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Abstract
The mid-infrared (MIR) region is attracting increasing interest for on-chip synchronous detection and free-space optical (FSO) communications. For such applications, a high-performance electro-optical modulator is a crucial component. In this regard, we propose and investigate a graphene-based electro-absorption modulator (EAM) and microring modulator (MRM) using the suspended germanium waveguide platform. The modulators are designed for the second atmospheric window (8 to 12 µm). The incorporation of double-layer graphene on the suspended slot waveguide structure allows for the significant enhancement of light-graphene interaction, theoretically achieving a 3-dB bandwidth as high as 78 GHz. The EAM shows a calculated modulation depth of 0.022-0.045 dB/µm for the whole operation wavelength range. The MRM exhibits a calculated extinction ratio as high as 68.9 dB and a modulation efficiency of 0.59 V·cm around 9 µm. These modulators hold promise for constructing high-speed FSO communication and on-chip spectroscopic detection systems in the MIR atmospheric window.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The mid-infrared (MIR) region, typically defined as the wavelength range of 2 to 20 µm, covers the molecular fingerprint of many molecules, making it a useful tool for molecular absorption spectroscopy in civilian and military applications. This region also includes two crucial atmospheric transmission windows at 3-5 µm and 8-12 µm, which make it an ideal choice for both terrestrial and space-based applications. Thus, the MIR region has great potential for chemical or biological sensing [1], astronomy [2], industrial processes control [3], thermal imaging [4], and free-space optical (FSO) communications [5]. To develop MIR photonics applications, a suitable waveguide platform is needed. Silicon photonics has gained significant attention for its potential in creating integrated devices at the near-infrared (NIR) telecom band [6–10], especially for optical interconnects and communication systems. However, the use of silicon-on-insulator (SOI) material platform for longer wavelengths (beyond 3.8 µm) is restricted due to the high absorption of silicon dioxide [11–12]. Fortunately, germanium, also a group IV material, offers an intrinsic transparent window (2-14 µm). As silicon starts to absorb light from 8 µm, germanium is the preferred material for integrated platforms particular for longer wavelengths up to 14 µm [13]. It has similar properties to silicon, such as wide transparency ranges, high refractive indexes, and mechanical robustness [14]. Moreover, germanium-based integrated devices can be fabricated using the mature CMOS fabrication technology.
Germanium-based passive integrated devices have been successfully demonstrated experimentally in the MIR region, such as grating couplers [15], resonators [16], arrayed waveguide gratings [17], crystal cavities [18], and polarization rotators [19]. However, active devices, which are crucial for the development of MIR integrated systems, such as high-speed light modulation and detection, are less explored. For example, high-performance modulators could offer significant potential for FSO transmission applications and spectroscopic detection systems. Despite its potential, MIR light modulation remains largely unexploited. In recent years, high-speed optical modulators have been demonstrated using external free-space Stark modulation [20] or directly-modulated quantum cascade lasers [21]. However, these modulators are not easily scalable due to their complicated fabrication processes, which rely on quantum wells. Furthermore, the electro-absorption modulator (EAM) based on the germanium-on-silicon (Ge-on-Si) platform has achieved modulation up to 8 µm [22], but its modulation bandwidth is limited to only 60 MHz due to unoptimized Ohmic contacts between doping areas and metal electrodes. Therefore, there is a pressing need to explore new effects that can facilitate the development of high-speed, integrated MIR modulators.
In the meantime, 2D materials, including graphene, hexagonal boron nitride (hBN), transition metal dichalcogenides (TMDs), and black phosphorus (BP), have emerged as promising materials for optoelectronic components in integrated photonics [23–26]. These materials can change the complex refractive index when an electric field is applied, making them useful for integrated light modulation applications [27–31]. Graphene, in particular, has been extensively studied for light modulation applications due to its strong interaction with light, gate-variable in-plane optical conductivity [32], high carrier mobility, and ultra-broadband compatibility [33]. It can be easily integrated on top of various photonic platforms, such as silicon, germanium, or other dielectric waveguides, to realize efficient light modulation. Although using graphene modulators based on group IV integrated platforms have been demonstrated experimentally over the last decade [34–39], waveguide-integrated graphene modulators at the MIR region have yet to be explored. Therefore, this study aims to exploit a high-speed germanium-based graphene modulator for the MIR atmospheric window.
