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We investigated the broadband operations of a silicon Mach-Zehnder modulator (MZM) based on a forward-biased-PIN diode. The phase shifter was integrated with a passive-circuit equalizer to compensate for the narrowband characteristics of the diodes, which consists of a simple resistance of doped silicon and a parallel-plate metal capacitance. The device structure was simple and fabricated using standard CMOS processes. The measured results for a 50-Ω driver indicated there was a small VπL of 0.31 V·cm and a flat frequency response for a 3-dB bandwidth (f3dB) of 17 GHz, which agree well with the designed values. A 25-Gb/s large-signal operation was obtained using binary signals without pre-emphasis. The modulator showed a linear modulation property to the applied voltage, due to the metal capacitance of the equalizer.
© 2015 Optical Society of America
1. Introduction
The size and power consumption of optical transceiver modules for short- to long-distance communications must be reduced to increase their transmission capacity. Silicon photonics is a promising technology for this purpose because it enables for the fabrication of photonic integrated circuits (PIC) on a silicon substrate [1–4]. A number of lasers, modulators, and detectors, as well as optical circuits for any polarization and wavelength division multiplexing, can be integrated on a single PIC chip for multi-channel transmissions [1]. A silicon modulator is key device for such a silicon PIC, because it converts electrical signals into optical ones [5]. In particular, Mach-Zehnder modulators (MZM) based on the free-carrier plasma effect are promising candidates because of their processing and structural compatibility in silicon PICs [1].
Silicon modulators should operate at high-speeds using a low-driving voltage and only encompass a small area of the PIC so that they can meet the requirements for transceiver modules. In other words, a broadband modulator with small VπL is needed. MZMs based on reverse-biased PN diodes, which are operated in the depletion mode, have most commonly been investigated [5–10]. A lot of effort has been put into achieving high-speed operations by optimizing the doping profiles of PN diodes. However, their modulation efficiency is not sufficiently large; VπL is typically larger than one V·cm [5–9]. The high modulation efficiency of a metal-semiconductor-silicon (MOS) capacitor modulator was recently reported, where the VπL < 0.3 V·cm. This modulator, however, has only a limited process compatibility with a silicon PIC due to the necessity of a poly-silicon layer, which is optimized for optical devices [11–13].
Silicon modulators based on the forward-biased operation of a PIN diode are promising for use in silicon PICs [14–19]. We reported on the 50-56 Gb/s operations using a forward-biased PIN diode and a small VπL of 1.3 V·cm at 25 GHz [17]. The fabrication of this type of MZM is simple and fully compatible with CMOS. One drawback of this type of MZM is that the optical frequency response drastically decays at frequencies larger than about 1 GHz due to its large capacitance. Therefore, all broadband operations of these modulators have been conducted using pre-emphasis signals, which need special circuitry.
We investigated the broadband operation of forward-biased PIN diodes in this work by integrating a frequency equalizer with the modulator to operate it using a standard none-return-to-zero (NRZ) signal [20]. The equalizer consists of a simple passive resistance-capacitance (RC) circuit [21,22] fabricated using a standard fabrication process [22]. We achieved a flat optical frequency response of the MZM up to 17 GHz for the 3-dB bandwidth (f3dB). The measured VπL was as small as 0.31 V·cm when the forward-biased operation mode was applied to the PIN-diodes.
This paper is organized as follows. The following section describes the circuitry of the equalizer and how it works with the PIN-diode for broadband operations. Section 3 presents the measured optical frequency response and 25-Gb/s large signal experiment using an MZM with the equalizer. In Section 4, we discuss the test element group (TEG) patterns of the PIN modulator and the equalizer. We designed the MZM with the equalizer using the parameters extracted from these TEG patterns.
2. Equivalent circuit and operation principle of RC passive equalizer for forward-biased PIN diode
Figure 1 (a) shows the equivalent circuit of the PIN diode. RS is the series resistance and CF and RF are the capacitance and resistance originating from the leak path at the intrinsic region of the PIN diode. For a modulator that is based-on forward-biased PIN-diodes, RF >> RS. In this case, the response of the modulator is expressed as follows [15–19].
