Research of Gate-Tunable Phase Modulation Metasurfaces Based on Epsilon-Near-Zero Property of Indium-Tin-Oxide

Abstract

In this paper, we proposed a reflection phase electrically tunable metasurface composed of an Au/Al₂O₃/ITO/Au grating structure. This antenna array can achieve a broad phase shift continuously and smoothly from 0° to 320° with a 5.85 V applied voltage bias. Tunability arises from field-effect modulation of the carrier concentrations or accumulation layer at the Al₂O₃/ITO interface, which excites electric and magnetic resonances in the epsilon-near-zero region. To make the reflected phase tuning range as wide as possible, some of the intensity of the reflected light is lost due to the excited surface plasmon effect. Simulation results show that the effect of optimal phase modulation can be realized at a wavelength range of 1550 nm by modulating the carrier concentration in our work. Additionally, we utilized an identical 13-unit array metasurface to demonstrate its application to the beam steering function. This active optical metasurface can enable a new realm of applications in ultrathin integrated photonic circuits.

1. Introduction

With the advancement of ultra-compact optical devices, there is an urgent demand for new structures that can realize the control of the phase and amplitude of the light dynamically [1,2,3,4,5,6,7,8]. Photonics based on 2-dimensional nanostructures, such as metasurfaces, can potentially provide a feasible solution for this specific challenge [9,10,11,12]. Metasurfaces are composed of periodic geometry arrays of subwavelength elements such that each element can impose a phase shift and amplitude change on the transmitted, reflected, and scattered light [13,14,15,16]. Additionally, there are three essential functions of metasurfaces: beam steering [17], focusing of light [18], and polarization conversion [19]. For example, Liu et al. summarized micromachined tunable metamaterials with mechanical actuation based on mechanical reconfiguration, which has required mechanical movement in recent years [20]. However, this method depends on processing conditions, and the modulation process is not flexible. To respond to the requirement of dynamic tunability, our work is based on optically tunable reflective metasurfaces that have a more comprehensive application prospect than passive metasurfaces [21,22].

The material of choice for the active metasurfaces needs to be quickly and controllably integrated into nanophotonic structures, and if possible, the selected material should be CMOS-compatible, thus allowing integration with on-chip platforms. In a vast regime of wavebands, transparent conductive oxides (TCOs) have been demonstrated as an ideal material that meets the requirements for many reasons, such as the low resistivity, controllable electro-optical property, and the epsilon-near-zero (ENZ) property [23,24,25,26,27]. Indium Tin Oxide (ITO) belongs to this class of material, which is an n-type semiconductor material formed by doping In₂O₃ with Sn in a specific proportion. The advantages of using ITO as an active material in metasurfaces are manifolds: ITO films can modulate the optical refractive index in a plasmonic cavity configuration and show strong electro-optic solid effects in epsilon-near-zero (ENZ) behavior due to the carrier concentration can be changed in the range of 10²⁰–10²¹ cm⁻³ [28,29,30]. To date, industrial advancements, such as magnetron sputtering systems, reactive evaporation, and electrochemical diffusion processes, have made a high yield and reliable process possible, contributing to the wide application of ITO [31,32].

Among the various physical mechanisms for regulating the complex refractive index of materials to achieve phase shifts, field-effect modulation is chosen to offer continuous tunability, shorter response time, and a relatively wide tuning range. It can also provide an amply significant carrier density change in doped semiconductors or conducting oxide, leading to a variable complex refractive index in the charge depletion or accumulation regions [33,34,35]. Based on the formation principle of charge depletion regions in doped semiconductors, field-effect modulation is a distinctly mature approach in the semiconductor process and is compatible with CMOS [36,37]. For example, Sherrott et al. demonstrated a 237-degree phase modulation range at an operating wavelength of 8.50 mm by using a gate-tunable graphene-gold resonator structure in 2017 [38]. Huang et al. demonstrated an active metasurface realizing the dynamic control of both amplitude and phase [39]. A phase shift of about 225 degrees can be observed at a wavelength around 1550 nm by applying a voltage of 4.6 V in their work. Inspired by these studies, the phase modulation range and the incident wavelength are optimized under a smaller voltage in our work.

