Hybrid plasmonic graphene modulator with buried silicon waveguide

Journal Pre-proof Hybrid plasmonic graphene modulator with buried silicon waveguide Yuan Zhu, Chunyu Deng, Lei Huang, Guohua Hu, Binfeng Yun, Ruohu Zhang, Yiping Cui

PII: DOI: Reference:

S0030-4018(19)30819-3 https://doi.org/10.1016/j.optcom.2019.124559 OPTICS 124559

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Optics Communications

Received date : 11 April 2019 Revised date : 8 September 2019 Accepted date : 10 September 2019 Please cite this article as: Y. Zhu, C. Deng, L. Huang et al., Hybrid plasmonic graphene modulator with buried silicon waveguide, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124559. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

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Hybrid Plasmonic Graphene Modulator with Buried Silicon Waveguide Yuan Zhu1,2, Chunyu Deng1, Lei Huang1, Guohua Hu1,*, Binfeng Yun1, Ruohu Zhang1, Yiping Cui1,* 1

Advanced Photonics Center, School of Electronic Science and Engineering, Southeast University, Nanjing,

Jiangsu 210096, China 2The

14th Research Institute of China Electronics Technology Group Corporation, Nanjing, Jiangsu 210039,

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China

Abstract: We propose a low-loss broadband modulator by combining plasmonic effect with

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graphene to realize highly efficient modulation on the SOI (Silicon-On-Insulator) platform. Due to a hybrid plasmonic waveguide including buried silicon waveguide and silver waveguides, the fundamental mode is mainly confined in two single-layer graphene sheets, and the electric field vector is parallel to the graphene sheets ensuring the high efficient light absorption of graphene.

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The specific hybrid structure makes it easy for graphene transfer. Also, non-coplanar structure of silicon waveguide and silver waveguides provides simplified fabrication process and fabrication tolerance. The simulation results demonstrated that modulation bandwidth of 346 GHz is obtained, and the 3 dB modulation length is only 9.493 μm. In addition, competitively low propagation loss

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of 0.85 dB was realized of the hybrid modulator.

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Keywords: Surface plasmon polaritions, Graphene, Silicon-On-Insulator, Broadband modulator

*Corresponding author. E-mail addresses: [email protected] (G. Hu), [email protected] (Y. Cui). 1

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1. Introduction An optical modulator is one of key components in a photonic system, which is applied to change basic properties of a light beam propagation in optical waveguide according to external

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electronics signals [1]. Silicon-based modulators receive more and more attention from all over the world and show infinite potentials for future optical interconnections, as these modulators are compatible with the complementary metal-oxide-semiconductor (CMOS) fabrication standard and

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have relatively low costs. However, weak electric-to-optic conversion efficiency of silicon-based modulators leads to their lower modulation efficiencies. New materials, which possess both compatibility with CMOS and highly electric-to-optic conversion efficiency, are in urgent demand for the development of silicon-based modulators.

Graphene, a single layer of carbon atoms arranged in a honey-comb lattice, has attracted a

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great deal of interest due to its excellent electrical and optical characteristics [2-10]. Due to its extremely high electron mobility and good compatibility with CMOS, graphene can be applied to realize high efficient modulation. Combined with high-index dielectric waveguides, graphene-

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based modulators have already been realized [11-18]. However, as optical modes are limited in high-index dielectric region and far away from the interface of graphene/dielectric waveguide, the interaction between light and graphene in this modulator is inherently weaker. In order to enhance the interaction between light and graphene, surface plasmon polaritions (SPPs) on graphene are used to design excellent optical modulators for the tighter spatial confinement and higher local field intensity [19~21]. Hybrid plasmonic modulators based on graphene have been explored for electro-optical modulation [22~25]. Hybrid SPPs can combine the ultra-compact mode size of SPPs waveguide and the ultra-fast modulation speed of graphene, thereby improving the performance of the modulators. Huang presented a hybrid plasmonic graphene-based modulator [24]. Two single-layer graphene sheets were placed on the slot formed by the horizontal hybrid plasmonic waveguide. With effect of the slot, modulation bandwidth has

