Energy-Efficient Forward-Biased PIN Silicon Mach–Zehnder Modulator With 50 μm Active Phase Shifter Length

We present the design performance validation of an energy-efficient silicon Mach-Zehnder modulator (MZM) with a forward-biased PIN junction by simulation and experiment. With a length of <inline-formula> <tex-math notation="LaTeX">$50~\mu \text{m}$ </tex-math></inline-formula>, the presented MZM exhibits at least four times smaller form factor for the active phase-shifter than the state-of-the-art. Furthermore, we recorded a remarkably low <inline-formula> <tex-math notation="LaTeX">$V_{\mathrm {\pi }}L$ </tex-math></inline-formula> of only 0.0025 <inline-formula> <tex-math notation="LaTeX">$\text{V}\times $ </tex-math></inline-formula>cm. By thermal tuning of an additional heater, segmented with the phase shifter, the measured DC extinction ratio of the MZM was 30 dB. Non-return-to-zero data transmission up to 5 Gb/s and the generation of sinc-shaped Nyquist pulse sequences with a bandwidth of 12 GHz is demonstrated. The very small footprint and power consumption make the presented MZM an ideal choice for various applications like Nyquist pulse generation, parallel analog signal processing, arbitrary waveform generation, etc.


I. INTRODUCTION
In recent years, the demand for large-scale integration has been increasing [1], [2].Due to their compatibility with the existing complementary metal-oxide-semiconductor (CMOS) technology, integrated silicon-on-insulator (SOI) electro-optic modulators have already been subjected to a lot of research [3].One such device is a Mach-Zehnder modulator (MZM) which is based on a Mach-Zehnder interferometer.In one or both interferometer arms the optical path is changed by a modulation-signal dependent phase change.This phase change is transferred to an intensity change of the optical wave by the interference between both arms.The modulation efficiency of the MZM can be calculated by the performance metric V π L, with V π as the The associate editor coordinating the review of this manuscript and approving it for publication was Stanley Cheung .required voltage to achieve a phase shift of π.In silicon MZM there are several ways to obtain a phase shift like the plasma dispersion effect, where an external voltage is applied to change the free-carrier concentration [4], [5].This voltage can be applied in the forward or reverse-biased direction.Depending on the system requirements, different configurations of MZMs can be designed.Up to now, in the field of optical communications, the preference has been predominantly towards the reversed-biased configuration, since these modulators can provide high bandwidths and therefore, high-speed communications [6], [7], [8], [9].However, in addition to their applications in optical communications, MZMs have attracted a lot of attention to be utilized in various other fields like microwave photonics [10], LiDAR [11], [12], quantum key distribution [13], [14], optical switches [15], [16], optical computing like reservoir computing [17], [18], etc.Some of these fields, for example, LiDAR do not require high bandwidth or modulation speed in the GHz range and should be operated with low power consumption [11], [12].However, they need large-scale integration.To satisfy these requirements, forward-biased MZMs become advantageous because they offer low power consumption as well as low insertion loss (IL) [19], [20], [21], [22], [23], [24], [25].Forward-biased modulators are also comparatively smaller in size and thus can be helpful for large-scale integration.
The performance of a modulator can be improved in terms of different figures of merit using special structures.For example, silicon-based ring modulators provide a low form factor.However, they lack thermal stability in a densely packed network of photonic integrated circuits [26].Alternatively, an MZM can be modified into compact structures like corrugated modulators, but the trade-off here is high insertion loss [27], [28], [29], [30], [31].However, to reduce the design and operation complexity, standard MZMs can be a very good choice.Standard MZMs while integrated can be directly utilized as analog to digital converters (ADC), arbitrary waveform generators (AWG), Nyquist pulse generators, etc. [32], [33], [34].In this paper, we present the characterization and design of a silicon MZM with a forward-biased PIN junction.The active phase-shifter length of this modulator is 50 µm.To the best of our knowledge, this is the shortest reported active phase shifter length for an MZM so far.An overview of forward-biased ultra-compact modulators with high ER along with low V π L is presented in Table 1.The presented modulator can achieve a high extinction ratio (ER) of 30 dB, which is very close to the DC ER of our previously reported forward-biased modulator (33 dB but with a 10 times longer active phase shifter length [20]) and 7 dB higher compared to other reported modulators.We also demonstrate that our modulator can transmit data with a bitrate of 5 Gb/s.This is lower than our previously reported 15 Gb/s modulator [20].However, due to the very short active phase-shifter length, more devices can be accommodated in the same area.This is especially important for integrated parallel systems, which utilize parallelization of the silicon modulators for high bandwidth signal generation or reception with low-speed electronics and photonics on a fully integrated module [35], [36].Since these methods are based on Nyquist sincpulse sequences, we also demonstrate our modulator as an integrated Nyquist pulse generator.
The paper is structured as follows.In section II, the design of the modulator is discussed together with static and direct current (DC) characterizations.The evaluation of the radio frequency (RF) characterization is presented in section III.In section IV, the results for Nyquist pulse generation are demonstrated and, finally, the paper is concluded in section V.

