We present high-speed operation of pin-diode-based silicon Mach-Zehnder modulators that have side-wall gratings on both sides of the waveguide core. The use of pre-emphasis signals generated with a finite impulse response digital filter was examined in the frequency domain to show how the filter works for different filter parameter sets. In large signal modulation experiments, VπL as low as 0.29 V·cm was obtained at 12.5 Gb/s using a fabricated modulator and the pre-emphasis technique. Operation of up to 25-Gb/s is possible using basically the same driving configurations.
©2012 Optical Society of America
Convergence of photonics and electronics will be essential for future computer systems to overcome current limitations, particularly in terms of interconnects . Silicon photonics is a promising technology for addressing this issue, as it can enable the fabrication of large-scale integrated circuits (LSIs) with high-capacity optical interconnects, by integrating a number of optoelectronic devices on a silicon substrate [1–4]. An array of high-speed silicon modulators plays a key role in converting a large amount of data from electrical to optical with multiple channels. Each modulator must be compact and power-efficient to achieve large-scale and high-density interconnects because they can use only a fraction of the total power and area allowed for interconnects . As a consequence, researchers have been investigating a number of different silicon modulators over the past decade to meet this requirement [5–29].
Mach-Zehnder modulators (MZMs), which use reverse-biased pn diodes, are most commonly investigated for near-future applications [5–11]. These diodes act as electrical capacitors for storing and releasing electrons and holes according to the applied voltage. These carriers change the refractive index of the waveguide using the free-carrier plasma (FCP) effect. This kind of modulator has already exhibited high-speed operation at 40 Gb/s . However, the active length of such modulators is equal to or longer than 1 mm and/or the amplitude of the driving voltage is larger than 1 V at speeds higher than 10 Gb/s. These characteristics are not always sufficient for the applications mentioned above. These performances are largely limited by the efficiency of the modulators: 0.71 V·cm had been the lowest VπL reported so far . Although efficiency may be improved using a higher electrical capacitance with high doping concentration at the pn junction, it will inevitably cause large free-carrier absorption of light.
In contrast, pin diodes, which have an undoped region between doped regions in the waveguide, provide much lower VπL when used in modulators with forward bias voltage, lower by two orders of magnitude than the above-mentioned pn-diode-based modulators [7,12–16]. For pin modulators, frequency dependence has been a major issue. Low VπL is possible only in a frequency range typically smaller than several hundreds of MHz, and it rapidly decreases above that frequency. Pre-emphasis signals have been successfully introduced to compensate for this frequency dependence, enabling broadband operation up to 16 Gb/s [12–17,21–23]. In this driving configuration, overall VπL differs from that measured at DC and low frequencies. Nevertheless, few papers have reported the VπL of such pin-diode-based modulators driven by pre-emphasis signals at 10 Gb/s or higher . In addition, it is not clear yet to what speed this technique can achieve for modulators beyond 16 Gb/s. Thus, the potential of pin-based modulators remains largely unexplored for the application of large-scale optical interconnects when operated using pre-emphasis signals.
We studied the operation of a pin-based silicon MZM in injection mode by using pre-emphasis signals, particularly using finite impulse response (FIR) digital filter-based emphasis signals, to reveal its potential. The relationships between the frequency response of the fabricated MZM and those provided from the FIR digital filter are shown for different parameter sets of the filter to show how this compensation works. Large-signal high-speed modulation experiments were conducted using such FIR-based emphasis techniques. As a result, we obtained clear eye-openings with a VπL as low as 0.29 V·cm for the pin-based MZM at 12.5 Gb/s, which is, to the best of our knowledge, the lowest VπL among silicon MZMs operated at 10 Gb/s or higher including pn- and pin-based modulators. Furthermore, we show that higher operations beyond 16 Gb/s are possible for pin-based modulators in injection mode using basically the same techniques.