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been improved to 0.4 THz with modulation length of 8.5 μm. Peng proposed a graphene-on-gap modulator theoretically [25]. Part of double-layer graphene is suspended upon the air gap. Due to the linear optical absorption of graphene, the modulation length of four single-layer graphene sheets can be decreased to only 3.6 μm and the bandwidth modulation can reach 0.48 THz. In these modulators, hybrid plasmonic effect greatly enhances the modulation efficiency of the device, also 2

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brings about difficulties in fabrication. To achieve a balance between modulation performance and fabrication process, we propose a graphene-based modulator with hybrid plasmonic waveguide. The plasmonic waveguide consists of Ag waveguides, Si waveguide and two single-layer graphene sheets embedded between. Non-

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coplanar structure can simplify the fabrication process, and provide more fabrication tolerance. Considering more layers of graphene may add to difficulty of fabrication, we compromise by choosing two single-layer graphene sheets formed as a capacitor. In principle, the transversal

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electric-field component of the modulated mode can enhance the optical absorption of graphene, rather than the longitudinal one [26]. Hybrid wedge SPPs (HWSPPs) [27-30] mode is introduced to enhance light absorption of graphene. As a result, an ultra-speed, broadband, low-loss graphenebased hybrid plasmonic modulator with small footprint is realized, which would provide new

2. Structure principle and device design

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methods for optoelectronic devices with enhanced light-graphene interactions.

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Fig.1. shows a schematic diagram of hybrid plasmonic modulator with buried silicon waveguide. The hybrid plasmonic waveguide is made of a buried silicon waveguide and two silver waveguides on SiO2 substrate. The refractive indices of Si and SiO2 are 3.44 and 1.446. The buried silicon waveguide is convenient to be planarized in fabrication process ensuring the transferring of graphene. Two silver waveguides are both 300 nm wide and 200 nm high with refractive index of 0.1453+11.3587i [31] at the wavelength of 1550 nm. The structure of capacitor is formed by two single-layer graphene and Al2O3. The thickness of graphene is specified as 0.34 nm, as used in [25]. The permittivity of Al2O3 is 1.732. The thickness of Al2O3 inter-layer is set as 10 nm after optimization [Discussion see Supplement Ⅰ], as used in [32]. The gap between Ag parts is denoted as D, which is also the overlap length of two single-layer graphene. The width of Si waveguide is

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denoted as W.

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Fig. 1. (a) 3D schematic of designed graphene hybrid plasmonic waveguide for electro-optical modulation, (b)

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The cross-section of the hybrid plasmonic modulator.

Graphene should be treated as an anisotropic material, whose out-of-plane permittivity ε⊥ is fixed as 2.5 [22] and in-plane permittivity is calculated as ε||=2.5+iσ||/(ωε0dg) [33]. The in-plane conductivity of graphene can be tuned by applied voltage [34,35], which can be expressed as:

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 ||   intra   inter

 intra =

  E i8 0 Eth ln  2 cosh  F  E ph  iEs   2 Eth

(1)   

2   E ph  2 EF   1 1 1  E ph  2 EF  i    inter = 0  tan    ln 2  2 Eth  2  E  2 E 2  4 E 2   ph F th  

(2)

(3)

The in-plane conductivity of graphene concludes the intra-band conductivity (σintra) and the inter-band conductivity (σinter). σ0 =e2/(4ћ) is the universal conductivity of graphene, e is the charge of an electron and ћ is the reduced Planck constant. Eth= kBT is thermal energy, kB is Boltzmann constant, and T is temperature. Es= ћ/τ is scattering energy in eV with the scattering time τ, which

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is assumed to be 0.1 ps [33].When the operation wavelength is 1550 nm and T=300 K, Eph is calculated to be 0.8 eV. EF is the Fermi level which can be tuned by applied voltage [36], described by the following equation:

EF  vF  V  V0

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(4)

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vF is the Fermi velocity of graphene, which is set to be 0.9×106 m/s. According to the capacitor model, η can be described to be εrε0/eT, in which V0 is voltage offset due to natural doping of graphene. When the applied voltage is low, the Fermi level is near the Dirac point (EF
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The inter-band transition is allowed from electron-occupied regions to unoccupied regions, resulting in a large optical loss of propagating light. When a larger negative voltage is applied, the Fermi level is lower than half the photon energy (EF<-hν/2), where there are no electrons available

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for inter-band transition. When a higher positive voltage is applied, the Fermi level is higher than half the photon energy (EF>hν/2), all electron states in graphene are occupied, and the transition is forbidden. In both of the last two cases, the transmission decreases [15]. As for the parallel capacitor formed by two single-layer graphene, a voltage applied can make one layer doped by

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holes and the other doped by electrons with the same doping level, which means that change of applied voltage can result in the different intensities of light absorption caused by graphene.