In this work, we propose and numerically investigate double-layer graphene (DLG) EAM and a microring modulator (MRM) based on suspended germanium slot waveguides. The suspended slot waveguide structure is utilized to minimize cladding material absorption and increase light interaction, which is expected to improve the modulation bandwidth as the overlap length of DLG is reduced. The DLG EAM is designed to have a wide operation window that covers the entire second atmospheric window, with a modulation depth ranging from 0.022-0.045 dB/µm. On the other hand, the MRM is designed to have a very high extinction ratio (ER) of approximately 68.9 dB and a modulation efficiency of 0.59 V·cm at around 9 µm. The calculated 3-dB bandwidth of these modulators using the equivalent resistor-capacitor (RC) circuit model is approximately 78 GHz, which indicates their potential for high-speed modulation applications.
2. Device design
Figure 1(a) schematically illustrates the proposed design for a high-speed DLG EAM based on a suspended germanium slot waveguide. The cross-section of the device is depicted in Fig. 1(b). The modulator is based on the Ge-on-Si platform. A dielectric layer of zinc sulfide (ZnS), which is transparent in the 1-14 µm range [40] is used as the top layer. Subsequent to the deposition and planarization of the ZnS layer, the silicon layer is removed using a tetramethylammonium hydroxide (TMAH) solution through etched holes. This step is crucial for eliminating the significant absorption of silicon in the second atmospheric window. The germanium layer has a thickness of 500 nm, and the entire device is etched to a depth of 400 nm to ensure efficient mode overlap with the DLG overlayer. The thickness of ZnS between the DLG is selected to tZnS = 30 nm. To maximize the evanescent coupling of the optical mode with the DLG, the thickness of the waveguide top cladding is te = 5 nm.
Figure 2(a)-(c) show the simulated mode profiles at graphene Fermi level EF (also chemical potential µ) = 0 eV in the Ge-on-Si rib, suspended germanium rib, and suspended germanium slot waveguide. Figure 2(d) shows the absorption of graphene in a suspended germanium rib waveguide and Ge-on-Si rib waveguide when the germanium layer height (hGe) is 1 µm and the etch depth (hetch) is 0.6 µm at a wavelength of 9 µm, calculated using the graphene Kubo formula [41]. As the energy distribution of the Ge-on-Si rib waveguide is leaked to the silicon substrate due to the relatively low index contrast between the germanium layer and silicon substrate, the mode overlap of the evanescent field with the upper graphene is weaker, resulting in lower light absorption [42]. Thus, suspended germanium waveguides and thinner germanium layers are employed to improve the light-graphene interaction. Figure 2(e) depicts the absorption of graphene in a suspended germanium slot and rib waveguide when the germanium layer height is 0.5 µm and the etch depth is 0.1 µm at the wavelength of 9 µm. The electric field is tightly confined in the slot region, enabling stronger interaction of graphene with the propagating fundamental TE mode in slot waveguides than in rib waveguides. Additionally, rib waveguides require a larger DLG overlap width (the width of the graphene-ZnS-graphene capacitor) than slot waveguides, resulting in limited electro-optical (EO) 3-dB bandwidth with increasing capacitance. Therefore, suspended germanium slot waveguides are used in our device.
Fig. 2. (a)-(c) The electric field magnitude |E| distributions of the fundamental TE mode at graphene Fermi level EF = 0 eV in the Ge-on-Si rib, suspended germanium rib, and suspended germanium slot waveguide, respectively. (d) The graphene absorption with different Fermi levels in (a) and (b). (e) The graphene absorption with different Fermi levels in (b) and (c).