2. Device structure
Figure 1 is a schematic of the fabricated MZM we used in the experiments . A Mach-Zehnder interferometer is formed using silicon-based waveguides and two multi-mode-interference (MMI) couplers on a silicon-on-insulator (SOI) substrate. The modulator has side-wall gratings on both sides of the waveguide core in the phase-shifter section to enable electrical connection between the core and metal electrodes. During operation of the modulator, free carriers, such as electrons and holes, are injected into or extracted from the core via the fins of the grating. The light propagating mainly in the waveguide core interacts with these carriers causing a phase shift due to the FCP effects. The waveguide has a uniform thickness of silicon over the entire modulator; hence, to form this waveguide, the top surface of the buried oxide (BOX) layer acts as a stopper in the etching process. Therefore, our MZM is easier to fabricate and obtain stable results from than conventional rib-waveguide-based modulators, in which the etching needs to be stopped by precisely controlling the time to leave a thin slab of a silicon layer.
As indicated in Fig. 1(b), the width and height of the waveguide core were set as 450 and 220 nm, respectively, so that the waveguide would be compatible with regular silicon photonic wire waveguides. As for the design of the grating, if small optical loss is needed, the fins should be as long and narrow as possible. However, if low electrical loss is needed, the fins should be as wide and short as possible. Therefore, we chose 2 um and about 60 nm, respectively, due to this constraint. We designed the pitch of the grating to be 285 nm, so that the operating wavelength of 1550 nm would become sufficiently larger than the Bragg wavelength of the gratings. With this condition, light propagates without serious reflection by the gratings and has almost uniform field distribution along propagation axis. Optical confinement of the guided mode in the 220-nm thick and 450-nm wide waveguide core was equal to 89% from a numerical simulation. The fins of the gratings and the silicon pads on both sides of the core were highly p- or n-doped. Both doping levels were about 1020 cm−3 in the pads, while they were expected to be several times smaller in the fins due to the dopants escaping during the processes. The space between the edge in the doped region of the fin and the side wall of the core was 450 nm. We fabricated such phase shifters with different active lengths ranging from 0.1 to 1.0 mm.
The MZM was fabricated in the Super-Clean-Room at AIST Tsukuba West by using process technology for CMOS devices. During fabrication, we used a variable-shaped-beam electron-beam (VSB-EB) writer to define the core of the waveguide including the grating. Figure 2 shows a scanning electron microscopy (SEM) image of the fabricated waveguide with side-wall grating. It exhibited uniform periodicity, as intended. To this side-wall grating waveguide, phosphorus (P+) was implanted to form n+-regions as shown in Fig. 1(b). The dopants were thermally activated by annealing for 15 min. at 1000 °C. Next, boron (B+) was implanted to the waveguide to form p+-region, followed by thermal annealing for 5 min. at 1000 °C. A 1-μm thick layer of silicon dioxide was deposited to cover the waveguide as cladding layer. Finally, contact windows were opened on silicon pads, and 1-μm thick aluminum was deposited to make contact. In the above processes, the thermal annealing was much longer than those in regular fabrication processes of silicon devices. During this long annealing, both phosphorus and born defused and got closer to the waveguide core from the edge of the original doped regions, which was 450 nm away from the side of the waveguide core. As a consequence, the concentrations of the dopants gradually decreased from the edge of the original doped regions toward the side of waveguide core, and this reduced effective width of unoped region on the waveguide core.
3. Static characteristics
3.1 Transmission spectrum
We characterized the fabricated MZM in various ways. Our MZM had two optical ports on both facets of the device chip as shown in Fig. 1(a). In optical measurements, we kept using one specific port to input optical continuous wave to the MZM on one of the facets. On the opposite facet, we used both of two ports, switching from one to another to detect optical power from the MZM, depending on type of the measurements. In this paper, we call one of output ports bar port when it is on the same side as input port, and call another output port cross port, as shown in Fig. 1(a). First, we measured the transmission spectrum of the MZM with an active length of 250 μm. Figure 3 shows the measured spectrum from the cross port of the device. The phase difference was corrected so that the output from the cross port was at maximum. For comparison, we measured a simple waveguide that had no MMI couplers, gratings, dopants, or electrodes. In the graph, a large dip was observed around 1460 nm for the MZM with the width of about 10 nm. We attributed the dip to the stopband of the gratings since the reference waveguide did not show such a dip in those wavelengths. As intended, the distance between the stopband and the operating wavelength of 1550 nm was sufficiently large, and the spectrum of the MZM had a smooth curve around 1550 nm, similar to that of the reference waveguide. Enhancement of the phase change could have been possible if we had set the wavelength of light to be near the band-edge of the stopband, as described by Brimont et al .
