Linear absorption coefficient of in-plane graphene on a silicon microring resonator

We demonstrate that linear absorption coefficient (LAC) of a graphene-silicon hybrid waveguide (GSHW) is determined by the optical transmission spectra of a graphene coated symmetrically coupled add-drop silicon microring resonator (SC-ADSMR), of which the value is around 0.23 dB/um. In contrast to the traditional cut-back method, the measured results are not dependent on the coupling efficiency of the fiber tip and the waveguide. Moreover, precision evaluation of graphene coated silicon microring resonator (SMR) is crucial for the optoelectronic devices targeting for compact footprint and low power consumption.

1. In order to measure the LACs induced by graphene, multiple stripe waveguides should be patterned with different lengths of graphene [14][15][16], of which the processes are burden some, time consuming and even expensive.
2. The coupling efficiencies between the fiber tips and the waveguides as well as waveguide end facets maintain non-uniformity. Moreover, such fiber-to-waveguide coupling losses are often comparable to or even much higher than the propagation losses in the waveguides [27], leading to high uncertainties in loss measurements, as stated in [30].
3. Because of the imperfect coverage of grapheme with cracks, the measured losses in these stripe waveguides deviate from the linear fit when the lengths of the transferred graphene are beyond 500 µm [14].
In addition to these disadvantages, the silicon microring resonator (SMR), which is a fundamental building block in silicon photonics, has been widely used in integrated optoelectronic devices owing to its compactness of footprint and low requirement of power [31]. Integrating graphene on SMR offers great opportunities in highperformance optoelectronic devices.
In this paper, we present a comprehensive method to determine the LAC of GSHW with a configuration of microring resonator using a small fraction of graphene, which suffers less cracks resulting from grapheme transfer process. A symmetrical add-drop SMR is introduced as a host for graphene. The monolayer grapheme grown by chemical vapor deposition (CVD) is transferred onto the fabricated SMR. The patterning of graphene is accomplished by an electron beam lithography (EBL) process following by a"lift-off" process. The experimental results are compared with a simulation model utilizing Finite Difference Method (FDM).