To optimize the modulation performance, different rib widths wrib and slot widths wslot are considered. Figure 3(a) shows the calculated absorption of the DLG on the suspended germanium slot waveguide with varying slot widths as a function of rib width at the graphene Fermi level EF of 0 eV and the wavelength of 9 µm. The figure suggests that wrib = 2.8 µm is the optimal width with maximum absorption. The calculated absorption and group index of the EAM as a function of slot width when the rib width is 2.8 µm are displayed in Fig. 3(b), showing that the interaction area reduces with the increasing slot width. While decreasing it will enhance the interaction strength, which in turn reduces the group index, leading to an increase in group velocity and resulting in a decline in interaction time, thus weakening the interaction between the mode field and graphene. Therefore, there is a trade-off between the enhancement of interaction strength and the reduction of interaction area, and we choose wslot as 200 nm to achieve the maximum absorption. Considering that the width of the DLG overlap (wm) is set to be the same as the slot width, we have optimized the graphene width wgraphene = 6.2 µm to maintain a proper distance between the metal contacts and the slot waveguide. This is important because longer wavelengths lead to larger mode fields, which could cause excess optical losses due to the metal contacts. All the parameters of the proposed EAM are presented in Table 1.
Fig. 3. (a) Absorption of the EAM for different slot widths as a function of rib width. (b) Absorption and group index of the EAM as a function of slot width of a rib width ∼ 2.8 µm.
Table 1. Parameters of the proposed EAM
3. Modulation performance
Figure 4(a) shows the calculated modulation depth of the proposed DLG EAM as a function of the Fermi level of graphene for different wavelengths, using the optimized structure. The modulation depth is defined as the difference value at graphene Fermi level EF = 0 eV and 0.15 eV, while the insertion loss (IL) is defined as the value at graphene Fermi level EF = 0.15 eV. The EAM's operation window covers the entire second atmospheric window (8-12 µm), with modulation depth ranging from 0.022 to 0.045 dB/µm and IL ranging from 0.0085 to 0.0095 dB/µm. For example, a 300-µm-long EAM can achieve 6.6-13.5 dB modulation depth in the 8-12 µm range, with a moderate IL of 2.55-2.85 dB. The calculated IL primarily comprises the absorption contributions from both graphene and the metal electrodes. The metal electrode structure consists of a 5 nm thickness of titanium (Ti) and a 35 nm layer of gold (Au), which introduces an intrinsic loss of approximately 0.0015 dB/µm to the total loss. Furthermore, it is worth noting that in an experimental device, the IL is likely to be higher than the calculated value due to additional losses originating from factors such as sidewall scattering, material defects at the Si/Ge interface, and the presence of a native oxide layer or imperfections on the germanium surface. However, previous measurements have reported losses in the range of 2-5 dB/cm for germanium waveguides operating within the wavelength range of 7-12 µm [42–44]. Considering the relatively short length of our device, we anticipate that the experimental loss will have a negligible influence.
Fig. 4. Modulation depth of the EAM as a function of graphene Fermi level with (a) different wavelengths at graphene scattering time = 100 fs (b) different graphene scattering times at wavelength λ = 9 µm.
The maximum achievable modulation depth per unit length depends on the mobility of graphene and previous research was based on a scattering time of 100 fs. In Fig. 4(b), the EAM modulation depth at the wavelength of 9 µm is illustrated for scattering times of 50 fs, 100 fs, and 1 ps. For a high mobility graphene (scattering time = 1 ps) with changing Fermi level from 0 to 0.15 eV, a value of 0.046 dB/µm is obtained, while for a low mobility graphene (scattering time = 50 fs) within the same Fermi level range, the value is 0.037 dB/µm.
To improve the modulation depth, an MRM is also investigated for wavelength near 9 µm, and its structure is presented in Fig. 5(a). An all-pass type microring resonator is proposed with a radius of 60 µm that incorporates a 50 µm overlap length of graphene on a section of the ring waveguide. The transmission spectra are characterized by:
Fig. 5. (a) Schematic of the proposed MRM. (b) Transmission spectra of the MRM with different applied voltages. (c) Modulation depth of the MRM with different applied voltages.
The incident light is modulated by changing the applied voltage V related to the graphene Fermi level EF, according to the following formula:
Fig. 6. (a) Drive voltage of the proposed modulators versus the graphene Fermi level. (b) The equivalent RC circuit of the proposed modulators.