To further examine the propagation loss of the waveguide with side-wall gratings, we measured the transmissions of waveguides with different active lengths at 1550 nm. The results are shown in Fig. 4 , in which the solid line indicates linear fitting for the measured points. The slope of the line was 3.9 dB/mm, corresponding to the propagation loss of the waveguide. This includes the losses from the free-carrier absorption in the doped region and scatterings by the gratings. Since our MZM was efficient and the active lengths below 1 mm were sufficient for high-speed operation, the measured propagation loss was relatively small.
3.2 DC extinction characteristics
Figure 5 is the DC response of our MZM with an active length of 250 μm when forward-bias voltage was applied to one of the two diodes. As the red curves in the graph show, our MZM had very efficient extinction characteristics. The voltage difference of the first bottom and peak of the curve was only 0.12 V for bar port, from which the VπL was calculated to be as low as 0.003 V·cm. As mentioned above and confirmed in the next section, this efficiency, however, rapidly decreases at frequencies higher than 100 MHz. Hence, a different method for estimating VπL is necessary for the modulator based on forward-biased diodes, which is one of topics of this paper. The extinction ratio (ER) was as high as 23 dB at maximum, which indicates that the imbalance of the MMI couplers was small enough and the Mach-Zehnder interferometer functioned as intended. The blue curve shows the forward current for the applied voltage. The device exhibited a normal rectifying property of pin diodes. The differential resistance was 14.6 Ω at 1.5 V, which was smaller than that of rib-waveguide-based modulators, if compared at the same active length . This indicates that the side-wall grating is suitable for modulators to electrically connect the core of the waveguide and the metal electrodes.
4. High-speed modulation characteristics
Next, we characterized the high-speed modulation of the fabricated MZM with an active length of 250 μm.
4.1 Small-signal response
First, we examined the frequency response of our MZM for small modulation signals. Figure 6(a) shows the measurement setup, where high-frequency signals were applied to one of the two phase shifters, and the modulated signals were optically detected from one of the two outputs of the modulator. A constant forward DC bias voltage of 0.9 V was applied to the diode of the driven arm with high-frequency signals, while only DC bias voltage was applied to the diode of the opposite arm. The latter voltage was adjusted so that the lightwaves propagating the two arms had the proper phase difference during the measurements. The black solid line of Fig. 6(b) shows the measured response of our MZM. The response was relatively high and flat at low frequencies below 100 MHz. This response is attributed to the large electrical capacitance that the pin diode has with forward bias voltage. However, as the frequency goes above 100 MHz, the response rapidly decreases with a slope of about 20 dB/decade up to around 20 GHz. This dependence indicates that the modulator behaves as a simple series resistor-capacitor (RC) circuit in the frequency range from DC to about 20 GHz; the response of such RC circuits is almost constant below the cut-off frequency and decreases by 20 dB/decade above that frequency. For the modulator, the resistance is attributed to the fins of the gratings, contact between the semiconductor and metal electrodes, and the load resistance of 50 Ω, while the pin diode mostly accounts for the capacitance.
A pre-emphasis signal was used to compensate for this and obtain flat response in the entire frequency band of the signal [12–17,21–23]. An FIR digital filter is particularly suitable for this purpose since it has already been incorporated in the electrical off-chip interconnect of LSIs [16,23]. Figure 6(c) shows a block diagram of the FIR-based pre-emphasis filter with two taps we used in the experiments. The FIR filter consisted of a broadband divider, constant delay, and multiplier and combiner. The transfer function of the filter is expressed as follows;
The suffix n corresponds to each tap of the filter, and N + 1 means the total number of taps. The notations hn and τ represent the coefficients of the multiplier and the delay of the FIR filter, respectively. The narrow red solid line of Fig. 6(b) is the calculated curve using the above function for the parameter set of (h0, h1, τ, N) = (1, −1, 80 ps, 1). The delay was chosen as the full-width bit slot for 12.5 Gb/s, at which large signal operation was performed as described in the later section. The calculated response is linear with a slope of 20 dB/decade from the lowest frequency up to around 3 GHz and became flat at 6.25 GHz, at which ωτ = π. This compensation is not necessarily sufficient for the MZM with the frequency response indicated by the black curve in Fig. 6(b), to obtain clear eye-openings in 12.5-Gb/s operation. In contrast, if the delay of the FIR filter is equal to a half-bit slot of 12.5 Gb/s, the response of filter maintains a slope of 20 dB/decade up to 7 GHz, which is double from the previous case; hence, it can sufficiently compensate for the response of the MZM at that bit rate. As for the low frequency component from DC, the filter exhibits a flat response, similar to the modulator, if h1 becomes smaller than h0, as shown with the red bold line in Fig. 6(b). Generally, if the h1 becomes smaller, the frequency response of the filter remains flat in wider frequency range from DC. Due to these adjustments of the parameter sets of the FIR filter, it can compensate for the response of the pin modulator in the full-frequency range for broadband signals.
