With the number of processing cores increasing in central processing units, the electrical interconnects gradually become the bottleneck for the further improvement of computing performances due to their large delay, low bandwidth, and high power consumption ^[1]. Optical interconnects based on silicon photonics have been regarded as a promising solution to this problem. Silicon optical modulators, which are used to encode electrical signals onto optical beams, are a major workhorse in optical interconnects ^[2,3]. Till now, the reported high-speed silicon modulators are dominantly based on two optical structures: the Mach–Zehnder interferometer (MZI) ^{[4–7" target="_self" style="display: inline;">–7]} and the resonant cavity ^{[810" target="_self" style="display: inline;">–10]}. Silicon modulators based on microrings and microdisks have the merits of small size, low modulation power, and high modulation speed of up to 50 Gb/s ^[11]. However, they also suffer from certain limitations, such as narrow optical bandwidth and high temperature sensitivity, which greatly limit their practical applications. Silicon modulators based on MZIs, on the other hand, have broad optical bandwidth and high tolerance to temperature fluctuations. Modulation speeds up to 70 Gb/s have also been recently demonstrated in MZI modulators (MZMs) integrated with reverse-biased p−n junctions ^[12]. A higher modulation speed can be expected by reducing the radio-frequency (RF) loss of transmission lines ^[13], as the modulation bandwidth is partially limited by the attenuation of RF drive signals.

Advanced modulation formats are necessary to increase the aggregation data rate within a limited spectral bandwidth. As the basis for advanced modulation formats, binary phase-shift keying (BPSK) modulation based on a silicon MZM has been reported ^[14]. In their design, separate traveling wave electrodes (TWEs) on the two MZI arms are used, requiring differential RF signals ^[15].

In this paper, we demonstrate a silicon BPSK modulator using a MZI structure driven by a single-drive push–pull TWE. The TWE has been optimized with numerical simulations. 32 Gb/s BPSK modulation is achieved with an error vector magnitude (EVM) of 18.9%.

To design a high-speed modulator, we consider three main factors that determine the modulation bandwidth. First of all, the characteristic impedance (Z0) of the TWE needs to approach 50Ω in order to avoid RF signal backreflection from the ends of the TWE. Second, the RF attenuation of the TWE should be small, since the electro-optic (EO) 3 dB bandwidth is related to the RF electro-electro (EE) 6.4 dB bandwidth ^[16]. Third, the electrical and optical waves need to be synchronized to provide the highest modulation efficiency ^[17]. For a lossless modulator with impedance-matched load and generator, its EO 3 dB bandwidth is determined by the velocity mismatch between the RF and optical signals and is given by ^[18] f3dB=0.18(neff−n0)l,(1)where l is the electrode length, neff is the microwave refractive index, and n0 is the group refractive index of the waveguide optical mode. To increase the modulation bandwidth, neff needs to approach n0.

Figure 1(a) shows the schematic structure of our BPSK modulator consisting of an asymmetric MZI integrated with a single-drive TWE. We adopt the asymmetric MZI structure because the bias point (π-phase difference) needed for BPSK can be conveniently obtained by tuning the input laser wavelength. In principle, a symmetric MZI structure can be used to provide a large optical bandwidth, but a phase shifter (e.g., based on a microheater) is also needed to set the bias point. The modulation arm length is 3 mm. Figure 1(b) shows the cross section of the MZM. Six key parameters related to the TWE need to be optimized, including the width of the metal lines WE, the separation of the metal lines SE, the width of the p+ doping region Wp, the width of the n+ doping region Wn, the separation of the via from waveguide Svia, and the separation of p+/n+ doping from waveguide Sdop. The silicon waveguide has a width of 500 nm and a height of 220 nm with a slab thickness of 60 nm. The separation between MZI arms is 120 μm. The p and n doping concentrations in the p−n junctions are ∼4×1017 and ∼1×1018cm−3, respectively. The n+ doping region in the center of the MZI has a doping concentration of ∼1020cm−3, connected with a DC bias terminal. The two p+ doping regions at the outer sides of the MZI have a doping concentration of ∼1020cm−3, connected with the RF signal (S) and ground (G) terminals. The equivalent circuit model of the single-drive TWE is shown in Fig. 1(c). The two p−n junctions (one for each arm) are back-to-back connected. The RF signal VRF is applied between S and G terminals. A common DC bias VB is applied to the middle n+ doping region. Hence, the voltages dropped on the two junctions are −VB+VRF/2 and −VB−VRF/2, respectively, forming a push–pull fashion with only a single RF input.

Fig. 1. (a) Schematic structure of the BSPK modulator. (b) Cross section of modulation arms showing the single-drive TWE. (c) Equivalent circuit model of the TWE.

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The large p−n junction capacitance makes it difficult to design a high-speed TWE to meet the three criteria mentioned above. The single-drive TWE design can effectively reduce the total capacitance to half, as the two junction capacitors in the two arms are connected in series. The push–pull scheme also reduces the modulation-induced frequency chirp ^[19].

In our first version of design, the TWE parameters are chosen according to the literature reports ^{[13,15–19" target="_self" style="display: inline;">–19]} and are listed in Table 1 (the device is denoted as MZI-1). Figure 2 shows the simulated EE-S21, Z0, and neff responses using the COMSOL RF module. The EO-S21 response is calculated from an equivalent circuit model ^[18]. The EE 3 dB bandwidth is 10 GHz, and the EO 3 dB bandwidth is 25 GHz. neff approaches 3.2 at high RF frequencies. Z0 is close to 50Ω at low frequencies but tends to increase with frequency. To further improve the modulator performance, we need to reduce RF attenuation and increase neff with all TWE parameters taken into consideration during optimization. It is impossible to scan all parameters simultaneously, and therefore we start from MZI-1 and vary only one TWE parameter at a time to simulate the change trend of RF attenuation, Z0, and neff. It should be noted that in SE scan, Svia is revised to 18 μm in order to ensure the metal lines are always connected with the contact holes. From the change trend and taking into consideration the three factors that affect the TWE performance, we can further improve the modulation bandwidth.

