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Abstract
This paper presents a simulation-based analysis on the performance of plasmonic ferroelectric Mach-Zehnder in a ring (MZIR) versus symmetric Mach-Zehnder modulators (MZMs) on Si3N4 targeting O-band operation. The detailed investigation reveals the tradeoff between Au and Ag legacy noble metals providing lower modulator losses and CMOS compatible Cu featuring low cost. The numerical models also show that by opting for the MZIR layout there is a reduction in the Vπ x L product of 46% for Ag, 39% for Au and 30% for Cu versus MZMs. Time-domain simulations verify the successful generation of 112 Gbaud PAM-4 Signals from both MZIRs and MZMs for as low as 2 × 1.3 Vpp and 5µm long plasmonic phase shifters (PSs) with MZIRs providing a ΔQ signal improvement over MZMs of 2.9, 2.4, and 1.3 for Ag, Au, and Cu metals respectively. To the best of our knowledge, this is the first theoretical demonstration of such a low-loss, low-voltage, high-speed, and CMOS compatible plasmonic modulator on Si3N4, in the O-band.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silicon photonic intra-Data-Center Interconnects (intra-DCI) have flourished during the last decade as cloud computing, high-performance computing, streaming and AI, have spearheaded great alterations to the traffic flow patterns, intensifying bandwidth requirements at ever decreasing distances [1]. In such a demanding environment, co-packaged silicon photonic based transmitters are a promising technology that can scale and evolve in terms of size, bandwidth, and power consumption [2] with demonstrations on legacy SOI solutions providing elevated speed metrics in combination with wavelength multiplexing, filtering or power splitting capabilities [3,4].
On the other side, the advent of Silicon Nitride (Si3N4) has brought forth a large variety of new possible applications leveraging its large transparency window, low propagation losses and excellent performance [5,6]. The first efforts were focusing on passive components such as filtering and multiplexing/demultiplexing modules for microwave photonics [7–9] and receivers for datacom [10]. Nevertheless, the true strengths of the Si3N4 were revealed with the invention of hybrid, heterogeneous [11,12] and monolithic [13,14] co-integration providing the realization of complex circuits incorporating also active components via efficient low-loss coupling interfaces [15–17]. In this way recently novel hybrid [18] and heterogeneously integrated lasers [19] and photodetectors [20] have been demonstrated.
However, a complete intra-DC integrated photonic link on Si3N4 still requires a modulator element capable of operating at high baud rates beyond 100 G per lane in conjunction with low power consumption and low losses. Additionally, CMOS compatibility should be a given targeting replacement of SOI modulators in today’s datacom applications where low cost is among the top priorities. As Si3N4 is a dielectric and cannot facilitate intrinsic electro-optic activation [5], hybrid and heterogeneous integration are the only ways for the realization of high-speed modulators [11]. These techniques employ a variety of materials in combination with Si3N4, so as to achieve the modulation of light in the phase domain, such as silicon [21], graphene [22,23], ferroelectric lead zirconate titanate [24], electro-optic polymers [25], lithium niobate [26–33] and barium titanate oxide [34–36]. Out of those, Si3N4-LNOΙ is the prevalent solution in most recent publications with results demonstrating simulated bandwidth up to 1200 GHz [29], 95 GHz experimental 3dB-bandwidth (BW) for a 10 mm PS length and Vπ of 3.75 V [32]. The highest data rates ever recorded on Si3N4 is 80Gbps in single-channel [27], 280 Gbps in a quad-channel NRZ array [31] and 128Gbps in a single channel PAM-4 signal transmission [33]. On the other side, ferroelectric barium titanate oxide (BTO) compared to all the other ferroelectric materials, exhibits the largest electro-optic coefficient, is CMOS compatible and can withstand high temperature variations [34–37] for subsequent post processing during packaging of the devices. The credentials of the high electro optic coefficient of the BTO material were demonstrated in [34] resulting in as low as 106nW/FSR power consumption in a racetrack resonator on Si3N4. Nevertheless, these devices, being purely photonic, are bound by large footprint incorporating 150 µm long PSs.
