Surface plasmons in metallic nanostructures have continuously attracted extensive research attention because of their ability to break the diffraction limit and confine electromagnetic fields at the subwavelength scale that can greatly enhance light–matter interaction [1,2]. This has triggered a series of breakthroughs in fundamental nanophotonic studies [3–7] together with the realization of highly compact nanophotonic devices, such as (bio)chemical sensors, nano-lasers, optical modulators, and photodetectors [8–18]. Recently, ultrathin (few nanometers in thickness) noble-metal films have sparked great research interest because they can support extremely confined plasmonic modes in the visible and near-infrared (vis-NIR) spectral regions, and provide an enhanced nonlinear optical response [19–26]. This is further driven by the development in fabrication technologies for high-quality ultrathin gold and silver films [21,22,26–28]. Combined with the advanced nanofabrication technology, these ultrathin noble-metal films can be patterned into ultrathin plasmonic structures [21,25,26], which allow access to the regime of extreme light–matter interactions for fundamental studies, as well as the development of applications such as surface-enhanced spectroscopy, spontaneous emission enhancement, high-sensitivity optical sensing, and optical modulation.

While the near- and far-field response of ultrathin plasmonic structures can be tailored by engineering the geometrical parameters, it is highly desired to have the ability to tune it dynamically [29]. On one hand, this is necessary for shifting the plasmonic resonance, which is highly sensitive to fabrication errors for ultrathin metallic nanostructures [26], to the designed wavelength; on the other hand, development of a dynamically tunable plasmonic resonance can enable an on-demand enhancement of light–matter interactions, which can remarkably extend the scope and applicability of ultrathin plasmonic nanostructures for applications such as surface-enhanced spectroscopy [12,30], spontaneous emission enhancement [31,32], and light modulation [33–36]. Among the various tuning approaches (e.g., based on thermal, electrochemical, mechanical, electrical, and optical mechanisms) [15,37–41] developed for metallic nanostructures, electric tuning is of great interest because of its advantages including fast response time and easy integration. Indium tin oxide (ITO), as a highly efficient electro-optical material, has been widely used for electric tuning of plasmonic response in metallic nanostructures [35,36,42–45]. However, due to the ultrathin thickness (few-nanometer scale) of the electrically induced accumulation layer (i.e., the active region with an electrically induced permittivity change), it is mostly exploited for electric tuning of metal–insulator–metal or metal–insulator–semiconductor plasmonic structures, in which a strong overlap between the plasmonic modes and the nanometer scale accumulation layer in ITO can be achieved.

Here, by combining the extreme light confinement capability in ultrathin plasmonic nanostructures with the efficient nanoscale electro-optical effect in ITO, we propose an all-solid-state electric approach to efficiently modulate plasmonic resonances in ultrathin gold nanoribbon arrays. We demonstrate that an ultrathin thickness of the gold nanoribbons, enabled by a recently developed fabrication technology, plays a crucial role in the efficiency of electric tuning of the plasmonic response. Exploiting the above advantages, we numerically show that a spectral shift in the plasmonic resonance up to 36 nm along with a 16% change in the intensity of the transmission dip of a 2-nm-thick gold nanoribbon array can be realized with an application of gate voltage below 1.7 V. These results open a new avenue towards the electric tuning of plasmonic resonances in ultrathin gold nanostructures and may find applications in miniaturized devices for surface-enhanced spectroscopy, spontaneous emission enhancement, and signal processing.

Recent developments in ultrathin monocrystalline gold films [26,46,47] with low loss and strong field localization allow for development of new nanophotonic designs. In this work, ultrathin gold nanoribbon arrays (GNRAs, nanoribbons in the array are not coupled with a period three times the nanoribbon width), which support ultraconfined dipolar plasmonic resonances and can be readily fabricated in a large scale [21,22,26], were exploited for the electric tuning investigation. Figure 1 shows a schematic illustration of the proposed design for electric tuning of plasmonic resonance in an ultrathin GNRA, which is embedded in a high-k dielectric, hafnium oxide (HfO2) and then sandwiched between two ITO layers. When normally incident light having polarization perpendicular to the nanoribbons illuminates the array, it excites nanoribbon dipolar plasmonic resonances, which results in a dip in the spectral dependence of the transmission. When a positive voltage is applied between the GNRA and the ITO layers (upper panel of Fig. 1), a nanoscale electron accumulation layer is induced in the ITO at the ITO/HfO2 interfaces [48], which leads to the modulation of the refractive index of the ITO in this region, including both real and imaginary (absorptive) parts. As the plasmonic resonance is highly localized around the nanoribbons and the thickness of HfO2 is just a few nanometers [35], there is a good overlap between the mode electromagnetic field and the region of the refractive index change in the ITO, which makes the plasmonic resonance of the GNRA very sensitive to the induced refractive index changes, providing the mechanism for its electric tuning (as schematically shown in the lower panel of Fig. 1). The implemented approach is based on a recently developed fabrication technology for single-crystal atomically smooth ultrathin gold layers, which has already been used for the experimental demonstration of low-loss plasmonic modes and enhanced nonlinear effects [26,46,49].