Fig. 2. Simulation results of MZI-1. (a) EE and EO S21 responses. (b) Z0 and neff versus RF frequency.

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Figure 3 shows the simulation results. The RF frequency is set at 28 GHz, and the p−n junction bias voltage is set at −4V. It can be seen that SE has the most significant influence on all three factors, and it is the only variable that can increase neff. Yet there is a trade-off between RF attenuation and velocity match. We choose a larger SE to let neff approach n0 at the cost of a higher RF attenuation. To compensate for the RF loss, WE is increased and Sdop is decreased as shown in Figs. 3(a) and 3(e). Increasing WE also helps to counteract the increase of Z0 after choosing a larger SE. Given the TWE geometry, the increasing SE requires simultaneously increased Svia and Wp to guarantee good metal contact. As shown in Figs. 3(d) and 3(f), Svia and Wp have little impact on TWE performance, and hence it is safe to increase them. Wn is finally fine-tuned to achieve a small RF loss and matched impendence.

Fig. 3. Effects of various TWE parameters: (a) WE, (b) SE, (c) Wn, (d) Wp, (e) Sdop, and (f) Svia on RF attenuation, Z0, and neff.

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The final optimized parameters are shown in Table 1 (MZI-2). Figure 4 shows the frequency responses of S21, Z0, and neff for the improved design. Compared with the original one, the EE 3 dB bandwidth is increased to 15 GHz, and neff is increased to 3.6 at high RF frequencies, closer to the optical waveguide group index of 4.023. The EO 3 dB bandwidth is hence improved to 35 GHz. It should be noted that the thickness of the buried oxide (BOX) layer HBOX also affects the modulator EO bandwidth. However, given that HBOX is determined by the silicon-on-insulator (SOI) wafers and thereby cannot be freely designed on the mask level like the other parameters, we did not specifically optimize this parameter.

Fig. 4. Simulation results of MZI-2. (a) EE and EO S21 responses. (b) Z0 and neff versus RF frequency.

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Our device was fabricated at the Institute of Microelectronics (IME) Singapore using complementary metal-oxide-semiconductor (CMOS) compatible processes. The starting material is a SOI wafer with a 220 nm thick top silicon layer and a 2 μm thick BOX layer. 248 nm deep ultraviolet photolithography was used to define the waveguide patterns, followed by anisotropic dry etch of silicon. The p+, p, n, and n+ doping was obtained by ion implantation followed by rapid thermal annealing at 1030°C for 5 s ^[16]. Silicon dioxide was then deposited and contact holes were etched. Finally aluminum was deposited and etched to form the metal connection.

Figure 5 shows the measured optical transmission spectra when the applied voltage on the lower arm is varied from 0 to −6V. The insertion loss is about 15 dB, including 4 dB/facet coupling loss, 6 dB waveguide loss, and 1 dB loss from the multimode interferometers that compose the MZI. The interference notch is shifted by half a free spectral range under a reverse voltage of 4.5 V, which indicates the modulation efficiency is VπL=1.35V·cm.

Fig. 5. Measured optical transmission spectra under various bias voltages.

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We measured the EE S-parameters of the TWE from DC to 26 GHz by using a vector network analyzer (Agilent N5247A) under various bias voltages, as shown in Fig. 6. The measured 3 dB bandwidth reaches 15.5 GHz when the MZM is biased at −4V, matching with the simulation result in Fig. 4(a). S11 is less than −15dB for the full measured frequency range, implying good impendence match.

Fig. 6. Measured (a) S21 and (b) S11 responses of MZI-2 with DC bias voltage varying from 0 to −4V.

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We then measured the eye diagrams of the BPSK modulated signals. A 32 Gb/s pulse pattern generator was used to generate the pseudo-random binary sequence RF drive signals with a 223−1 pattern length. The peak-to-peak voltage (Vpp) was ∼6V after amplification. The RF signal was applied to the TWE through a 40 GHz GS probe. The other end of the TWE was terminated with a 50Ω resistor by using another SG probe. −3V DC bias voltage was applied to the device through a print circuit board wire-bonded with the chip. The input laser light with 12 dBm optical power was coupled to the modulator. The output light with around −10dBm optical power was amplified by an erbium-doped fiber amplifier followed by a 1 nm bandwidth optical filter to compensate for the device insertion loss. The amplified optical signal was then fed into a digital oscilloscope for eye-diagram measurement or to an optical modulation analyzer for constellation diagram measurement. Figure 7 shows the measured results. The constellation diagram measurement suggests the BPSK signal Q-factor is 7.2 and EVM is 18.9%.

Fig. 7. (a) Measured BPSK signal eye diagram. (b) Measured BPSK constellation diagram. The signal data rate is 32 Gb/s.

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In conclusion, we have demonstrated a 32 Gb/s BPSK modulator with an optimized 3 mm long single-drive push–pull TWE. Numerical simulation was carried out to analyze the effect of various TWE geometric parameters on the TWE performance. The measured modulation efficiency is VπL=1.35V·cm. S-parameter characterization reveals that the 3 dB EE bandwidth of the TWE is 15 GHz, corresponding to 35 GHz EO bandwidth of the modulator. The 32 Gb/s BPSK constellation diagram was also measured with an EVM of 18.9%.