We calculated bandwidths of our MZM when it was driven with the FIR filter with the parameter of (h0, h1, τ, N) = (1, −0.98, 40 ps, 1). We first calculated summation of the black solid and the red bold line in Fig. 6(b) at each frequency. For the summation, we defined maximum response in whole frequency range as 0 dB. We next extracted low and high frequency limits at which the responses first fell below −3 dB. As a result, 3-dB bandwidth was from 281 MHz to 7.89 GHz, which was sufficient for 12.5 Gb/s operation as confirmed in the following section. In the same way, we calculated 6-dB bandwidth of the MZM, which was from 16.5 MHz to 12.5 GHz. In Fig. 6(b), vertical axis was defined for optical signals as 20⋅Log10ΔP(f), in which ΔP(f) means the amplitude of the optical power variation and f is frequency. Note that in this notation, ΔP(f) became half of its maximum at the low and high frequency limit in the 6-dB bandwidth rather than 3-dB bandwidth.
4.2 Large-signal modulation experiment
From the results of the small-signal frequency responses, we performed large-signal broadband operations of our MZM using a pseudorandom binary sequence (PRBS). Figure 7 shows the experimental setup, in which DATA is a PRBS of 27-1 in standard non-return-zero (NRZ) form generated using a pulse pattern generator (PPG), and xDATA is the inverted pattern of DATA. DATA and xDATA are combined to obtain the same function of the FIR digital filter. The amplitudes of DATA and xDATA were independently set to determine the coefficient of h0 and h1 in Fig. 6(c). The relative delay between xDATA and DATA was adjusted using the PPG to provide the τ in the filter. Figures 8(a) and 8(b) are the measured electrical waveforms of DATA and xDATA before the combiner in Fig. 7. xDATA had slightly smaller amplitude and was delayed with 80 ps corresponding to one bit of 12.5 Gb/s, so that (h0, h1, τ, N) = (1, −0.86, 80 ps, 1) in the configuration in Fig. 6(c).. The two signals were then re-combined, amplified, and split into two identical signals. Figure 8(c) is the waveform of one of the split signals, from which the amplitude of the pre-emphasis signal was determined to be 2.3 Vpp in a 50-Ω system. Finally, forward DC bias voltages of 0.74 V and 0.81 V were added to the signals by using bias-Ts. The resultant two signals were applied to both arms of the MZM to drive it in a push-pull configuration. The polarities of the two signals were the same, whereas those of the diodes of the two arms were opposite. The phase difference of the lights between the two arms was adjusted using the DC bias voltages, so that the average output power from the bar and cross ports would become identical.
Figure 8(d) is measured optical waveform output from the bar port of the MZM at a bit-rate of 12.5 Gb/s. Clear eye-openings were obtained with a dynamic extinction ratio of 8.0 dB. This configuration of the pre-emphasis signal, based on constant one-bit delay, is compatible to those used in electrical interconnects of LSIs. Therefore, the results indicate that pin-diode-based modulators can easily be implemented for interconnects of standard LSIs.