Co-packaged optics on the other side require extremely small dimensions, especially if they are going to be connected directly to the ASIC’s pins for driverless operation. Plasmonic modulators fit ideally in this need combining ultra-high bandwidth and a footprint matching ASICs’ pin pitch of a few micrometers. Starting from the lithium niobate platform, plasmonic LNOI modulators have demonstrated low half-wave voltage length products of 0.23Vcm for a footprint less than 1mm2 and a bandwidth over 10 GHz [38]. By integrating Plasmonic Organic Hybrid (POH) PS on SOI photonic waveguides, a C-band modulator was demonstrated for a racetrack design with on-chip BW over 110 GHz, 1 dB insertion loss (IL), sub-volt operation and enhanced stability [39–41]. Going to BTO, its frequency response was measured up to 270 GHz [42]. Relying on the above advantages, in [35,36], the first Si3N4-BTO plasmonic-slot based MZM was demonstrated experimentally delivering 216Gb/s PAM-2 and a 256Gb/s PAM-4 error free signal transmission in the C-band. However, the plasmonic metal was Au, not suitable for CMOS mass fabrication, the Si3N4-to-plasmonic coupling losses were over 6.5 dB and a Vπ x L product of 144 Vµm was measured at 40 GHz.
In this work, we numerically analyze the first fully O-band CMOS compatible, in terms of material stack, Copper (Cu) based Si3N4-plasmonic MZIR modulator design capable of operating at above 100Gbaud rates and compare its performance versus two identical devices exploiting noble metals i.e. Au and Ag, which are not CMOS compatible but are the most commonly utilized plasmonic metals in plasmonics research. The whole analysis presents in detail the penalty induced in the performance of the modulator for going to CMOS by the higher propagation losses induced by the Cu metal in the plasmonic PSs. In addition, the work highlights the advantages the MZIR layout in terms of power savings versus symmetric MZMs in agreement with a similar conclusion from the LNOI platform [43]. Assuming a 5µm long PS of the MZM or MZIR for all three material platforms, the best performance is obtained as expected for Ag achieving insertion losses of 3.56 dB and Vπ x L product 46% lower than the standard MZM. The Au based MZIR is very close to this with insertion losses of 4.74 dB, and Vπ x L product 39% lower than the conventional MZM. Finally, the CMOS compatible Cu based MZIR exhibits insertion losses of 6.85 dB and Vπ x L product 30% lower than its symmetric MZΜ counterpart. The drop in the performance of the Cu based MZIR is coming from the lower Q-factor of the resonance peaks due to the higher propagation losses in the plasmonic phase shifter equal to 0.78 dB/µm versus 0.33 dB/µm for Ag and 0.5 dB/µm for Au. In high-speed operation for the same PS length and 2 × 1.3Vpp driving voltage at 112Gbaud PAM-4 modulation format, the signal quality improvement measured by the ΔQ of MZIR versus MZM is calculated as 2.9, 2.4 and 1.3 approximately for Ag, Au and Cu plasmonic metals, respectively. By lowering the driving voltage to 2 × 0.8Vpp the ΔQ metric is equal to 0.88 for Cu, 2.2 for Au and 2.78 for Ag. The absolute Q value for the Cu based MZIR is higher than 5.2 even for 2 × 0.8Vpp driving voltage confirming error free transmission under FEC. All Q values in these calculations are for 10dBm at the input of the modulator and no biasing. For a degraded r42/2 the proposed MZIR retains a voltage reduction higher than 18% for Cu-, 28% for Au- and 37% for Ag-based designs. These performance metrics render this modulator technology an ideal optical engine for co-packaged optics solutions compatible with next generation 51.2 Tb/s switching routers featuring 224Gbps SerDes interfaces.
The organization of the rest of the paper is the following: Section 2 presents the overall MZIR modulator layout and demonstrates the device-level analysis and results from all the various elements employed in the circuitry. Section 3 shows the static and frequency-domain analysis of the plasmonic modulator for the three plasmonic metals, Ag, Au, and Cu and the various design parameters, highlighting all performance trade-offs. Section 4 describes the results from the time-domain analysis at the system-level, elucidating the capabilities of the MZIR modulator for 112Gbaud PAM-4 Signal Transmission. Section 5 studies the impact of a degraded r42 value of the BTO due to fabrication to the MZIR performance metrics. Section 6 discusses and compares the results of this paper with other modulators in the literature.
