Multi-Parameter Optimization of a Shallow Ridge InP Traveling Wave Mach-Zehnder Modulator for Beyond 200 Gb/s Optical Datacom Applications

We present multi-parameter optimization of a shallow ridge InP-based traveling wave Mach-Zehnder modulator (MZM) for ultra-wide modulation bandwidth by velocity and impedance matching and microwave attenuation minimization. Relationship between MZM microwave loss and p-cladding layer doping profile is quantitatively analyzed and incorporated in device optimization. We propose a systematic analysis methodology allowing the full optimization of an InP shallow ridge MZM capable of 200 Gb/s PAM4 operation, compatible with high-volume low-cost manufacturing. Our design is expected to achieve 4.3 V half-wave voltage and 81 GHz 3-dB bandwidth with simplified fabrication process and improved long-term reliability.


I. INTRODUCTION
F IBER optic datacom technologies have experienced significant bandwidth growth over the past two decades, driven by exponential internet traffic and hyperscale data center I/O bandwidth demand growth, which in turn require ever higher speed modulator technology to deliver the necessary optical data transmission bandwidth [1]. Beyond 100 Gb/s, high speed traveling wave Mach-Zehnder modulator (MZM) on InP is the most likely solution delivering the necessary operating speed and supporting higher modulation formats [2]. The high-speed performance of a traveling wave MZM is limited by characteristic impedance matching, optical and electrical velocity matching, and microwave loss associated with both RF electrode and underlying semiconductor layers [3], [4]. In most reported InP traveling wave MZM design analysis, only the impedance and velocity matching are considered, with the microwave loss effect implicitly ignored, resulting in unrealistic bandwidth estimations (infinite for the ideal matching case) [5], [6]. The best reported InP MZM deploying a back-to-back p-i-n deep-etched ridge design has been demonstrated with 42 GHz 3-dB bandwidth by utilizing a simultaneously velocity and impedance matched capacitive-loaded (CL) Traveling Wave Electrode (TWE) [7], based on the Quantum Confined Stark Effect (QCSE). The deep etching process past the multiple quantum well (MQW) active region results in higher optical confinement and modulation efficiency, but is very sensitive to sidewall etch quality that can produce high scattering loss and surface defect states. Monolithically integrating the deep etched ridge structure with a shallow etched DFB laser source will also result in complicated integration process that is not compatible with high-volume low-cost manufacturing requirement of optical datacom applications. Other reported InP traveling wave MZM deploying special n-i-p-n epitaxial designs [8] also will be difficult to fabricate, especially when integrated with a DFB laser source similar to an EML laser chip that is currently mass deployed in optical datacom applications. A possible way to decrease fabrication difficulty is deploying a shallow ridge waveguide structure [9], which has been demonstrated with a robust fabrication process. However, the previously published shallow ridge MZM result was based on a design with relatively low modulation speed without systematic design parameter optimization which is the focus of this article.
In this work, we report the multi-parameter optimization of a high speed InP MZM design, deploying a shallow ridge p-i-n type waveguide, which offers advantages of monolithic integration with a ridge waveguide DFB laser, also avoiding sidewall roughness related optical scattering loss and potential surface defect state reliability issues which could be highly detrimental in deep-etched designs, resulting in a more robust and scalable manufacturing process. Comparing with state of the art InP MZM design utilizing a deep ridge waveguide structure [7], the shallow ridge MZM design optimized in this work is insensitive to sidewall roughness induced optical scattering loss and easier to integrate with a ridge waveguide DFB laser source monolithically. Additionally, for the RF traveling electrode design Benzocyclobutene (BCB) planarization is utilized to reduce fabrication complexity compared to previous designs based on air bridge process [10]. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ We also developed a rigorous design methodology, that optimizes for modulation efficiency and high frequency response, taking into considering not only velocity and impedance matching but also metal electrode and semiconductor material current induced microwave losses, with variations across the full microwave frequency range, with we believe significantly improved accuracy of our simulation results compared to the simplistic empirical approach used in previous works [6], [11]. It should be noted that the optimization method we propose is not only applicable to a typical InP MZM structure but also to other designs such as deep ridge waveguide.
