Fast response and high responsivity realization of microcavity enhanced graphene photodetector using subwavelength grating electrodes

Optics Communications 457 (2020) 124684

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Fast response and high responsivity realization of microcavity enhanced graphene photodetector using subwavelength grating electrodes Haixia Liu, Yujie Lei, Yizhen Wang, Hua Shen, Yanxiong Niu ∗ School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China

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Keywords: Subwavelength grating Graphene Responsivity Response time

ABSTRACT Graphene photodetectors (GPD) have been studied since the first discovery of graphene, and microcavity enhanced graphene photodetector (MEGPD) is one of the structure of GPDs with many advantages. Additionally, MEGPDs can reach fast response with well-designed electrode structure. Subwavelength grating (SWG) shows extraordinary optical transmission (EOT) phenomenon, making it a potential structure for MEGPD electrodes. Responsivity of MEGPD can be kept at its origin value due to high transmittance of SWG structure while response time of MEGPD could be significantly reduced. In this paper, a design and analysis of MEGPD with SWG electrodes is presented. Theoretical analysis shows that structure parameters including period, height and width of slits are the key factors to influence both the transmittance and response time. Silver is selected as the material of electrodes to obtain high conductivity. Transmittance is determined through a transmission model of SWG structure. SWG structure is confirmed through optimization, and the result is presented below: The period is 730 nm, the height is 580 nm and the width of slits is 330 nm. At a nominal operating wavelength of 1.55𝜇m, the transmittance can reach 0.9927 to maintain the responsivity at 1.23A/W and the response time can reach picoseconds. This design may provide an idea to gain high response speed when fabricating high responsivity GPD.

1. Introduction Graphene photodetector (GPD) has been studied since the first discovery of graphene in 2004 and has attracted much attention due to its unique characteristics such as fast response and wide detective range. Applications of GPD on long-wavelength photons detection, especially in terahertz detection, are attractive to researchers, though in infrared and visible light detection graphene suffers from weak absorption and large dark current [1–7]. Microcavity enhanced GPD (MEGPD) can approach high responsivity with narrow spectral width and high Q-factor, which has bright prospects in visible light and infrared detection, and also has great potential in wavelength division multiplexing (WDM) system [8–10]. However, the design of the electrodes has not yet been taken into account in time, and well-designed electrode structure can highly reduce the response time while keep the responsivity at high level. Metal–graphene–metal (MGM) electrode structure, similar to that of traditional MSM photodetectors, is easy to be fabricated and integrated [11]. Besides, the response time of MGM structure GPD is much lower than that of traditional structure GPD [12]. However, MEGPD can reach high responsivity with small area of interdigital electrodes, but with larger area of electrodes MEGPD can reach high response speed. Subwavelength grating (SWG) shows extraordinary

optical transmission (EOT) phenomenon [13]. MEGPD can reach high responsivity and high response speed with SWGs serve as electrodes. Researches of SWG began in 1998 when Ebbesen and his co-workers reported the EOT phenomenon [13]. Over the next few years appeared some theoretical studies about two main factors that affect EOT phenomenon: surface plasmon polaritons (SPPs) and cavity modes [14–17]. In 2011, Romanato reported the analysis of near- and far-field optical distribution of light transmitted through SWG [18]. Besides, researches about photodetectors based on SWG structure were also reported. In 2008, Hu demonstrated different microcavity structure with different SWG structures as top reflectors, which can enhance the absorption 20 times [19]. In 2014, Zhao and his co-workers presented a GPD based on deep metal grating, which can enhance the absorptance of graphene to nearly 70% [20]. However, Hu and Zhao made SWG as top reflector, requiring the absorbing layer to achieve certain thickness, which cannot be applied on MEGPD. Though grating structure has been applied on some other photodetectors [21], no research about MEGPD integrated with subwavelength grating electrodes is proposed. In this article, a MEGPD integrated with SWG electrodes is proposed. The microcavity structure is proposed in our previous work [22] and the design and performance simulation of SWG electrodes are the main targets. Based on model analysis presented by García-Vidal [23],

∗ Corresponding author. E-mail address: [email protected] (Y. Niu).

https://doi.org/10.1016/j.optcom.2019.124684 Received 22 July 2019; Received in revised form 1 September 2019; Accepted 1 October 2019 Available online 4 October 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.