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3. Theory analysis and optimization

By using finite element method, we studied the eigenmodes of the hybrid plasmonic waveguide @ 1550 nm. For the configuration with width of silicon (W) and gap between Ag parts (D) both fixed at 200 nm, two main modes in the hybrid plasmonic waveguide are shown in Fig.2 (a-b). Here, the red arrows represent the electric field vectors. We define fundamental mode in Fig.2 (a) as hybrid wedge SPPs (HWSPPs) mode [23] with two poles. And mode in Fig.2 (b) consists of 4 poles, so named as high order HWSPPs mode. HWSPPs mode obtains higher |𝐸(𝑦)| intensity in the graphene region than high order HWSPPs mode. Recent studies have shown that electric field component parallel to the graphene sheet can greatly enhance the interacting between graphene and propagating mode [26]. The electric field vector of HWSPPs mode is practically parallel to double-layer graphene structure between the two poles. For high order HWSPPs mode,

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electric field vector paralleled to double-layer graphene is relatively weak, and electric field vector near the outboard two pole is almost perpendicular to single-layer graphene. Thus, it can be indicated that HWSPPs mode can achieve stronger absorption of light.

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Fig. 2. (a-b) |𝐸(𝑦)| intensity distribution of HWSPPs mode and high order HWSPPs mode. (c) Real and imaginary part of the effective modal index of the graphene-based hybrid plasmonic waveguide for HWSPPs mode. (d) Optical loss per length α curves for HWSPPs mode with respect to Fermi level, where the applied voltage is also displayed (blue curve).

We select HWSPPs mode as modulation mode. Fig.2 (c) depicts the effective modal index (neff) of HWSPPs mode, including the real and imaginary part as functions of the Femi level (EF) of graphene. When Femi level varies from 0 to 1 eV, Real(neff) of HWSPPs first rises to the maximum value at EF =0.4 eV (hν/2), and then falls. According to the Puali blocking mechanism of graphene when EF >0.4 eV, Imag(neff) shows a rapid drop around EF=0.4 eV. Also, Imag(neff) indicates the optical loss for propagating mode. In order to quantify the optical absorption of the

[29]:

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graphene-based hybrid plasmonic waveguide, we further calculate the optical loss per length α by

 =40 lg(e) Im(neff ) / 

(5)

where λ=1550 nm. From Fig.2 (d), the optical loss per length α also experiences distinct decline when EF=0.4 eV, corresponded to that of Imag(neff). Therefore, we set EF=0.2 eV (α=0.363 dB/μm) 6

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and EF=0.6 eV (α=0.087 dB/μm) respectively as “ON” and “OFF” state of our designed modulator. We define modulation efficiency as the difference of optical loss per length α between “ON” and “OFF” state. Then, the modulation efficiency (ME) can be calculated as: ME=α(EF=0.2 eV)α(EF=0.6 eV), represents the modulation depth per length. Fermi level of graphene can be gated dB/μm by switching the applied voltage between 0 and 4.588 V.

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by applied voltage, as shown in Fig.2 (d). As a result, the ME of the hybrid waveguide is 0.276

To obtain the highest ME, we first take the gap between Ag parts (D) into consideration. Here

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we set D=W and D sweeping from 10 to 600nm.The curve between D and the effective modal index of HWSPPs mode is shown in Fig.3 (a). Real(neff) differences between EF=0.2 eV and EF=0.6 eV is negligible for HWSPPs mode. And Imag(neff) of “ON” and “OFF” state vary as the D changes, indicating the modulation depth differ for different configuration of D. Based on

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Imag(neff), the curve between ME and D is shown in Fig.3 (b).

Fig. 3. (a) Real part (solid line) and imaginary part (dashed line) of the effective modal index with respect to D at EF=0.2 eV and EF=0.6 eV. (b) The modulation efficiency and FoM curve as functions of D.

