Design of a Dual-Mode Graphene-on-Microring Resonator for Optical Gas Sensing

On-chip optical gas sensors, which use resonant shifts of cavities to detect molecular concentrations, have the advantages of high sensitivity, real-time detection, and compact footprint. However, such sensors are usually limited by a serious cross-sensitivity issue induced by environmental temperature variations. To overcome this limitation, we study a dual-mode graphene-on-microring resonator to accurately measure gas concentrations without suffering from temperature variations. To be specific, the influences of gas-induced graphene’s optical conductivity changes and environmental temperature variations on effective refractive indices of TE0 and TE1 modes in the resonator can be decoupled based on the modal linear independent responses. With this method, we designed a nitrogen dioxide sensor with a sensitivity of 0.02 nm/ppm and a limit of detection of 0.5 ppm. Our study paves the way for developing on-chip optical gas sensors with excellent sensitivity and temperature stability.


I. INTRODUCTION
Compact and low-cost gas sensors have wide applications in consumer electronics, industrial safety, medical diagnosis, environmental monitoring, vehicle exhaust measurement, and public security. To date, different types of gas sensors have been demonstrated, such as electrochemical gas sensors [1], semiconductor gas sensors [2], [3], and optical gas sensors [4]- [7]. Among these sensors, optical gas sensors, namely, fiber sensors [8], [9], surface plasmon resonance sensors [10], [11], and waveguide-integrated sensors [12], [13], have the advantages of high sensitivity, fast response, and electromagnetic immunity [14]. Taking advantage of state-of-the-art CMOS technology, siliconbased waveguide-integrated sensors are most promising to be integrated with optoelectronic and electronic devices for achieving monolithically chip-integrated sensing, signal The associate editor coordinating the review of this manuscript and approving it for publication was Maged Abdullah Esmail .
processing, and communication [15]. Therefore, they have attracted great attention in the past decades.
On the other hand, graphene is an intriguing material to develop optical gas sensors [16]. Adsorbed gas molecules act as charge-carrier donors or acceptors to change graphene's optical conductivity, which leads to phase or intensity changes of photonic devices. Moreover, by integrating graphene on a waveguide, the graphene sheet can interact with light in the waveguide through the evanescent field coupling [17], [18], significantly elongating the light-molecules interaction length. As a result, optical gas sensors based on graphene-covered photonic integrated circuits (PICs) have been a hot research topic. Based on this platform, researchers have developed structures, such as electrically gated graphene-on-silicon nanowires [19], grapheneon-germanium slot waveguides [20], and graphene-on-silicon microring resonators (MRRs) [21] for the trace gas detection.
Moreover, with the advantages of high sensitivity, fast response, and label-free detection, refractive index (RI) sensors have been widely demonstrated for gas sensing. In such VOLUME [24]. However, the temperature variation condition is commonly present in industrial RI sensing applications. Several works have proposed methods to solve this issue based on microwave sensors for the liquid RI sensing, such as using a reference mode to compensate for the temperature change [25] and developing an artificial neural network model to restore the sensor's response to the material under test regardless of the varying temperature [26]. It is necessary to develop a method to eliminate the influence of the temperature variation for the RI gas sensor.
In this paper, we studied a dual-mode graphene-on-MRR RI gas sensor to overcome the cross-sensitivity problem. We theoretically analyzed the influences of gas-induced graphene's optical conductivity changes and environmental temperature variations on effective RIs of the TE 0 and TE 1 modes in the graphene-on-MRR. Our study shows that graphene and temperature-induced RI variations can be extracted separately due to the modal linear independent responses to these two factors. Based on this model, we designed a nitrogen dioxide (NO 2 ) gas sensor with a sensitivity of 0.02 nm/ppm and a limit of detection (LOD) of 0.5 ppm. Our study paves the way for developing sensitive on-chip optical gas sensors without suffering from temperature fluctuations.