H. Liu, Y. Lei, Y. Wang et al.

Optics Communications 457 (2020) 124684

Fig. 1. (a) Schematic structure of MEGPD integrated with SWG electrodes, the SWG structure is on the upper layer of graphene, the other parts of the MEGPD remains unchanged (b) Top view of electrodes layer and graphene layer, subwavelength grating structure is constituted by the electrode fingers.

simulation, the saturation velocity is assumed as a constant. So the transit time can be expressed in the following equation:

transmittance of SWG can be expressed as a function of three parameters: the period, the height and the width of slits. Silver is selected as the electrode material. At a nominal operating wavelength of 1.55 μm, the transmittance of SWG can reach 0.9927 to keep the responsivity of MEGPD in our previous work at 1.23 A/W. Besides, the response time of MEGPD can reach picoseconds. Further analyses including the influences of three parameters are presented at the end of this paper.

𝜏𝑖 =

The structure of MEGPD is presented in Fig. 1a with the main structure coming from our previous work. Comparing to the MEGPD structure presented in paper mentioned above, the electrodes of this MEGPD are fabricated above the graphene layer. The top view of electrodes and graphene layer is given in Fig. 1b. The interdigital arrangement of the two electrodes alternately constitutes a grating structure. Here the period of SWG p and the width of SWG slits w are defined in Fig. 1b. The response time of this photodetector consists times of different procedures [24] and here two main times are taken into consideration: RC charging time and transit time of photogenerated carriers [25]. To calculate RC charging time, the capacitance and resistance should be calculated first. Capacitance can be given in the following expression: 𝐾(𝑘) 𝐴 ⋅ 𝜀 (1 + 𝜀g ) ⋅ 𝐾(𝑘′ ) 0 𝑝

𝜓(𝑥, 𝑧) = 𝛼𝜓0+ 𝑒−𝑖𝑘0 𝑛𝑒𝑓 𝑓 𝑧 + 𝛽𝜓0− 𝑒−𝑖𝑘0 𝑛𝑒𝑓 𝑓 (ℎ+𝑧)

where and represent the electromagnetic field forward and backward. 𝑘0 represents the wave vector while 𝑛𝑒𝑓 𝑓 represents the effective refractive index of SWG. The coefficient 𝛼 and 𝛽 can be expressed below: 𝛼 = 𝜏12 + 𝛽 ⋅ 𝜌21 𝑒𝑖𝑘0 𝑛𝑒𝑓 𝑓 ℎ 𝛽 = 𝛼 ⋅ 𝜌23 𝑒

1 𝑑𝜑 √( ) 1 − 𝑘2 sin2 𝜑 ( ) 𝜋𝑤 𝑘 = tan2 4𝑝 √( ) ′ 𝑘 = 1 − 𝑘2

𝑡 = 𝜏23 exp(𝑖𝑘0 𝑛𝑒𝑓 𝑓 ℎ)𝛼

(1)

𝐾(𝑘)𝐴 ⋅ 𝜀 (1 + 𝜀g ) 𝐾(𝑘′ )𝑝 0

(8) (9)

(10)

According to Eqs. (8), (9) and (10), t can be written in the following form [23]: 𝑡=

𝜏12 𝜏23 exp(𝑖𝑘0 𝑛𝑒𝑓 𝑓 ℎ) 1 − 𝑟21 𝑟23 exp(𝑖2𝑘0 𝑛𝑒𝑓 𝑓 ℎ)

(11)

This is the ideal transmission coefficient of SWG structure. In practical application, several factors such as the phase alternation on the interface of I and II, II and III, and the loss in SWG slits, the transmittance should be expressed below [18]:

(2)

(3)

1 𝑇 = √ 𝜀𝑚

(4)

The resistance of electrodes mainly comes from the metal–graphene junction resistance and it could reach 110 Ωμm [26]. So the RC charging time is given below: 𝜏𝑅𝐶 = 𝑅𝑠 𝐶 = 𝑅𝑠 ⋅