In this paper, a dynamically tunable metasurface with a metal–medium–metal grating structure is proposed. We chose ITO as the active material to reach an expansive phase change due to the Fabry–Perot resonance and zero-crossing effect of the permittivity of the ITO accumulation layer. In addition, we simulate a dynamical beam steering device implemented with 30°, 20°, and 10° modulation functions. This optical array will find potential applications in the focusing lens, beam steering device, and polarimeters.

2. Theoretical Models and Design Considerations

A schematic representation of the proposed metasurface structure is shown in Figure 1. We designed tunable metasurfaces composed of an Au back-reflector, on top of which an ITO layer is deposited. This layer is followed by the deposition of a dielectric spacer Al₂O₃ layer and Au nanoantennas. In designing the metasurface element, the physical parameters for the ITO layers should be obtained [40,41]. In our calculations, we assume that the carrier concentration of the active material is N₀ = 3.2 × 10²⁰ cm⁻³.

When no external bias is applied, the real part permittivity of the ITO layer is positive at a wavelength of 1550 nm. Once under bias, a charge accumulation layer is formed in the ITO, reaching the epsilon-near-zero (ENZ) region with the voltage increasing, which results in a considerable electric field enhancement occurring in the accumulation layer for near-infrared wavelengths. The permittivity dispersion of generic TCO can be described by the Drude model:

$$\epsilon ={\epsilon }_{\infty }-\frac{\omega p^2}{{\omega }^2+i\omega \gamma }$$

(1)

$${\omega }_p{}^2=\frac{N_0{e}_c{}^2}{{\epsilon }_0{m}_t}$$

(2)

where ${\epsilon }_{\infty }$ = 3.95 is the high-frequency permittivity [42]; $\gamma$ = 180 THz is the collision frequency; ${\omega }_p$ is the plasma frequency, and $\omega$ is the angular frequency of incident light. ${\epsilon }_0$ is the vacuum permittivity; $m_t=0.35\times m_0$ is the effective mass of electrons in ITO; $m_0$ is the electron rest mass [43]; $e_c$ is the electron charge, and the initial electron concentration N₀ is set to be 3.2 × 10²⁰ cm⁻³. Based on Formula (2), the plasma frequency is found to be 1.84 × 10¹⁴ rad·s⁻¹.

Another parameter that determines performance is the choice of the plasmonic metal. The relative permittivity of Au is 1.59 [44,45], and our work function of Au is 5.1 eV, which is higher than that of ITO (4.4 eV) when the carrier concentration N₀ = 3.2 × 10²⁰ cm⁻³. In addition, selecting Au as a metal electrode in our metasurfaces ensures that the phase change is stable and continuous. The other is the choice of gate dielectric material. Alumina (Al₂O₃) exhibits high DC permittivity and almost perfect interfacial properties with Si-based substrates. It is often employed in field-effect transistor fields as high dielectric constant gate dielectric materials and has a high breakdown field of up to 10 MV/cm. The average thickness $t_{acc}$ of the accumulation layer related to the carriers injected into the ITO layer in a standard metal–insulator–semiconductor structure [46] is given by:

$$t_{acc}=\frac{\pi }{\sqrt{2}}\sqrt{\frac{k_{B}T{\epsilon }_0{\epsilon }_c}{N_0{e}_c{}^2}}$$

(3)

where $k_B=1.38\times {10}^{-23}\mathrm{J}/\mathrm{K}$ is the Boltzmann constant; T = 300 K is the Kelvin temperature; $e_c$ = 1.6 × 10⁻¹⁹C is the electron charge; ${\epsilon }_0$ is the free space permittivity, and ε_c = 9.3 is the relative static permittivity of ITO [47]. Due to the aforementioned N₀ = 3.2 × 10²⁰ cm⁻³, the thickness of the accumulation layer is found to be $t_{acc}$ = 0.7 nm. Then, we can find the carrier concentration N_acc in the accumulation layer. Assuming a uniform carrier distribution in the accumulation layer [48], the injected carrier concentration can be calculated as:

$$N_{acc}=\frac{V_g{\epsilon }_0{\epsilon }_{ins}}{e_c\times t_{acc}\times t_{ins}}$$

(4)

where t_ins = 5 nm is the thickness of the insulator spacer, ${\epsilon }_{ins}$ = 9 is the relative permittivity of Al₂O₃ [49], and V_g is the applied voltage.