2. MZI-ring modulator layout and component analysis
2.1 MZIR layout analysis
The plasmonic ferroelectric MZIR modulator is based on the traditional 2 × 2 MZI circuit with the adjustment of a dielectric waveguide loop connection from one input of the 2 × 2 input MMI to one of the outputs of the 2 × 2 output MMI. Figure 1(a) presents the corresponding layout of the MZIR modulator, while Fig. 1(b) shows the cross section of the plasmonic PS. The design employs three waveguiding levels: the Si3N4 dielectric waveguide forming the main device circuitry, the aSi interposer waveguide used as an intermediate layer for optimum light transfer between the Si3N4 waveguide, and the plasmonic slot PS filled by a ferroelectric barium titanate oxide (BTO) material. The plasmonic slot waveguide, due to its waveguide symmetry, supports a TE plasmonic mode, therefore the polarization of interest in the MZIR operation is also TE. The Si3N4 waveguide has a width of 800 nm and an equal thickness value of 800 nm, supporting both a TE and a TM mode, with the TE one exhibiting an effective index with a real part Re{neff} = 1.773 and propagation losses (PL) of 0.2 dB/cm at a wavelength λ = 1310 nm. The Free Spectral Range of the MZIR is controlled by the total length of the cavity formed by the waveguide loop, the Multimode Interference (MMI) couplers, the Si3N4-to-plasmonic-slot coupling interfaces, and the plasmonic slot PS. The total cavity length is kept as low as possible to achieve the highest possible FSR value. The loop length is large enough to enclose two MMIs approximately 300µm long, two coupling interfaces approximately 186µm long and a PS of variable length. Finally, there is a length difference between the two branches of the MZI equal to ΔL = LFSR/2 = λ0/2Re{neff(Si3N4)} for λ0 = 1310 nm inducing an extra π phase shift in the loop for reasons that will be better analyzed and illustrated in Section 4.
Fig. 1. (a) 3D schematic of the tri-layer Si3N4-BTO plasmonic slot based ferroelectric modulator and (b) plasmonic slot (MIM) phase-shifter utilizing a ferroelectric BTO material.
The analysis of the MZIR plasmo-photonic circuit is starting from the optimization through 3D-FDTD simulation of the MMI-Couplers, the plasmonic slot PS and the Si3N4-to-plasmonic slot coupling interfaces. Then the transfer function of these components is inserted in a circuit level simulator towards maximization of the MZIR modulator performance. The whole study also includes a comparison versus normal MZMs, so as to reveal the power savings coming from the MZIR without any penalty in the obtainable bandwidth, contrary to Ring or Racetrack Resonators.
2.2 MMI coupler design and broadband response
The MZIR device design was initiated with the MMI couplers. Consecutive 3D-FDTD numerical calculations have been utilized in order to obtain maximum coupling efficiency to the two output ports simultaneously with minimum imbalance. The output width, MMI length, and position of the input and output tapers have been varied in a systematic manner to reach the optimum performance in terms of efficiency. These were identified as 6 µm for the MMI width and 108 µm for the MMI length. The taper output width has been increased to 2.5 µm to collect all the field at the two outputs, while the taper length has also been increased to 20 µm. Figure 2(a) depicts the simulated device in a 3D-manner. The MMI inputs and outputs were placed at a distance dw = 1.5µm from the center of the MMI. The |E| field distribution for a wavelength of 1.31 µm for a TE- mode input is shown in Fig. 2(b) indicating efficient operation in the TE polarization. Figure 2(c) shows the corresponding transfer functions extracted from broadband 3D-FDTD simulations. In both graphs the losses per port are below 0.2 dB near 1310 nm, with the imbalance being lower than 2%. The scattering matrix for this design was obtained and inserted in circuit simulations analyzed in Section 3.
Fig. 2. (a) 3D schematic of designed MMI coupler. (b) Top view of |E| field distribution for a TE mode excitation from input 1 to the 2 × 2 MMI. (c) Numerically calculated transfer function at the two outputs of the MMI for the TE mode excitation.
2.3 Plasmonic slot phase-shifter analysis
The second element of the MZIR circuit that is thoroughly analyzed in this work is the plasmonic MIM slot PS capable of supporting highly confined plasmonic modes in the BTO. This material features an approximately 3x-10x higher effective electro-optic coefficient versus LiNbO3 [44]. The optical mode in the slot was calculated by solving the eigenvalue problem at λ = 1310 nm at the 2D-plane for each voltage V with the Finite Difference Method (FDE).
Towards the analysis of the plasmonic slot PS, by sweeping the applied voltages, Poisson’s Equation was initially solved at the cross-sectional plane of the slot employing FEM simulations for the calculation of the RF electric field distribution |ERF|. Then the effective index neff = Re{neff} + iIm{neff} was calculated at each voltage V, by applying the RF field distribution with the interpolation of the 2D-FDE mesh. The calculation of the neff considers the following equations with r13 = r23 = 8 pm/V, r33 = 33 pm/V and r42 = 807.53 pm/V [44,45]. The material refractive index elements were derived from [44,45].
