1. Introduction

Oxides and their interfaces have been investigated in the last two decades as potential platforms for a wide variety of applications in photonics, biology, and catalysis [1–5]. The surfaces and interfaces of ferroelectric oxides with nonpolar oxides are interesting because of their strong electric polarization [1]. Cutting a ferroelectric along the direction perpendicular to the polarization axis results in two oppositely polarized surfaces with macroscopic electric dipole moments. Depolarization fields are formed in the surrounding environment to stabilize the ferroelectric surfaces [1]. Surface metallization can occur as a result of stabilization occasionally [6,7]. Recently, metallization was found in ferroelectric lithium niobate (LiNbO₃, LN) doped with transition and rare earth metals [8,9]. The metallization of the surfaces is essentially due to the formation of 2D electron gas (2DEG), which is suitable for supporting surface plasmon polaritons (SPPs) [8,9]. Usually, the metallization of ferroelectric oxides is hidden because ions in the ambient environment tend to be adsorbed on the surfaces and screen the electric field well, concealing the metallization layer falls in the nanometer scale [1]. However, this condition changes when nonpolar oxides are deposited on the LN surfaces with magnetron sputtering methodology [8,9]. In the sputtering atmosphere, high energy noble gas ions are used to bombard off, with high probability, the adsorbed ions from the LN surfaces before deposition. When depositing indium-tin-oxide (ITO) on the Z-cut LN surfaces, the metallization was restored and demonstrated unambiguously by monitoring the very first reflection (VFR) from ± Z-faces. As polar catastrophe [10,11] occurs at the interfacial layer between LN (high polar) and ITO (nonpolar), the electrons swarm at the interface, forming 2DEG as a screening layer [9], similar to electron redistribution across MOS structures under voltage [12]. Meanwhile, plenty of ab initio theoretical investigations have been carried out to comprehend intriguing findings regarding LN surfaces [1]. From an alternative band alignment perspective, a staggered bandgap alignment was observed to be formed between the ITO and LN when seen as a heterostructure [13]. Consequently, the electrons will accumulate near the ITO/LN interfaces to equalize the Fermi levels, resulting in metallization, which can be studied with optical means to study striking differences of the two interfaces. The metallization is inherently suitable for designing metasurfaces in tuning plasmonic resonance for many applications, such as high-resolution full color display [14], without resorting dissipative metals [15,16]. Moreover, the giant light-light modulation can serve as nanometric optical logical gates.

2. Theoretical analysis

Band alignment has been applied to analyze the charge transfer and accumulation of the oxide ferroelectrics and semiconductor based heterostructures [13]. Thus, the knowledge of the band structure of adjacent materials is required. Density functional theory (DFT) was used to estimate the electron distribution from an atomistic view and to calculate the band gaps of ITO and Fe-LN. Our structural optimizations of the most stable geometries and charge distributions were calculated via the CASTEP [17,18] module based on DFT. We chose plane wave ultra-soft pseudopotential (PWPP), generalized gradient approximation (GGA), and Perdew–Burke–Ernzerhof (PBE) approaches to take electronic effects into account. The cutoff energy is 561.4 eV in calculation and k points are 6×6×2 for continuity of bandgap.

To raise absorption in the shorter visible waveband of LN to light, dopants like Fe²⁺, Fe³⁺, and Cu²⁺ were chosen [19] and introduced expedient to recording photorefractive (PR) phase gratings as means in exciting SPPs at the modified surface [20,21]. These bands from doped elements separate the bandgap of pure LN in the middle and increase the Fermi energy. This is the reason why the band gap of Fe-LN is 2.2 eV, smaller than that of pure LN (4.5 eV). Similarly, the band structure of ITO was calculated. Comparing the two band structures [Fig. 1(a)], a typical staggered band alignment forms as a heterostructure [13]. As a result, the electrons will transport from the LN to the ITO side and accumulate in a very thin layer near the LN/ITO interface. In fact, the alignment of the Fermi levels of ITO and LN differs greatly at the ± Z-faces owing to different surface polarization, resulting in different Fermi bending.

 

Fig. 1. (a) Band structures for Fe-LN and ITO. (b) Schematic of the local electric field distributions at the two interfaces. (c) Charge density in ITO. z=0 refers to the ITO/LN interface. Orange and yellow lines represent charge density in Au and Ag, respectively.