Based on the above analysis, we can perform optical measurements to illustrate the phase change of incident light with the applied voltage. All the simulations were performed using the numerical simulation software COMSOL Multiphysics based on the finite element method (FEM).

3. Results and Discussion

The metal-insulator-semiconductor field-effect structure was utilized to observe the ENZ region and injected electron density in the ITO accumulation layer. We simulated reflectance and phase modulation of the periodical antenna structure under normal incidence illumination with transverse magnetic (TM) polarization (H-field along with the stripes) based on Figure 1. Electromagnetic waves and frequency domain modules were utilized in our simulation, and the boundary condition was set to a periodic boundary condition. For the ITO layer, we used extremely refined mesh division and free triangular mesh for other areas. Figure 2a,b show the distribution of electromagnetic fields at different applied voltages for a fixed wavelength (1550 nm). The metal grating excites surface plasmon resonance, causing the electric field to converge on the ITO layer, and then changing the dielectric constant of ITO at this time can make the phase changes. At 0 V, symmetrical electric fields between the Au antenna and Au backplane can be observed due to ITO optically behaving as a dielectric (ε > 0). In the case of an applied voltage of 2.6 V, the ENZ condition takes up the accumulation layer at the interface of the ITO and Al₂O₃, and the enhancement of the z-component of the electric field in the accumulation layer is magnified in Figure 2c. As one can see, the real part of the active layer’s permittivity (ε_acc) is 2.093, and the carrier concentration is 3.2 × 10²⁰ cm⁻³ at no bias for the incident wavelength λ = 1550 nm in Figure 2d. Based on the carrier concentration model in ITO materials [50,51], it shows that the concentration of carriers within the active layer could rise to 1.1 × 10²¹ cm⁻³ with the increasing gate bias, which leads to the permittivity of the accumulation layer changing from a positive one to a negative one. For applied bias values larger than 3.0 V, the permittivity of the accumulation layer is negative, similar to metal. In the case of an applied bias around 2.6 V, ε_acc is close to zero (ε_acc = 0.041–0.58i), which stimulates the resonance of the local surface plasma, resulting in a steep change of phase shift. This is in line with our expectations of achieving the ENZ region. Figure 2e shows the reflectance and phase shift spectra as a function of the applied voltage. The dotted lines indicate the ENZ region in the accumulation layer at the Al₂O₃/ITO interface. With the gate bias increasing, the magnetic dipole plasmon resonance couples to the ENZ region in the ITO accumulation layer can induce a significant phase shift in reflection [52]. According to this feature, we can study the phase change that conforms to the present description.

As shown in Figure 3a, the designed element phase tuning range (the blue line) is more significant than 300° at λ = 1550 nm, which is obviously better than the phase modulation of the other wavelengths. At 2.65 V bias, the accumulation layer preliminarily reaches the ENZ region, leading to a phase shift of 247°. Based on Formula (5), the phase change is related to the applied voltage [53]. In the ENZ region, the electric field energy is highly confined inside the ITO thin film and fully interacts with the ITO layer. The locally concentrated electric field is very sensitive to changes in the surrounding electromagnetic environment parameters. Therefore, when doping ITO through the bias electrode due to the change in the ITO film’s conductivity, the light scattering phase will change sharply, resulting in electrical modulation of the phase. Figure 3b shows the variation between the reflectance of the metasurface and the applied voltage at different wavelengths. With the ENZ condition holding, the plasmonic resonance enhancement is generated in the active layer, leading to the minimum reflectance of 5.9% at 3.35 V shown in Figure 3b. Because critical coupling occurs at the Al₂O₃/ITO interface, the incident wave is absorbed, and the stronger the absorption, the more severe the phase mutation, i.e., the phase change is the most obvious when the amplitude is the lowest.