First, as a key precursor of the tuning effect, the change in the optical characteristics of ITO in a gold-HfO2-ITO structure was investigated under the application of external gate voltages, with the thickness of the HfO2 layer surrounding the ultrathin GNRA set to a technologically achievable value of 2 nm. Generally, the optical properties of ITO are described by the Drude model [50]. The application of an external bias across the gold-HfO2-ITO structure lowers the potential and leads to the accumulation of electrons in the nanoscale ITO region adjacent to the HfO2/ITO interfaces. Self-consistent electrostatic simulations reveal that the distribution of the carrier density at the interfaces closely follows an exponential decay function under various applied voltages as shown in Fig. 2(a), presenting an agreement with the Thomas–Fermi approximation [35,51]. Notably, upon the application of a gate voltage as low as 2 V [purple line in Fig. 2(a)], the maximal carrier density is increased by ∼100 times to the value of n∼1027m−3 at the HfO2/ITO boundary, which significantly alters the local plasma frequency ωp2=nq2/ε0m* (where m*=0.35me, and q and me are the electron charge and mass, respectively). The change of the plasma frequency then drastically modifies the ITO permittivity, εITO=ε∞−ωp2/(ω2+iωγ) (see Appendix A for details), where γ is the electron scattering rate and ε∞ is the high-frequency dielectric constant. As shown in Fig. 2(b), with the increase of the gate voltage from 0 to 2.5 V, at the wavelength of 1.55 μm, the real part of the permittivity of ITO right near the HfO2/ITO boundary decreases from a positive value of 3.90 to a negative value of −4.46, while the corresponding imaginary part increases from essentially 0 to 1.24. Specifically, with the application of a gate voltage of approximately 1.4 V, the ITO can reach a highly attractive epsilon-near-zero (ENZ) regime [marked in Fig. 2(b)] [52]. Overall, due to the exponential decay of the electron density in the ITO near the interface, an ITO layer thickness of 3 nm is large enough for efficient tuning.

The interaction strength between the plasmonic GNRA and the active ITO layer determines the characteristics of the electric tuning of plasmonic resonance in ultrathin GNRA. Therefore, it is important to study the plasmonic properties of the ITO-integrated GNRA (with a 2-nm-thick HfO2 layer and a 3-nm-thick ITO layer having a free electron concentration of 1025m−3). To carry out accurate electromagnetic simulations, additional optical loss related to the thickness-dependent electron scattering on the ultrathin GNRA boundaries was considered. Particularly, permittivity of single-crystalline gold from Ref. [53] was corrected with the impact of the boundary scattering using the Fuchs theory [54,55] (see Appendix B for details). As shown in Fig. 2(c), to obtain a plasmonic resonance around 1.55 μm, GNRAs with various thicknesses and widths (keeping the period a=3w) can be used. Specifically, with the gradual decrease in the thickness of the nanoribbons, the required width of the nanoribbons also decreases. The corresponding near-field distributions for plasmonic structures constructed using GNRAs with thicknesses of 1, 5, and 10 nm for the resonance wavelength of 1.55 μm are presented in Fig. 2(d). One can see that the near-field maps for GNRAs with a smaller thickness demonstrate better relative localization of the electromagnetic field in the active ITO region. To quantitatively illustrate this trend, the ratio between near-field intensity integrated within the ITO layer adjacent to the nanoribbon and the entire integrated near field was calculated [Fig. 2(e)]. The results confirm tighter field confinement and consequently a higher overlap between the mode electromagnetic field and the active ITO layer for smaller nanoribbon thicknesses, which is highly beneficial for greater interaction of the plasmonic mode with the nanoscale permittivity change in ITO to obtain better electric tuning of the plasmonic resonance. Ultrathin GNRAs can be fabricated by patterning a large-size ultrathin gold flake into a nanoribbon array using electron-beam lithography and plasma etching techniques as demonstrated in our previous work [26]. Particularly, the thickness of a single-crystal gold flake currently achieved is as small as approximately 2 nm. Therefore, the electric tuning of ITO-integrated GNRAs with nanoribbon thickness of 2 nm is first investigated. For the plasmonic resonance in the telecom spectral range, the width of the nanoribbons for the 2-nm-thick GNRA is determined to be 102 nm [Fig. 2(c)].