The equivalent RC circuit of the EAM is shown in Fig. 6(b), and the EO 3-dB bandwidth of the modulator can be calculated by [45,46]:
where RC is the contact resistance between graphene and metal, RS is the sheet resistance of graphene, and Cgraphene is the capacitance of the graphene-ZnS-graphene structure. Among them, RC is given by: where contact resistivity ρc is selected as ρc = 500 Ω·µm and L is the length of the modulator. And RS is given by: where sheet resistance R□ is selected as R□ = 500 Ω/□. Besides, the Cgraphene can be calculated by:Consequently, the calculated 3-dB bandwidths of the EAM and the MRM are as high as 78 GHz by subtitling RC, RS and Cgraphene into Eq. (2), which exhibit a splendid dynamic characteristic. We acknowledge that the experimental bandwidth of the proposed modulators may be slightly lower than the calculated value due to the load impedance [45].
4. Discussion
Figure 7 illustrates the dependence of graphene's complex relative permittivity on the Fermi level for various wavelengths, using the graphene Kubo formula. When the graphene Fermi level EF is lower than half the photon energy of incident light µc (about 0.40 eV, 0.14 eV, 0.08 eV, 0.05 eV at 1.55 µm, 4.5 µm, 8 µm, and 12 µm, respectively), graphene exhibits significant absorption, and the absorption rapidly decreases if the EF is larger than half the µc. At 9 µm, the graphene absorption reduces with increasing graphene Fermi level from 0-0.15 eV. This reduction in absorption could allow effective light modulation. Conversely, the absorption of DLG magnifies when graphene Fermi level exceeds 0.18 eV (as shown in Fig. 2(e)), this is because the surface plasmons polaritons (SPP) of graphene is excited on the waveguides. Therefore, our graphene modulators operate within the Fermi level range of 0-0.15 eV, eliminating the presence of graphene SPP. Consequently, these modulators require an ultra-low drive voltage of 1.8 V.
Fig. 7. Complex relative permittivity (real part and imaginary part) of graphene versus Fermi level with different wavelengths.
Table 2 compares the latest integrated MIR modulators designed for the 8-12 µm range. MIR light modulation was achieved based on Ge-on-Si and Graded SiGe waveguide using the free-carrier plasma dispersion effect [22,48]. Until now, very few broadband MIR modulators have been demonstrated, except for the recent report of the Stark EAM with a bandwidth of up to 9 GHz [5]. However, these quantum wells-based Stark modulators require relatively complex fabrication processes that are impractical for large-scale integration. In theory, it is possible to achieve MIR modulators with very large 3-dB bandwidths [47,49,51]. The EAMs relying on the free-carrier plasma dispersion effect necessitate long lengths (typically a few millimeters) to achieve a modulation depth higher than 1 dB, resulting in significant IL [50,52]. Additionally, the manufacture of graphene hybrid plasmonic EAMs, as described in Ref. [47] and [49], requires precise dimensional parameters and extremely high-quality graphene. In contrast, our proposed EAM and MRM could provide high modulation depth, low IL, and large 3-dB bandwidth, and more importantly, they can be manufactured by well-established CMOS fabrication technology and thus are cost-efficient.
Table 2. Performance comparison of on-chip integrated MIR electro-optic modulators operating at the second atmospheric window (8-12 µm)
5. Conclusion
To summarize, suspended germanium slot waveguide-based MIR modulators (EAM and MRM) using DLG for the second atmospheric window are investigated. Suspended slot waveguides are introduced to reduce propagated loss, strengthen the graphene absorption, and increase the modulation bandwidth. The simulations show that the modulation depth of the EAM is 0.022-0.045 dB/µm for the 8-12 µm wavelength region. And the calculated results of the MRM show a very high extinction ratio of ∼ 68.9 dB, and modulation efficiency of ∼ 0.59 V·cm at around 9 µm. The EO 3-dB bandwidth of the modulators is up to 78 GHz. It is believed that the proposed modulators can promote the development of spectroscopic detection systems and FSO communications in the MIR atmospheric window.