$$\varphi \left(V\right)=\frac{2\pi \Delta nL}{\lambda }$$

(5)

Where $\Delta n$ is the change in the refractive index of the material caused by the voltage, L is the waveguide length, and $\varphi$ is the phase change. In this case, the reflectance of field-effect modulation is observed at different biases from −2 V to 6 V, which can be understood from the continuity of the normal component of the electric displacement at the field-effect modulation interface. In modern electronic communication, the integration of electronic scales usually requires a nanoscale, and the reduction of device size also requires further energy consumption reduction [52,53]. The designed antenna arrays realized smooth and extensive phase regulation over 300° at near-infrared wavelengths under a smaller voltage condition. Therefore, voltage reduction in our structure is of great significance for future device design.

As demonstrated in the above results, a significant phase change can be achieved in this gated active reflective metasurface. We further employed 13 independent unit cells to illustrate the function of beam steering. These tunable beam steering components have an identical antenna structure of Au/Al₂O₃/ITO/Au planar layers with a periodicity of 400 nm operating at a wavelength of 1550 nm. Thus, the 13-element metasurface operating over the 1550 nm band has a length of 10 μm. The array surrounded by air is at the bottom of the simulation region, and the boundary condition is set to the scattering boundary condition. The incident wave propagates vertically from the z-direction, and the electromagnetic beam shown in Figure 4 is reflected by the entire antenna structure. The maximum delay required to steer the antenna over an angle $\theta$ is given by [54]:

$$\theta =\arcsin \frac{{\phi }_n}{n{k}_{r}d}$$

(6)

where θ is the deflection angle of the reflected beam, $k_r=\omega /c$ represents the relationship between the phase of the incident wave and the distance, $n$ is the element number, $d$ is the spacing of adjacent array elements, and ${\phi }_n$ is the degrees of the adjacent unit’s phase shift. We define a positive scan angle when the antenna looks to the left of the boresight. For our present scenario (where $n$ = 13 and θ = 10 deg), the maximum delays required for the angle +10 deg with respect to elements $n$ = 0, 1, 2, … are 0, 16.1°, 31.8°, … The simulation results are consistent with our analysis above, which demonstrates the function of beam steering successfully, i.e., each element can satisfy the condition for a fixed phase shift when the incident wave frequency is fixed. The direction of the reflected beam toward 30°, 20°, and 10° has shown in Figure 4. This shows that the beam deflection of 30°, 20°, and 10° corresponds to a single element phase difference of 46.5°, 31.8°, and 16.1°, respectively. This efficient electronically tunable beam steering system will have potential value in the development of ultrathin on-chip applications and sensing devices.

4. Conclusions

In summary, gate-tunable metasurfaces based on Indium-Tin-Oxide were studied in our work. The simulated phase shift can reach 247 degrees by applying a 2.65 V gate bias at a wavelength of 1550 nm, whose maximum phase shift can reach 320 degrees at 5.85 V. This continuous and smooth phase modulation is more than 20 degrees greater than other mid-IR metasurface systems [38,39], which only need a smaller applied voltage. In addition, beam steering with different angles was demonstrated by controlling the phase shift of 13 unit cells, i.e., the phase shift of the adjacent unit moves by 16.1 degrees, and the reflected beam deflects by 10 degrees. This strong light–matter interaction can be explained by the critical coupling of incident waves to the metasurface. The incident light excites eigenmodes through radiative coupling, and the energy is converted into resistive losses under critical coupling conditions so that the reflections are sufficiently suppressed. Phase modulation is a transition state that occurs in under-damped and over-damped oscillations, which means that this transition inevitably passes through a critical coupling region. Therefore, a wide range of phase modulation will be strongly coupled with absorption strength, i.e., with the range of phase tunability increasing, the absorption intensity will also increase, and the phase tunability comes at the expense of energy loss. Due to the critical coupling condition of perfect absorption during the phase change process, in the part with the most severe phase change, the corresponding light absorption is the strongest, and the reflection amplitude is the smallest, at only about 1%. Such a two-dimensional array could enable guidance on devices, such as dynamic holograms, ultrathin lenses, nanoscale light modulators, and polarimeters.