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Alternatively, the 2DEG formation and charge distribution can be studied with diffusion function by treating the spontaneous polarization (SP) of LN as a source. Because of its proximity to the ITO film, the SP field of the + Z-face is screened by the electrons coming both from the ITO and LN. Consequently, electrons are redistributed near the interface. As illustrated previously [22], the potential φ(z) relates to the total free carrier density by

3. Experiments and discussions

We have previously reported that the VFR is dramatically reduced when monitored it reflection from the –Z-face of ITO coated LN slab [8]. We obtained an exponential gain coefficient (EGC) as large as –78525 cm^-1 under the illumination of two counterpropagating laser beams [8]. The absolute value of EGC was significantly enhanced with the help of 2DEG and SPPs coupling with the incident light. In this study, we have raised the EGC by 2.2 fold to –172700 cm^-1 with the same configuration. Surprisingly, when we checked the VFR of a weak laser beam incident on the + Z-face, its reflectivity was raised by up to 60%. Meanwhile, the reflectivity of the VFR could be reduced to as low as 1.6% at the –Z-face. The striking trend difference between the two cases needs to be investigated to understand the working of the two ITO/LN interfaces.

The Z-cut LN slab used in this study was cut from the middle of a slug grown by the conventional Czochralski technique along the Z-direction from the congruent melt with Li/Nb=48.6/51.4 and doped with iron (0.05 wt% Fe₂O₃). More details regarding the growth and poling treatment can be found in [24]. The LN slab dimensions were 0.59×11.8×14.9 mm³, with the ± Z-faces (11.8×14.9 mm²) optically polished. After the slab is ultrasonically cleaned, 150 nm thick ITO films were deposited onto both the ± Z-faces by magnetron sputtering. The ITO target was made of SnO₂ and In₂O₃ with 90 wt% and 10 wt%, respectively. The sample-to-target distance was 15 cm and the vacuum chamber was evacuated down to a base pressure of about 5×10⁻⁶ Torr prior deposition. The deposition was carried out at a growth temperature 180 °C and argon gas pressure 0.3 Pa with high purity and with low power (∼110 W) for ∼10 min. Then the slabs were annealed at 520 °C for 15 min. The thickness of ITO film was measured as 150 nm by a scanning probe microscope. The thickness and resistance of ITO films are ∼150 nm and ∼56 Ω/cm, respectively.

The schematic of the experimental setup is shown in Fig. 2(a). Two coherent laser beams (532 nm) impinge on the ITO coated Z-cut Fe-doped LN slab described above. The beam power ratio was P₂/P₁=104.2 mW/13.1 mW = 7.95. P₁ is the weak beam and illuminates the testing surface (+ or – Z-faces). P₂ is the strong beam and propagates in the direction opposite to P₁. Owing to the small wedged angle during sample preparation, there are multiple reflections when P₁ is on. We only monitored the very first reflection (VFR) of P₁ with a power meter (Thorlabs, PM110D) because it indicated the testing surface conditions directly in the half wavelength range [25]. When changing the incidence angle θ, the two laser beams were kept collinear and counterpropagating to each other. Then, the slab was turned by 180° to monitor the other VFR of P₁ from the other surface with the same operations.

 

Fig. 2. (a) Schematic illustration of setup for monitoring the VFR from the two interfaces. 2θ is the angle between the incident and VFR beams. BS: beam splitter; Pr: prism; M: mirror. (b) Dynamic curves of VFR of P₁ at ± Z-faces under different illumination conditions. (c) Variation of EGC values with incidence angle obtained by measuring the VFR variation.

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The results are shown in Fig. 2(b). The VFR signal of –Z-face (2θ = -25.0°) was reduced greatly when the two laser beams illuminated the slab simultaneously (red line in stage I and V). The VFR can be reduced from 1.2 mW to as low as 0.21 mW (R=1.6%) by P₂ illumination, namely, anti-reflection. The VFR of + Z-face with only P₁ on is identical with that of the –Z-face (stage IV, the difference is because of multiple reflections and incident angle). However, sharply different from that on the –Z-face, the VFR of + Z-face (2θ = 1.7°) was enhanced greatly from 1.73 mW (R=13.2%) to 7.70 mW (R=58.8%) under the effects of P₂ (blue line at the end of stage IV and beginning of V). Stage IV shows the typical tendency of VFR with only P₁ illumination. The VFR was enhanced by 4.4 fold when compared to the reading with a sole laser beam for + Z-face, corresponding to EGC of +115800 cm^-1, at least 463 times higher than the best results previously reported in Fe-doped LN slab [26]. From the VFR dynamics, it can be seen that there was energy competition between the laser beams and the SPPs in both ± Z-faces. The competition energy (CE) can reach 2.06 mW. Meanwhile, the dynamic curves (stage IV) with only the weak beam were a lot smoother than that with two laser beams on simultaneously, suggesting energy couplings between laser beams with SPPs mediation. In experiments (not shown in figures), after exposure with P₂, followed by turning on P₁ and shutting off P₂ immediately, the VFR jumped to as high as 80% and decayed gradually over time. This means that beam P₂ and its multiple reflected beams can write phase gratings. Once the phase gratings are read with P₁, the diffraction light can excite SPPs, which could couple energy back to its VFR. The fall in signal was the indirect result of erasure of the phase gratings. It is worth mentioning that VFR enhancement/reduction has been previously observed from PR materials and some physical explanation was proposed [27]. However, the physical explanation proposed here can give an alternative and better insight regarding this mechanism.