Appendix 1: Schematic illustration of the proposed fabrication processes
The schematic illustration of the fabrication processes for our proposed devices is shown in Fig. 8. First, a germanium slot waveguide is fabricated on the Ge-on-Si wafer via electron beam lithography (EBL) and inductively coupled plasma (ICP) etching processes (Figs. 8 (a) and (b)). Then, the ZnS film is deposited on the chip using electron beam evaporation (EBE) (Fig. 8 (c)) [53]. After the ZnS film deposition, a flat surface of the chip can be achieved using chemical mechanical polishing (CMP) to ensure a good attachment of graphene The Ge and ZnS layers are then etched using ICP to form wet etched holes (Fig. 8 (d)) [54], after which the silicon substrate is removed using TMAH solution through the aforementioned holes (Fig. 8 (e)). Subsequently, the bottom layer graphene is transferred onto the chip's flat surface using a wet transfer method (Fig. 8 (f)), and then patterned via EBL and oxygen ion etching processes [55]. An electrode that establishes contact with the bottom layer graphene is created using a lift-off method (Fig. 8 (g)). Subsequently, a very thin ZnS dielectric layer is deposited using EBE (Fig. 8 (h)), and the ZnS film on the electrode can be removed by wet etching using acid. Finally, the top layer graphene and electrode are fabricated once more using the aforementioned method (Figs. 8 (i) and (j)). Although our design incorporates a suspended structure, the deposition of the ZnS film and CMP process on the germanium slot waveguide enhance the feasibility of fabrication. Additionally, the deposition of a very thin dielectric layer, along with the transferring and patterning of the graphene layer, as well as the lift-off process of the electrodes, have already been successfully demonstrated on suspended waveguides in Ref. [45].
Fig. 8. Fabrication steps for the proposed graphene modulators. (a) Ge-on-Si wafer. (b) germanium slot waveguide. (c) ZnS deposition and planarization. (d) Wet etch holes etching. (e) Si trenches etching. (f) Bottom layer graphene transferring and patterning. (g) Bottom layer graphene contact electrode. (h) ZnS dielectric layer deposition and the ZnS on the electrode surface removing. (i) Top layer graphene transferring and patterning. (j) Top layer graphene contact electrode.
Appendix 2: Analysis of the overlay accuracy with the graphene layers
Practically, the overlay accuracy in EBL during the fabrication processes could result in variations to the graphene overlap of the fabricated devices. we have considered six cases of fabrication tolerances related to the overlay accuracy: (a) shifting the bottom layer graphene forward by 50 nm while keeping the top layer graphene unchanged, (b) shifting the bottom layer graphene backward by 50 nm while keeping the top layer graphene unchanged, (c) shifting the top layer graphene forward by 50 nm without altering the bottom layer graphene, (d) shifting the top layer graphene backward by 50 nm without altering the bottom layer graphene, (e) shifting both the top and bottom layer graphene forward by 50 nm, and (f) shifting both the top and bottom layer graphene backward by 50 nm. In Fig. 9, we compare these six cases and observe only slight changes in the modulation depth of the device due to variations in the overlay accuracy. Additionally, in our calculations, the bandwidth of all six cases, dependent on the width of the double-layer graphene overlap (wm), is calculated to > 53 GHz, enabling high-speed modulation in the mid-infrared range. Thus, despite the potential impact of overlay accuracy on device performance, our proposed devices still exhibit good performance.
Fig. 9. Modulation depth of the EAM at wavelength λ = 9 µm with the overlay accuracy consideration. Case a: shifting the bottom layer graphene forward by 50 nm while keeping the top layer graphene unchanged. Case b: shifting the bottom layer graphene backward by 50 nm while keeping the top layer graphene unchanged. Case c: shifting the top layer graphene forward by 50 nm without altering the bottom layer graphene. Case d: shifting the top layer graphene backward by 50 nm without altering the bottom layer graphene. Case e: shifting both the top and bottom layer graphene forward by 50 nm. Case f: shifting both the top and bottom layer graphene backward by 50 nm.
Funding
Key Technologies Research and Development Program (2022YFB2803600); National Natural Science Foundation of China (62175080); Key Research and Development Program of Hubei Province (2021BAA005).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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