It is worth noting that the gap D is also the overlap length of two single-layer graphene, resulting in the decline of modulation bandwidth with the increasing of D. To achieve a trade-off between

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modulation efficiency and bandwidth, we choose the optimized configuration with D less than 300 nm. In order to obtain a balance between ME and insertion loss (IL), we calculate the figure of merit curve as shown in Fig.3 (b). Figure of merit (FoM) is defined as: FoM=ME/IL, where insertion loss is equal to the optical loss when EF=0.6 eV. And, ME curve reaches its peaks at D=75 nm and D=200 nm. Taking both ME and FoM into consideration, we choose D=200 nm due to its relatively higher ME and FoM as the optimized D for the structure. 7

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Then we set D at 200 nm, and focus on the optimization of the width of Si waveguide(W). Fig.4 (a) illustrates the effective modal index of HWSPPs mode as a function of W at EF=0.2 eV and EF=0.6 eV. ME and FoM can be calculated by Imag(neff) as shown in Fig.4 (b). The ME reaches its maximum at W=150 nm, FoM of which is also the highest. The optimized structure

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parameters of the proposed hybrid waveguide should be chosen as W=150 nm and D=200 nm. For the optimized configuration, modulator with 9.493 μm long waveguide can realize 3 dB

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modulation depth, and the IL is 0.826 dB.

Fig. 4. (a) Real part (solid line) and imaginary part (dashed line) of the effective modal index with respect to W at EF=0.2 eV and EF=0.6 eV, for HWSPPs mode. (b) The modulation efficiency and FoM curve as functions of W. (c)The modulation efficiency and 3 dB modulation bandwidth curve as functions of d. (d) Modulation

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efficiency of the configuration (W=150 nm and D=200 nm) with ±10nm fabrication error.

Take fabrication error into consideration, Fig.4 (c) shows the modulation efficiency of the structure (W=150 nm and D=200 nm) with ±10 nm fabrication error. The maximum loss of ME is 0.0085 dB/μm, which is negligible. It shows the fabrication tolerance of proposed structure. Also, 8

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non-coplanar structure means the deposition of silver waveguides is upon the buried silicon waveguide and graphene. The fabrication process is simplified, compared with that in [24~25].

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4. Modulation bandwidth and power consuming The hybrid plasmonic waveguide length is set as 10 μm, and the wavelength of incident light range is broadband from 1.2 to 1.9 μm. Fig.5 (a) shows the transmission and modulation efficiency

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of the modulator at both “ON” and “OFF” states. All materials’ dispersions are taken into consideration. The conclusion can be drawn that for this configuration of modulator the modulation depth is over 3 dB and IL is less than 1.09 dB, when the optical wavelength varies from 1.260 to

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1.675 μm (all the O to U bands included).

Fig. 5. (a) Transmission spectra of “ON” and “OFF” states for λ varying from 1.2 μm to 1.9 μm, and modulation efficiency of proposed modulator. (b) The equivalent circuit model of this device.

For the electrical characteristics of an electro-optical modulator, modulation bandwidth and power consumption are two important merits. As for capacitor structure formed by two single-

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layer graphene and dielectric Al2O3, the modulator structure can be simplified as Fig.5 (b). Then, 3 dB modulation bandwidth of the modulator can be estimated by [37]: f3dB 

1 2 RC

(6)

Furthermore, R is the serious resistance of the structure including the graphene’s sheet resistance (Rg,sh) and the contact resistance (Rg,c) of both top and bottom single-layer graphene. 9

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CGIG comprises the oxide capacitance (COX) and quantum capacitance (Cq) of top and bottom single-layer graphene, where COX can be calculated by COX=εrε0S/d. And the theoretical value of Cq is 0.8 μF/μm2 [38]. The graphene’s sheet resistance Rg,sh is varied between 100 and 300 Ω/sq, corresponding to the carrier mobility of between 6900 and 2300 cm2/V·s. Here, we assume Rs=100

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Ω/sq as used in [37]. The graphene-metal contact resistance is assumed to be Rg,c =150 Ω·μm. The total resistance and total capacitance is 44.24 Ω and 10.409 fF. The 3 dB modulation bandwidth of the modulator is calculated to be 346 GHz.

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The power consumption of the modulator can be obtained by P=C·V2/4, where V is calculated to be 4.588 V. As a result, the power consumption is 54.787 fJ/bit.