Based on our simulation results, we systematically optimized a shallow ridge InP MZM design which we believe is capable of achieving 81 GHz 3-dB bandwidth and 4.3 V half-wave voltage (V π ) with 1 mm long electrode, sufficient for supporting beyond 200 Gb/s 4-Level Pulse Amplitude Modulation (PAM4) operation. Fig. 1(a) shows a schematic view of the TWE MZM in the InP/InGaAsP material system designed to operate TE polarized near 1550 nm investigated in this article, utilizing a periodically capacitive loading TWE with a 50 Ω termination in a series push-pull configuration. The fraction of loaded TWE section active length (L a ) within a period length (L p ) is defined as fillingfactor (FF), which is a key parameter in designing the loading capacitance to eliminate velocity mismatch between the optical and electrical waves [5]. Fig. 1(b) shows a detailed cross-section view of the optical waveguide, with a 2.2 µm wide shallow-etched ridge stopping at the undoped upper spacer layer. In the baseline design, the epitaxial structure of the MZM is grown on a semi-insulating (S.I.) InP substrate, including from bottom up a 1.7 µm InP n-mesa layer (1 × 10 18 cm −3 ), an unintentionally doped optical waveguiding layer, a 1.3 µm InP p-cladding layer (5 × 10 17 cm −3 ) and a 0.2 µm In 0.53 Ga 0.47 As p-contact layer (1 × 10 19 cm −3 ). The unintentionally doped optical waveguiding layer consists of a lower InP spacer layer, 1.40Q (λ = 1.4 µm) MQW active region and an upper InP spacer layer. The MQW region is composed of several 8 nm wide barriers (In 0.81 Ga 0.19 As 0.41 P 0.59 ) and 12 nm wide wells (In 0.64 Ga 0.36 As 0.76 P 0.24 ), and sandwiched between two undoped InP spacer layers. The upper and lower InP spacer layers have unequal thicknesses, creating a 50 nm offset in the MQW center position towards the n side, in order to minimize the p-type doping free-carrier absorption loss which is a much stronger effect than that from n-type doping in InP material system [12]. In the following section, both modulation efficiency (half-wave voltage length product) V π L and 3-dB bandwidth based on our shallow ridge MZM design are optimized by design trade-offs between key parameters, including MQW number, unintentionally doped optical waveguiding layer thickness (UDT), p-cladding layer doping concentration, TWE length and TWE filling-factor (FF = L a /L p ) as shown in Fig. 1(a). The TWE consists of 1.5 um thick Ti/Au metal, biasing the pair of MZM waveguides in a back to back p-i-n configuration laterally as shown in Fig. 1(c), while co-propagates with the optical signal down the waveguide pair in the longitudinal direction, terminating with a 50 Ω on-chip resistor.

A. Modulation Efficiency Optimization
In order to ensure sufficient RF driving voltage in real world applications, the half-wave voltage of the proposed MZM device is quantitatively analyzed by MQW number and UDT active region thickness optimizations. We first perform MQW carrier transport simulation and obtain absorption coefficient and index change using APSYS 3D finite element semiconductor device modeler. Fig. 2 shows the simulated absorption spectra of an MZM baseline design consisting of twenty 1.40Q MQW within 1.15 µm thick UDT under varying applied electric field as an example. The absorption edge is intentionally designed 150 nm shorter than the operation wavelength, accepting small amount of residual interband absorption at 1550 nm. Under applied external electric field, the conduction band and the valence band of a quantum well structure will tilt and cause absorption band edge red-shifts to longer wavelength due to QCSE [13]. Two absorption peaks can be observed in each curve in Fig. 2, corresponding to the MQW light-hole absorption and heavyhole absorption peaks respectively.