II. DESIGN AND DC CHARACTERIZATION
The cross-section of the modulator is designed based on a simulation to maximize the change of refractive index and subsequently the phase shift with a certain applied voltage, as well as to keep the linear loss to a tolerable level.
For evaluation, several cross-sections like PN and PIN with various intrinsic region widths were simulated.The length of the active phase shifter was fixed to 50 µm to minimize the size of the MZM.As the chips were fabricated by the Advanced Micro Foundry (AMF), the thickness and width of the rib waveguide are 220 nm and 500 nm respectively, as per the foundry standard.The doping concentration, buried oxide thickness, etc. were also selected according to the foundry specifications.The simulations were carried out with the Lumerical software package, considering forward-biased configuration.The voltage is swept from 0 to 3.4 V.
First, the charge distribution for these cross-sections was evaluated by a static simulation with the DEVICE package.The surface recombination is set to 10 7 cm/s and is considered a boundary condition.The same crosssection is also simulated by the MODE package.The mode profile is computed by importing the charge distribution achieved in the previous step.To optimize the modulator design, simulations considering several cross-sections were carried out.We simulated five different designs with various widths of the intrinsic region.We started with zero (PNjunction diode), and then we gradually increased the width to 2.5 µm.The results are presented in Fig. 1.As can be seen in Fig. 1(a), the highest phase shifts can be achieved for high bias voltages and low widths of the intrinsic region.However, this results in a higher loss (as depicted in Fig. 1(b)).Other very important parameters, i.e. junction capacitance and resistance were simulated for the same voltage range and are presented in Fig. 1(c) for the five cross-section designs mentioned before.It is evident from Fig. 1(c) that the junction capacitances increase as the PIN diode turns on.After it reaches a maximum at a certain voltage, the capacitance decreases slowly and will gradually reach a saturation point at higher bias voltages.Fig. 1(c) also shows the behavior of the junction resistances.While the value of the resistance is very high when the PIN diode is off, it starts to decrease exponentially as the PIN diode turns on around 0.7 V. Additionally, the resistance of the junction decreases with   Comparing all five configurations, a trade-off was made and the PIN cross-section with a 0.46 µm of intrinsic width was chosen for fabrication.The final cross-section of the active phase shifter is presented in Fig. 2(d).
In the next step, the fabricated chips were characterized.Several chips were used for the initial DC characterization to ensure the correctness of the results.All the chips provided almost similar results.Therefore, we randomly chose one of them for wire bonding on a printed circuit board (PCB) for further investigation.The fabricated chip wire-bonded and glued on a printed circuit board (PCB) is shown in Fig. 2(b).Only the results acquired from this single chip, achieved with the setup in Fig. 3, are reported here.As an optical source, a fiber laser (FL) from NKT Photonics with a center wavelength of 1550.116nm and an optical power of 12.3 dBm was used.A grating coupler (GC) on the chip couples the light into the modulator.A polarization controller (PC) ensures the polarization alignment.The coupling losses of the input and output couplers were measured with a reference waveguide placed on the same chip to be 15.4 dB.The output power was measured to be −4.3 dBm, which corresponds to a total optical loss of the forward-biased silicon modulator of 1.2 dB.
Two bias tees were used at the two arms of the modulator to combine the DC and the input electrical signals and pass them to the electrical ports of the modulator.As depicted in Fig. 2(c), each phase shifter of the modulator has one ground (G) and one signal (S) port.These two ports work as RF and DC input ports.One additional DC port (T) at each arm of the modulator is utilized for thermal tuning.For both thermal tuning ports, there is a common ground (T GND).One arm of the modulator receives a fixed voltage, where the voltage is swept using the signal port on the other arm.RF and DC connectors are soldered on the PCB for this purpose.To compensate for the coupling losses, an Erbiumdoped fiber amplifier (EDFA) followed by a bandpass filter (BPF) for filtering out the amplified spontaneous emission noise was used at the output.The signal was detected with a 40 GHz Photodiode from Optilab.
In Fig. 4, the DC characterization results without any thermal tuning are presented in comparison with the simulation for the current-voltage (IV)-characteristics and the output optical power of the modulator.Here, the normalized transmission through the MZM was simulated considering the plasma dispersion effect.The normalized transmission is evaluated using Eq. ( 1).
In Eq. ( 1) σ is the splitting ratio (the ratio of the power in each phase-shifter), L 1 and L 2 are the lengths of the two arms, and n eff1, and n eff2 are their refractive indices, respectively.V 1 and V 2 represent the voltage applied to the respective arms.The detailed analysis of this equation is discussed in our previous publication [20].
Figure 4(b) represents the change of the output optical power as a function of the applied bias voltage for an optical input power of 12 dBm.As shown, the simulation and experimental results fairly match.By changing the bias of the active phase shifters, we get the first transmission minimum with an ER of 10 dB around 2.5 V for a current of 15 mA (Fig. 4(a)).The second transmission minimum appears around 3 V.That means the difference between the two dips is 0.5 V, which corresponds to the required voltage for the π-phase shift.Therefore, the V π L of this modulator can be assumed as 0.5 V × 50 µm = 0.0025 V×cm, which to the best of our knowledge is the lowest V π L reported for forward-biased Mach-Zehnder modulators.
In the next step, thermal tuning is applied to improve the ER.The result is presented in Fig. 5.In this case the voltage  required at the phase-shifter for the π phase-shift is 3.8 V.However, the DC ER in this case is about 30 dB and the transfer function is more linear.The change in the ER is due to an imbalance (length or width) between the two arms, which results in different phase shifts induced by each arm [20].When there are some imbalances, the arm of the modulator used for modulating may already have a phase shift induced.This means the transmission maxima might start with a lower value than expected, which subsequently results in a lower ER.With thermal tuning, this imbalance can be compensated, and the transmission maximum starts with the expected value (balanced arms), resulting in a higher ER.