A 2D-Schematic of the plasmonic slot PS can be seen in Fig. 3(a). The plasmonic metal is either Cu, Au, or Ag and has a thickness of 100 nm. The slot width is 100 nm for Au and Cu, and 90 nm for Ag, considering the practical limitations of standard low cost 193 nm DUV lithography [46]. The slight difference in the width of the Ag slot is coming from the optimization of the coupling to the Si3N4 layer [16]. The numerically calculated RF electric field for an applied voltage of 1 V and optical modal field can be seen in Fig. 3(b) and (c), respectively, where a great overlap between the RF and optical field in the slot filled by the BTO material is revealed. The effective index change ΔRe{neff} for increasing voltage values can be seen in Fig. 3(d). From there it is evident that the three materials exhibit almost the same slope, indicating an almost identical half-wave voltage length product (Vπ x L). Indeed, the calculations show for Ag and slot width 90 nm, the Vπ x L is 25.51 Vµm, for Au and slot width 100 nm it is 28.06 Vµm, while for the CMOS Cu and 100 nm slot again, the Vπ x L is 27.33 Vµm. These low values are justified by the high RF and optical electric field confinement in the BTO material of the slot waveguide as seen in Fig. 3(e). The same figure reveals that the confinement factor in the slot ranges from 80% to 45% independent from the type of metal and defined almost exclusively by the slot width. However, Fig. 3(f) shows a clear tradeoff between CMOS compatibility and propagation performance as the propagation losses vary from 0.33 dB/µm for Ag, to 0.5 dB/µm for Au and finally to 0.78 dB/µm for Cu. It should be noted that Cu PS losses is more than double versus the Ag based one with subsequent degradation of the overall performance. Finally, alternative interesting CMOS compatible plasmonic metals, Al and TiN, were examined as possible solutions for plasmonic phase shifters. Nevertheless, the calculated propagation losses of TiN were above 10 dB/µm, while the losses for Al were 1.47 dB/µm for slot widths of 100 nm. For this reason, Copper (Cu) was chosen as the most favorable CMOS compatible metal.
Fig. 3. (a) Cross section of the designed Cu/BTO/Cu (MIM) plasmonic slot PS. (b) Calculated RF-electric field |ERF| (c) and optical modal field |EOPT|. (d) Effective index change ΔRe(neff) vs applied voltage V. (e) Confinement factor (%) of the optical mode in the plasmonic slot. (f) Propagation losses (dB/µm) for increasing slot widths.
2.4 Tri-layer low-loss Si3N4-to-plasmonic slot coupling interfaces
A tri-layer coupling interface from a Si3N4 waveguide to the plasmonic slot waveguide was strategically designed targeting ultra-low coupling losses to the plasmonic slots presented above. The schematic and the numerical results from 3D-FDTD simulations of the configuration for Au, Ag and Cu can be seen in Fig. 4. The interface follows a two-step approach: (a) an adiabatic coupler from an 800 × 800nm2 Si3N4 to an aSi interposer waveguide with a width of 350 nm and a thickness of 220 nm, and (b) a directional coupler from the aSi waveguide to the plasmonic slot PS. Two 100 nm thick intermediate dielectric SiO2 layers are deployed to separate the three layers. Figure 4(b) and (c) present the simulated electric-field distribution for the adiabatic coupling and the directional coupling step, respectively. The losses induced from the adiabatic coupler are as low as 0.06 dB per transition, while for the directional coupler, the lowest coupling losses ensue for Ag having a value of 0.71 dB for a coupling length Lc = 2.78 µm. For Au this value increases to 0.86 dB per directional coupler for Lc = 2.71 µm, while for CMOS Cu the coupling losses increase to 1.23 dB. More details for the coupling interface are provided in a previous work [16], also highlighting the tolerances of the device to fabrication variations.
Fig. 4. (a) 3D-depiction of Si3N4-to-plasmonic slot two-step interface geometry. (b) Numerically calculated electric field |E| for the adiabatic coupling step from Si3N4-to-aSi and (c) for the directional coupling step from aSi-to-Cu-plasmonic-slot.