II. SENSING PRINCIPLE OF THE DUAL-MODE GRAPHENE-ON-MRR
First, the influence of the gas doping on graphene's Fermi level (E x ) can be expressed as follows [16], where V F is the Fermi velocity, g v = g s = 2 are the valley degeneracy and the spin degeneracy, respectively. n i is the graphene's initial carrier concentration (before gas doping). n is the change of the graphene's carrier concentration due to the gas doping. As for NO 2 molecules, n can be given by the following empirical formula [16], where C NO2 (ppm) is the concentration of NO 2 . Besides, due to the selectivity of the gas adsorption, the change of the Fermi level of graphene is related to gas species [16]. Therefore, the selective responses of graphene optical gas sensors could be used for sensing multiple gas molecules. Second, based on the graphene's Fermi level, the optical conductivity (σ ) of graphene can be calculated by Kubo formula [27], where is the optical frequency, = 7.6 × 10 12 s −1 is the scattering rate, n F (ω) is the Fermi distribution function, ω is the energy of the relativistic Landau levels, and is the exciton gap of Landau level energies. Assuming a finite thickness (d) of 0.7 nm of the graphene sheet, the relative permittivity of the graphene sheet can be calculated from the following equation, where ε 0 is the relative permittivity of vacuum. Based on Eqs.
(1)-(4), we calculated the relative permittivity of the graphene sheet with different initial Fermi levels and gas concentrations, as shown in Figure 1. The real part of the relative permittivity represents the phase change of light when interacting with graphene, while the imaginary part of the relative permittivity represents the optical loss induced by the graphene sheet. As shown in Figure 1(a), the real part of the relative permittivity decreases more rapidly at lower initial doping levels, so the incident light has a larger phase shift. Moreover, the variation of the imaginary part of the relative permittivity is relatively low for all the doping levels, since there is no interband transition in graphene when the Fermi level is beyond half of the photon energy (0.4 eV), as shown in Figure 1(b). Consequently, we chose the initial doping level of 0.41 eV in this work. Besides, the adsorbed gas molecules were strongly attached to the graphene devices at room temperature [16]. Graphene could be recovered to the undoped state by annealing at a high temperature, namely, from 323 K to 423 K in experiment [16], [28]. Finally, dual-mode resonance responses of the grapheneon-MRR to the gas concentration can be analyzed by using the transfer matrix method [29]. Different from single-mode MRRs, both TE 0 and TE 1 modes have phase changes (ϕ 0 and ϕ 1 ) with gas concentration (G) and temperature variation (T ), which could be assumed as, where K 0G and K 1G are the gas concentration sensitivities of the TE 0 and TE 1 modes, respectively, and K 0T and K 1T  are the temperature sensitivities of the TE 0 and TE 1 modes. If the two modes have linearly independent responses to the variations of the gas concentration and temperature, the influences of these two factors can be decoupled by solving the following equation, Phase signals ϕ 0 and ϕ 1 of the TE 0 and TE 1 modes, which are sensitive to the gas concentration and temperature variation, can be characterized by using a cavity, namely, MRR. As a result, we can separate graphene and temperature-induced RI variations in NO 2 molecular sensors based on the dual-mode graphene-on-MMR.

