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Abstract
Electro-optical modulators are essential for scalable photonic integrated circuits and are promising for many applications. The convergence of silicon (Si) and lithium niobate (LN) allows for a compact device footprint and large-scale integration of modulators. We propose a sandwiched Si/I/LNOI modulator for broad modulation with CMOS-compatible fabrication tolerances. There is a thin film SiO2 spacer sandwiched between Si and LN, which is engineered to tailor optical and electrical properties and enhance index matching. Moreover, the SiO2 spacer is also exploited to inhibit the radiation loss induced by mode coupling. The modulator shows a bandwidth of ∼180 GHz with a halfwave voltage of 3 V. Such a device is considerably robust to the fabrication deviations, making it promising for massive and stable manufacturing.
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1. Introduction
Integrated photonics promises an optical solution to a wide range of applications including communication, microwave photonics, as well as optical computing [1–4]. The realization of these applications requires electrical-to-optical signal conversion. Electro-optic modulators (EOMs) for mapping electrical signals to an optical carrier are of high importance. Various materials have been utilized for integrated EOMs, including silicon (Si), graphene, indium phosphate (InP), and ferroelectric material. Out of these ferroelectric materials, lithium niobate (LN) has been employed for decades. Recent development of fabrication technology enables the manufacturing high-quality thin film LN, which has boost researches on the thin film LN platform. In previous researches, thin film LN EOMs proved to be efficient solutions for achieving beyond-100-GHz modulation bandwidth (BW), which is based on direct etching or combining LN with other materials. For direct etching, the thin film LN EOMs come with slanted sidewall and compared with silicon-based materials, are more difficult to micro-structure [5–7]. The hybrid silicon nitride (SiNx)/LNOI EOM is a promising candidate for avoiding the necessity of LN etching [8], but the SiNx/LNOI EOMs have to be manufactured with large footprints since the low refractive index of SiNx and the large anisotropy of LN lead to hundreds of micrometers of bend radius [9]. Si shows great promise to realize compact and scalable photonic integrated circuits (PICs). Recent efforts include that the thin film LN is bonded to the pre-patterned Si PICs to realize EOMs [10]. However, the bonding approach suffers from complex fabrication. To tackle this issue, a schematic of the heterogeneous Si/LNOI EOM is proposed, in which the Si waveguides are loaded on the thin film LN [11]. The dimensions of Si must be engineered to confine more light in the thin film LN. However, it should be noted that the performance of the EOM is sensitive to the fabrication deviations, which restricts the scalable utilities of this device. Moreover, the optical loss is also an impediment to the performance of the EOM. Although studies on structures with reduced optical losses have been reported [12,13], the loss behavior is still worth exploring.
In this work, we investigate the sandwiched Si/I/LNOI waveguide structure with a Mach-Zehnder interferometer push-pull configuration to achieve a broadband operation free of the fabrication deviations. Moreover, we study the radiation loss depending on mode coupling. The thin film SiO2 spacer provides additional freedom to tailor the properties of the optical signal and the electrical signal, making it easier to obtain perfect index matching and suppressing the radiation loss. Besides, fabrication tolerances are relaxed by employing the SiO2 spacer. Our work offers an elegant path for broadband modulation in photonics and a unique potential to build scalable PICs.
2. Concept and theory
The schematic layout of the sandwiched Si/I/LNOI Mach-Zehnder electro-optic modulator (MZ-EOM) in push-pull configuration is depicted in Fig. 1(a). The input optical signal is equally split into two waveguide arms and then the two arms combine. The multimode interferometric (MMI) couplers are used for a splitter and a combiner. The optical signals in the two arms experience the opposite electric field. Meanwhile, the applied voltage, via co-planar waveguide traveling-wave electrodes (CPW-TWEs), is aligned along the Z-axis of the thin film LN to strengthen the EO interaction. In the EO interaction region, the Si waveguide is designed to confine more light in the thin film LN, serving as the phase shifter. Outside the EO interaction region, the Si waveguide keeps the thickness of 220 nm to confine light in the Si waveguide, achieving compact waveguides and sharp bends. A bi-level taper can be used to guide the optical fundamental TE mode from the Si waveguide to the sandwiched Si/I/LN waveguide (and vice versa) [11]. The cross section of the sandwiched Si/I/LN waveguide in the EO interaction region is illustrated in Fig. 1(b). The stack consists of a Si substrate, a buried oxide layer (BOX) with a thickness of 2 µm, a thin film LN layer with a thickness of 600 nm, a thin film SiO2 spacer, and Si waveguides.
