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Abstract
Advanced coding formats can improve the spectral efficiency in optical transmission systems, while the generation can be expensive and power hungry when electrical digital-to-analog converts (DACs) are utilized. Optical segmented modulators can supersede electrical DACs with the merits of low cost and power efficiency. However, due to their compact size, the leakage current between the adjacent segments results in considerable electrical crosstalk, which impairs the linearity of the modulators and distorts the modulated signal. Here, we propose and demonstrate an electrical crosstalk suppression scheme for optical segmented modulators by introducing a complementary doped region as an insulator. Two depletion regions with high impedances are formed, resulting in the decrease in leakage current and crosstalk. Qualitative and quantitative analysis are performed, and experimentally, in a ring based segmented modulator, more than 5 dB crosstalk improvement is successfully achieved within the 30 GHz range.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays, the growing data traffic demands in data centers and trunked communication systems motivate the investigation of high capacity, low-cost optical transmission systems. Improving the spectral efficiency (SE) is a feasible way to realize the high capacity optical transmission. Advanced coding formats, such as four level pulse amplitude (PAM-4) and 16-ary quadrature amplitude modulation (16-QAM) can improve the SE and have already been accepted as the coding formats of the choice in optical transmission systems [1,2].
In order to generate advanced coding formats, digital-to-analog converters (DACs) are usually used [3]. To date, realization of 100 Gb/s beyond PAM-4 has been reported [4,5], assisting by the electrical DAC. However, the utilizing of electrical DACs increases the power consumption and system cost, and high-speed electrical DACs are difficult to design and realize. In order to mitigate this issue, PAM-4 generation in optical domain without using electrical DACs has been developed, using dual Mach-Zehnder modulators (MZMs) with footprint of serval millimeters [6]. On the other hand, PAM-4 generations based on dual parallel [7] and cascaded [8] micro-ring modulators (MRMs) have also been demonstrated, with the merit of compact footprint. However, precise alignment of resonances of multiple MRMs will be difficult, and the thermal tuning increases the power consumption. To further minify the footprints and reduce the power consumption, segmented modulators are proposed, and PAM-4 generation utilizing segmented MZM with 1.5 mm length [9] or segmented MRM with 12 µm radius has been demonstrated [10]. Since there exists only one micro-ring resonator in segmented MRM scheme, the precisely wavelength aligning is not an issue any more, and the power consumption in thermal tuning can be reduced. Likewise, the 16-QAM generation scheme has a similar evolution process as PAM-4 does [11].
Although segmented modulators have advantages in terms of low-cost and power consumption, they have to face the challenge in suppressing electrical crosstalk within a narrow region. When a segmented modulator is loaded with driven signals, there exist leakage currents between adjacent segments, resulting in electrical crosstalk and distortion of the modulation linearity. Pre-equalization in electrical domain can compensate the nonlinearity at the cost of adding complexity of the driver design [10]. Increasing the distance between adjacent segments can suppress the electrical crosstalk [12], however, this sacrifices the length of modulation region.
In this paper, we propose and demonstrate that, by substituting the complementary doped region for the intrinsic region, an insulator can be formed between segments to suppress the leakage current and the resulting crosstalk. For a proof-of-concept demonstration, a compact segmented MRM with a radius of 9 µm is fabricated and characterized, and more than 5 dB crosstalk improvement is achieved up to 30 GHz, indicating an effective suppression.
To thoroughly investigation the crosstalk generation and suppression, the segmented MRM used in PAM-4 generation is discussed and characterized in this paper. Section 2 introduces the generation of electrical crosstalk and its impact. Section 3 presents the proposed method of suppressing electrical crosstalk. Section 4 describes the experimental results. Section 5 concludes this paper.
2. Electrical crosstalk generation and impact
2.1 Crosstalk generation and definition
The structure of conventional two-segments MRM is presented in Fig. 1. The modulation region is separated into two segments, namely the most significant bit (MSB) part and the least significant bit (LSB) part. Intrinsic silicon is utilized to insulate the MSB segment from LSB segment. Synchronous non-return zero (NRZ) signals, VM and VL, with same amplitude are loaded on the two segments separately.
