1 Introduction

Scaling down electronic device dimensions has led to significant improvement in terms of speed, power consumption, cost and footprint area. However, devices cannot be further scaled down due to several short channel effects. Today, commercial high-performance processors offer a compute power to memory bandwidth ratio of 5–10 TDP-FLOP/Byte [1]. This shows the need to increase the bandwidth to meet the higher data rate requirements of data-intensive applications like artificial intelligence, machine learning so that the overall clock frequency of the system improve. Due to electronic interconnect delay time issues and losses, achieving quicker electronic circuits running above 10 GHz is a major challenge. Light is believed to be one of the most promising possibilities for replacing electronic signals as information carriers [2]. Optical devices facilitate high operation speed due to high optical frequencies and possess a tremendous data-carrying capacity because of the wide bandwidth [3, 4]. Photonic devices find applications in energy-efficient lighting, high-performance computing, environmental monitoring, chemical, and biological sensing and many more [5]. However, miniaturization of optical devices is a big challenge due to diffraction limitations in the subwavelength region. Hybrid Plasmonic Waveguide (HPW) is proven to be a promising candidate in confining the light in deep subwavelength region and offering low propagation losses combining the properties of both Surface Plasmon Polariton (SPP) and photonic waveguides [6,7,8,9,10,11,12,13,14].

Silicon photonics involving active functionalities like switching, tuning, modulation and detection the basic mechanism to induce refractive index change is plasma dispersion effect based on depletion or injection type p–n junctions. However, Si photonics have poor electro-refractive effect associated with larger footprint, losses and high energy consumption [15]. Graphene a two-dimensional allotrope of carbon, consisting of carbon atoms packed in a hexagonal lattice structure, has unique electro-optical properties [16, 17] useful in a broad range of photonic applications. Graphene is a zero-bandgap semiconductor whose fermi level can be adjusted by electrical gating which results in a change in refractive index. Graphene can be used as an active material in silicon photonics to achieve more efficient light modulation, switching and detection [18,19,20,21,22,23]. Furthermore, graphene can be integrated into silicon photonic devices in a CMOS compatible manner [24, 25].

Ring resonators play a significant role in reducing the footprint area of Si photonics. A ring resonator is made up of an optical waveguide looped back on itself, with a resonance occurring when the resonator’s optical length is an integer multiple of wavelengths [26, 27]. Ring resonators are extensively used in optical modulators/switches, optical filters, light sources and optical sensing [28,29,30,31]. Hybrid plasmonic microcavities have recently been suggested as a viable alternative for achieving nanoscale light confinement [32,33,34,35].

In this paper, an optical switch based on electrically tunable graphene–silicon ring resonator is proposed. The suggested ring resonator shows electrically controllable characteristics taking advantage of gate tunability property of graphene. The Hybrid Plasmonic Waveguide (HPW) design of the ring tightly confines the mode in the nanoscale SiO2 layer by overcoming diffraction limitations. The subwavelength confinement and placing of graphene over the ring provide strong interaction of light with the graphene layer. In this paper, we measured the shift in resonance wavelength of micro ring as a function of graphene gating. As, voltage is varied from 0 to − 15 V, a maximum resonance wavelength shift of 2 nm is obtained. The variation in chemical potential of graphene w.r.t applied voltage is also observed. The coupling gap and length of the ring resonator are optimized for improving the Extinction Ratio (ER) [7, 36].