Experimental details
The symmetrically coupled add-drop silicon microring resonator (SC-ADSMR) consists of a SMR and dual stripe waveguides working as through and drop ports. The SMR, with a width of 500 nm and a height of 220nm,has a radius of R=15 µm, which is fabricated on a SOI wafer with a buried oxide (BOX) layer of 3 µm using EBL and inductively coupled plasmon (ICP) etching. The stripe waveguides, which are laterally coupled with the SMR, has the same dimensions with that of the SMR and the corresponding gaps are 125 nm and 117 nm respectively. The nearly identical gaps show that the fabricated add-drop silicon microring resonator is symmetrically coupled. In Fig. 1, the monolayer graphene transfer and the SC-ADSMR device fabrication processesare illustrated. CVDgrapheneis grown on both sides of the copper foil (Cu). Next, a 200-nmthick poly (methyl methacrylate) (PMMA)(Allresist, AR-P 672.045) film is spin-coated onto the upper surface of the layered backside graphene/Cu/monolayer graphene to protect the monolayer graphene from damage. The sample consisting of layered backside graphene/Cu/monolayer graphene/PMMA is floated on marble's etchant with 15 grams of copper(II) sulfate pentahydrate (CuSO 4 ·5H 2 O), 50 ml of deionized water (DI), and 50 ml of concentrated hydrochloric acid (HCl). The backside graphene is totally removed after 2-min chemical etching. Then the Cu/monolayer graphene/PMMA sample is floated on marble's etchant with 15 grams of copper(II) sulfate pentahydrate (CuSO 4 ·5H 2 O), 50 ml of deionized water (DI), and 50 ml of concentrated hydrochloric acid (HCl). The backside graphene is totally removed after 2-min chemical etching. Then the Cu/monolayer graphene/PMMA sample is floated on DI for about 3 minutes to remove the chemical impurities. Another marble's etchant with the same chemical recipe is applied for removal of the Cu beneath the monolayer graphene, of which the etching time is about 1.5 hours. The remained sample consisting of layered monolayer graphene/PMMA is last rinsed in DI, leaving it ready for transferring. We employ the following processes to transfer the monolayer graphene to specific region of the SC-ADSMR by ripping out the abundant monolayer graphene: a 450-nm thick PMMA film is spin-coated on the SOI wafer containing the fabricated SC-ADSMR device and the specific region with a 45 degree sector area is patterned using EBL, followed by developing and fixing of the PMMA photo resist. At the time, the prepared monolayer graphene/PMMA sample is transferred onto the chip followed by drying with a mild nitrogen blow. Subsequently, a "lift-off" process is introduced to form the graphene coated SC-ADSMR device. The whole chip is baked at 180°C for 15minutes, after which the PMMA is dissolved in hot acetone for about 1hour. The removal of the PMMA also results in cutting-away of the monolayer graphene resting on the450-nm thick PMMA, which is similar to the lift-off [32] process. Finally, the chip is rinsed in isopropyl alcohol (IPA) for further cleaning and dried again by a mild nitrogen blow. A scanning electron micrograph (SEM) picture of the graphene coated SC-ADSMR device with partial part of the stripe waveguides is shown in Fig. 2(a), in which secondary-electron contrast is obtained. The possible reason for imaging contrast lies in different secondary-electron-generation efficiencies of silicon, silicon oxide and monolayer graphene. At the boundary of the patterned graphene, the random roughness of the monolayer graphene is large due to the coarse-controlled "lift-off" process.
The detailed SEM picture of our fabricated GSHW is shown in Fig. 2(b). At the top of the waveguide, the monolayer graphene is covered. In addition to that, the monolayer grapheme naturally extends to the surface of the BOX layer, forming a trapezoid configuration. Figure 2(c) shows the photonic crystal grating coupler, which is optimized for TE mode coupling exhibiting an insertion loss of 7.5dB per facet. Adopting the experimental setup in Fig. 3(a), the SC-ADSMR is characterized by an amplified spontaneous emission (ASE) light source (Amonics, AEDFA-300-B-FA) ranging from 1535nm to 1565nm, and the transmission spectra of the through port before and after graphene transfer (noted as woGr and wGr respectively) are recorded by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370),which is shown inFig. 3(b). It shows that the resonator before and after graphene transfer have an identical free spectral range (FSR) of 5.8 nm. The significant reduction of extinction ratio and broadening of the resonances in Fig. 3(b) are the result of increased propagation loss (absorption) induced by the monolayer graphene. The red shift of the resonances are probably caused by the residual PMMA and the chemical impurities introduced by the graphene transfer and "lift off" procedure (the residual PMMA does not attribute to additional loss [24]). The explicit characterization of monolayer graphene relies on the Raman spectrum. In Fig.3(c), we measure the Raman spectra of the graphene coated SC-ADSMR device using LabRAMHR800 (France, Jobin-Yvon). The blue curve represents the Raman spectrum of the area where graphene is lifted off, of which the typical Raman peaks are missing. And the red curve shows a G peak (~ 1586cm -1 ) with a full width at half maximum (FWHM)of~ 18cm -1 and a 2D peak(~2700 cm -1 ), of which the 2D-to-G peak intensity ratio is about 1.2, implying that the transferred graphene is a monolayer and the corresponding chemical potential is around 0.2 eV [33]. Moreover, a weak D peak is also found at ~1350 cm -1 , indicating the transferred monolayer graphene is of high quality. We also measure the Raman spectra in some other regions. The results turn out to be the same with the Raman spectra of Fig. 3(c).