𝑖𝑘0 𝑛𝑒𝑓 𝑓 ℎ

The transmission coefficient t is given below:

𝜋∕2

∫0

(7)

𝜓0+

𝜓0−

where A represents the area of electrodes, p is defined as the period above, 𝜀0 is the relative dielectric constant of air, 𝜀𝑔 is the relative dielectric constant of graphene. The expressions of K, k and 𝑘′ are: 𝐾(𝑘) =

(6)

Several methods are used to calculate the transmission properties of SWG structure [27–29], and here a simplified analytical SWG model presented by García-Vidal is selected to calculate the transmission properties. Fig. 2a shows the structure of SWG while Fig. 2b indicates the transmission model of SWG. Electromagnetic field distribution in the SWG slits can be expressed in the following equation:

2. SWG structure and theory analyses

𝐶=

𝑤 2𝑣

|𝜏12 |2 |𝜏23 |2 exp(−2 |𝑘′′ ℎ|) | | | | | | |1 − |𝜌12 𝜌23 | exp(𝑖𝜙𝑡𝑜𝑡 )|2 | | | |

(12)

where 𝛷𝑡𝑜𝑡 represents the phase alternation inside the slits: 𝜙𝑡𝑜𝑡 = 𝜙21 + 𝜙23 + 2𝑘0 𝑛𝑒𝑓 𝑓 ℎ

(5)

(13)

The parameters n and 𝑘0 can be expressed below:

Transit time mainly depends on the saturation velocity of photogenerated carriers and the width of slits. The saturation velocity v depends on many parameters, such as bias voltage. In order to simplify the

𝑛𝑒𝑓 𝑓 = 𝑘′ ∕𝑘0 𝑘 = 𝑘′ + 𝑖𝑘′′ 2

(14) (15)

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Optics Communications 457 (2020) 124684

Fig. 2. (a) Schematic structure of SWG electrodes (b) Schematic of the transmission model of SWG.

w = 50 nm, but it falls to 1.2 when w = 100 nm. If the width increases, the refractive index will be close to 1, and the SWG structure has no EOT phenomenon anymore. The transmission and reflection factors 𝜌 and 𝜏 can be calculated through boundary conditions for electromagnetic fields on different interfaces [23]: 2𝑆0 cos 𝛼 1 ⋅ cos 𝛼 + 𝑍𝑠 1 + (1 − 𝑍𝑠 )𝑓 cos 𝛼 − 𝑍𝑠 2𝑆0 𝑆̃0 (1 − 𝑍𝑠 ) cos 𝛼 1 𝜌12 = − ⋅ cos 𝛼 + 𝑍𝑠 1 + (1 − 𝑍𝑠 )𝑓 (cos 𝛼 + 𝑍𝑠 )2 1 − (1 + 𝑍𝑠 )𝑓 𝜌21 = − 1 + (1 − 𝑍𝑠 )𝑓 2𝑆̃0 1 𝜏21 = ⋅ cos 𝛼 + 𝑍𝑠 1 + (1 − 𝑍𝑠 )𝑓

𝜏12 =

Fig. 3. Effective refractive index as a function of width of the slits.

(17) (18) (19) (20)

Considering the SWG structure is sandwiched between air layers, 𝜌23 = 𝜌21 and 𝜏23 = 𝜏21 . 𝛼 represents the incident angle. The phase alternation 𝛷21 and 𝛷23 can be dropped from the equation given below (r is the modulus of 𝜌21 ):

where 𝑘′′ represents the loss inside the slits. The wave factor k inside the slits can be found from the characteristic equation given below: √ √ 𝑤 𝑘2 − 𝑘20 𝜀𝑔 𝜀𝑔 𝑘2 − 𝑘20 𝜀𝑚 tanh( )=− √ (16) 2 𝜀𝑚 𝑘2 − 𝑘20 𝜀𝑔

𝜌21 = 𝑟𝑒𝑖𝜙

(21)

The other parameters are given below:

𝜀𝑔 and 𝜀m respectively represent the relative permittivity of graphene and metal. According to Eqs. (14), (15) and (16), the effective refractive index of SWG can be found related to the width of the slits, the relative permittivity of both graphene and metal. In this paper, 1.55 μm wave is selected as the operating wavelength to match the parameters in our previous work. Silver is selected as the material of electrodes for its high conductivity, and its relative permittivity is 𝜀m = −112.37 + 6.64𝑖 [30] when the incident wavelength is 1.55 μm. Fig. 3 shows the relationship between the effective refractive index of SWG and the width of slits. The refractive index decreases when the width is increasing. The effective refractive index can reach 1.4 when

√ sin(𝑘𝛾𝑛 𝑤∕2) 2𝜋𝑛ef f 𝑤 𝜀m , 𝑆𝑛 = , 𝑆̃n = 𝑆n , 𝛾𝑛 = sin 𝛼 + , 𝑘𝛾𝑛 𝑤∕2 𝑝 𝑝 ⋅ 𝑘0 ∞ ∑ 𝑆𝑛 𝑆̃𝑛 𝑓= . √ 𝑛=−∞ 1 − 𝛾𝑛2 + 𝑍𝑠

𝑍𝑠 =

3. Simulation and results According to Eq. (12) and the following equations, the transmission properties of SWG mainly depend on three parameters: the period p,

Fig. 4. Transmittance as a function of the height of SWG, Fig. 4b is part of Fig. 4a.

3

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Optics Communications 457 (2020) 124684

Fig. 5. Transmittance as a function of the period of SWG, three different lines indicate three different height value.

Fig. 8. Schematic of the MEGPD structure with the length of microcavity and buffer layer recalculated.

different period values when height differs. This is because p and w both affect the transmittance according to Eqs. (12) and (17)–(20). To further calculate the best values of p and w, Fig. 6 is given as the relationship between transmittance and period and height. The 𝑥-axis represents the height while 𝑦-axis represents the period, and different colors incidents different transmittance. It can be seen that only when the period matches the height can transmittance reach a high value. When the two parameters mismatches, transmittance falls rapidly. The peak transmittance appears when p = 730 nm and w = 580 nm according to Fig. 6. The effect of w on transmittance remains to be discussed since it affects not only 𝜌 and 𝜏 but also the effective refractive index. Fig. 7 shows the relationship between w and transmittance with Fig. 7b serving as the enlargement of part of Fig. 7a. Two peaks appear in Fig. 7a, but only the left one meets the requirement. Because 𝑤 = 𝑝 at the right peak and SWG no longer exists. When w increases, the transmittance rapidly reaches to the first peak, then falls down slowly and increases again. In the fast rising stage, the EOT phenomenon plays a leading role. When w keeps increasing, the EOT phenomenon weakens. However, when the width of the slits becomes larger, the incident light can travel directly through the slits, so the transmittance will keep high. According to Fig. 7b, when w = 330 nm, the transmittance can reach the peak, and the peak value T = 0.9927. The parameters of MEGPD is presented here: AlAs/Al0.1 Ga0.9 As and TiO2 /SiO2 serve as reflector, Al2 O3 serves as buffer layer, the microcavity length is 467.4 nm and bilayer graphene is located in the middle of the microcavity. However, the microcavity length should be enlarged

Fig. 6. Transmission as a function of both the period and the height of SWG.

the height h and the width of slit w. Here in Fig. 4 the relationship between the height and the transmittance is presented. Fig. 4b is the enlargement of part of Fig. 4a. The transmittance of SWG varies periodically with the height of SWG. Actually according to Eq. (13), the phase alternation varies periodically with h when 𝛷21 and 𝛷23 are constants. When the parameters p and w are constants, 𝜌21 remains, so 𝛷21 and 𝛷23 remain invariant. The transmittance reaches the maximum when phase alternation 𝛷𝑡𝑜𝑡 is an integer multiple of 2𝜋. However, the peaks of transmittance decrease when height increases, because metal will absorb part of the incident light. So height should be chosen as the value which makes the transmittance reach the first peak. Furthermore, the relationship between the period of SWG and the transmittance is presented in Fig. 5. Peak transmittances appear at

Fig. 7. Transmission as a function of the width of SWG slits, Fig. 7b is part of Fig. 7a.