QF represents the stored charge on the PIN-diode, which corresponds to the phase change of the modulator. The time constant, CFRS, largely determines the 3-dB bandwidth, f3dB, of the modulator. Since the CF is large for the RS for a forward-biased PIN diode, the f3dB is usually about several-hundred MHz [15–19].
Fig. 1 Equivalent circuit of forward-biased PIN-diode (a) without and (b, c) with RC passive equalizer. (b) and (c) are equivalent when CERE = CFRF.
We introduce the RC passive equalizer to increase the f3dB of the modulator, as shown in Fig. 1 (b). We set the circuit parameters of the equalizer so that CERE = CFRF. The equalizer and diodes under this matching condition are equivalently expressed using the same circuitry as shown in Fig. 1 (a), by using a composite capacitance and resistance, as Fig. 1 (c) shows. When CF >> CE, the composite capacitance can be replaced by the small capacitance CE of the equalizer in Fig. 1 (c). A small CE increases the f3dB at the expense of a decreased in efficiency, as indicated by the above equation.
Figure 2 shows the calculated modulation efficiency of the PIN diode with (all colored lines) and without (black line) the equalizer. Both the frequency and the response are normalized when using the CF. The results clearly show the operating principles of the RC equalizer. The smaller the CE becomes, the larger the f3dB is obtained at a reduced level of efficiency, compared with the modulator without the equalizer. The dotted lines indicate the response of the modulator with the equalizer when the CERE deviates from the CFRF. In this case, the flatness of the low-frequency region deteriorates, as the figure shows.
Fig. 2 Calculated results of modulation efficiency of PIN diode with (all colored lines) and without (black line) equalizer. For the modulator with the equalizer, the CERE equals the CFRF for the solid lines, whereas there is mismatching between them for the dotted lines.
3. Fabricated MZM with equalizer
3.1. Device structure
Figure 3 (a) shows a top view of the fabricated MZM embedded with the RC passive equalizer. The phase shifter, which is loaded on each arm of the MZM, is based on a side-wall grating waveguide and the PIN diodes [15–19]. A number of narrow fins are periodically placed on both sides of the waveguide core for use as the electrical channels for the electrons and holes, as Fig. 3 (b) shows. The structural details of the phase shifter including the doping profiles are the same as those in our previous works [18]. The interaction length of the phase shifter (Lact) was 60 μm.
Fig. 3 (a) Top-view of fabricated silicon MZM modulator based on PIN-diode-based phase shifter combined with RC passive equalizer, (b) Close-up of phase shifter based on side-wall grating waveguide. (c) Top view of resistance of equalizer (RE), where length is defined as L_RE. (d) Cross section of one of two phase shifters. Its position is indicated by the dotted line in (a).
The RC passive equalizer in this work was connected to each of the two phase shifters. The capacitor CE of the equalizer consists of parallel metal plates. The length of the CE is the same as Lact and the width of the CE (W_CE) is 40 μm. The CE was set at 100 fF. As shown in Figs. 3 (c) and (d), the gap between the top and bottom metal layers is 1 μm, which was filled with SiO2. The RE consists of a thin doped silicon layer that is 1-μm wide and the RE (L_RE) is 25-μm long. As shown in Fig. 3 (c), we ensured that the RE laterally bends to reduce the lateral space of the equalizer. The doping conditions of the RE for both arms are the same as the n- region of the PIN diode. The RE was set at 16 kΩ.
We fabricated these modulators using the standard processing technologies for complementary metal-oxide semiconductor (CMOS) devices.
3.2. Optical frequency response and modulation efficiency
We evaluated the fabricated modulator to verify the operating principle of the embedded RC equalizer for a PIN diode. Figure 4 shows the measured optical frequency response of MZMs with and without the RC equalizer under a forward-biased condition. The responses are normalized at f3dB = 17 GHz. The bias current (Ibias) was 120 μA in this experiment. We obtained flat and wide-bandwidth responses for a MZM (red line) with an RE of 16 kΩ. We also show the response curves for 4.8 kΩ (orange line) and 32 kΩ (blue line). We confirmed from these results that the flatness of the low-frequency response is determined by the value of RE.