Although they are clearly opened, the eye diagram of Fig. 8(d) deteriorates from the original NRZ signals in Figs. 8(a) and 8(b). The transition between 0 and 1 levels is not so fast that both levels construct bold lines at the center of the eye pattern. This deterioration is thought to be due to insufficient compensation of the one-bit-delay-based pre-emphasis signal. To improve the eye patterns, we used an FIR-digital filter based on a half-bit delay. The configurations are the same as the previous one-bit delay case, except the delay between DATA and xDATA. We set the delay as 40 ps this time. After fine adjustment of the amplitude of DATA and xDATA, the parameter was set as (h0, h1, τ, N) = (1, −0.98, 40 ps, 1), which was exactly same as that of the red solid line of Fig. 6(b). Figures 9(b) and 9(c) are the eye patterns for this pre-emphasis signal, obtained from the bar and cross ports of the MZM. The eye diagrams show improved openings compared with those in Fig. 8(d). Levels 0 and 1 maintain a constant value regardless of the successive sequences of the data. This improvement is because the compensation circuit with half-bit delay maintains a slope of 20 dB/decade to higher frequencies; hence, the optical signals have more high-frequency components compared with the previous case of one-bit delay. As for the dynamic ERs, they were 4.1-4.2 dB and smaller than those in Fig. 8(d). This is due to the slight difference in ratio of -h1/ h0 between the two driving configurations. In Fig. 8(c) the ratio is less close to 1, which means pre-emphasis signals contained more low frequency components, compared with that in Fig. 9(a). In this case, eye diagram opened wide when each of 0 and 1 level is constantly applied to the MZM without transitions between two levels, which caused small increase of dynamic ER.
As mentioned in the previous section, the modulator maintains a relatively linear decrease up to 20 GHz, as shown in Fig. 6(c). This implies that higher operation than 12.5 Gb/s is possible if compensation techniques maintain a slope of 20 dB/decade in the higher-frequency range. We used an in-line type RF differentiator (Picosecond Pulse Lab, Model 5206, passive impulse forming network) instead of the FIR filter to conduct this experiment. The reason we did not use the FIR filter described above was that the RF components, such as the combiner, did not have sufficient bandwidth for higher operation, while the differentiator nicely maintained the slope of 20 dB/decade up to 20 GHz. The experimental configurations were, otherwise, basically the same as those in Fig. 7. In this case, 3-dB and 6-dB bandwidths of the MZM were estimated to be from 320 MHz to 12.5 GHz and from 116 MHz to 22.1 GHz, respectively, in the same way as explained in section 4.1. The peak-to-peak voltages of the driving signal were 3.32 V and 3.07 V, respectively for 20-Gb/s and 25-Gb/s operations. We used a larger amplitude than that of 12.5 Gb/s because the modulation efficiency decreased at higher frequencies. In addition, we changed the DC phase difference of the light between two arms from π/2 to obtain larger extinction ratios at the expense of the optical insertion loss (IL). Figures 10(a) and 10(b) show optical waveforms obtained at 20 Gb/s and 25 Gb/s, respectively. Although they deteriorated more than those at 12.5 Gb/s, the opened areas are still recognized for both rates with dynamic extinction ratios of 6.8 dB and 4.5 dB, respectively. As far as we know, 25 Gb/s is the highest speed that silicon modulators based on forward-biased pin-diodes are operated.
4.3 VπL and optical IL in 12.5 Gb/s operation
From the results of Fig. 9, we evaluated the performance of our MZM in 12.5-Gb/s operation in detail. First, from the measured dynamic ER, we estimated the VπL. When the MZM is driven around its quadrature point, the ER is given as:Fig. 9, by optical IL.