4

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Optics Communications 457 (2020) 124684

Fig. 9. The change of transmittance as a function of three parameters (a) of the period of SWG (b) of the height of SWG (c) of the width of SWG slits.

to become larger than the height of SWG. Here the microcavity length should be selected as 1.5𝜆eq , which is 1402.2 nm. The length of bottom buffer layer should be 𝐿𝑏𝑜𝑡 = 0.5 × 1402.2 nm = 701.1 nm. The length of top buffer layer should be 𝐿𝑡𝑜𝑝 = (1.5 × 𝜆∕2 − ℎ × 𝑛𝑒𝑓 𝑓 )∕𝑛𝑏𝑢𝑓 = 326.8 nm. The structure of MEGPD is presented in Fig. 8. Photovoltaic (PV) effect and photo-thermoelectric (PTE) effect both contribute to photocurrent generation [31]. However, the efficient photocurrent generation of MEGPD presented below mainly results from the internal E-field according to paper [11]. The responsivity of this MEGPD is 𝑅0 = 1.24 A/W without the effect of SWG. So the responsivity of MEGPD integrated with SWG is 𝑅 = 𝑇 ⋅ 𝑅0 = 1.23 A∕W, which means the SWG structure has little impact on the performance of MEGPD. Here a simple comparison of RC charging time and transit time between the MEGPD presented in our previous work and in this paper is given below. The saturation velocity is assumed as a constant and here the value 𝑣 = 5.5 × 105 m∕s in the paper [11] is selected as the constant. The results of the response time are not consistent with the actual situation, they are only applied in the comparison. Besides, the number of finger electrodes is assumed as 10 pairs, and the area of the graphene is assumed as 14.6 μm × 14.6 μm. The RC charging time can be calculated as: 𝜏𝑅𝐶 = 𝑅𝑠 𝐶 = 𝑅𝑠 ⋅

𝐾(𝑘)𝐴 ⋅ 𝜀 (1 + 𝜀g ) = 0.13 ps 𝐾(𝑘′ )𝑝 0

It is much larger than the sum of RC charging time and transit time of the MEGPD presented in this paper. Assuming times of other procedures are the same, the SWG structure can highly decrease the response time of MEGPD. During fabrication process, errors inevitably occur. To further analyze the errors that influence the transmittance of SWG structure, results of simulations are illustrated below. Here the change of transmittance is selected as the parameter to measure the influences of errors. Fig. 9a presented the relationship between the changes of transmittance and the parameter p. Transmittance could be easily affected by the error of period if 𝑝 > 730 nm but could tolerant little error if 𝑝 < 730 nm. Fig. 9b presented the relationship between the changes of transmittance and the parameter h. Transmittance could be easily affected by the error of height, because height directly determines the phase alternation inside the slit according to Eq. (14). If the phase alternation is not an integer multiple of 2𝜋, the transmittance could reduce greatly. Fig. 9c illustrated the relationship between the changes of transmittance and the parameter w. Actually the width of SWG slit affects little on the transmittance. 4. Conclusion An optimized MEGPD structure with well-designed SWG structure electrodes is presented in this paper whose responsivity keeps at a high level and response speed is strongly enhanced. At the operating wavelength of 1.55 μm, the responsivity of MEGPD can remain at 1.23 A/W since the transmittance of SWG structure can reach 0.9927, while the response time can reach picoseconds. This paper focused on the transmission model and the design of SWG structure. The period, the height and width of slits have critical effects on the performance of SWG, so the fabrication of SWG and graphene deserves to be emphasized. Errors of these parameters have different effects on the performance of SWG. These results provide a prospective solution

(22)

The transit time can be calculated as: 𝜏i =

𝑤 330 nm = = 0.3 ps 2𝜈𝑑 11 × 105 m∕s

(23)

The transit time of MEGPD presented in our previous work can be calculated as (the width of the electrodes is assumed as 1 μm): 𝜏i =

(14.6 − 2 × 1) μm 𝑤 = = 11.5 ps 2𝜈𝑑 11 × 105 m∕s

(24) 5

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Optics Communications 457 (2020) 124684

of fast response and high responsivity MEGPD and may facilitate the application of graphene photodetector. In practical application, many other factors could also limit the response time and several methods have been reported to solve these problems [32,33]. These would also be taken into consideration and solved in our future researches.