According to the Kramers-Kronig relationships, the absorption coefficient shift will cause a corresponding change of refractive index [3], the small absorption changes with bias voltage beyond the MQW absorption band edge still create sufficient index and phase changes for MZM operation at 1550 nm in TE mode. For active region design with more quantum wells, higher index change at a given electric field intensity causes larger phase shift of the propagating optical wave along the MZM waveguide, contributing to lower half-wave voltage length product (V π L). However, when taking the epitaxy growth quality deterioration and material uniformity for larger quantum well numbers into account, we chose twenty-quantum-well structure as a compromise between achieving low drive voltage and maintaining sufficient MOCVD epitaxial quality, which becomes increasingly challenging with very high number of QW's. Another important variable is UDT. An MZM design with a thinner UDT will produce a higher built-in electric field intensity under the same bias voltage, which will generate greater phase shift and result in lower V π L, but thinner UDT generally introduces extra optical free-carrier absorption (FCA) loss due to increased optical mode profile and free-carrier distribution overlap, calculated using optical mode simulator Lumerical [14]. In Fig. 3, simulated V π L and free-carrier absorption loss for FF = 0.2, 0.5 and 1 are shown, the device operates with higher V π L for lower FF value of the periodical capacitance loading RF electrode design. In general, the FF of a well-designed MZM is greater than 0.5 to maintain sufficient modulation efficiency. Assuming the acceptable upper limit for V π L is 4.5 V·mm and FCA optical loss upper limit of 0.5 dB/cm for a capacitive loading electrode with FF between 0.5∼1, we select UDT = 1.1 µm for our design with the goal of meeting realistic operation requirements including meeting commercial IC driver voltage output limit and minimizing optical insertion loss. Fig. 4 is the simulated optical  mode (white line contour) and microwave signal electrical field (colormap) profiles of the selected waveguide design, indicating the optical waveguide supports single mode propagation whose group index (n opt ) is 3.7, quantum well optical confinement factor (Γ QW ) is 0.4 and electrical and optical field profile overlap (Γ EO ) is 0.6.

B. Modulation Bandwidth Optimization
A key part of the traveling wave InP MZM design optimization is the high frequency TWE design. To maximize modulation bandwidth, a traveling wave InP MZM electrode shown in Fig. 1(a) should simultaneously has 50 Ω characteristic impedance (Z 0 ) matching external drive circuit and the termination resistor, microwave index (n 0 ) equals to the optical waveguide mode group index (n opt ) in order to achieve velocity matching between the electrical and the optical wave signals traveling along the waveguide pair, and low microwave attenuation along the transmission line. The proposed TWE shown in Fig. 1 is an external coplanar strip (CPS) electrode connecting with inner active periodic loading electrodes for meeting velocity and impedance matching requirements [6]. Fig. 5 shows the schematic diagram of a single period of the periodic TWE structure (1.5 µm thick Ti/Au) with important parameters CPS width W, CPS space S, period length L p and active length L a identified. In this case, W, S and L p are 160 µm, 60 µm and 250 µm as default, while L a is a variable correlating to filling-factor selected (FF = L a /L p ).