3. MZI-ring frequency-domain analysis
3.1 Semi-analytic numerical calculations
For the initial study of the physical characteristics of the MZIR modulator, a semi-analytic model was formulated and applied as a starting point towards better understanding of the device physics, as presented in our previous work in [47]. The energy efficiency and the voltage reduction of the MZIR with respect to the symmetric MZM for the same material platform and equal PS length is dependent on the total cavity losses. The metric signifying the Voltage Reduction Factor (VRF) of the MZIR with respect to the equivalent MZM modulator is related to the comparison factor CF and is provided by the following relations:
The voltage reduction factor VRF (%) defined in Eq. (3) and (4) is the percentage reduction to the Vπ value of an MZIR modulator versus an equivalent non-resonant symmetric MZI. The CF value is dependent on the total losses in the MZIR cavity included in the parameter Atot calculated from (3) and the Vπ x L product for each PS in the MZIR is reduced with respect to the symmetric MZM according to (5):
Equation (5) refers to the voltage that needs to be applied in each of the two PSs for the maximization of the ER in the MZIR. The calculated total device Insertion Losses (IL), Voltage Reduction Factor (VRF), critical coupling voltage Vcrit for Eqs. (3) and (5) are illustrated in Fig. 5 for different PS lengths. As seen in Fig. 5(a), the insertion losses are the lowest in Ag-based MZIRs with the value retained below 5 dB for slot lengths up to 10 µm. For Au, the IL are a little higher ranging from 2 up to 7.3 dB and for Cu, the IL increase to 11 dB for a slot length of 10 µm that was expected from the simulations results in the previous Section. Figure 5(b) and Fig. 5(c) present the voltage reduction factor and the critical coupling voltage results, respectively, where it is evident a clear trade-off exists between the two metrics. For lower plasmonic slot PS lengths the total cavity losses are lower, therefore the VRF is higher. However, the critical coupling voltage is also higher as it is inversely dependent on the PS length, originating from the Vπ x L product of (5). For Ag, the reduction factor VRF ranges from 55.9% down to 40% for slot lengths between 1 µm and 10 µm. However, the critical coupling voltage Vcrit becomes sub-Volt for lengths higher than 7 µm, rendering feasible driving these modulators directly from ASICs. For Au, the VRF varies from 52% to 28.5% with the Vcrit becoming sub-Volt for lengths higher than 9.5 µm. Finally, for the Cu CMOS metal, the VRF is as high as 44.9% for Lslot = 1 µm and decreases to 18.7% for 10 µm long PSs. The critical coupling voltage, on the other side, decreases to 1.1 V at Lslot = 10µm.
Fig. 5. (a) MZIR insertion loss IL (dB). (b) Voltage reduction factor VRF (%). (c) Critical coupling voltage Vcrit(V) for increasing plasmonic slot PS lengths Lslot (µm).
3.2 Frequency-domain circuit analysis
The broadband scattering matrices for all the designed components presented in the previous Section were inserted in Ansys-Lumerical INTERCONNECT for system level simulation evaluation. The S-matrices of the coupling interfaces allow for the study of any effects that may occur due to potential parasitic reflections. All the photonic and plasmonic waveguides were represented as compact models with a variable length. The model takes into account all the parameters such as effective index neff, group index ng, propagation loss PL and dispersive characteristics. Figure 6(a)-(c) present the simulated power transfer functions in for all three metals for 5 µm long PS. The calculated Free-Spectral Range (FSR) in all cases is approximately 75.17 GHz. The static responses of Fig. 6(a)-(c) indicate optimum performance for Ag as it was expected. For a 5 µm plasmonic slot PS, the IL are as low as 3.56 dB with the ER being higher than 30 dB for total absolute differentially applied voltage of 2 × 1.3 Vpp. The VRF is 46% versus the symmetric MZI with the same PS length. For the same length in Au, the IL increase to 4.74 dB, while the ER is 11 dB for the same voltage. Due to the slightly increased cavity losses, the VRF is decreased to 39%. Finally, if CMOS compatibility is mandatory, the Cu-based MZIR with the same length induces IL of 6.85 dB, still below than a 10 dB minimum value common in plasmonic modulators and an ER of higher than 7.7 dB for 2 × 1.3Vpp voltage. The VRF in this case is 0.3 indicating at least a 30% voltage reduction compared to Cu-based MZIs.
Fig. 6. (a) Calculated power transfer functions of the MZIR Cu-based slot, (b) Au-based slot, and (c) Ag-based slot for PS length Lslot = 5 µm for various applied voltages at each of the two MZI arms.
4. System-level modulator performance
4.1 Electro-optic bandwidth analysis
This section presents the simulation and circuit analysis in the time-domain. The MZIR modulator bandwidth has been theoretically studied in [48] and applied in [49] for Si-MZIRs and [43] for a low-FSR based LiNbO3 MZIR. As the supplement of [43] mentions in a detailed manner, for an input wavelength aligned at the MZIR wavelength peaks, the MZIR FSR creates resonances at the EO response of the modulator, having a negligible effect on its 3 dB cutoff frequency. Even with low FSR, the calculated EO bandwidth of the MZIR device of [43] can extend up to 40 THz. Based on [43] the PS bandwidth is the sole limiting factor contributing to the overall modulator bandwidth. In this MZIR design optimization, the plasmonic slot PSs are lumped elements with a length of 5µm, much lower than the RF wavelength. Their 3 dB bandwidth can reach up to 500 GHz in plasmonic slots employing the POH technology [50]. The capacitance of the 100 nm wide slot is calculated between 44.3 fF for 5 µm to 177fF for 20µm long PSs.