Fig. 1. Schematic layout of the sandwiched Si/I/LNOI EOM and its optical and electric field distributions. (a) Schematic of the Si/I/LNOI EOM. The Si layer keeps the thickness of 220 nm where the MMIs and input/output waveguides are located. The Si layer gets thinner in the EO interaction region. (b) The cross section of the waveguide structure in the EO interaction region. (c) The color profile shows the optical mode field distribution (in logarithmic scale) and the arrow shows the static electric field distribution, where hSi = 90 nm, wSi = 500 nm, G = 7 mm, hi = 150 nm, wtr = 0 nm, hLN = 600 nm, and the optical loss is 1.36 dB/cm. (d) The horizontal cut of the optical mode profiles in the middle of the thin film LN. The shaded region indicates the continuum of the slab radiations. (e) The top view of the waveguide structure in the EO interaction region, the red line indicates the guided optical mode and the blue line indicates the slab radiation modes.
Since the refractive index of Si is larger than that of LN, the thickness of the Si waveguide must be thin enough to confine more light in the thin film LN. The cross section should therefore be carefully optimized for a low Vπ and a broad BW. Vπ is determined by the EO interaction length L as well as the EO interaction strength of VπL. Provided the push-pull configuration, VπL is given by [14]
As depicted in Fig. 1(c), the electric field, which overlaps with the optical field, can be quasi-uniformed in the thin film LN. ΓLN, the optical confinement in the thin film LN, is defined as
The EO bandwidth is characterized by the frequency response. For the EOM with CPW-TWEs, the frequency response is modeled as [15]
Figure 1(c) shows the distributions of the optical field and the electric field. The slab radiations are excited at the metal-SiO2 interface. The radiation mode also can be understood by surface plasmon polariton (SPP) mode [16]. Figure 1(d) illustrates the horizontal cut of the optical mode profile and the refractive index distribution. Shown at the top is the conventional guided mode (illustrated as the black line in Fig. 1(d)), which is outside the continuum (neff > nslab). This guided mode remains uncoupled with the slab radiations (illustrated as the dashed line in Fig. 1(d)). Inside the continuum (neff < nslab), the optical mode can be coupled to the slab radiations [17,18]. However, under some special conditions, the optical mode remains localized with fewer radiations, leading to lossless propagation (illustrated as the red line in Fig. 1(d)). Inherently, the lossless mode is formed by destructive interference of the slab radiations. As seen in Fig. 1(e), the destructive interference can be engineered by the dimensions of the SiO2 spacer.
3. Characteristics of the sandwiched structure
For the design of strong EO interaction and targeted frequency response, analysis of the electrical signal is necessary. The material properties used in the simulations are listed in Appendix A. To analyze the effect of the SiO2 spacer thickness (hi) and the electrode gap (G), the variations of the electric field and the microwave properties are simulated. The electric field is depicted in Fig. 2(a). Ez (c, m) is a value of the electric field at the center of the thin film LN when the applied voltage is 1 V. A thicker SiO2 spacer would give a smaller Ez (c, m) since the electrodes get farther away from the thin film LN in the vertical direction. The microwave properties, which are frequency dependent, include the microwave effective index (nm), the microwave loss (αm), and the characteristic impedance (Re(Z0)). Since αm decreases quickly as the thickness of the electrodes (hAu) increases until 0.8 µm (see Appendix B), the hAu is fixed at 0.8 µm in the following analysis. These simulated results in Figs. 2(b)–2(d) are performed at the frequency of 100 GHz. Here, the width of the signal electrode (ws) is set to be 12 µm. It is clear that nm is sensitive to hi, while more robust to the change of G. Besides, by increasing hi and G, αm decreases whereas Re(Z0) increases.
Fig. 2. Simulated results versus G and hi. (a) The electric field (Ez (c, d)) at the center of the thin film LN, (b) the effective index (nm), (c) the microwave loss (αm), and (d) the characteristic impedance (Re(Z0)) of the microwave signal at a frequency of 100 GHz (ws = 12 µm, hAu = 0.8 µm).