With the determined optimal parameters of the ITO-integrated ultrathin plasmonic structure, its electric tuning performance was investigated. The transmission spectra of the ITO-integrated ultrathin plasmonic structure having nanoribbons with a thickness tGNRA=2nm and a width w=102nm for various gate voltages are presented in Fig. 3(a). To expose the dependencies in detail, Fig. 3(b) provides a zoomed-in view of the transmission spectra in the wavelength region spanning from 1.45 to 1.6 μm. Then, the values of resonance wavelength and minimum transmission for various gate voltages are extracted [Fig. 3(c)]. With the rise of the voltage from 0 to 1.4 V, the plasmon resonance dip exhibits a blue-shift for about 36 nm from 1.55 to 1.514 μm, which is due to a gradual decrease in the real part of the permittivity of ITO with an increasing gate voltage. When the voltage increases further, ITO near the HfO2 interface enters the ENZ regime, which introduces a significant optical loss in the ITO layer due to ENZ-related field enhancement (which will be explained in detail later) and the increase of the imaginary part of ITO permittivity, overall resulting in a rapid decrease of the transmission [Fig. 3(c)]. Particularly, the transmission drops to a minimum value of 24.8% at the bias voltage of 1.7 V. At the same time, the ENZ behavior causes a significant change in the field distribution of the plasmonic mode, which leads to a disruption in the monotonic trends of both characteristics around 1.7 V [Fig. 3(c)]. With a following increase of the voltage from 2.1 to 2.5 V, when the ENZ region moves inside the ITO layer further away from the HfO2 interface, their behavior is gradually restored to a monotonic decrease. Noting that from the point of view of practical applications, excessively high voltage is more likely to induce the occurrence of tunneling phenomena [35], we restrained the simulated voltages to values below 2.5 V. Overall, the transmission change (ΔT=Tnon-gated−Tgated) and the corresponding modulation depth (1−Tgated/Tnon-gated) of the ITO-integrated ultrathin plasmonic structure at various wavelengths are shown in Fig. 3(d). One can see that the two characteristics are well correlated. Notably, upon application of a gate voltage of just ∼1.7V, the transmission change can lie in the region of 10%–16% in the broad wavelength range from 1.4 to 1.54 μm, with the maximum value of ∼16% at the wavelength of 1.47 μm, corresponding to the modulation depth of 0.34. The achieved tunability in resonance wavelength and transmission can be considered to be very substantial as they arise from only a ∼1-nm-thick active region in the ITO layer and undoubtedly benefit from the ultraconfined optical field of the nanoribbon plasmonic dipolar resonance. Moreover, to improve the tunability of the plasmonic resonance of the structure, a smaller array period that enhances the density of the nanoribbons together with their coupling can be implemented (see Appendix C for details). At the same time, it is worth noting that the smaller gaps would increase the challenge in device fabrication.

To further elucidate the nature of such electric tuning efficiency, the near-field distributions of the electric field around the nanoribbons at the resonance wavelengths of 1.55 μm and 1.516 μm and gate voltages of 0 and 1.7 V are presented in Figs. 3(e) and 3(f), respectively. The enlarged views of the regions of the field localization shown in Figs. 3(g) and 3(i) demonstrate that under the application of the voltage the optical intensity starts to be confined in the ITO charge accumulation layers. More precisely, the plots of the normalized electric field intensity along the dashed lines in Figs. 3(g) and 3(i) clearly show the pronounced induced electric field in these regions [Fig. 3(h)]. This is related to the increase of the local electric field component normal to the boundary in the ENZ region (present inside the accumulation layer at the applied voltages above 1.4 V; see Fig. 1) due to the continuity of the corresponding component of the dielectric displacement. Thus, due to the induced field enhancement, the ENZ effect can introduce significant optical loss, which is translated to a rapid decrease of the transmission [Fig. 3(c)]. Therefore, a substantial modulation can be obtained at gate voltages below 1.7 V, which are (1) easily achievable, (2) safe in terms of the dielectric breakdown, and (3) at which tunneling effects can be neglected [35].