Fig. 4 Measured optical frequency response of MZM with equalizer under forward-biased condition, where RE and CE are set at 16 kΩ and 100 fF. The orange and blue curves are the response curves, where the REs were 4.8 kΩ and 32 kΩ. The responses are normalized at 17 GHz. The black curve is the response of the reference PIN diode without the equalizer.
Next, we derived the modulation efficiency VπL of the MZM at DC with the equalizer from the shift in the measured transmission spectrum according to the applied DC bias voltage. Figures 5 (a) and (b) show the measured optical responses and the VπL at DC, where the Ibias ranges from 20 to 200 μA. The low-frequency responses below 200 MHz in Fig. 5 (a) are different for each Ibias. Therefore, the measured VπL at DC increases in accordance with the Ibias in Fig. 5 (b). The VπL is 0.31 V·cm for the Ibias of 120 μA, at which the flatness of the response curve in Fig. 5(a) is the best so that we determined the modulation efficiency of the MZM from the VπL at DC. This is a small value in comparison with the previously reported results for the PN-diode-based phase shifters [9]. For other Ibiass, the circuit parameters deviate from the matching conditions of the equalizer, and the response at low frequencies changes, just like that shown in Fig. 4. These deviations are considered to cause the changes in VπL with the Ibias in Fig. 5 (a).
Fig. 5 (a) Measured optical frequency response and (b) VπL of MZM at DC under forward-biased condition. The RE and CE of the equalizer are 16 kΩ and 100 fF. The VπL with a bias current of 120 μA is 0.31 V·cm, at which the frequency response shows flat responses in the low frequency region.
3.3. 25-Gb/s large-signal experiment
Figure 6 (a) shows the experimental set up of the 25-Gb/s large-signal modulation with two drivers with a 50-Ω output impedance. We used the fabricated modulator with a Lact, RE, and CE of 60 μm, 16 kΩ and 100 fF. The modulator was operated by using a pseudorandom binary sequence of 231-1 in a standard NRZ signal form in a push-pull configuration. The 50-Ω impedance driver was used in this experiment. We used RF cables with the same length and commercial RF probes to input two driving signals in time. The values of peak-to-peak-voltage amplitudes (Vpps) of the input signals applied to the one of the phase shifter are from 1.71 to 3.31 V for a 50-Ω input impedance, which we measured 25-Gb/s eye patterns for each Vpp. The input wavelength was adjusted to sustain the quadrature point. In this experiment, we fixed the bias current instead of voltage to maintain the same bias condition of the PIN modulator as small signal experiment in Fig. 4-5.
Fig. 6 (a) Set up of 25-Gb/s large signal modulation experiment. (b) 25-Gb/s output optical waveform of PIN-diode-based phase shifter with RC passive equalizer operated using 2.8-Vpp NRZ standard signals.
The 25-Gb/s optical signal waveforms for a Ibiass of 120 μA and 200 μA are shown in Fig. 6 (b), where clear eye openings are confirmed. We consider that the optical frequency responses of 120-μA and 200-μA conditions are almost flat. In addition, the modulation efficiencies of both conditions are same at high frequency. In terms of the linearity, however, 200-μA bias condition is the best in our experiment. As for the characterization of the RF modulation efficiency from the DC VπL, we used the 120-μA condition because the flatness of the response curve is better than 200-μA one.
The measured extinction ratio (ER) is 1.9 dB and 2.1 dB for each bias condition. However, the estimated ER from the DC VπL at 120 μA and 200 μA were 2.7 dB and 2.2 dB, respectively. For the case of 120 μA, there is 0.8 dB difference between experimental ER and estimated one. This difference can be caused by nonlinearity in large signal experiment, as shown in the next paragraph.