III. RF CHARACTERIZATIONS OF THE MZM
With an RF signal generator (Agilent Technologies E8257D) as electrical input to the MZM, we measured the BW and the data modulation speed of the modulator.The electrical input power of the modulator for the frequency sweep from 100 kHz to 5 GHz was 5 dBm or 1.125 Vpp.A radio frequency spectrum analyzer measures the electro-optic response of the modulator.The measurement result in comparison to the simulation with Lumerical INTERCONNECT is presented in Fig. 6(a).Due to the forward-biased operation, the roll-off is fast.Therefore, the 3-dB BW is around 500 MHz, and the 10-dB BW is 1 GHz.
In the next step, the data modulation capability of the modulator was evaluated.An arbitrary waveform generator (AWG) generates a non-return-to-zero (NRZ) PRBS-7 binary phase shift keying modulation (BPSK) signal.Here an electrical amplifier with 26 dB gain was used to amplify the electrical signal generated by the AWG to a modulator input power of 8 dBm.The bias was set to 2V, to remain in the linear zone of the π-phase shift curve of the modulator shown in Fig. 4.This method reduces the DC power consumption, although it needs a higher RF swing voltage.Different peakto-peak voltage swings were applied to find the lowest possible bit error rate (BER).Here the lowest BER was found for the swing of 1.125 V pp .The electrical signal was converted to an optical signal and measured by a 20 GHz photodiode.To track and analyze the waveform in real-time, a real-time oscilloscope (Tektronix DPO73304) was utilized.All analyses were conducted for 3 Gb/s, 4 Gb/s, and 5 Gb/s NRZ PRBS-7 BPSK modulations.In the case of 3 Gb/s, no bit error was recorded for the transmission of 15,000 bits.Therefore, the BER is calculated from the measured Q-factor To compare the performance metrics, the Q-factors, BERs, and EVM are presented in Table 2. Considering 5 Gb/s speed, the power consumption is calculated to be 4.12 mW/Gb/s.All the performances reported in this manuscript can be improved  by pre-distorting the signal with an arbitrary waveform generator.However, we did not use any electronic preor post-processing to show the real performance of this modulator.