The effect of nanoribbon thickness on the electric tuning performance was further investigated. Here, for consistency, the resonance wavelength of the ITO-integrated plasmonic structures with various nanoribbon thicknesses at zero gate voltage is fixed at 1.55 μm by adjusting the nanoribbon widths. Figure 4(a) shows the dependence of the shifts of the plasmonic transmission dips on the gate voltage for ITO-integrated plasmonic structures with various nanoribbon thicknesses. It can be seen that for the same applied gate voltages, the shift of the dip wavelength decreases with the increase of the nanoribbon thickness tGNRA. In addition, Fig. 4(b) shows the corresponding increase in the change of the value of the transmission dip minimum (the corresponding absolute value of the transmission dip is shown in the inset). These results suggest that the tunability of the ITO-integrated nanoribbon array progressively improves with the decrease of the nanoribbon thickness. Specifically, when the thickness of the GNRA is decreased to 1 nm, it gives a spectral shift up to 55 nm and a transmission change of ∼13% at a gate voltage of 1.7 V at 1.55 μm. This can be explained by the observation that thinner nanoribbons produce tighter optical field confinement; therefore a much larger portion of plasmonic field interacts with the nanoscale permittivity change in ITO [Fig. 2(e)]. At the same time, for the ITO-integrated nanoribbon arrays constructed using nanoribbons with a thickness of 10 nm and above, the electric tuning effect almost disappears.

The HfO2 thickness is also a key parameter in determining the self-consistent distributions of the electric potential and the induced carrier density and therefore the distribution of the permittivity change inside the ITO layers. For consistency, the effect of the HfO2 thickness on the electric tuning performance was investigated by slightly modifying the width of the nanoribbons to keep the same resonance wavelength at 1.55 μm (with the other parameters set as tGNRA=2nm, tITO=3nm, and a=3w). As can be seen from Figs. 4(c) and 4(d), the alteration of both the resonance wavelength and the magnitude of the plasmonic transmission dip occurs at smaller applied voltages for smaller thicknesses of HfO2. This can be expected, as in this case there is a larger drop in the potential inside the ITO layers, which leads to a higher induced carrier concentration and therefore a more dramatic change in permittivity. In addition, the accompanying smaller overlap between the ultraconfined plasmonic field and the nanoscale electron accumulation layer in the ITO for thicker HfO2 layers also contributes to the degradation of the electric tunability. Overall, it can be concluded that an ITO-integrated nanoribbon array with smaller nanoribbon and insulator thicknesses has better electric tuning performance. It is worth noting that, for certain applications such as surface-enhanced spectroscopy and spontaneous emission enhancement, the direct access to the optical near fields of ultrathin GNRAs is required. Therefore, the electric tunability of 2-nm-thick GNRA with only a bottom ITO layer was also investigated (see Appendix D for details). Under a gate voltage of 1.7 V, a spectral shift of 24 nm and a transmission change of ∼10% can be obtained at the wavelength of 1.49 μm.

In conclusion, by leveraging the resonant extreme light confinement capability of the ultrathin nanoribbons and a dramatic electro-optical effect in ITO, having a particular synergy in the proposed ultrathin design, we have demonstrated an electrically induced 36 nm spectral shift in the plasmonic resonance along with ∼16% change in the transmission for a 2-nm-thick GNRA. The operation speed of this electrically tunable plasmonic structure is estimated to be at approximately 2 GHz, as determined by the RC time of the structure (with a device size of 2μm×2μm, a gate capacitance of ∼0.3pF, and a realistic contact and wiring resistance of ∼2kΩ). Being ultrathin and all-solid-state, the proposed electrically tunable ultrathin plasmonic structure is prospective for various applications such as surface-enhanced spectroscopy, spontaneous emission enhancement, and optical modulation.