The electrical crosstalk derives from the leakage currents between the adjacent segments. When the MSB segment is driven, the considerable current flows through the intrinsic silicon (marked by purple line), resulting an undesirable voltage drop in the LSB segment. This undesirable voltage drop is the electrical crosstalk Slm exactly. Similarly, the leakage current (marked by golden line) from the LSB segment results crosstalk Sml in the MSB segment.
Figure 2 shows the equivalent circuit of conventional two-segments MRM. RSM and RSL, which equal to 50 Ω, are the source resistances. RMSB and CMSB are the series resistor and junction capacitor of MSB segment, while RLSB and CLSB are the series resistor and junction capacitor of LSB segment, respectively. Usually, the series resistance of PN junction in silicon ranges from dozens ohms to a few hundreds ohms, and the capacitance is about dozens femto-farad [4]. Ri is the resistance of the intrinsic silicon insulator. When the MSB segment is driven, the undesirable voltage drop VLSB on the LSB segment is
Fig. 2. Equivalent circuit of the conventional two-segments MRM and its crosstalk simulation results. RMSB = 14 Ω, RLSB = 23 Ω, CMSB = 11 fF, CLSB = 19 fF.
Similarly, the expression of crosstalk Sml, which characterized the voltage measured at the MSB segment when the LSB segment is loaded with driving voltage, can also obtained.
The simulated crosstalk-frequency curve is presented in Fig. 2, where only Slm is shown for simplicity. It can be found that a higher impedance of Ri results a smaller crosstalk. This result is readily comprehensible, as an insulator with a higher impedance leaks a weaker current, and the corresponding crosstalk would be smaller.
According to the law of resistance, Ri can be expressed as
where rsi is the sheet resistance of silicon insulator, lsi is the length and wsi is the width of the insulator. To suppress the crosstalk, a long and narrow insulator with high sheet resistance is excepted. However, the width of intrinsic silicon insulator wsi equals to the width of ohmic contact region, and it cannot be too small. Otherwise, the series resistances of segments will increase and the bandwidth of the modulator will be reduced. In compact segmented MRM, increasing the lsi will shorten the total length of segments and degrade the modulation efficiency. As to the sheet resistance rsi, it relates to the purity and lattice integrity of silicon insulator. Generally, high-purity silicon with a complete lattice has a high sheet resistance. However, in the process of forming ohmic contact regions, the lateral diffusion of ion implantations and thermal diffusion during the annealing reduce the purity of the silicon insulator. Besides, the lattice damage introduced by the ion implantations breaks the lattice integrity of the silicon insulator [13]. Hence, the intrinsic silicon insulator is not a perfect insulator to suppress the electrical crosstalk.2.2 Crosstalk impact
When there exists crosstalk, the aggerate phase shift generated by the segmented MRM has the following relationship with the driving signals,
where k is the modulation efficiency of PN junction, lLSB and lMSB are the length of LSB and MSB segments, respectively. In Eq. (4), the first and second components are the phase shifts generated by LSB segment and MSB segment respectively.Considering the case that the crosstalk is negligible (Slm = 0, Sml = 0), Eq. (4) can be simplified to the following form.
Obviously, Eq. (5) is the output expression of a 2-bit DAC, where lLSB and lMSB are the weight coefficients, VL and VM are the input coding values, and k is the output gain of DAC. A 2-bit DAC can generate PAM-4 signals naturally.
By contrast, in the case that the crosstalk is considerable (Slm ≠ 0, Sml ≠ 0), the phase shift generated by a segment is not only related to the corresponding driving voltage but also to the one on the adjacent segment, as shown in Eq. (4). This means the DAC is nonlinear and the linearity of the modulated PAM-4 signal is degraded. In other words, the level separation mismatch ratio RLM [2] will deviate from ‘1’, if the electrical crosstalk is considerable. RLM is a parameter to characterize the linearity of PAM-4 signal, and for an ideal PAM-4 signal, RLM is equal to ‘1’.