Empirical formulae and lossless transmission line models readily available for n 0 and Z 0 design estimations are typically used in other InP MZM works [11], we believe they are inaccurate and furthermore could not accurately model our shallow ridge MZM design because of the presence of fringing field capacitance extending laterally into the underlying planar n-doped layers and parallel with the MQW junction capacitance [15]. To achieve quantitative transmission line analysis with feasible computation requirements, we first performed full-wave optimization using commercial 3D EM simulation software (HFSS) of a single period of TWE MZM in Fig. 5, with the design goals of simultaneous velocity and impedance matching and also minimizing TWE microwave loss. Then we fed the HFSS simulated s-parameter into an electrical circuit simulator (ADS) to obtain the frequency performance of the entire periodic structure. The microwave loss has been typically neglected in other published InP MZM analysis, which also in general assumed n 0 and Z 0 are frequency independent [5]. Yet in reality the above parameters are strongly frequency dependent as shown in our work, and can cause large inaccuracy in predicting the RF performance of the MZM device if not accounted for. Fig. 6 shows the HFSS simulated n 0 (at 60 GHz) and Z 0 (at 5 GHz) contour plots for TWE MZM design with various FF-UDT pairs. As practical design guideline, in a semiconductor waveguide-based traveling wave electrode, the impedance should in general be matched at a low frequency (e.g., 5 GHz) to avoid ripple in the electro-optic response and electrical reflections, while the microwave and optical index should be matched at a high frequency close to targeted bandwidth (e.g., 60 GHz in our case) because the effect of velocity mismatch is amplified for higher frequencies due to the shorter electrical signal wavelength [3]. We define the acceptable ranges of n 0 (3.7 ± 0.1) and Z 0 (50 Ω ± 1.5 Ω) as simultaneous velocity and impedance matching. In Fig. 6, the regimes covered in green represent the optional values for FF and UDT, which are expected to meet the velocity and impedance matching requirements. As previously discussed in Fig. 3 we already fixed UDT = 1.1 µm as part of the MQW active region design optimization, accordingly the RF electrode design FF is selected to be 0.5 at the white dot in Fig. 6. FF = 0.5 means that the TWE active length on the back to back p-i-n waveguides is halved by periodically capacitive-loading as shown in Fig. 5, hence the corresponding V π L is 4.3 V·mm (FF = 0.5) referring to Fig. 3.
For an InP MZM design implementing our FF-UDT optimization result, we performed HFSS broadband simulations of both microwave index and the characteristic impedance (DC -100 GHz), as shown in Fig. 7(a) and (b) respectively. While velocity matching at 60 GHz and impedance matching at 5 GHz are achieved, the strong frequency dependence of n 0 and Z 0 vary can be clearly observed, in particular toward the high frequency limit. For InP MZM systematic design optimization, in addition to velocity and impedance matching, we also performed explicit microwave loss calculations of the entire structure. The path of microwave signal propagating down the ridge pair structure in Fig. 1(c) is quite complicated, and can be broken down into several current components each with its associated microwave loss contributions, including current traveling longitudinally down the Ti/Au metal electrode, with its associated frequency dependent skin effects, current flowing laterally between G and S electrodes through the back to back p-i-n MQW junctions, and less obviously a third current component [16] traveling longitudinally along the ridge waveguides inside the semiconductor material underneath the electrode, which exhibits with no frequency dependent skin effects, but parallel to the electrode current component and optical mode propagation. The relative distribution of these three current components is also strongly frequency dependent, and can be qualitatively studied using equivalent circuit analysis similar to what is done for single ridge waveguide traveling wave phase modulators [4], [16]. Key parameters include vertical series resistance of the waveguide p-cladding layers (R p ) and longitudinal cladding resistance parallel to the waveguide (R sc ), both result in resistive loss. The above mentioned two semiconductor microwave loss contributions are both highly sensitive to the p-cladding layer doping profile. For a low contribution from R p , the waveguide cladding conductivity should be high. However, a high cladding conductivity can lead to an increased microwave loss due to additional shunted longitudinal semiconductor current modeled by R sc , parallel to the current flow inside the metal electrode. The semiconductor waveguide p-cladding layer doping profile strongly affects the overall InP MZM microwave loss, yet it has not been quantitatively accounted for in previously published works. The n-cladding doping plays a much smaller role for microwave loss, due to the much higher electron mobility compared to hole.
We explicitly calculated microwave loss of the MZM structure in Fig. 1, including electrode structure and semiconductor materials induced loss, with varying p-cladding layer doping concentration using HFSS. As an example Fig. 8 shows that at 60 GHz increasing the waveguide p-cladding layer doping concentration from 1 × 10 17 cm −3 to 1 × 10 18 cm −3 improved microwave loss from 4.7 dB/mm to 2.6 dB/mm, which will significantly affect the mm scale TWE MZM modulation bandwidth at high frequency. We note that changing the doping of the waveguide semiconductor layer to first order has a negligible effect on the inductance (L) and capacitance (C) of the traveling wave electrode, and thus does not invalidate the velocity and impedance matching optimization results discussed earlier.