5. Conclusion

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In summary, a hybrid plasmonic modulator based on graphene has been proposed with excellent modulation bandwidth (346 GHz), short modulation length (9.493 μm) and low energy consumption (54.8 fJ/bit). Specific hybrid plasmonic waveguide consists of Si waveguide and

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silver waveguides. The non-coplanar structure reduces the difficulties of graphene transfer process and provides more fabrication tolerance. Meanwhile, by combing the hybrid plasmonic effect with graphene, HWSPPs mode greatly enhances the interacting between graphene and light. After the geometrical optimization, it is shown that the modulation efficiency is further increased to 0.316 dB/μm, with the propagation loss less than 0.09 dB/μm. Also, 3 dB modulation depth can be reached for the whole O to U Band in case of 10 μm long waveguide. The modulator holds a great

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potential as a reliable on-chip device for optical communications and links.

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Supplementary Ⅰ: Optimization of distance between graphene layers The distance between the graphene layers has an impact on modulation bandwidth and the modulation efficiency of the proposed device. Fig.6 (a) schematically shows the structure of Al2O3-

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graphene-Al2O3 capacitor, including three layers of Al2O3. Thickness of the three Al2O3 layers are all the same, which is denoted as d. The upper layer is used to electrically isolate the contact

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between graphene and Ag. The lower layer is for the convenience of fabrication.

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Fig. 6. (a) schematic of the capacitor structure (b) Modulation efficiency and 3 dB modulation bandwidth at d=5,7,10,15 nm. (c) |𝐸| intensity distribution of propagating mode.

For the optimized configuration of modulator (W=150 nm and D=200 nm), the characteristics of the modulator at different values of d (5,7,10,15 nm) are shown in Fig.6 (b). As the propagating mode is restricted in the gap formed by the edge of Ag waveguide and Si waveguide show in Fig.6 (c), the graphene layer is further away from the center of the propagating mode with d increasing. Thus, the interaction between graphene and the propagating light is getting weaker, leading to the drop of the modulation efficiency. At the same time, according to the formula of the oxide capacitance COX=εrε0S/d, S is the area of capacitor, and d is the thickness of capacitor. As d increases, the oxide capacitance decreases, resulting in the rise of 3 dB modulation bandwidth and

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the power consumption.

To achieve a balance between modulation efficiency and 3 dB modulation bandwidth of the proposed device, we choose d at the value of 10 nm with modulation efficiency of 0.316 dB/μm and 3 dB modulation bandwidth of 346 GHz.

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Supplementary Ⅱ: Possible fabrication method of the device Our device is designed based on the commercial SOI wafers with a top silicon layer of 220 nm and a buried silica layer of 3 μm. The waveguide can be made by the standard SOI processing,

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including e-beam lithography (EBL) and inductively coupled plasma (ICP) etching. To provide a flat surface for graphene transfer, which can avoid the damage of graphene across the waveguide, PECVD silica is deposited and planarized to the top of waveguide using standard chemical

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mechanical planarized (CMP) techniques [16]. Then, the wafer should be coated with 10 nm thermal ALD Al2O3 to form the substrate for graphene transfer. After this, the first graphene sheet (grown by CVD) can be wet-transferred [39,40] on the top of the chip. The transferred graphene can be patterned by standard ultraviolet (UV) lithography and oxygen plasma etching [11]. Following this, the metal contacts can be patterned by UV lithography, and Au/Ti electrode can be

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made by electron-beam evaporation and a lift-off process [32]. Due to the hydrophobic nature of graphene basal plane, it is difficult for direct deposition of high dielectric constant material through ALD growth on graphene [12]. Instead, 1nm layer of Al should be thermally evaporated, which

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can be immediately oxidized into Al2O3 upon exposure to the air. Using the oxidized aluminum as a seed, 9 nm of Al2O3 can be successfully deposited by ALD machine [12,16,32]. Afterwards, the transfer, dielectric and metallization processes should be repeated for the second graphene layer. The plasmonic Ag waveguides can be manufactured using the similar fabrication method of the electrode.

Acknowledgments

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This work was supported in part by the National Key Research and Development Program of China (2018YFB2201903), the National Key Research and Development Program of China (2018YFE0201000) and the State Key Program of National Natural Science Foundation of China (61535012).

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