Considering two critical coupled segmented MRMs, the simulated PAM-4 eye diagrams are shown in Fig. 3, using reported dynamic model [14] and parameters listed in Table 1. In Fig. 3(a), the crosstalk of the segmented MRM is about −8dB. It can be seen that the level separations are unequal and the corresponding RLM is 0.72. By contrast, the level separations in Fig. 3(b), generated by segmented modulator with −18dB crosstalk, are uniform and the corresponding RLM is 0.96. According to IEEE standard [2], the RLM of PAM-4 signal should be larger than 0.95 to ensure that the four levels can be well differentiated.
Fig. 3. 10 GBaud eye diagrams of the segmented MRMs with (a) −8 dB crosstalk and (b) −18 dB crosstalk. ${\Delta _{\textrm{12}}}$ and ${\hat{\Delta }_{\textrm{12}}}$ are the level separation of the middle eyes.
Table 1. Parameters used in eye diagrams simulation
2.3 Parasitic parameters
In section 2.1, parasitic parameters introduced by handle wafer and electrodes are not discussed. Qualitative discussion about parasitic parameters will be presented in this section.
Figure 4(a) shows the sectional view and the parasite impedances of the segmented MRM. LM, LL and Lcp denote the inductances introduced by the electrodes; CM, CL and Ccp model the capacitances between the electrodes; CMox and RMh model the current path through the buried oxide (BOX) and handle silicon around MSB segment, while CLox and RLh model the current path through the BOX and handle silicon around LSB segment. Figure 4(b) illustrates the equivalent circuit including parasitic parameters. The crosstalk S’lm and S’ml in LSB and MSB segments can be derived.
Comparing Eqs. (2) and (6), it can be found that they are similar in form, Thus, we suppose that the measured crosstalk-frequency curve (with parasitic impedances) will be similar to the one in simulation (without parasitic impedances). Compared with the capacitive impedances ZLSB and ZMSB, cascaded inductors are introduced into the equivalent impedances Z’LSB and Z’MSB, resulting resonances at certain frequencies. Hence, dips and ripples would be found in the measured crosstalk-frequency curve.
As shown in Fig. 4(b), the resistor Ri is paralleled with a branch containing capacitor Ccp and inductor Lcp. Usually, the cascaded impedance of Ccp and Lcp is capacitive, and the impedance decreases with the increase of frequency. Hence, the impedance of insulator is lower in high frequency, resulting an increasing crosstalk in high frequency range.
3. Crosstalk suppression
To suppress the crosstalk in segmented MRM, we substitute complementary doped silicon for the intrinsic silicon as an insulator. The proposed segmented MRM is shown in Fig. 5. The LSB and MSB segments inside the micro-ring are N type doped, accordingly the complementary implantation, namely P type implantation, is used inside the micro-ring to form the insulator. The segments outside the micro-ring are P type doped. All the P type doped regions are connected in common ground. Two PN junctions are formed at the interface between the P type doped region and the adjacent N type doped regions inside the micro-ring, indicated as crosstalk-suppression-diode-pair (CSDP) in Fig. 5. The CSDP works as the insulator.
Usually, the LSB and MSB segments are reverse biased for a high-speed operation [15], and the voltage potential in N type doped regions is higher than that in P type doped region. Hence, the PN junctions in CSDP are operated in depletion mode and their impedances can be as high as several million ohms due to the depletion regions. The diffusion dopants and lattice defects introduced by fabrication process may affect the distribution of PN junctions. Nevertheless, the depletion regions still exist and can be used as a high impedance insulator. As mentioned in section 2.1, a high impedance insulator results in a small electrical crosstalk. Consequently, the proposed method can suppress the electrical crosstalk.
Besides, the length of depletion regions can be as small as dozens of nanometers [16], thus the length of complementary doped region can have a compact size that limited by the critical dimension of fabrication process.
The equivalent circuit of the proposed segmented MRM is shown in Fig. 6. RG denotes the series resistance of the complementary region. CLr and CRr are the depletion-layer capacitances in the CSDP, and RLr and RRr are the depletion resistances. In this circumstance, the crosstalk ${\hat{S}_{lm}}$ and ${\hat{S}_{ml}}$ in LSB and MSB segments have the following expressions.
Fig. 6. Equivalent circuit of the complementary doped segmented MRM and its crosstalk simulation results. CLr and CRr are 5 fF; RLr and RRr are 10 MΩ; RG is 1.5 KΩ.