Next, we extracted the phase shifts at the phase shifter between the on and off levels from the ER for various driving-voltage amplitudes for a Ibias from 100 to 200 μA, as shown in Fig. 7. In this analysis, we neglect the effect of small optical loss because the phase shifter of our MZM is very short and the voltage swing on the PIN diode is small. As the graph indicates, the phase shifts are linear ones for the applied driving voltage, with a relatively large Ibias. Our modulator showed linearity in the phase shift up to 0.076 π during this experiment when applying a driving voltage of up to 3.31 Vpp. The measured optical propagation loss of the phase shifter was α = 8.3 dB/mm when a Ibias of 200 μA was applied. Considering the push-pull operation, the length of phase shifter for a π phase shift (Lπ) is determined to be Lπ = π/(0.076π*2)*60*10−4 mm = 0.395 mm. Therefore, our modulator could provide a linear π-phase change with an optical loss of αLπ = 3.28 dB. For any type of modulator, linear phase shift can be obtained for sufficiently small driving voltage. In this case, however, the phase shifter should be long enough to obtain the required phase shift, and the optical loss increases.Thus, we consider απ as a figure of merit to compare the linearities among different types of MZMs. As explained in Section 2, the CE determines the amount of current flow to the modulator and the stored charge in the PIN-diode when CF >> CE holds true. The CE attributes to the metal parallel plates and has a completely linear response to the applied voltage. Therefore, the use of the equalizer is considered to cause the high linearity in the modulation for our modulator.
Fig. 7 Phase-shift caused in each arm of MZM during 25-Gb/s operations as function of driving-voltage amplitude for various bias conditions Ibias. The inset shows the I-V curve of the one phase shifter with equalizer.
The longer phase shifter than the 60-μm one is more suitable to lower the driving voltage. In this case, however, the lower impedance drivers are required to operate the long phase shifter. Otherwise, the bandwidth becomes smaller due to the increased RC-time constant. Use of segmented phase shifters is another way, which are operated by a number of 50-Ω drivers, respectively [9]. In our experiments, only 50-Ω drivers were available. Therefore, we used the short 60-μm phase shifters. We also have to consider the tradeoff between phase-shift efficiency and optical loss. Too-long phase shifter provides the smaller optical modulation amplitude (OMA) due to the increased loss [19]. For our phase shifter, 520-μm phase shifter would provide the largest OMA, which is calculated by using the measured VπL and optical loss constant.
4. Equivalent circuit analysis
4.1 Extraction of circuit parameters of PIN diode
We investigated the PIN-diode-based phase shifter to determine the circuit parameters of the equalizer. We measured the electrical-S11 reflection of the electrodes on one of the MZM phase shifters under forward biased condition. We used a 60-μm-long reference phase shifter without an equalizer. Figure 8 shows the real and imaginary parts of the impedance derived from the measured-S11. We fitted the impedances by assuming the circuit shown in Fig. 1 (a) for all these bias currents. For example, we show the fitting results of 120 μA and 200 μA in Fig. 8 as dotted curves. The impedances are well reproduced by its equivalent circuit.
Fig. 8 Real and imaginary parts of extracted impedances of one of phase shifters of fabricated MZM, extracted from measured S11-reflection with Ibiass of 120 μA and 200 μA (solid curves). The dotted lines are the fitting curves obtained using the equivalent circuit shown in Fig. 1 (a).
We determined the circuit parameters of the forward-biased PIN diode from these results. In Figs. 9 (a-c), the circuit parameters of the PIN diode are shown for a Ibias from 10 to 200 μA. The time constant CF*RF is plotted in Fig. 9 (d) using the extracted CF and RF. The CF*RF is the important parameter for determining the electrical parameters of the RC passive equalizer because the CE*RE should match this value. The CF*RF parameter of the PIN diode shows almost a constant value in the Ibias range of 120-200 μA. Figure 9 (e) presents the I-V characteristics. The experiments were conducted near the built-in voltage of the PIN diode throughout this paper. As shown in Fig. 9 (f), we calculated the Qπ = VπL*CF/Lact of the phase shifter, which is defined as the stored carries for the π-phase shift 3 pC that was obtained in the Ibias range of 120-150 μA.
