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An electro-absorption optical modulator based on dual-graphene-on-graphene configuration is presented and investigated. Four graphene layers are embedded in a silicon-on-insulator (SOI) waveguide, the total metal-graphene contact resistance of this structure is reduced 50% by the graphene layers co-electrode design. By optimizing the position of each graphene-on-graphene (GOG) layer in the waveguide, a strong interaction between graphene layers and light is obtained, which leads to a significant change of the effective mode index (EMI) in the waveguide. Calculations show that an electro-absorption optical modulator can achieve 34 dB extinction ratio (ER) and 100 GHz modulation bandwidth with 5 µm-long active region and 17.6 fJ/bit consumption.
© 2014 Optical Society of America
1. Introduction
Graphene, a two-dimensional version of graphite with its carbon atoms arranged in a hexagonal lattice, has stirred great interest in recent years due to its distinctive and intriguing electrical and optical properties. It has high carrier mobility of more than 200000 cm2/(V•s) at ambient temperature, as well as wide operational bandwidth, covering the infrared and visible light ranges [1]. Furthermore, the conductivity of graphene can be effectively tuned by electrostatics [2]. The applications of those excellent properties of graphene have been investigated [3,4]. Graphene has been proved to be an ideal material for realizing novel modulators [5] with ultra wide operational bandwidth, high speed, small footprint and CMOS compatibility. So far, both graphene-based electro-optic modulators [6–8] and electro-absorption modulators [9–13] have been proposed, based on single graphene layer or double graphene layers schemes. Since the operating bandwidth of graphene-based modulator is mainly limited by the parasitic resistance and capacitance of the structure [9,10,14,15], in order to achieve high-speed operation, it is essential to design a structure with low resistance and capacitance.
In this paper, an electro-absorption optical modulator based on dual-GOG configuration is presented. Four graphene layers are embedded in a SOI waveguide, in which two graphene layers sandwiched by three insulating dielectric spacers form GOG layer, the other two graphene layers form another GOG layer. The influence of graphene layers on propagating mode is studied. The more layers of graphene reside in waveguide, the stronger the effect is imposed on propagating mode. The total metal-graphene contact resistance of this structure is reduced 50% by graphene layers co-electrode design. This reduction is much larger than the method of forming cuts in the graphene within the contact region, which shows a 32% reduction in Cu-graphene contact resistance [14]. By optimizing the position of each GOG layer in waveguide, a maximum interaction between graphene layers and light is obtained, causing a significant change of the EMI in the waveguide. The simulation results show that an electro-absorption optical modulator can achieve 34 dB ER and 100 GHz modulation bandwidth with only 5 µm-long active region and 17.6 fJ/bit consumption.
2. Optical and electrical properties of graphene
The complex conductivity of graphene can be dynamically tuned by applied voltage [2], which can be deduced from the Kubo formalisms [16,17]
where δintra , δinter are intraband conductivity and interband conductivity respectively where ħ is the reduced Planck constant, and ω is the angular frequency. The chemical potential µ can be tuned by applied voltage, |µ| = ħνF(πa0|Vg-VDirac|)1/2 [2,18,19], the Fermi velocity νF≈1.1 × 106m/s, a0 = εrε0/de is yielded from the simple capacitor model, |Vg-VDirac| would be the applied voltage. Γ1 = 1/τ1, Γ2 = 1/τ2, where τ1, τ2 are intraband relaxation time and interband relaxation time respectively. Here δ0 = e2/(4ħ) = 60.8 µS is the optical conductivity of undoped graphene. For all the following calculations, the incident light is λ = 1550 nm, τ1 = 1.2 ps and τ2 = 10 fs. The conductivity of graphene is shown in Fig. 1(a).
Fig. 1 The graphene's conductivity and permittivity as a function of chemical potential for λ = 1550 nm, T = 296 K (room temperature).
For pristine graphene, the variation of conductivity is symmetry for positive bias and reverse bias. Therefore, in the following sections, only the positive biased graphene's behavior is considered. The permittivity of graphene can be calculated by using ε = 1 + iδ/(ωε0dg) as shown in Fig. 1(b), dg = 0.7 nm is the thickness of single graphene layer. The µ can be dynamically tuned by the applied voltage. Around µ = 0.4 eV, the imaginary part of ε shifts sharply, as does the real part of ε. At µ = 0.51 eV, the absolute value of graphene's permittivity ε approaches zero. When µ<0.51 eV, both the real part and imaginary part of ε are positive, and the graphene acts like a dielectric material. However, the graphene shifts to metallic material when µ>0.51 eV. Then the imaginary part of ε is still close to zero and the real part of ε becomes negative. The changes of graphene's permittivity ε influence the EMI in the waveguide [5,6,8,11]. The real part of the EMI affects the phase of light, known as electro-refraction, and the imaginary part of the EMI induces light absorption, defined as electro-absorption. Therefore, it is important to investigate the EMI in the waveguide when the optical modulator is designed.