The simulated crosstalk-frequency curve of ${\hat{S}_{lm}}$ is shown in Fig. 6. In low frequency band, the impedance of the proposed insulator is decided by the depletion resistances. The insulator with high resistance reduces the leakage current and the crosstalk is suppressed significantly. While in the high frequency band, the depletion-layer capacitances dominate the impedance of proposed insulator and it decreases with the increase of frequency. Therefore, the crosstalk is higher in high frequency band.
4. Experiments
The experimental setup is shown in Fig. 7(a). A two-port vector network analyzer (VNA) is utilized to measure the crosstalk between LSB and MSB parts in segmented MRM. The two segments are connected to the two ports of the VNA through two bias-tees, respectively. The DC source is utilized to provide bias voltage to the LSB and MSB segments. The bias voltages are set to a same value. The S21 and S12 measured by the VNA are the crosstalk Sml and Slm, respectively. The conventional segmented MRM and the proposed segmented MRM (both with radii of 9 µm and 1 µm insulators) are fabricated and measured. Both devices were fabricated on the same silicon-on-insulator (SOI) wafer. The silicon waveguide was fabricated by a partial silicon etching followed by a full etching to form a ridge waveguide with 220 nm height rib and 90 nm thickness slab [17]. The doping concentrations are $\textrm{6} \times \textrm{1}{\textrm{0}^{\textrm{17}}}$ cm−3 for P and $\textrm{5} \times \textrm{1}{\textrm{0}^{\textrm{17}}}$ cm−3 for N. Photoresist masks were used to create the different doping regions. Figure 7(b) shows the optical micrograph of the fabricated device. The conventional device has the same physical structure with the proposed device, and only the proposed device is shown here.
We measured the crosstalk of conventional device and the proposed one biased at 0, −1V and −2V. The crosstalk-frequency curves of Slm and Sml of the two devices are shown in Figs. 8(a) and 8(b), respectively. The curves in Fig. 8(a) are similar to those in Fig. 8(b), and the slight distinctions are generated by the different impedances of LSB and MSB segments. The experimental results demonstrate that the crosstalk can be suppressed significantly in low frequency band by introducing the 1 µm complementary doped region as an insulator, and the crosstalk is suppressed more than 5 dB up to 30 GHz. Some dips and ripples can be seen in Fig. 8. They are introduced by the resonances of parasitic impedance as we discussed in section 2.3.
Fig. 8. (a) Slm and (b) Sml of segmented MRM utilizing intrinsic silicon and complementary doped region as insulators when biased at 0, −1 V and −2 V.
The crosstalk in the proposed device is higher than that in the conventional device when frequency is higher than 33 GHz. This is because the impedance of the proposed insulator is lower than that in the conventional insulator in high frequency band. As discussed in section 3, the capacitances dominate the impedances of CSDP in high frequency band. The capacitances decrease with the increase of frequency, and would be lower than the impedance of conventional insulator when frequency is higher than 33 GHz. Nevertheless, the performance degradation in high frequency band can be ignored for 28 GBaud signals. Moreover, the frequency performance might be optimized by reducing the capacitances of CSDP, which can be implemented by reducing the doping concentration of the complementary doped region [16].
Furthermore, the crosstalk suppression performance of the proposed insulator is immune from the bias voltage when being operated in depletion mode. Hence, the bias voltage can be used to optimize the other performances of modulator such as modulation bandwidth [18,19] and spurious-free dynamic range [20].
5. Conclusions
We demonstrate that, by introducing a complementary doped region as an insulator, the electrical crosstalk in segmented modulator can be suppressed more than 5 dB within 30 GHz frequency range. The length of complementary doped region is only 1 µm in the demonstrated device, and theoretically it can be shortened to tens to hundreds of nanometers. The proposed method is a promising way to realize a low crosstalk segmented modulator with compact footprint for high capacity, low-cost optical transmission systems.
Funding
National Key Research and Development Program of China (2019YFB1803801, 2019YFB2203502); National Natural Science Foundation of China (61775073, 61922034); Key Research and Development Program of Hubei Province (2020BAA011); Program for HUST Academic Frontier Youth Team (2018QYTD08).
Disclosures
The authors declare no conflicts of interest.
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