO₃. It also accounts for the significant differences in ferroelectric domain reversal between congruent and stoichiometric (defect free) LiNbO₃ crystals, namely, one order of magnitude of reduction in the coercive field value for stoichiometric crystals [19]. In Raman experiments, the effect of the internal electric field results into changes in the energy of the vibrational modes through the piezoelectric tensor of LiNbO₃, according to the linear relationship between the deformation of the crystal structure and the applied electric field. Thus, confocal Raman spectroscopy can be used as a fine optical microprobe to characterize the presence of strain and/or additional defects associated with the involved switching mechanism [20,21].

In the particular case of DEBW, the observed spectroscopic changes displayed in Fig. 4 are well correlated with the intensity variations and frequency shifts reported for conventional electrical poling using electrodes [14, 22] hence indicating that the formation of string-like shaped domains via ferroelectric domain breakdown does not influence the final lattice rearrangement. Additionally, the presence of strain and/or additional defects due to electron bombardment can be also ruled out in the whole charge density range employed in this work (600-3000 µC/cm²). At this point it is important to mention that the observed change in the local internal field after polarization reversal is not limited to the ferroelectric axis, but it also varies along the transverse (orthogonal) component as manifested by the frequency shift of both, A₁ and E modes. Note that in LiNbO₃ the ionic motion associated with the A₁ relates to ionic displacements along the polar axis, Z, while the E phonons are associated with the motion along the Y (or X) axis [23,24]. Further, since the vibrational energy of E(TO)₁ and E(TO)₈ Raman modes also shifts at domain walls, an interaction between intrinsic defect and domain walls can be concluded.

On the other hand, the intensity changes observed at domain walls can be explained by simply considering symmetry arguments. In fact, an ideal domain wall can be considered as a planar defect (interface) where a strong symmetry breaking takes place. As a result, a depolarization effect occurs at the wall resulting in intensity variations of the polarized Raman modes [25,26]. This fact along with the overlapping of certain modes explains the intensity increase observed for the E(TO)₉, E(TO)₇ and A(LO)₄ modes. We will go back to this aspect on section 3.4 (Second harmonic generation).

3.3 Characterization of inverted domains: Fluorescence spectroscopy

As a complementary tool to evaluate the role of electron bombardment within the domain inversion process, room temperature Yb³⁺ fluorescence imaging experiments were performed. It has been established that trivalent rare earth ions (RE) substitute for Li⁺ in LiNbO_3. These ions are off-centered from the regular Li position due to the presence of different charge compensation mechanisms, and so they may exhibit a multi-center distribution due to their slightly different local environment [27]. Due to the lattice rearrangement during polarization reversal, the optical properties of the non-equivalent rare earth centers can be also modified, allowing the study of local perturbations by luminescence spectroscopy as optical probe. In this sense, low temperature excitation/emission experiments have been successfully employed to study the role of extrinsic defects – mainly Nd³⁺ and Er³⁺ rare earth ions, during polarization reversal in LiNbO₃. More specifically, it has been shown that the lattice rearrangement for the non equivalent optically active centers into the Li⁺ octahedra can be altered by the polarization switching [28–30]. Because of the small ionic radius of Yb³⁺ ion compare to others RE ions, its incorporation into the LiNbO₃ lattice produces a minor distortion and a single emitting center occupying the regular Li⁺ cationic site has been reported [14].

Figure 5(a) shows the room temperature emission spectrum of Yb³⁺ ions in LiNbO₃ obtained after excitation at 920 nm. It consists of five main optical bands at 950, 980, 1005, 1030 and 1060 nm, which are associated with the transitions from the ²F_5/2(0') and ²F_5/2(1') excited Stark energy levels of the excited state to each of the four Stark levels of the ²F_7/2 (0,1,2,3) fundamental state, respectively. Figure 5(b) displays the corresponding energy level scheme of Yb³⁺ ions in LiNbO₃ where the main optical transitions have been highlighted. The fluorescence spatial maps after scanning an individual hexagonal inverted ferroelectric domain are shown in Figs. 5(c) and 5(d). They were obtained under excitation at 920 nm. The analyzed transitions correspond to those in which laser action has been demonstrated (at 1035 nm and 1064 nm). As seen, there is a clear contrast between the inverted and non inverted areas which show a slight red shift of the fluorescence bands of about 0.5 nm. A similar analysis was performed for the ²F_5/2(0') → ²F_7/2(0) line (~980 nm). For this transition, all the spectroscopic features namely, peak position, lack of spectral satellites, intensity and spectral linewidth, were unaltered.

 

Fig. 5 (a) Emission spectrum obtained from a z-cut Yb³⁺ doped LiNbO₃ crystal under excitation at 920 nm. (b) Energy level scheme of Yb³⁺ ions in LiNbO₃. The main optical transitions are highlighted with arrows. Absorption lines (blue arrows), emission lines (red arrows). (c) Fluorescence map of a hexagonal domain obtained after plotting the frequency shift of the ²F_5/2(0') →²F_7/2 (2) optical transition centered around 1030 nm. (d) Fluorescence map of the same inverted domain associated with the frequency shift of the ²F_5/2(0') →²F_7/2 (3) optical transition centered around 1060 nm. Dotted lines are guide for the eye.