4.2 System-level simulations
A system-level simulation setup illustrated in Fig. 7 was created for the evaluation of the signal quality at 112 Gbaud PAM-4 targeting compatibility with next generation 51.2Tb/s ASIC routers SerDes interfaces. The S-parameters of the laser input/ fiber output coupling elements were excluded from the model, so as to evaluate the modulator performance exclusively. In the setup, a laser optically feeds the MZIR modulator with its wavelength aligned to a resonance of the MZIR transfer function near 1310 nm. The laser output optical power Pin is variable with the laser linewidth equal to 1 MHz assuming normal low-cost GaAs DFB technology. A PRBS-13 electrical signal from a Pulse Pattern Generator is fed to a PAM-N symbol mapper that correlates each of the PAM-4 symbols to each voltage value differentially applied to the MZIR device. The rise and the fall time of the driving electrical pulses is equal to 0.35 of the bit period i.e. 3.3ps. After modulation, the signal is received by a PIN photodiode (PD) with a responsivity of 0.55A/W, a dark current of 10 nA, and a thermal noise equal to -173.8dBm/Hz. The signal finally passes from a 4th order Low-Pass Bessel Filter of 84 GHz 3 dB bandwidth and then it is recorded on the oscilloscope. An optical spectrum analyzer monitors the signal before the OE conversion at the PD. It should be highlighted that no DSP is applied on the transmitter or receiver side for enhanced signal quality.
Fig. 7. Time-domain system level simulation setup for the evaluation of the signal quality received from MZIR modulators.
Figure 8 presents the numerical results of the system level simulations regarding the quality of the signal generated by the MZIR and MZM modulators. Figure 8(a) shows the initial calculations of measuring the output power from the modulator by sweeping the applied voltage to the MZMs or MZIRs for the three plasmonic metals. The resonance peaks in the MZIRs assist to the exhibition of significant higher extinction ratios relative to the MZMs even for low driving voltages. As such the Ag MZIRs present an extinction ratio 22.4 dB higher than the Ag MZM, while this value decreases to 19.6 dB for Au, and to 16.251 dB for Cu. Figure 8(b) shows the calculated Q-factor with respect to the input power Pin injected by the laser to the modulator for 2 × 1.3Vpp applied to the two PSs assuming a high-power ASIC. The improvement in the signal quality of the MZIR versus the MZM at 10dBm input power is 2.9, 2.4 and 1.3 for the Ag, Au and Cu based modulators, respectively. The bias is equal to 0 V in all scenarios targeting equivalent power consumption comparison. In terms of absolute values, the Q-factor is 9.4 for Ag, 7.15 for Au and 5.66 for Cu at 10dBm, easily surpassing the error free transmission threshold under FEC at up to 2 km [51]. The Q-Factor has been defined through the BERQ value as in [51], where N = 4:
Fig. 8. (a) Output power (dBm) vs. applied voltage per PS (V) for 0 dBm input power. (b) Q-factor vs. input power Pin for Cu, Au, and Ag MZIRs and MZMs with Lslot = 5 µm for 2 × 1.3Vpp driving voltage. (c) Q-factor vs. input power Pin for Cu, Au, and Ag MZIRs and MZMs with Lslot = 5 µm for 2 × 0.8Vpp driving voltage. (d)–(f) Eye diagrams of signal generated by the MZIR at 112 Gbaud PAM-4 for 2 × 0.8Vpp applied voltage and 10 dBm input power for Ag, Au, and Cu metal on the plasmonic slot.