For the optical signal at 1550 nm traveling in the EO interaction region, we perform the optical properties including the confinement in LN (ΓLN) and the group index (ng). Figure 3 depicts these properties as functions of the thickness of the Si waveguide (hSi) and that of the SiO2 spacer (hi). Here, the width of the Si waveguide (wSi) is chosen to be 500 nm. As presented in Fig. 3, ΓLN drops with the increase of hSi whereas ng goes up. It can be inferred that hSi should be less than 130 nm to obtain a larger ΓLN. Meanwhile, the value of hi also affects ΓLN and ng. It can be seen that for hSi < 130 nm, the SiO2 spacer serves as a barrier to confining more light in the thin film LN as the SiO2 spacer becomes thicker. Furthermore, by adopting the SiO2 spacer, the sensitivity of ng to hSi can also be effectively suppressed. Hence, we tend to engineer the SiO2 spacer and inhibit the negative effect caused by the randomness of the Si waveguides.
Fig. 3. Simulated results versus hSi and hi. (a) The confinement in the thin film LN (ΓLN) and (b) the group index (ng) of the optical signal (wSi = 500 nm).
It is worth noting that the electrical and optical properties determine the modulation performance. According to the above demonstration, the electrical properties vary with G and hi. Therefore, the thickness of the SiO2 spacer and the electrode gap should be jointly optimized. The variation of VπL versus different G and hi is analyzed and plotted in Fig. 4(a). Here, the dimensions of the Si waveguides are set to be 90 nm × 500 nm. It is presented that VπL exhibits a linear function of G, and a smaller G leads to a lower VπL. Besides, it can be found that VπL can be less sensitive to hi with a certain value of hSi.
Fig. 4. Simulated results of (a) the halfwave voltage length product (VπL) and (b) the EO bandwidth (BW) versus G and hi. (hSi = 90 nm). Simulated results of (c) the halfwave voltage length product (VπL) and (d) the EO bandwidth (BW) versus hSi and hi (G = 7 µm). Inset in Fig. 4(c) shows VπL as a function of hSi in a range from 60 nm to 120 nm.
According to Eq. (3), a shorter EO interaction length will result in a broader BW, but leads to a higher Vπ. To balance the intrinsic tradeoff between BW and Vπ, BW can be optimized with a fixed halfwave voltage of Vπ = 3 V. Assuming index matching is obtained, the BW performance is presented in Fig. 4(b). A larger G, however, results in a broader BW. In this sandwiched structure, the electrode gap of G is chosen to be 7 µm to ensure a larger BW and a smaller VπL. BW can be adjusted by changing the width of the signal electrode (ws). The dependance of BW with ws is discussed in Appendix B.
Index matching matters at high frequencies. The SiO2 spacer can offer additional freedom to tailor the optical properties, making it easier to achieve perfect index matching between the optical field and the electric field by adjusting hi. We also analyze VπL and BW as functions of hSi and hi, which are plotted in Figs. 4(c) and 4(d). Here, the simulated results correspond to the electrode gap of G = 7 µm. It can be found that VπL decreases considerably as hSi decreases until 130 nm. Moreover, the inset of Fig. 4(c) presents VπL as a function of hSi in a range from 60 nm to 120 nm. It implies that a thicker SiO2 spacer may lead to a lower VπL, even though there is a degradation of the electric field as discussed above. Maximal values of BW are achieved when index matching is obtained with different hSi and hi. Based on the index matching condition, hSi is selected to be 67 nm, 80 nm, 90 nm, 90 nm, and 90 nm with different SiO2 spacer thicknesses of hi = 0 nm, 50 nm, 100 nm, 150 nm, and 200 nm. It is worth noting that BW is especially sensitive to hSi when hi = 0 nm, 50 nm, and 100 nm since ng changes quickly with the varied hSi, and index mismatch causes the decrease of BW. However, the rapid decrease may be avoided by utilizing a thicker SiO2 spacer, since index matching can be maintained with a certain range of hSi, when hi = 150 nm and 200 nm.