Increasing p-type dopant will cause extra optical free-carrier absorption loss due to its overlap with the optical mode confined in the UDT region, also shown in Fig. 8. To tradeoff between microwave and optical loss due to p-type dopant, we propose a gradient-doped scheme with a 3 × 10 17 cm −3 to 7 × 10 17 cm −3 p-type linear doping ramp from MQW toward the upper layer electrodes over 1.3 µm in depth, obtaining 2.65 dB/mm microwave loss at 60 GHz and 0.3 dB/cm optical waveguide absorption loss for the MZM structure, based on Lumerical optical mode calculations. Fig. 9. ADS simulated electrical S21 and S11 parameters of the optimal MZM design with a 1 mm length traveling wave electrode. Based on our extensive simulation analysis, InP MZM design shown in Fig. 1 is optimized with key parameters including MQW number (n = 20), MQW active region thickness (UDT = 1.1 µm), TWE filling-factor (FF = 0.5) and waveguide p-cladding layer linear ramped doping concentration (3∼7 × 10 17 cm −3 ) with optical insertion loss of 0.3 dB/cm. The detailed HFSS simulation results over 0-100 GHz, including the s-parameter, frequency dependent microwave index, impedance and microwave loss are then fed into ADS and Lumerical in sequence for full Electrical Optical (EO) response simulation in the frequency and time domain. In Fig. 9 we present the ADS simulated electrical S21 and S11 parameters of the optimal MZM design with a 1 mm length traveling wave electrode, demonstrating electrical bandwidth of 81 GHz and S11 below 15 dB up to 89 GHz. Fig. 10(a) shows the EO responses of the optimized MZM with 1 mm, 2 mm and 3 mm TWE lengths, with 3-dB bandwidths results of 81 GHz, 65 GHz and 54 GHz respectively. The half-wave voltages for the corresponding designs are 4.3 V, 2.15 V and 1.43 V with V π L of 4.3 V·mm. The 1 mm TWE design (V π = 4.3 V, f 3dB = 81 GHz) represents our best design performance and in principle is capable of supporting 100 Gbaud PAM4 (200 Gb/s) digital data modulation meeting both bandwidth and IC driver voltage requirements. Fig. 10(b) and (c) show the simulated clean and wide eye opening obtained at 100 Gb/s (50 Gbaud) and 200 Gb/s (100 Gbaud) PAM4 data modulation rates respectively, even before applying FFE or DFE equalizations, which is standard for eye quality improvements during PAM4 data transmission. Overall our simulation results demonstrate an optimal TWE InP-based MZM expected to be capable of beyond 200 Gb/s ultrahighspeed modulation with 4.3 V half-wave voltage and 81 GHz 3-dB bandwidth. Based on our systematic optimization methodology, it is viable to design a shallow ridge waveguide InP MZM capable of beyond 100 GBaud transmission using robust and scalable fabrication process for high-volume low-cost optical datacom networks.

IV. CONCLUSION
In conclusion, based on systematic design parameter analysis and integrating a multitude of quantitative optical and microwave EM simulation results, we optimized a shallow ridge InP-based MZM design which is expected to be capable of beyond 200 Gb/s ultrahigh-speed modulation with 4.3 V halfwave voltage and 81 GHz 3-dB bandwidth. Strong frequency dependence of microwave index, impedance and microwave loss are explicitly calculated and incorporated into our design performance analysis, resulting in a more sophisticated and accurate device model compared to previous works. As part of our design methodology, TWE MZM microwave loss optimization based on waveguide p-cladding layer doping profile is also proposed and implemented in HFSS simulation. Our shallow ridge p-i-n design is expected to be capable of high-speed performance surpassing the state-of-art deep ridge designs, while providing unique advantages including greater process tolerance and improved long-term reliability, making it suitable for high volume commercial applications.
We are currently working on the fabrication and experimental verification of our optimized design. We believe the works presented here represents an important step in exploring the high-speed performance potentials of InP MZM for medium reach optical datacom applications, including high speed optical data links inside and between large data centers over distance of 10 km and beyond.