3. Dual-graphene-on-graphene electro-absorption modulator
3.1 The influence of graphene on EMI
Figure 1 shows that the permittivity ε of graphene can be changed by chemical potential µ. This means the EMI of the waveguide with graphene layer can be dynamically tuned by applied voltage. Modulators based on single-layer graphene or double-layer graphene schemes have been proposed [9,13]. The more layers of graphene reside in waveguide, the stronger effect is imposed on propagating mode. In order to impose a strong effect on the propagating mode, the graphene layers should be placed at the center of the waveguide with maximum light intensity [20]. The impact of the number of graphene layer on EMI is investigated by the finite element method (FEM). The proposed design of this waveguide is based on commercial SOI wafers with 0.34 µm thick and 0.4 µm width Si waveguide. For single layer scheme, the graphene is placed in the middle of the Si ridge. For both double layers and triple layers schemes, the graphene layers are placed between Si layer (slab) and Si ridge. In the four layers scheme, two graphene layers form a GOG structure, placed between Si layer (slab) and Si ridge, the other two graphene layers form another GOG structure, imbedded in the middle of the Si ridge. For the five layers scheme, with its three graphene layers placed between Si layer (slab) and Si ridge, the other two graphene layers form a GOG structure, imbedded in the middle of the Si ridge.
As shown in Fig. 2(f)-2(i), it is obvious that the applied voltage has a much stronger effect on TM mode than on TE mode, both towards Neff and α. The Neff corresponds to the real part of EMI, whereas α is the imaginary part of EMI. In each of the schemes, the NTM has a dip at µ = 0.495 eV. However, afterwards the NTM increases rapidly and reaches a peak at µ = 0.53 eV. Both αTM and αTE have a lowest value at the point µ = 0.40 eV, and afterwards the αTM reaches its maximum at µ = 0.51 eV, whereas the αTE is still suppressed at a low level. At the “metallic graphene” point (µ = 0.51eV), for TM mode, the strongest absorption is presented. The embedded graphene layers show relatively small influence on TE mode. Therefore, for the rest of our work, we only consider TM mode.
Fig. 2 The impact of the number of graphene layers on EMI with the dielectric spacers of Al2O3 (the refractive index is 1.732). (a)~(e) Field distribution plot of the magnitude of the power flow of TM modes for considered single-layer, double-layer, triple-layer, four-layer and five-layer structures with chemical potential µ = 0.51 eV. (f)~(g) The Neff of TE and TM modes as a function of chemical potential. (h)~(i) The α of TE and TM modes as a function of chemical potential.
For single layer scheme, the variation of Neff of TM mode is ΔNTM = 0.0701, whereas, for five layers scheme the variation of Neff is ΔNTM = 0.1799. The four layers scheme also shows a large variation of Neff = 0.1632. For four layers scheme and five layers schemes the α are 0.164262 and 0.181038 respectively. Waveguides with fewer graphene layers show smaller variation of the Neff and α. However, the more graphene layers reside in waveguide, the more difficulties in manufacturing. Next, only the four layers scheme based modulator is investigated.
3.2 Dual-graphene-on-graphene waveguide
As shown in Fig. 3, the four layers scheme is based on commercial SOI wafers with Si layer (slab) and Si ridge, in which two graphene layers, sandwiched between three thin layers of insulating dielectric spacer form a simple model of capacitance. These are placed between Si layer (slab) and Si ridge, namely the lower GOG. The other two graphene layers are also isolated by three thin layers of insulating dielectric spacers, imbedded in the Si ridge waveguide and correspond to the upper GOG. An electrode connects one graphene layer of the lower GOG and one graphene layer of the upper GOG as a positive electrode. Another electrode connects the other two graphene layers as the ground electrode. All the graphene layers are first transferred to spacers, then the metals are deposited on to the graphene layers.
Better performance for 0.08 µm-thick Si layer (slab) and 0.26 µm-thick Si ridge was shown [21]. In order to impose a strong effect on the propagating mode, the upper GOG should be placed in a proper position with maximum light intensity. The material of insulating dielectric spacer also plays an important role in affecting the propagating mode. The insulating dielectric spacers separate the graphene layers from Si layers or Si ridge, to prevent potential graphene layers' carrier from injecting into the silicon. The influence of these two factors has been estimated, the results are shown as Fig. 4.
Fig. 4 The variations of Neff and MPA as a function of the distance D between upper GOG and lower GOG in the waveguide for different types of insulating dielectric spacer.
A maximum effect on the propagating mode is observed when the distance D between upper GOG and lower GOG is 0.1 µm in this waveguide. The variation of Neff reaches its maximum at this position, as does the mode power attenuation (MPA) for all the different types of insulating dielectric spacer. The thinner and higher refractive index n dielectric spacer shows a stronger effect with larger variation of Neff and MPA. In the following part, all calculations are based on this structure in which the upper GOG is placed 0.1 µm higher than lower GOG. So far, among all the schemes of proposed graphene-based waveguide modulators, the maximum variation of EMI of the waveguide, ΔNeff or α, is smaller than our proposed scheme which is based on four graphene layers.