[14] I.R. Hooper, J.R. Sambles, Surface plasmon polaritons on thin-slab metal gratings, Phys. Rev. B 67 (2003) 235404, http://dx.doi.org/10.1103/PhysRevB.67.235404. [15] K.G. Lee, Q.H. Park, Coupling of surface plasmon polaritons and light in metallic nanoslits, Phys. Rev. Lett. 95 (2005) 103902, http://dx.doi.org/10.1103/ PhysRevLett.95.103902. [16] F. Marquier, J. Greffet, S. Collin, Resonant transmission through a metallic film due to coupled modes, Opt. Express 13 (2005) 70–76, http://dx.doi.org/10.1364/ OPEX.13.000070. [17] P.B. Catrysse, G. Veronis, H. Shin, Guided modes supported by plasmonic films with a periodic arrangement of subwavelength slits, Appl. Phys. Lett. 88 (2006) 031101, http://dx.doi.org/10.1063/1.2164905. [18] F. Romanato, T. Ongarello, G. Zacco, Extraordinary optical transmission in onedimensional gold gratings: near- and far-field analysis, Appl. Opt. 50 (2011) 4529, http://dx.doi.org/10.1364/AO.50.004529. [19] X. Hu, M. Li, Z. Ye, Design of mid-infrared photodetectors enhanced by resonant cavities with subwavelength metallic gratings, Appl. Phys. Lett. 93 (2008) 241108, http://dx.doi.org/10.1063/1.3052893. [20] B. Zhao, J.M. Zhao, Z.M. Zhang, Enhancement of near-infrared absorption in graphene with metal gratings, Appl. Phys. Lett. 105 (2014) 031905, http://dx. doi.org/10.1063/1.4890624. [21] L. Wang, X. Chen, Top-gated black phosphorus phototransistor for sensitive broadband detection, Nano. 10 (2018) 5852–5858, http://dx.doi.org/10.1039/ C7NR09545G. [22] H.X. Liu, Y.J. Lei, Design and performance simulation of microcavity enhanced bilayer graphene infrared photodetector, Opt. Commun. 447 (2019) 24–29, http://dx.doi.org/10.1016/j.optcom.2019.04.067. [23] F.J. García-Vidal, L. MartinMoreno, Transmission and focusing of light in onedimensional periodically nanostructured metals, Phys. Rev. B 79 (2002) 145–150, http://dx.doi.org/10.1103/PhysRevB.66.155412. [24] C. Liu, L. Wang, X. Chen, Room-temperature photoconduction assisted by hotcarriers in graphene for sub-terahertz detection, Carbon 130 (2018) 233–240, http://dx.doi.org/10.1016/j.carbon.2018.01.020. [25] J.B.D. Soole, H. Schumacher, Ingaas metal–semiconductor-metal photodetectors for long wavelength optical communications, IEEE J. Quantum Electron. 27 (1991) 0–752, http://dx.doi.org/10.1109/3.81384. [26] F. Xia, V. Perebeinos, Y.M. Lin, The origins and limits of metal–graphene junction resistance, Nat. Nanotechnol. 6 (2011) 179–184, http://dx.doi.org/10. 1038/nnano.2011.6. [27] L. Li, New formulation of the fourier modal method for crossed surface-relief gratings, J. Opt. Soc. Amer. A 14 (1997) 2758–2767, http://dx.doi.org/10.1364/ JOSAA.14.002758. [28] J.A. Porto, F.J. García-Vidal, J.B. Pendry, Transmission resonances on metallic gratings with very narrow slits, Phys. Rev. Lett. 83 (1999) 2845–2848, http: //dx.doi.org/10.1103/PhysRevLett.83.2845. [29] Z. Chen, I.R. Hooper, J.R. Sambles, Strongly coupled surface plasmons on thin shallow metallic gratings, Phys. Rev. B 77 (2008) 761–768, http://dx.doi.org/ 10.1103/PhysRevB.77.161405. [30] P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6 (1972) 4370–4379, http://dx.doi.org/10.1103/physrevb.6.4370. [31] X. Xu, N.M. Gabor, J.S. Alden, Photo-thermoelectric effect at a graphene interface junction, Nano Lett. 10 (2010) 562, http://dx.doi.org/10.1021/nl903451y. [32] J.A. Robinson, M. Labella, M. Zhu, Contacting graphene, Appl. Phys. Lett. 98 (2011) 053103, http://dx.doi.org/10.1063/1.3549183. [33] A.D. Franklin, S.J. Han, A.A. Bol, Double contacts for improved performance of graphene transistors, IEEE Electron. Device Lett. 33 (2012) 17–19, http: //dx.doi.org/10.1109/led.2011.2173154.