IV. MZM AS NYQUIST PULSE GENERATOR
A sinc pulse sequence is the unlimited summation of ideal sinc pulses with a distinct time shift [34] and is just a rectangular frequency comb, which can be generated quite easily by driving the modulator with n equally spaced electrical input frequencies [35], [38].Such sinc-pulse sequences can be used to down-convert high-bandwidth signals into several parallel low-bandwidth ones, which can then be processed with low-bandwidth electronics [34].Due to its compactness, the presented modulator can be very beneficial for such an application.Therefore, we show how it can be used for the generation of sinc-pulse sequences.
Figure 7(b) shows a sinc pulse sequence with two zero crossings (one sinusoidal input frequency and a DC bias) generated by the modulator (black solid) compared to the calculated ideal trace (red dashed).As can be seen, although the 3dB bandwidth of the modulator is just 0.5 GHz, it can be used to generate sinc pulse sequences with a bandwidth of up to 12 GHz, which corresponds to a pulse width of 250 ps.Therefore, the modulator can be used for the processing of signals with a symbol rate of 12 GBd [39].
We previously demonstrated Nyquist pulse generation using reverse-biased on-chip modulators with lengths of 3.2 and 1 mm [32], [33].The demonstration in this paper proves that an ultra-compact forward-biased MZM with an active phase shifter length in the micrometer range can also be utilized for Nyquist pulse generation.Therefore, it is possible to take advantage of the compact size of the active phase shifter to accommodate more modulators in the same chip area, which is especially important for parallel signal processing based on Nyquist pulses.The presented silicon modulator enables high-bandwidth pulse generation with the smallest possible silicon footprint presented till now.Therefore, it is an ideal candidate for designing photonic DAC and ADC [36].

V. CONCLUSION
We have demonstrated, for the first time, to the best of our knowledge, a forward-biased PIN junction-based silicon MZM with an active phase shifter length of only 50 µm which is able to modulate normal data at 5 Gb/s.This modulator can be utilized to process signals with symbol rates up to 12 GBd by orthogonal sampling.With thermal tuning, the modulator can achieve a high DC ER of 30 dB.The MZM also has a very low insertion loss of 1.2 dB and a good modulation efficiency (V π L) of 0.0025 V.cm.

FIGURE 1 .
FIGURE 1. Cross-section analysis.Subfigures (a)-(d) present different parameters against the applied bias voltage for 5 different cross sections which varies the width of the intrinsic region.(a) Change of refractive index vs.voltage, (b) linear loss vs. voltage, (c) Resistance and capacitance vs. voltage, and (d) Cut-off frequencies vs. voltage.Intrinsic = 0 µm corresponds to a PN-junction diode, which is shown in (e).Intrinsic = 0.1 and 0.46 µm mean that there is an intrinsic region of various lengths in the middle of the waveguide, as shown in (f) for 0.1 µm.For an intrinsic width of 2.5 µm, the whole WG and 1 µm on each side of the WG (in the slab regions) belong to the intrinsic region, which is shown in (g).

FIGURE 2 .
FIGURE 2. (a) Microscope image of the fabricated MZM, (b) PCB with the fabricated chip glued on it (the white circle indicates where the modulator is placed), (c) Detailed top view of the circuit (GDS layout) including the modulator.The black circle marks the active phase shifter in one arm of the modulator, (d) A cross-sectional view of the active phase shifter for the fabricated MZM.

FIGURE 3 .
FIGURE 3. Experimental setup for the characterization of the integrated modulator wire-bonded on a PCB; FL: fiber laser, PC: polarization controller, AWG/RFG: arbitrary waveform generator or radio-frequency generator, respectively, two DC sources are used for two arms of the modulator, subsequently two bias tees are used to combine DC and RF input for two arms of the modulator, the Balun splits the AWG/RFG into two parts to be fed into two bias tees.EDFA: Erbium-doped fiber amplifier, BPF: bandpass filter, PD: photodiode, RFSA: radio-frequency spectrum analyzer.The red lines are optical paths, and the dotted blue ones are electrical paths.

FIGURE 4 .
FIGURE 4. DC characterization of the MZM for different bias voltages: (a) current-voltage characteristics, (b) transmitted optical power as a function of the applied voltage without any thermal tuning.

FIGURE 5 .
FIGURE 5. Transmitted optical power of the modulator as a function of the applied bias voltage with active thermal tuning.

FIGURE 7 .
FIGURE 7. (a) 4 GHz input signal, (b) Generation of 12 GHz Nyquist pulses.The solid black line represents the experimentally generated pulses, while the dashed red line represents the mathematically calculated ideal sinc pulse.

TABLE 1 .
Comparison of the performance metrics for forward-biased standard MZM.

TABLE 2 .
Comparison of the performance metrics.