2 Proposed device design

The proposed electrically tunable optical switch is as shown in Fig. 1. It is based on SOI architecture and consists of an input Si photonic waveguide which is connected to an output hybrid plasmonic waveguide via a tapered waveguide that converts photonic mode into a hybrid plasmonic mode. The input Si bus waveguide’s width and thickness are 450 and 220 nm, respectively. The hybrid plasmonic waveguide consists of a metal–insulator–semiconductor (MIS) structure. Gold is preferred as it offers lower losses in near-infrared region [37, 38] and gold’s thickness and width are chosen to be 100 and 300 nm, respectively. SiO2 being CMOS compatible is considered as the oxide layer and easily formed by Si oxidation, it’s thickness and width are 20 and 300 nm, respectively. On a SiO2 substrate, a Si layer with width and thickness of 300 and 200 nm is constructed. A micro ring resonator having a similar MIS structure as the hybrid plasmonic waveguide with a radius of 3.1 µm is designed. At the interface of gold and SiO2, a single layer of graphene is incorporated into the ring. The coupling length and gap between the hybrid plasmonic waveguide and the ring are optimized for higher ER to be 1.5 μm and 100 nm. In the proposed hybrid plasmonic ring, light is tightly confined in the SiO2 dielectric layer thereby providing a significant interaction between the graphene and the light.

Fig. 1
figure 1

a Three-dimensional image of the proposed optical switch based on electrically tunable graphene–Si ring resonator; thickness of gold, SiO2, and silicon are 100, 20 and 200 nm, respectively, inset shows the electric field confinement in 220 nm-thick Si photonic waveguide, and b cross section of the device shows the coupling region between ring and hybrid plasmonic waveguide separated by a gap of 100 nm, inset shows the electric field confinement in 20 nm-thick SiO2 layer of hybrid plasmonic ring and the hybrid plasmonic waveguide

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3 Electrically tunable characteristic

The device design, simulation and analysis are done with Lumerical using Finite Difference Eigenmode (FDE) and Finite Difference Time Domain (FDTD) solvers. Figure 1a inset depicts the photonic waveguide’s electric field confinement. Figure 1b inset shows field confinement in the hybrid plasmonic waveguide and the ring at the overlap region. This shows the strong confinement of the field with the graphene layer hence electrical gating of graphene effects the optical mode characteristics. Figure 2a shows the propagation of electric field down the waveguide when the ring is resonating, i.e., ON resonance state (− 15 V) and Fig. 2b depicts the field propagation when the ring is in OFF resonance state (− 3 V). In the resonant state, light gets coupled into the ring and resonates whereas in the OFF resonant state light is not coupled into the ring and reaches the throughput port.

Fig. 2
figure 2

Electric field propagation along the waveguide in a ON resonance state, i.e., − 15 V is applied across graphene, and b OFF resonance state, i.e., − 3 V is applied across graphene

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Electrical and optical properties of graphene are highly tunable by means of electrostatic gating or doping which shifts the Fermi energy level (EF). Light resonating in the ring strongly interacts with graphene hence electron–hole pairs are generated. For a given input wavelength, carriers generated varies depending on position of the fermi level which results in a change in ƞeff of the ring thereby shifting resonant wavelengths of the ring w.r.t applied voltage across the graphene. This phenomenon of tuning the resonant wavelengths of the ring with applied voltage [39, 40] can be used to switch an optical signal on and off and hence this device can be utilized as an optical switch. The graphene modelling is done using the surface conductivity approach. The surface conductivity model with all its equation is described below in a detail as

$$\left( {\omega ,\Gamma ,\mu_{c} ,T} \right) = \sigma_{{{\text{int}} ra}} \left( {\omega ,\Gamma ,\mu_{c} ,T} \right) + \sigma_{{{\text{int}} ra}} \left( {\omega ,\Gamma ,\mu_{c} ,T} \right),$$
(1)
$$\sigma_{{{\text{int}} ra}} \left( {\omega ,\Gamma ,\mu_{c} ,T} \right) = \frac{{ - ie^{2} }}{{\pi h^{2} \left( {\omega + i2\Gamma } \right)}}\int\limits_{0}^{\infty } {\left( {\frac{{\partial f_{d} \left( \xi \right)}}{\partial \xi }} \right)} - \frac{{\partial f_{d} \left( { - \xi } \right)}}{\partial \xi }d\xi ,$$
(2)
$$\sigma_{{{\text{int}} ra}} \left( {\omega ,\Gamma ,\mu_{c} ,T} \right) = \frac{{ie^{2} \left( {\omega + i2\Gamma } \right)}}{{\pi h^{2} }}\int\limits_{0}^{\infty } {\frac{{f_{d} \left( { - \xi } \right) - f_{d} \left( \xi \right)}}{{\left( {\omega + i2\Gamma } \right)^{2} - 4\left( {{\raise0.7ex\hbox{$\xi $} \!\mathord{\left/ {\vphantom {\xi {h^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${h^{2} }$}}} \right)}}d\xi } ,$$
(3)
$$f_{d} \left( \xi \right) \equiv \frac{1}{{\exp \left( {\left( {\xi - \mu_{c} } \right)/\left( {k_{B} T} \right)} \right) + 1}},$$
(4)