Acknowledgment This study was supported by the CAST Innovation Foundation, China (Grant No. CAST-BISEE2019-027). References [1] K.S. Novoselov, V.I. Fal’Ko, L. Colombo, A roadmap for graphene, Nature 490 (2012) 192–200, http://dx.doi.org/10.1038/nature11458. [2] Y. Zhang, Z. Wu, Y. Cao, Optical properties of one-dimensional fibonacci quasiperiodic graphene photonic crystal, Opt. Commun. 338 (2015) 168–173, http: //dx.doi.org/10.1016/j.optcom.2014.10.059. [3] J.T. Liu, X.J. Li, Y.Y. Wu, Effect of thickness deviation on the absorption of graphene in photonic crystal microcavity, Optik 164 (2018) 610–616, http: //dx.doi.org/10.1016/j.ijleo.2018.03.058. [4] N. Papasimakis, Z. Luo, Z.X. Shen, Graphene in a photonic metamaterial, Opt. Express 18 (2010) 8353–8359, http://dx.doi.org/10.1364/OE.18.008353. [5] D. Spirito, D. Coquillat, S.L.D. Bonis, High performance bilayer-graphene terahertz detectors, Appl. Phys. Lett. 104 (2014) 97–105, http://dx.doi.org/10.1063/ 1.4864082. [6] W. Tang, L. Wang, X. Chen, Dynamic metamaterial based on the graphene split ring high-Q Fano-resonnator for sensing applications, Nanoscale 8 (2016) 15196–15204, http://dx.doi.org/10.1039/C6NR02321E. [7] C. Liu, L. Wang, X. Chen, Room-temperature high-gain long-wavelength photodetector via optical-electrical controlling of hot Carriers in graphene, Adv. Opt. Mater. 6 (2018) 1800836, http://dx.doi.org/10.1002/adom.201800836. [8] J.T. Liu, Y. Cao, H. Tong, Broad-spectrum enhanced absorption of graphenemolybdenum disulfide photovoltaic cells in metal-mirror microcavity, Nanotechnology 29 (2018) 144001, http://dx.doi.org/10.1088/1361-6528/aaab13. [9] M. Engel, M. Steiner, A. Lombardo, Light–matter interaction in a microcavitycontrolled graphene transistor, Nature Commun. 3 (2012) 906, http://dx.doi. org/10.1038/ncomms1911. [10] M. Furchi, A. Urich, A. Pospischil, Microcavity-integrated graphene photodetector, Nano Lett. 12 (2012) 2773–2777, http://dx.doi.org/10.1021/ nl204512x. [11] T. Mueller, F. Xia, P. Avouris, Graphene photodetectors for high-speed optical communications, Nat. Photonics 4 (2010) 297–301, http://dx.doi.org/10.1038/ nphoton.2010.40. [12] J.H. Kim, H.T. Griem, R.A. Friedman, High-performance back-illuminated ingaas/inalas MSM photodetector with a record responsivity of 0.96 A/W, IEEE Photonics Technol. Lett. 4 (1992) 1241–1244, http://dx.doi.org/10.1109/68. 166955. [13] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, Extraordinary optical transmission through sub-wavelength hole arrays, Nature 391 (1998) 1114–1117, http://dx. doi.org/10.1038/35570.

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