## Abstract

The traditional Mach-Zehnder modulator (MZM) figure of merit (FOM) has been defined as (V_{π}^{2})/υ_{3dBe}, and works effectively for LiNbO_{3} long haul modulators. However, for plasma dispersion based electro-optic modulators, or any modulator that has an inherent relationship between its bandwidth, required drive voltage, and optical insertion loss/gain, this FOM is inappropriate. This is particularly true for short reach links with no optical amplification. In the following, we propose a new modulator FOM (M-FOM) based on device metrics that are essential for short-reach links, such as the peak-to-peak drive voltage, modulator rise-fall time, and relative optical modulation amplitude. Link sensitivity measurements from two MZMs that have different bandwidths and optical losses are compared using our M-FOM to demonstrate its utility. Furthermore, we present a novel application protocol of our M-FOM to provide deeper insight into the relative system impact that modulator performance has on data links with no optical amplification, by taking the ratio of M-FOMs from two modulators driven with the same radio frequency drive power.

© 2017 Optical Society of America

## 1. Introduction

CMOS Integrated Nano Photonics (CINPs) has the potential to make a disruptive impact on multiple market sectors, including datacom/metro-telecom communications, real-time sensing for health diagnostics, and national security applications, by bringing dramatic hardware cost reduction and semiconductor industry efficiency to these ventures [1,2]. Technology solutions range from the hybrid approach [3–9], where electrical and optical components are built on separate chips and in different technologies, to a full monolithically integrated solution [1,10–17]. Hybrid and monolithic platforms each offer unique advantages. Monolithic platforms have the advantage of being able to address both monolithic and hybrid technology approaches, since one can simply choose which components are relevant for a given application. However, in contrast to a photonics-only CMOS compatible platform, developing a monolithic technology presents the additional challenge of optimizing and guaranteeing the performance of both optical and electrical devices manufactured simultaneously through one common process flow. IBM has developed a monolithic sub-100nm CINP technology (CMOS9WG) that minimizes processing steps, mask levels, component parasitics, and packaging/assembly complexity, by monolithically integrating optical components into the CMOS circuit analog and mixed-signal front end [10].

CMOS compatible transmitters have been a topic of significant research. Mach-Zehnder modulators (MZMs) and ring modulators based on plasma dispersion electro-optic phase shifters have been demonstrated, and significant progress in performance metrics such as bandwidth and optical loss have be realized [3–40]. Silicon photonic MZMs provide relatively good temperature stability, but when free carrier plasma dispersion PN junction optical phase shifters are used, devices generally become large requiring traveling wave electrode or segmented electrode designs, in order to maintain high speed operation [11, 17, 21, 28–30,40]. Lumped element ring modulators tend to be very efficient from the perspective of RF power consumption, and have relatively small footprints, but are generally more temperature sensitive and require thermal stabilization strategies that can be power hungry and/or processing intensive [34, 37].

In the following, we first consider what performance metrics are most appropriate to include in a CMOS compatible modulator figure of merit (M-FOM) that is specifically targeted for shorter reach data transport without optical amplification, and apply these critical link performance metrics in a new M-FOM. We then demonstrate the utility of this newly derived M-FOM by making a direct comparison between two MZMs with different types of electro-optic phase shifters as a function of bit rate and drive conditions.

## 2. The use of Vπ in a modulator figure of merit

Historically M-FOM has been defined as the modulator bandwidth, ν_{3dB}, divided by the square of the voltage required to create a relative π phase shift within the device and turn the device from maximum to minimum optical transmission (V_{π})^{2} [41], as follows:

This M-FOM is aptly applied to LiNbO_{3} modulators, typically used in longer haul systems with optical amplification, where the length of the modulator does not change modulator loss much, but mostly impacts bandwidth and drive voltage. For typical silicon photonic plasma dispersion-based devices, changing MZM length not only impacts device bandwidth and drive voltage, but also significantly changes modulator optical loss. As such, there is an optimal MZM design length that gives a maximum relative optical modulation amplitude (ROMA), where the ROMA is simply defined as the optical modulation amplitude (OMA) from the transmitter (that results from the combination of optical loss and modulation extinction ratio created by the MZM from the applied drive voltage) divided by the input laser power going into the modulator. In essence, this can be thought of as taking the MZM output OMA and normalizing it by the optical power at the MZM input. We also note that the ROMA should be measured at a relatively low bit rate so the MZM extinction ratio is not significantly impacted by the MZM bandwidth. This quantity captures both the loss from the MZM and any OMA limitation created by not driving the MZM with a full Vπ. This ROMA definition is equivalent to multiplying the fractional change in the modulator transmission by the fractional linear optical transmission through the modulator [17]:

_{10}{(% trans of ‘0’)/(% trans of ‘1’)} = 10*log

_{10}(0.333/0.666) = −3dB. The $\Delta Tran{s}_{MZM}^{lin}$ quantity is the linear transmission of the MZM such that the MZM loss in dB is given by α

_{MZM}= 10* log

_{10}($\Delta Tran{s}_{MZM}^{lin}$). We note that in [17] we refer to this quantity as the relative transmitter penalty (RTP). The ROMA gives a direct quantitative indication of the impact a transmitter choice has on link budget, which is very useful insight for unamplified short reach optical links. Therefore, in the context of assessing modulators for short reach unamplified optical links, the use of modulator ROMA provides very significant insight.