Download Full Size | PDF

The obtained results contrast with those previously obtained at low temperature in which the emission spectra collected inside and outside the inverted areas were found to be identical [12]. The different behavior observed here can be associated with the strong electron-phonon coupling characteristic of Yb³⁺ ions. It is well known that the ²F_5/2(0’)→ ²F_7/2(1,2,3) transitions of Yb³⁺ are strongly coupled to lattice phonon modes. This is particularly true for LiNbO₃ where most of the structure observed in the absorption and emission spectra of Yb³⁺ ions has been correlated with different Raman modes [31]. Thus, the slight variations obtained in the energy of the vibrational modes after domain reversal are also reflected in the luminescence spectrum of Yb³⁺. That is, the strongly coupled electronic transitions of Yb³⁺ will show a much more noticeable shift than the zero phonon line. Further, the lack of spectroscopic changes obtained for the zero phonon line, ²F_5/2(0’)→ ²F_7/2(0) electronic transition, when scanning the inverted and non inverted areas, supports that the domain inversion process does not alter the local environment of Yb³⁺ ions, and therefore, the spectroscopic and laser properties of Yb³⁺:LiNbO₃ will remain unaffected.

3.4 Characterization of inverted domains: Second Harmonic Generation

SHG is an nonlinear process that involves the creation and detection of a second harmonic polarization $P_i^{2\omega }=d_{ijk}{E}_j^{\omega }{E}_k^{\omega }$ at frequency 2ω in a material by a light field at fundamental frequency, E^ω. It is therefore extremely sensitive to the symmetry of materials and consequently, to the symmetry breaking occurring at domain walls. In particular, SHG has been extensively used in nonlinear microscopy to visualize surfaces and interfaces, image domain structures with different orientations or for visualization of cell and tissue structure [32–35]. Here, SHG microscopy is employed to evaluate the influence of mechanical stress in the vicinity of domain walls as well as the presence of intrinsic defects in domain inverted Yb³⁺:LiNbO₃ crystals.

Antiparallel (180°) ferroelectric domains are equivalent with respect to the generated second harmonic response, i.e they exhibit the same SHG efficiency and therefore they should not be observed in the SHG spatial map unless the crystal structure has been somehow modified during polarization reversal. However, that is not the case for ferroelectric domain walls, where as mentioned above, a strong symmetry breaking occurs leading to an intriguing enhancement of the nonlinear response. In fact, it has been demonstrated that the change in the nonlinear coefficients at domain walls result into an extraordinary enhancement of the Cerenkov-type SHG allowing to generate simultaneous nonlinear processes or broadly tunable multicolor radiation in a conical geometry [5,15,36]. Indeed, nonlinear Cerenkov radiation (in the form of two discrete symmetrically distributed SH spots) has been recently observed at a single localized domain wall [37,38]. Cerenkov SHG has been recently employed to map ferroelectric domain walls in a three dimensional geometry as well as to study the intrinsic crystal symmetry properties of the crystal [39–41]. The study of the localized SHG response at both domains and domain walls, is therefore of significant interest.

Figure 6(a) shows the micrometric spatial map obtained for an individual hexagonal ferroelectric domain when the SHG intensity was analyzed in back reflection geometry. Two main features can be observed: i) the SHG response cannot distinguish between up and down ferroelectric domains, in agreement with the lack of changes in the crystal structure. ii) The SHG signal is strongly enhanced at domain walls pointing out the interface-like behavior of domain walls. The generated SHG intensity across an inverted domain is shown in Fig. 6(b). As seen, the FWHM of the SHG cross section signal extends over 1.5 μm, being this value limited by our spatial resolution in the z direction.

 

Fig. 6 (a) Micrometric spatial map obtained for an individual hexagonal ferroelectric domain when the SHG intensity was analyzed in confocal back reflection geometry. (b) Integrated SHG intensity scanned across the diameter of the inverted domain.

Download Full Size | PDF

4. Summary and conclusions

To summarize, large areas of regular alternate ferroelectric domains ordered in a two dimensional geometry have been fabricated in Yb³⁺ doped LiNbO₃ bulk crystals after polarization reversal by electron beam writing. Additionally, the possibility to obtain sub-micrometric inverted domains ordered in a two dimensional geometry is demonstrated. The obtained domains were found to be stable during months, crossing the whole sample thickness (0.5 mm). Further, the size and shape of the irradiated areas was found to be preserved at both crystal faces, pointing out the capability of the DEBW technique to provide high quality photonic devices with sub-micrometer domain size in a bulk configuration. In this respect we would like to note that DEBW can also be employed to predefine large areas of ferroelectric domain structures ordered in different geometries, namely, line shaped 1D structures, two dimensional hexagonal arrays.., without the need of any previous masking step.

The effect of electron bombardment within the domain inversion process has been also evaluated at the micrometer scale by combining spatially resolved confocal Raman, Fluorescence and Second Harmonic Generation experiments. The obtained results show that the linear and nonlinear spectroscopic signatures of the inverted domains do not suffer structural changes other than those associated with the polarization inversion. Hence, in addition to the possibility of obtaining non invasive spectroscopic images of domains and domain walls by using optical tools, the feasibility of DEBW technique on the fabrication procedure is confirmed. Moreover, by using a combination of linear and nonlinear optical probes we have shown that the formation of string-like shaped domains via ferroelectric domain breakdown does not influence the final lattice re-arrangement thus maintaining the laser properties and nonlinear optical response of rare earth doped LiNbO₃ crystals unaffected. We note that even though the spectroscopic analysis was performed on relatively large reversed areas (~15 μm), similar results are expected for sub-micrometer inverted domains.

The obtained results provide a comprehensive study of the relationship between the processing, the structure and the optical properties of domain inverted nonlinear ferroelectric structures which can be further exploited to develop novel photonic and optoelectronic devices using optically active ferroelectric crystals as multifunctional substrates.