Power consumption is another important factor for optical modulators. We next estimated the electrical power dissipated in the MZM during high-speed operations. During 12.5-Gb/s operation, DC forward bias voltage of 0.86 V was applied to both diodes of two arms of the Mach-Zehnder interferometer. The measured DC currents were 0.44 mA and 0.57 mA, respectively. Then, DC power consumption PDC was equal to about 0.87 mW. AC power consumption PAC can be estimated from input voltage waveform V(t) in Fig. 9(a). The PAC is given by a time integral as
We estimated the optical IL during 12.5 Gb/s operation in the following way. First we measured optical outputs from bar and cross ports of the MZM at initial state when no bias voltage or RF signal was applied to the MZM. We defined P0 as the summation of the measured two output powers. Note this P0 already suffered from 1-dB propagation loss since the side-wall grating waveguides had 3.9-dB/mm propagation loss, as mentioned in section 3.1. Next we measured optical outputs power from bar and cross ports respectively when bias voltage and RF signals were applied to the MZM in the configuration as described in the previous section during the measurement of Fig. 9. We defined these two output powers as Pbar and Pcross, respectively. Using these P0, Pbar and Pcross, P0/Pbar and P0/Pcross were calculated to be 3.1 dB and 3.2 dB, respectively. These values contained 3-dB switching losses. In the high-speed operations in section 4.2, the input optical power was equally distributed to bar and cross port, which caused 3-dB losses to both Pbar and Pcross. We call this switching loss in this paper. This assumption of 3-dB loss is reasonable because the measured Pbar and Pcross were almost identical and we set the Mach-Zehnder interferometer at quadrature state during high-speed operations. Finally, by adding the 1-dB propagation loss at initial state to the P0/Pbar and P0/Pcross, we estimated the IL during the high-speed operation to be 4.1 dB and 4.2 dB for bar and cross port, respectively, as indicated in Fig. 9. In the above discussion, it is clear that those ILs did not include optical coupling losses with lensed fibers used in the experiments and the excess loss of the MMI couplers. The 3-dB switching loss does not depend on the structure of the MZM and is excluded for the comparison in different structures. If we subtract this 3-dB from the ILs, the rest of losses were 1.1 dB and 1.2 dB, for bar and cross ports, respectively.
Table 1 summarizes the performances of our MZM and recently reported MZMs based on the FCP effect. The VπL of 0.29 V⋅cm in this work was, to the best of our knowledge, the lowest among silicon MZMs operated at 10 Gb/s or higher, as indicated in the table. This means the use of forward-biased pin diodes with pre-emphasis signals is effective in obtaining high modulation efficiency around 12.5 Gb/s. One reason for this low VπL is the use of forward-biased pin diodes. As mentioned in section 3.2, the response of pin-diode based modulators rapidly decreases in GHz range by 20 dB/decade. However, since the response at DC was exceptionally large, it maintains relatively large efficiency around 10 GHz. Therefore, by properly compensating for the slope, it is possible to operate forward-biased pin-diode in broadband with high modulation efficiency. Another possible reason is the doping profile of the pin diodes of our MZM. As described in this paper, p- and n-type dopants defused from the edge of the original implanted region toward the waveguide core by long-time thermal annealing, to form narrow undoped region on the waveguide core. This doping profile is different from those in other pin-diode based modulators . The size of the core of the side-wall grating waveguide and the optical confinement factor in it were both comparable to those of conventional rib-waveguides. Thus, our MZM has better overlapping between injected free carriers and optical guided mode, which can be another reason for the low VπL obtained in our experiment.
Note that modulator in the reference 24 had the smallest power consumption in Table 1 because it used ring resonator to increase modulation efficiency. In the other non-resonant modulators with wide optical bandwidth, our MZM had the smallest power for its operation speed. The small power consumption of our MZM was achieved by the smallest VπL.
The optical IL of our MZM was also small compared with the other MZMs in Table 1. The reason for this small loss was attributed to the use of the relatively short, 250-μm phase shifter and the pin-diodes. The core of the waveguide was undoped for the pin diodes. Therefore, our MZM does not exhibit loss of the background dopants, unlike pn-diode-based silicon modulators, which require medium-level doping in the core. These two features of high modulation efficiency and small optical loss together with the small active length suggest that our MZM is promising for application of large-scale and high-density optical interconnects.
We investigated pre-emphasis operations of pin-diode-based silicon modulators to evaluate their application to interconnects. We showed how the FIR digital filter-based pre-emphasis technique works for pin-modulators in the frequency domain. Using two-tap emphasis signals, 12.5-Gb/s operation was achieved with low VπL of 0.29 V⋅cm, which was, to the best of our knowledge, the highest modulation efficiency among silicon-based MZMs operated above 10 Gb/s including pn- and pin-diode-based devices. Up to 25-GHz operation is possible by using basically the same pre-emphasis technique.
This research is granted by the Japan Society for the Promotion of Science (JSPS) through the “Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program),” initiated by the Council for Science and Technology Policy (CSTP).
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