Fig. 9 Extracted electrical parameters of PIN-diodes from equivalent-circuit analysis. (a) CF, (b) RF, (c) RS, (d) CF*RF parameters of PIN diode under forward-biased condition, (e) I-V curve, and (f) Qπ of PIN diode.
4.2 Characterization of equalizer
We investigated the circuit parameters of the equalizer from the electrical measurement of the TEG pattern. Its capacitance consists of a parallel plate metal capacitor whose lateral size is determined by its 60-μm length (Lact) and W_CE.
Figure 10 shows the equivalent circuit and its circuit parameters for the TEG pattern. The total capacitance (Ctotal) is the summation of the CE and the parasitic capacitance, which is defined as CPAD. The results are 2.5 fF/μm, which is a reasonable value compared to the analytical calculation results when using a parallel plate capacitor. The resistance of the equalizer changes linearly for the L_RE in Fig. 10 (c). The measured RE is 0.7 kΩ/μm, which is sufficiently large for this equalizer.
Fig. 10 (a) Equivalent circuit of equalizer. (b) Total capacitance of equalizer TEG. The blue dotted curve shows the analytical calculation results of the Ctotal when using the parallel plate capacitor. (c) Measured resistance of RE from I-V measurements.
4.3 Calculated response of modulator
Figure 11 (a) shows the equivalent circuit of the modulator. This circuit has a complicated circuit diagram compared with the ideal case described in Fig. 1 (a). In this experiment, the amount of parasitic capacitance between the metal pads and the substrate silicon layer (CPAD) is comparable with the CE. Thus, the influence of this capacitance should be considered. The CDS corresponds to the capacitance between the bottom metal pad of the CE and the substrate silicon layer. The CGD is the component between the ground metal pad and the substrate. The influence of the CDS and CGD is quite small because the impedance of the PIN diode is much smaller than those derived from the CDS and CGD. The values of these parameters are listed in Fig. 11 (a).
Fig. 11 (a) Equivalent circuit of MZM with embedded RC passive equalizer and circuit parameters of 60-μm-length phase shifter. (b) Calculated optical frequency responses under forward-biased condition, where Ibias ranges from 20 to 120 μA.
Figure 11 (b) shows the calculation results for the normalized frequency response of the modulator under the forward-biased condition, where the Ibias ranges from 20 to 120 μA. We used the circuit parameters of the PIN diode in Fig. 4 in this calculation. The results show flat frequency responses under these bias conditions. The response curves of around 10 GHz are similar to the measured one. This indicates that the response property of our modulator with the equalizer can be predetermined from the circuit parameters of the equalizer TEG pattern and PIN diode. The 120-μA response curve below 300 MHz, however, is slightly different from the results shown in Fig. 4. The cause of this mismatch possibly comes from the subtle difference in the circuit parameters of the PIN diode as shown in Fig. 11(a).
5. Conclusion
We investigated the broadband operation of a silicon MZM that is based on the forward-biased PIN diodes, by integrating a passive RC equalizer with the diodes. The equalizer consists of a simple parallel circuit of a resistance-line and parallel-plate metal capacitance using standard CMOS processes, and was designed to compensate for the narrowband characteristics of the diode. The fabricated device showed a 3-dB bandwidth of 17 GHz, which was close to the designed value, and the VπL was as small as 0.31 V·cm for a 50-Ω driver. The results from large modulation experiments indicated the high linearity of the modulator during the phase change against the applied voltage, due to the metal capacitance of the equalizer as a linear element. These results indicate that our device is suitable for advanced multi-level modulation formats such as QPSK, QAM, PAM, and DMT for the next-generation of transceivers. These formats need a high-modulation linearity with a large phase change. The small-VπL characteristics enable for the use of a relatively short phase shifter with a power-efficient lumped driving configuration. In addition, a special process is not required for the fabrication of our device, which makes it easy to use standard CMOS foundry services.
Acknowledgment
This research is supported by the New Energy and Industrial Technology Development Organization (NEDO).
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