Fig. 4. Scheme of theSC-ADSMR with patternedmonolayer graphene
We adopt an analytical model proposed by Shijun Xiao et al. [30] to characterize the propagation loss in our graphene covered SC-ADMMR device. In Fig 4, the schematic diagram of the model is presented.κ 2 t and κ 2 d are coefficients representing the fraction of the optical power coupled into and out of the SMR through the input and drop port respectively. κ 2 p is the fraction of power losses per round-trip in the SMR due to intrinsic losses mainly resulting from grapheme absorption, roughness induced scattering. In our case, κ t =κ d is satisfied and optical response of the through port is given as [30]: Where T through (λ )is the power transmission of the through port, FWHM t is the FWHM of the optical transmission spectrum at the through port and λ 0 is the resonant wavelength. When the input wavelength is at resonance (λ=λ 0 ), T through (λ) has a minimal value of γ t which satisfies: ( ) ( ) 10 10 log , With ER t and γ t the extinction ratio and the minimal power transmission at the through port respectively. The coefficients κ p , κ t and κ d are described as: In the proposed sample, an eighth part of the resonator is covered with monolayer graphene. The total losses of the graphene coated SMR includes the linear absorption (LA) of the GSHW and the LA of the silicon waveguide. Assuming that the graphene "lift off" processdoes not induce extra LA in the silicon waveguide, the LAC of the GSHW can be written as: whereα wGr and α woGr correspond to the loss per round-trip before and after graphene transfer respectively, and n=1/8 corresponds to the fractional coverage length ofthe monolayer graphene. Table 1 shows the detailed experimental results before and after graphene transfer of the fabricated SC-ADMMR device deduced by the transmission spectra in Fig. 3(b), including the resonant wavelengths of the SC-ADSMR before and after graphene transfer, the corresponding extinction ratio and the FWHM of the transmission spectra. Utilizing the analytical method, the LAC of the GSHW in our case has a mean value of 0.23 dB/µm, which is comparable to the results in literature [23,24].

Simulation Model
Graphenecan be treated electromagnetically through its surface dynamic conductivity in a complex form consisting of interband and intraband contributions [34]: The intraband contribution can be evaluated as: , the interband contribution can be expressed as: where e is the electron charge, k B is the Boltzmann constant, ħ is the reduced Planck's constant, ω is the angular frequency of incident light, T is the temperature, μ c is the chemical potential, and τ is the momentum relaxation, respectively. In thesimulation, we use the values for the incident wavelength of λ s =1550 nm, the temperature of T=300K, and the momentum relaxation of τ=12 fs [35]. The surface dynamic conductivity of graphene σ (ω, μ c, τ, T) is plotted as a function of the chemical potentialμ c in Fig. 5. Taking the monolayer graphene as a boundary surface can be a good approximation in the simulation. We model graphene as a 2D anisotropic boundary and employ the 2D FDM to simulate the propagation loss in a stripe waveguide in Fig. 6(a). Since the graphene is not closely attached to the sidewall of the stripe waveguide, the interaction between the bilateral graphene and light is ignored. The physical boundary condition at the graphene/waveguide interface is expressed as [36]: wheren 12 is the vector normal to the interface, with direction from medium 1 to medium 2,Hand E is the normalized magnetic and electrical field at the interface respectively, J s is the surface current density of graphene, and here subscript // denotes in-plane field component.Adopting the waveguide width of 500 nmand height of 220 nm, the corresponding losses of the GSHW are plotted with different chemical potentials, of which the value is 0.07dB/µmfor TE mode when the chemical potential of graphene is around 0.2eV ( Fig. 6(b)). The simulated LAC of the GSHW is lower than the experimental result. This deviation probably lies in the following reasons: 1. The commercially available chip-sized monolayer graphene grown by CVD has some unpredictablemulti-layer domains [37], which could result in extra loss.
2. Chemical impurities are left after the wet etching transfer of monolayer graphene [38]. These chemical impuritieswill give rise to the surface roughness of the GSHW, leading to extra scattering loss.Moreover, the chemical impurities themselves may contribute to additional absorptionloss.

Conclusion
We propose a comprehensive way towards direct determination of the LACs of in-planemonolayer grapheneintegrated with SC-ADSMR device, whichdoes not depend on the coupling efficienciesbetween the fiber tips and the waveguides as well as the waveguide end facets. We design and fabricate a SC-ADSMR with patterned monolayer graphene.Themeasured result is larger than that of the simulation, which attributes to the imperfection of monolayer graphene and the scattering loss of the abundant chemical impurities introduced by graphene transfer and "lift off" procedures. Our workprovide efficient method to evaluate the linear optical performances of high-performance graphene-comprising waveguides targeting for compact footprint and low power consumption PICs.