where ω angular frequency, Γ scattering rate, μc chemical potential, T temperature, e electron charge, ℏ reduced Planck constant, and kB Boltzmann constant.

Figure 3 shows the variation in chemical potential of graphene w.r.t applied voltage across graphene. A change in chemical potential of 0.95 eV is observed for a − 15 V change in voltage. The chemical potential analysis w.r.t. applied voltage is done using the Lumerical device, in which charge transport and graphene modeling is used to extract the data mentioned in Fig. 3. The coupling length and the gap are highly optimized to achieve higher ER. The shift in resonance and ER for a fixed gap of 100 nm and various coupling lengths are shown in Table 1. A minimum gap of 100 nm is fixed to achieve less device footprint area and only the coupling length is optimized. The throughput port power versus the wavelength characteristics of the ring resonator for a coupling gap and length of 100 nm and 1.5 μm is as shown in Fig. 4. It also depicts an extinction ration of 10.94 dB. The device shows a maximum transmission and a minimum reflection.

Fig. 3
figure 3

Variation in chemical potential of graphene with voltage applied across graphene; a change in chemical potential of 0.95 eV is observed for a − 15 V change in voltage

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Table 1 Shift in resonance and ER for various coupling lengths
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Fig.4
figure 4

Throughput port power characteristics of the ring resonator showing the variation in resonance wavelengths of the ring with voltage applied across graphene; a shift in resonance of 2 nm and ER of 10.94 dB is observed for a − 12 V change in voltage at 1550 nm

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A resonance shift of 2 nm and an ER of 10.94 dB is observed. The real and imaginary effective index of the ring resonator for a length and gap of 1.5 μm and 100 nm are as depicted in Fig. 5a, b. The real effective index indicates phase shift and is a measure of shift in resonance of the ring. From 0 to − 3  V range which corresponds to a chemical potential of less than 0.4 eV we observe an increase in real effective index hence there is a red shift in resonance wavelengths whereas from − 3 to − 15 V range we observe a decrease in real effective index hence there is a blue shift in resonance wavelengths. The imaginary effective index indicates losses in the ring and for voltages less than − 3 V there is a decrease in imaginary effective index hence the losses decrease which is clearly evident from a sharper dip in the throughput port characteristics of Fig. 4, i.e., the dip corresponding to − 15 V is much sharper compared to − 3 V indicating low losses and good resonance. The main focus in the losses is propagation loss. We also calculated the error in terms of variation in terms of gap (g) and ring radius which is low.

Fig. 5
figure 5

a Variation in real effective index with voltage applied across graphene, and b variation in imaginary effective index with voltage applied across graphene, for a length and gap of 1.5 μm and 100 nm

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4 Conclusion

A nanophotonic switch based on electrically tunable graphene–silicon ring resonator is proposed. Optical switching is realized by tuning the resonant wavelength of the guided hybrid plasmonic mode in ring resonator. The shift in resonant wavelengths of the ring is achieved through modulation of fermi energy level of graphene by means of electrical gating. The gap and length of the ring are optimized for improved extinction ratio of 10.94 dB at a wavelength of 1550 nm. A minimum gap of 100 nm and a smaller ring radius of 3.1 μm offers minimal footprint area. The ƞeffreal and ƞeffimg of the ring w.r.t voltage across the graphene is observed. The reported results open the way for more optical switches, modulators based on electrically controllable characteristics of the graphene and the ring resonator. The proposed design can be used in various applications like optical interconnects, optical SRAM’s and other integrated photonic devices.