Figure 8(c) illustrates the same results under the assumption of 2 × 0.8Vpp driving voltage from the ASIC, considering a more conservative approach for high speed SerDes interfaces. The signal improvement now is 2.77 for Ag, 2.23 for Au and 0.88 for Cu and come in agreement with the results of Fig. 8(a). The lower voltage swing does not enable now reaching the resonance peak at the MZIRs, however the improvement in the signal quality from the MZIR is still valid. The absolute values for 10dBm input power are now 8.3 for Ag, 6.9 for Au and 5.2 for Cu. It should be highlighted that the Cu based MZIR is error free under FEC even in this highly demanding scenario revealing the high-quality signal generated by the MZIR modulator at such low voltages. The higher drop in the ΔQ of the Cu versus the Ag and Au when driving the modulator with 2 × 0.8Vpp instead of 2 × 1.3Vpp is coming from the lower Q factor of the resonance peaks in the Cu MZIR due to the higher propagation losses in the plasmonic PSs. Again, no biasing is considered assuming direct drive from the ASIC. Finally, Fig. 8(d)-(f) present the corresponding eye diagrams for the three MZIR modulators for 2 × 0.8Vpp driving voltage and 10 dBm input power. The recorded eyes are clearly open in all cases with Ag exhibiting the best performance due to the lowest overall losses. The asymmetry in the eyes for the three metals is due to the manual setting of the four levels from the driver. Higher Q-factor values are expected with proper optimization tools. Also, the effect of the extra π difference induced in the MZI branches of the MZIR is also noted here, setting the initial state of the MZIR to the highest output power.
5. Degradation of BTO EO-coefficient
In the work presented so far in this article, the main electro-optic coefficient element r42 has a value of 807.53pm/V. However, various experimental studies have reported the variability of r42, resulting in different values for the effective electro-optic coefficient, reff, as mentioned in Ref. [44]. This is related with the variability of r42 due to surface effects and stress induced phenomena [52]. In [44] the reported r42 for the stress-free and stressed BTO was 1300 ± 100pm/V and 730 ± 100pm/V, respectively. In [52], 2D-FEM simulations were performed considering a value of 923 ± 215pm/V. This section of the paper aims to assess the performance degradation of the proposed MZIR modulator design under degraded r42 coefficients. Initially, in Fig. 9(a), the Vπ x L product of the phase-shifter is calculated for increasing r42 coefficient values as r42/N with N equal to 1,2, and 4. For N = 2, corresponding to an effective electro-optic coefficient reff of 300pm/V, the Vπ x L is close to 49Vµm for Ag, 53.65Vµm for Cu and 54.44Vµm for Au, still considerably low compared to other plasmonic modulator demonstrations in the literature. Figure 9(b) and (c) illustrate the MZIR insertion loss and the VRF (%) for varying plasmonic slot lengths. Again, the choice of the PS length determines the total losses and the energy advantage of the MZIR versus symmetric MZI-modulators. For Ag, the most favorable plasmonic metal among the three, the losses remain below 10 dB even for lengths up to 20 µm, while the voltage reduction factor exceeds 25% when compared with symmetric MZI designs. Figures 9(d)-(f) illustrate the voltages required per phase shifter (PS) to achieve maximum extinction ratio (ER) in the resonant modulator for Ag, Au, and Cu, with slot lengths ranging from 5µm to 20µm. The electro optic coefficient of the BTO is varied between r42, r42/2 and r42/4. For an r42/2 and a PS length of 10µm, the corresponding critical coupling voltages for the MZIR are 1.55Vpp for Ag, 1.95Vpp for Au, and 2.18Vpp for Cu. With this slot length the reduction factor would become 18% for Cu, 28% for Au and 37% for Ag. Considering an upper voltage of 1.8Vpp from typical ASICs, then the length of the PS should be increased to 15 µm or even higher for Cu. The high insertion losses then limit the VRF to 11.88%, drawing the limit of where CMOS compatible MZRIs provide a viable advantage over symmetric MZIs. For r42/4 the critical coupling voltages are higher than 2.807Vpp for Cu even for 20 µm long PSs rendering this technology not compatible with CPO.
Fig. 9. (a) Half-wave voltage-length product VπL (Vµm) for varying electro-optic coefficient r42 (pm/V) value. (b) MZIR insertion loss (dB) and (c) voltage reduction factor (VRF) (%) for increasing plasmonic slot length Lslot (µm), and critical coupling voltage Vcrit (V) for (d) Ag-MZIR, (e) Au-MZIR, and (f) Cu-MZIR for increasing plasmonic-slot length and for r42, r42/2 and r42/4.