The optical loss is also a limiting factor of the EOMs. Here, the optical loss is dominated by the radiation loss and the metal-induced absorption loss, while the scattering loss is not considered. Here, the index difference between the optical fundamental TE mode and the slab radiation (Δneff = neff − nslab) is calculated to characterize the radiation loss. The simulated results in Fig. 5(a) imply that the optical mode is inside the continuum, since Δneff < 0. As mentioned above, the radiation loss can occur inside the continuum and lossless propagation can be obtained by engineering the trench width of the SiO2 spacer (wtr). Simulation results in Fig. 5(b) reveal that a thicker SiO2 spacer comes up with a higher optical loss. This is because a thicker SiO2 spacer makes more optical mode confined in the thin film LN and more optical mode can be coupled to the slab radiations. However, SiO2 etching helps suppress the radiation loss. As presented in Fig. 5(b), the loss of the optical mode changes as wtr varies. It can be observed that the optical loss becomes lowest when wtr is chosen to be 1.5 µm at different hi. Consequently, the SiO2 etching is employed to break the limitation of the thickness of the SiO2 spacer.
Fig. 5. (a) The index difference between the optical fundamental TE mode and the slab radiation (Δneff) versus hi. (b) The optical loss versus wtr with different hi.
The EO responses of the Si/LNOI modulator and the sandwiched Si/I/LNOI modulator are compared in Fig. 6. The optimized parameters are summarized in Table 1. The simulated microwave indexes (nm) are presented in Fig. 6(a). Here, the optical group indexes for the Si/LNOI modulator and the sandwiched Si/I/LNOI modulator are 2.33 and 2.21 (see the black dashed line). It can be seen that the index matching is very good. Figure 6(b) shows the microwave losses (αm), around 6 dB/cm at 100 GHz. The simulated characteristic impedances (Re(Z0)) are presented in Fig. 6(c), which is slightly larger than 50 Ω. Figure 6(d) reveals the EO responses when Vπ = 3 V. The EO response in dB is 20log10(m(ω)). There is a rapid roll-off at low frequency due to the impedance mismatch. It also can be seen that the Si/LNOI modulator and the sandwiched Si/I/LNOI modulator achieve the nominal 3-dB EO bandwidths of ∼170 GHz and ∼180 GHz, respectively.
Fig. 6. Simulated microwave properties and EO responses for the Si/LNOI modulator and the Si/I/LNOI modulator. (a) The effective indexes (nm), (b) the microwave losses (αm), (c) the characteristic impedances (Re(Z0)), and (c) the EO responses versus frequency.
Table 1. Comparison of the structural parameters of the Si/LNOI EOM and the Si/I/LNOI EOM
4. Tolerance to fabrication deviations
Another aspect to consider is the performance deteriorations induced by the random fabrication deviations, which are inevitable in massive/scalable productions. Considering of a low optical loss and robust fabrication, we choose hi = 150 nm. The simulated results aforementioned suggest that the thickness of the SiO2 spacer shows a tolerance of ±50 nm when hSi = 90 nm as depicted in Fig. 4(b). Meanwhile, the trench width of the SiO2 spacer shows a tolerance of ±1 µm, maintaining a low optical loss under 0.5 dB/cm. In other words, the optical distribution tends to be less sensitive in a range of wtr. Simulations are investigated to demonstrate the effect of Si dimensional variations on the performance deteriorations. Here, we compare the performances of the sandwiched Si/I/LNOI EOM with those of the Si/LNOI EOM without the SiO2 spacer. The width and the thickness deviations of the Si waveguide are set to be ±50 nm and ±10 nm. Figure 7 shows the sensitivities of the device to the variations of Si dimensions. It reveals that the Si/I/LNOI EOM is robust to the fabrication deviations. Such a behavior can be understood since the optical mode is better confined in the thin film LN by the SiO2 spacer and the deviations of the Si waveguide hold less effect on the distribution of optical mode and thus the modulation performance.
Fig. 7. Analysis of sensitivities to the variation in Si dimensions due to fabrication deviations. (a) Simulated random VπL, (b) BW with a fixed halfwave voltage, and (c) the loss as functions of δh and δw for the Si/LNOI EOM. (d) Simulated random VπL, (e) BW with a fixed halfwave voltage, and (f) the loss as functions of δh and δw for the Si/I/LNOI EOM.