The dramatic variation of VFR indicates the occurrence of high EGC, which in turn indicates energy coupling with SPPs. We measured the EGC values under different incidence angles (Fig. 2(c)). The pure gain is defined as γ = (VFR with P₂ on)/(VFR (initial) with P₂ off). The EGC is defined as Γ = (1/d) ln γ. Here, d is chosen as half the wavelength of 532 nm because the VFR is mainly dictated by mechanisms within the reach of evanescent waves [25]. The EGC values marked with Γ₁₀ were obtained with only P₁ on. The values marked with Γ_max and Γ_min were obtained by reading the highest and lowest reflectivity, respectively, at each incidence angle with both P₁ and P₂ on. One sees that these numbers are nearly three orders of magnitude greater than that reported in the doped LN slab [26]. The dynamic range was high (looks much noisy) for all incidence angles, implying the occurrence of fierce competition between the laser beams and the SPPs. A viewing screen was placed perpendicular to the slab upper edge (optical path is in Fig. 2(a)) and the recorded scattering pattern is shown in Fig. 3(a). One sees that the crests of the fringes on the left coincide with the troughs of the fringes on the right (inset of Fig. 3(a)), suggesting a π phase shift between the two sets of fringes. When strong energy transfer took place, scattering power as strong as 15 mW was recorded [Fig. 3(a)]. This means that the SPPs propagating along the interface was very strong and also explains why energy transferred to the laser beams is strong enough to reach the high EGCs obtained on ± Z-faces. It is also because of the ultra-low loss that the upper edge scattering can be so strong [28]. The significant difference between the two interfaces causes the opposite trends in VFR dynamics.

 

Fig. 3. (a) A typical scattering pattern on a viewing screen placed perpendicular to the composite slab under the illumination of two beams. The inset shows enlarged view of the red box in (a) rotated 90° clockwise. (b) and (c) are electric field components along the x-direction at the two faces, originating from the photovoltaic induced charge nonuniformity.

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To understand the mechanism behind the opposite trend of the VFRs from the ± Z-faces and the π phase shift between the two sets of fringes in the scattering pattern in Fig. 3(a), we have to take a closer look at the SP and photovoltaic fields [29,30] on the ± Z-faces. When an LN slab is illuminated by a laser beam with strong absorption in LN, the photovoltaic current will flow from its –Z-face to + Z-face [29,30]; hence, electrons will flow in the opposite direction. As a result, in the ITO, the electron density will decrease on the + Z-face side and the opposite process will take place on the –Z-face side. Consequently, the SP field is modulated by the photovoltaic field [29,30]. Thus, the Ez field in Fig. 1(b) was also slightly modulated because of the changed SP, resulting in an x component of the total electric field, shown in Fig. 3(b) and Fig. 3(c). This x component of the electric field is not as high as Ez in Fig. 1(b), but could cause a significant phase grating in the electrooptic LN. Considering that the photovoltaic induced electron increase/decrease occurs at the –Z/+Z-faces, leading to phase gratings with π phase shift, resulting in the opposite trend of the VFRs, and the π phase shift scattering pattern (Fig. 3(a)).

4. Conclusion

In conclusion, from ab initio theory, the band alignment of ITO coated Fe-LN indicated the charge transformation and the 2DEG formation. By considering the impact of the local fields on the band bending, the electric field showed the different conditions at ± Z-faces, forming two sets of 2DEGs. Considering the modulation of SP by the photovoltaic field, two sets of thin phase gratings were recorded on the ITO/LN interfaces with π phase shift, serving as the key to the significantly different trends in the VFRs and also to the two sets of scattering fringes recorded on the screen placed perpendicular to the slab upper edge. This study conducted in the LN/ITO combination is by no means limited to itself and could be generalized to any ferroelectric/transparent semiconductor combination. The super low loss 2DEGs are suitable for supporting visible SPPs, without using any metal part, highly desirable for plasmonic applications. The proposed technique is compatible with existing photonics circuits in LN, paving the way towards implementing ultrathin devices, such as optical modulator and surface optical circuits, especially light-light logical gates.