6. Discussion and comparison with other modulator devices
Table 1 summarizes the main outcomes of this work and compares them with significant work presented in the literature on high-speed photonic and plasmonic modulators in the Si3N4 platform. As noted in the table, resonant modulators in the Si3N4-Si [21] and the Si3N4-graphene [22] platform, are all based on carrier effects and cannot deliver baud rates over 30Gbaud. Going to ferroelectric modulators on Si3N4, the PZT-on-Si3N4 platform is limited by a much larger PS length and the baud-rates achieved do not surpass 40Gbaud for NRZ modulation [24]. On the other side, the Si3N4-LNOI platform has achieved sub-volt voltages [26], but with the PS length surpassing 2 cm and very high single-channel baud rates of 80Gbaud in OOK [27] and 64Gbaud in PAM-4 modulation [33]. Photonic Si3N4-LNOI MZMs with an ultra-high bandwidth of 1.26THz numerically [29] and 95 GHz experimentally [32] have also been demonstrated. Nevertheless, the designs are bound by either a high required voltage over 7Vpp for a 3 mm PS length, or by 10 mm long PS for lower voltage of 3.75 V. In [41], a plasmo-photonic Si-POH micro-racetrack design has broken the power-bandwidth limitations in the C-band achieving 160 Gbaud PAM-4 transmission with only 1.2Vpp driving voltage and 1.2 dB insertion losses. The POH though technology suffers from the aging and maximum temperature envelope of all polymers. The sole work to overcome the footprint, voltage, and bandwidth trade-offs on the Si3N4 platform is [35,36] utilizing plasmonic slot BTO PS, achieving ultra-high baud rates of 128Gbaud with PAM-4 modulation using a voltage of 3.6Vpp and a 3 V bias. Nevertheless, the design is based on Au and therefore not suitable for the potential mass-production, promised by the CMOS technology. Also, the MZM requires a higher PS length, and the circuit is optimized for the C-band. The simulated insertion loss value of [35,36] is significantly lower (<6.5 dB PS), with the Au propagation loss being only 0.3 dB/µm. However, this comes at a cost of a less confining plasmonic slot, leading to larger lengths and a hybrid Si3N4-BTO cross-sectional design exhibiting sensitivity of the Vπ x L value to material thickness variations. For the first time, herein, the performance of three MZIR modulators featuring plasmonic slot BTO PS based on Cu, Ag, and Au is presented for the O-band. This work demonstrates devices with the lowest footprint, capable of operating at ultra-high baud rates, while requiring low voltages compatible with co-packaging applications in the O-band. The performance of the MZIR is highlighted by the at least 30% lower Vπ x L product required versus the symmetric MZM in order to obtain the same extinction ratio confirmed by the time domain simulations revealing a signal improvement of ΔQ between 1.3 and 2.9 for 10dBm input power and 2 × 1.3Vpp driving voltage.
Table 1. Comparison of the presented CMOS plasmo-photonic modulators with the state of the arta
7. Summary
This work presents a detailed performance analysis of plasmonic slot ferroelectric Mach-Zehnder in Ring (MZIR) modulator on Si3N4 capable of operating at above 100Gbaud in the O-band. The whole study investigates the tradeoff associated with going to CMOS Cu metal for the formation of the plasmonic PS targeting low cost, versus the legacy Ag and Au metals exhibiting the lowest plasmonic propagation losses. In addition, the paper calculates the power energy saving coming from opting for the MZIR layout versus the symmetric MZM in agreement with other recent works in other material platforms. Considering a 5µm long plasmonic PS at each arm of the MZM or MZIR the best results are obtained as expected for Ag, where the insertion losses of the MZIR are 3.56 dB and the Vπ x L product is 46% lower than the standard MZM. The Au based MZIR metrics are very close with insertion losses of 4.74 dB and Vπ x L product 39% lower than the conventional MZM. Finally, the CMOS compatible Cu based MZIR exhibits insertion losses of 6.85 dB and Vπ x L product 30% lower than its symmetric MZΜ counterpart. In high-speed operation, the MZIR is generating PAM-4/112 Gbaud signals for 5µm PS length and 2 × 1.3Vpp driving voltage with a ΔQ of 2.9, 2.4 and 1.3 versus symmetric MZMs for the Ag, Au and Cu plasmonics metals, respectively revealing the clear benefits of the MZIR layout. By lowering the driving voltage to 2 × 0.8Vpp the signal improvement is 0.88 for Cu, 2.2 for Au and finally 2.78 for Ag. The absolute Q factor is above 5.2 even for Cu metal and 2 × 0.8Vpp driving voltage indicating an error free link under FEC. All Q factors values mentioned above are for 10dBm at the input of the modulator and no additional biasing. The degradation of the r42 value due to thin film effects was also studied through simulations. For r42/2 the voltage reduction values become >18% for Cu, > 28% for Au and >37% for Ag. Our results pave the way for the adoption of plasmonic modulators as optical engines for co-packaged optics in next generation 51.2 Tb/s switching ASIC routers.
Funding
H2020 LEIT Information and Communication Technologies.
Acknowledgments
We would like to acknowledge the European H2020 NEBULA (contract no. 871658) and the Horizon-RIA ALLEGRO (contract no. 101092766) project.
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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