III. DESIGN AND SIMULATION RESULTS
Based on the above principle, we designed an optical gas sensor based on the graphene-on-MRR, as shown in Figure 2(a). A racetrack MRR was designed on a silicon-on-insulator wafer with a 220-nm thick top silicon layer (H1) and 3 µm buried oxide (BOX) (H2). As shown in Figure 2(b) and Figure 2(c), a waveguide width (W) was set as 1 µm with an etching depth (H3) of 200 nm, simultaneously supporting the TE 0 and TE 1 modes, while a bending radius (r) of the MRR was set as 20 µm introducing negligible radiation losses to the two modes. The waveguide is embedded in silicon oxide. A graphene sheet could be integrated on the surface of the MRR isolated by using a thin silicon oxide layer (H4). By adjusting the thickness of the isolation layer, it is possible to control the interaction strength between the propagating light and graphene sheet. In this work, we fixed the thickness of the isolation layer as 10 nm, which is feasible for experimental fabrication [30]. At the wavelength of 1550 nm and Fermi level of 0.41 eV, the effective RIs of the TE 0 and TE 1 modes were simulated as 2.7338 and 2.4129, respectively, by using a commercial finite element method (FEM) software tool (COMSOL Multiphysics). The optical loss coefficients are related to the imaginary parts of the complex effective RIs and are calculated as 0.0085 dB/µm and 0.01 dB/µm for the TE 0 and TE 1 modes, respectively. Figure 2(d) shows the simulated electrical field distributions of the two modes.
Since the TE 0 and TE 1 modes have different effective RIs and optical losses, we need to properly design the coupling length (L) and gap width (g) of the MRR to satisfy the critical coupling conditions for the two modes. The fabrication of the device is CMOS-compatible. The silicon devices can be fabricated by electron beam lithography (EBL) followed by dry etching. A thick silicon oxide layer could be deposited by using plasma-enhanced chemical vapor deposition (CVD). After that, the waveguide devices could be planarized by using chemical mechanical polishing to reach the top silicon layer. The commercial CVD graphene can be transferred onto the silicon device by using the standard wet transferring process. In the wet transfer process [17], the CVD graphene deposited on a copper foil could be first spin-coated with a layer of polymethyl methacrylate (PMMA). Then the copper foil could be etched away by using the ammonium persulfate solution. After rinsed in deionized water, the graphene supported by the PMMA layer could be transferred onto the silicon chip. The chip could be dried in the air and baked on a hot plate to allow better contact between graphene and waveguide devices. The EBL could be used to define the areas where the graphene layer should be exposed [17]. Then the O 2 plasma could be used to remove the exposed graphene areas. Finally, the remaining PMMA could be removed by acetone. The silicon waveguide could be used as a bottom gate to electrically tune the Fermi level of the graphene sheet.
Based on the proposed structure, we first numerically studied the dual-mode graphene-on-MRR. We simulated the cross-coupling power ratio (k 2 ) as a function of coupling length (L) under a fixed gap width (g) of 300 nm, as shown in Figure 3(a). With the L of 289.2 µm, the TE 0 and TE 1 modes have the same k of 0.4, which provides similar extinction ratios (ERs) for the two modes in the MRR. Moreover, we calculated the L needed to achieve the same k of the two modes for the different g, as presented in Figure 3(b).  indicates that with increasing the g, the L increases while the k decreases. Finally, we employed the above optical coefficients obtained to calculate quality (Q) factors [31] and ERs of the MRR, as shown in Figure 3(c) and Figure 3(d). By increasing the g, the Q factors quickly increase first and then become almost saturated. As RI sensors usually prefer a large Q factor, large ER, and small device footprint [32], we chose the g of 300 nm and L of 289.2 µm to develop the optical gas sensor.
Based on the designed dual-mode graphene-on-MRR device, we explored its application in NO 2 sensing under different temperatures. The shift of the resonance wavelength λ res is essentially caused by a change of the effective RI of the resonant mode n eff with λ res = n eff L eff /m [32], where L eff is the effective length of the MRR, and m is the order of the mode. We first calculated the effective RIs, optical loss coefficients, and transmission spectra of the TE 0 and TE 1 modes with 0 ppm and 20 ppm NO 2 gas doping at a room temperature of 300 K, as shown in Figure 4(a) and Figure 4(b). When gas molecules are adsorbed on the graphene sheet, the Fermi level increases, leading to the decrease of effective RIs and optical losses, the resonant wavelengths, therefore, have blueshifts while the Q factors and ERs become larger. The resonant wavelengths of the two modes with different gas concentrations are shown in Figure 4(c) and Figure 4(d). The sensitivities from the linear fittings are −0.018 nm/ppm for the TE 0 mode (K 0G ) and −0.025 nm/ppm for the TE 1 mode (K 1G ), respectively. The LOD of the sensor is 0.5 ppm, which reaches the requirement of the Occupational Exposure Limit for NO 2 sensing in Europe (1ppm) [33]. By adjusting the waveguide geometry, the interactions between the waveguide modes and graphene can be tailored to modify the sensitivity and LOD. Then we calculated the temperature sensitivity of the sensor. In our model, we applied the thermo-optic  coefficients of 1.8 × 10 −4 /K of silicon [34] and 0.96 × 10 −5 /K of silicon oxide [35] and simulated the effective RIs and optical loss coefficients of the two modes. The calculated resonant wavelengths at different temperatures are shown in Figure 4(e) and Figure 4(f). As the temperature increases, effective RIs of the two modes increase, leading to the redshifts of the resonant wavelengths. The temperature sensitivities are fitted as 0.106 nm/K for the TE 0 mode (K 0T ) and 0.130 nm/K for the TE 1 mode (K 1T ), respectively. The temperature sensitivities are four times larger than those of the gas concentration. Consequently, it is critical to eliminate the temperature variation when measuring the gas concentration by the RI sensing devices.
Finally, with the obtained gas concentration sensitivities (K 0G and K 1G ) and temperature sensitivities (K 0T and K 1T ) of the two modes, we demonstrated the optical gas sensor without suffering from the cross-sensitivity of temperature variations problem. Based on the above graphene-on-MRR design, the resonant wavelengths are 1546.99 nm for the TE 0 mode, and 1544.86 nm for the TE 1 mode, respectively, under a temperature of 300 K, as indicated by the black solid curves in Figure 5(a) and Figure 5(b). Then, we assumed a sensing condition with a gas concentration of 2 ppm and a temperature increase of 2 K. Based on Eqs. (1)-(4), the resonant wavelengths of the TE 0 and TE 1 modes shift to longer wavelengths by 0.16 nm and 0.19 nm, respectively. Based on the resonant wavelength shifts, we calculated gas concentration and temperature variations by using Eq. (6). The gas concentration and temperature increase were calculated as 2.1 ppm and 1.9 K, respectively, which are well consistent with the setting values. As a result, we theoretically demonstrated that the graphene-induced and temperature-induced RI variations could be decoupled by using the graphene-on-MMR. We compared the sensing performance of the proposed device with previous studies based on various approaches, such as the fiber-optic sensor [36], metal oxide semiconductor sensor [37], and solid-electrolyte gas sensor [38], as shown in Table 1. The LOD of the proposed device is comparable with those of the fiber-optic sensor and metal oxide semiconductor sensor but lower than that of the reported YSZ based solid-electrolyte gas sensor. It is worthwhile to know that the metal oxide semiconductor and solid-electrolyte gas sensors have to be operated at a high temperature. While the proposed device could work at room temperature and is not affected by the electromagnetic intervention.

IV. CONCLUSION
In summary, we theoretically studied the dual-mode graphene-on-MRR for gaseous NO 2 sensing. The device has a sensitivity of 0.02 nm/ppm and a LOD of 0.5 ppm. By using the dual-wavelength demodulation method, the gas concentration can be measured without suffering from temperature fluctuations. Our study is expected to boost the development of on-chip sensitive sensors with high temperature-stability for gas sensing.