5. Conclusion
We have proposed a sandwiched Si/I/LNOI modulator and demonstrated a detailed analysis of the electrical and optical properties. The broad bandwidth is achieved by engineering the thickness of the Si waveguide and the SiO2 spacer. Moreover, due to the mechanism of coupling from the guided mode to the slab radiations, the thickness limitation of the SiO2 spacer can be relaxed by utilizing SiO2 etching, which thus improve fabrication tolerances. The performance comparison of LN-based EOMs with CPW-TWEs summarized in Table 2. It reveals that this sandwiched Si/I/LNOI modulator exhibits a broad bandwidth of ∼180 GHz and a halfwave voltage of 3 V, resulting in a higher bandwidth-voltage performance. For further optimization, the bandwidth-voltage performance can be enhanced by utilizing the capacitively load traveling wave electrodes (CL-TWEs) since CL-TWEs take advantage of a reduced microwave loss. We believe that the sandwiched Si/I/LNOI structure has opened a new avenue for complex and scalable photonic integration circuits. Furthermore, the demonstration of such a CMOS-compatible and fabrication-friendly structure paves the way for the development of practical photonics in the future.
Table 2. Performance comparison of EOMs with CPW-TWEs
Appendix A: Design procedure for the sandwiched modulator
In order to analyze the characteristics of the EO interaction and the EO response, we first calculate the electric field distribution at a certain voltage in commercial software (COMSOL). Then, the EO response is determined by the microwave properties including microwave index (nm), the microwave loss (αm), and the characteristic impedance (Re(Z0)). Thus, such three factors are calculated in the ANSYS HFSS. Next, we calculate the optical confinement in LN, the optical group index, the effective index, and the slab index at a wavelength of 1550 nm in an optical mode solver (Lumerical Mode solution). Note the slab index is performed with the Metal-SiO2-LN structure. Based on the electric and the optical properties extracted from these simulations, the halfwave voltage length product (VπL) and the bandwidth (BW) with a fixed halfwave voltage can be calculated. Finally, we evaluate the optical loss. Here, the material properties used in these simulations are listed in Table 3. The material dispersion is considered when we calculate the optical group index.
Table 3. Material properties
Appendix B: The electrode geometry for the sandwiched modulator
The electrode geometry plays an important role when we tailor the microwave properties except for the waveguide dimensions. αm can be reduced by increasing the thickness of the electrodes. As presented in Fig. 8, αm decreases quickly as the thickness of electrodes (hAu) increases until 0.8 µm. Thus, we adopt 0.8 µm in our structure. The electrode gap (G) is chosen to be 7 µm based on the consideration of a broader BW and a lower Vπ. Once the gap of electrodes (G) is fixed, the width of the signal electrode (ws) can be optimized to adjust the microwave properties and the EO response. Dependance of the microwave properties and the EO response (Vπ = 3 V) on the width of the signal electrode are plotted in Fig. 9. Figures 9(a)-(d) show the simulated results of the Si/LNOI EOM, and Figs. 9(e)-(h) indicate that of the Si/I/LNOI EOM with hi = 150 nm. nm is less sensitive to ws. Moreover, a narrower ws results in an increased αm and an increased Re(Z0). Given that index matching is achieved, the simulated results of the EO response are plotted in Figs. 9(d) and (h). There is a rapid roll-off at low frequency due to the impedance mismatch. Besides, impedance mismatch also causes ripples in EO response, indicating the power of the microwave signals is back-reflected. In addition, the EO BW increases slightly, when the characteristic impedance is slightly large. For the optimized EO response coupling with less reflection and a broader BW, we choose a slightly smaller value of ws = 12 µm. A narrow signal electrode can help to increase the characteristic impedance and may outweigh the penalty paid by the higher microwave loss.
Fig. 8. (a) The microwave loss (αm) versus the thickness of the electrodes (hAu) and the thickness of the SiO2 spacer (hi) at a frequency of 100 GHz.
Fig. 9. Simulated results of microwave properties and EO response, when hAu = 0.8 µm, G = 7 µm. (a) the effective index (nm), (b) the microwave loss (αm), (c) the characteristic impedance (Re(Z0)) of the microwave signal, and (d) the EO response in a frequency range from 1 GHz to 200 GHz for the Si/LNOI EOM. (e) the effective index (nm), (f) the microwave loss (αm), (g) the characteristic impedance (Re(Z0)) of the microwave signal, and (h) the EO response in a frequency range from 1 GHz to 200 GHz for the Si/I/LNOI EOM.
Funding
National Key Research and Development Program of China (Program No. 2019YFB2203700); National Natural Science Foundation of China (Grant No. T2225023).
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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