The equivalent circuit of this proposed waveguide is shown in Fig. 5. The Rc is the metal-graphene contact resistance, C = εrε0S/d is the capacitance which is calculated by a simple capacitor model, where εr is dielectric constant of insulating dielectric spacer, S is the overlap area of two graphene layers, and d is the thickness of insulating dielectric spacer. For the present fabricated modulators, the operation speed is limited by resistance and capacitance [9,10], where resistance is mainly contributed by the metal-graphene contact resistance [10,13]. As shown in Fig. 5, the total metal-graphene contact resistance and capacitance of this structure are written
The 3-dB modulation bandwidth is estimated by [8,13]where R is the resistance of this system, and can be obtained by Rtotal [13]. The metal-graphene contact stems from the unique physical interactions that take place between the contact metal and the atomically thin graphene layer [12]. The value of metal-graphene contact resistance varies with metal used. Here we use Rc = 400Ω-µm [13,15]. Compared with single GOG scheme [10,13], the total metal-graphene contact resistance is reduced 50% by this configuration, as well as having a stronger effect on propagating mode.3.3 Electro-absorption optical modulator
The configuration of the proposed electro-absorption optical modulator is shown in Fig. 6. The α corresponds to the propagation loss. It is noteworthy that the RF dielectric constant of 7 nm-thick Al2O3 is about 7 instead of the square of its optical refractive index [22]. Dielectric spacer with higher dielectric constant would induce a larger capacitance and lower the modulation speed. In order to achieve high modulation speed, the 7 nm-thick hBN (εr = 3.92) is preferred as an insulating dielectric spacer. The dielectric constant of 7 nm-thick hBN is much smaller than that of 7 nm-thick Al2O3. At the point of µ = 0.51 eV, the αTM = 0.198094, whereas at the point of µ = 0.405 eV, the αTM = 0.0008378. This is much smaller than that at the point of µ = 0.51 eV. Thus, it is an ideal property for designing an electro-absorption modulator.
As shown in Fig. 7, at the chemical potential µ = 0.405 eV, the modulator is at “ON” state. The light passes through the waveguide with very little loss. When the chemical potential µ shifts to µ = 0.51eV, it is at “OFF” state, and large amount of light is absorbed by the waveguide. The electro-absorption modulator works at these two points, µ = 0.405eV and µ = 0.51eV. The ER for TM mode can achieve 34 dB by using only L = 5 µm long active region. The variation of voltage ΔV = 1.89 V, and the estimated capacitance is 19.8 fF. The energy per bit Ebit for a 5µm long active region and 0.4 µm-wide electro-absorption optical modulator is reckoned on the order of 17.6 fJ/bit. The 3-dB modulation bandwidth is estimated to be f3dB = 100 GHz.
As mentioned above, |µ| = ħνF(πa0|Vg-VDirac|)1/2 and C = εrε0S/d, where |Vg-VDirac| is the applied voltage. The material and thickness of insulating dielectric spacer play a role in determining the modulation speed and consumption. This is because the refractive index and thickness of insulating dielectric spacer directly determine the value of C and ΔV. The modulator with higher refractive index of insulating dielectric spacer shows lower consumption and higher extinction ratio at the cost of 3-dB modulation bandwidth. The higher 3-dB modulation bandwidth is exhibited for modulator with thinner insulating dielectric spacer. The detailed performance of the modulator varying with dielectric spacer is presented in Table 1.
Table 1. The performances of proposed modulator (L = 5µm) varies with dielectric spacer
4. Conclusions
In summary, we investigated the influence of multiple graphene layers on EMI. Results indicate that the more graphene layers reside in waveguide, the stronger effect on EMI was obtained. An electro-absorption optical modulator based on dual-GOG waveguide is presented. By optimizing the position of each GOG layer in the waveguide, a strong interaction between graphene layers and light is obtained, which leads to a significant change of the EMI in the waveguide. The total metal-graphene contact resistance of this structure is reduced 50% by graphene layers co-electrode design. This reduction is much larger than the method of forming cuts in the graphene within the contact region. We also investigate the influence of the insulating dielectric spacers on the performance of proposed modulator. The results show that an optical modulator with higher refractive index of insulating dielectric spacer shows lower consumption and higher extinction ratio at the cost of 3-dB modulation bandwidth. The proposed optical modulator with the refractive index εr = 3.9 and 7 nm-thickness of insulating dielectric spacer can achieve 34 dB ER by using only 5 µm-long active region. The estimated consumption is 17.6 fJ/bit, and the 3-dB modulation bandwidth f3dB for the proposed optical modulators can be as high as 100 GHz.
Acknowledgments
This work was funded by Chinese 973 Program under Grant No. 2012CB315701 and 2011CB301705, National Nature Science Foundation of China (No. 61090393, 61421002, 61307070, 61307031) and Science and Technology Innovation Team of Sichuan Province (No. 2011JTD0001). The work was also partly supported by KNAW, The Netherlands China exchange program (No. 12CDP008).
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