We have previously shown that, neglecting bandwidth considerations, there is an optimum design point for the expected ROMA from a plasma dispersion MZM, based on the MZM electro-optic phase shifter efficiency-loss FOM (EL-FOM) and peak-to-peak drive voltage (V_{pp}) as shown in Eq. (3) [17],

_{π}L and optical propagation loss, which results in a quantity with units of V-dB.

Using this analytic expression ROMA can be plotted as a function of the derived extinction ratio (ER). When this is done, an optimum design point becomes evident, which is indicative of an MZM design that provides a maximum attainable ROMA [17]. Taking the derivative of Eq. (3) with respect to the MZM ER, setting the result equal to zero, and solving for the resulting MZM ER gives the optimum ROMA attainable for a given EL-FOM and available V_{pp}, the result of which is shown in Eq. (4). Therefore, solving for Eq. (4) gives the extinction ratio at which an MZM will provide the maximum possible ROMA. We note that this approach does not take into account the resulting bandwidth of the MZM, but rather solely focuses on achieving the maximum ROMA for a given V_{pp} drive voltage and EL-FOM.

*a*and

*b*are the input and output field coupling coefficients, ${e}^{-{\sigma}_{1}L}$and ${e}^{-{\sigma}_{2}L}$account for optical propagation loss, where σ

_{1}and σ

_{2}characterize the optical loss, L is the length of the electro-optic phase shifter, and Δϕ

_{1}(

*t*) and Δϕ

_{2}(

*t*) are the relative optical phase changes in each MZM arm, and calculating the optimum ROMA for the considered MZM designs. These two methods gave identical results, which verified our methodology. Figure 1 is a plot of the MZM extinction ratio (left y-axis), and fraction of a π phase shift (right y-axis), that gives the optimum ROMA from plasma dispersion MZMs as a function of the phase shifter EL-FOM assuming a 1.6 V

_{pp}push-pull RF drive, and this plot shows that the maximum ROMA is obtained when the MZM is designed such that it is driven with less than a Vπ drive. This can be seen in Fig. 1, since a value of ‘1’ on the right y-axis represents a π phase shift in the MZM, and the optimum ROMA design is never driven with a full Vπ phase shift. Therefore, plasma dispersion MZM designs with an optimized ROMA do not use a full Vπ voltage swing. We note that optimizing the ROMA from the MZM is a critical design feature in short reach links that do not have optical amplification, and that the amount of phase shift required for a ROMA optimized design depends on the phase shifter EL-FOM. From this discussion, it follows that using Vπ in a M-FOM for such applications is not appropriate since a Vπ phase shift does not provide an optimized design, and the amount of phase shift that does provide an optimized design depends on the EL-FOM of the electro-optic phase shifter.

We suggest that the Vπ metric, which is used in the traditional MZM FOM, be replaced by a relation between the applied MZM Vpp drive and ROMA, since these metrics are of greatest relevance for unamplified shorter-reach optical data links. By substituting the MZM V_{pp} drive divided by the ROMA for the Vπ value, we incorporate the modulator V_{pp} drive, the OMA from the modulator, and the optical loss caused by the modulator into the M-FOM, along with the device rise-fall time (τ) as such:

In this M-FOM we divide the V_{pp}^{2} value by 50 Ω so it represents the power consumption of the traveling wave modulator. Even though many plasma dispersion MZMs have electrode characteristic impedances of less than 50 Ω, we use this value since test equipment used to characterize a given RF driver would have this impedance. So even though the RF drive may have a different V_{pp} within the MZM electrode than that measured in a 50 Ω environment, using the 50 Ω impedance value in the M-FOM will scale the modulator power consumption appropriately, and is a convenient approach from a test and implementation perspective. Also, the V_{pp} value within the MZM electrode is not important for the M-FOM since the ROMA metric captures the impact of both device sensitivity and V_{pp} on the link budget. We also note that when the M-FOM is in the form given in Eq. (6) and Eq. (7), the M-FOM gets smaller as the M-FOM improves. This is in contrast to the M-FOM given in Eq. (1), which gets larger as the M-FOM improves. We choose this convention because we are essentially defining the M-FOM so it will scale with power consumption.

The discussion above focuses on traveling wave MZMs. However, segmented MZMs or ring modulators can be a preferred solution for a given application, which are both lumped-element devices (as opposed to traveling wave devices). The power consumption for a lumped element modulator scales as ¼*C*V_{pp}^{2}, where C is the capacitive load seen by the modulator driver. Therefore, for a lumped-element segmented MZM, or ring modulator, the M-FOM takes the form:

We now touch on the use of modulator rise-fall time versus bandwidth in the M-FOM. Bandwidth measurements in intra-cavity ring modulators can be problematic due to resonant interactions of the modulation sidebands within the resonator, which can give bandwidth results that significantly exceed that expected from the optical cavity lifetime, particularly if the bandwidth is on the order of the free spectral range of the ring modulator [26,42]. Under these circumstances bandwidth measurements in ring modulators become problematic, and the use of rise-fall time is preferred for the M-FOM.

## 3. Mach-Zehnder Modulator Characterization

In this manuscript, we compare two different MZMs using our derived M-FOM. To compare the two MZMs the basic modulator characteristics of rise-fall time, optical loss, and extinction ratio were measured, and the ROMA was calculated, as shown in Figs. 2(a)-2(d).

The two MZMs considered, labeled MZM1 and MZM2, have the same general layout, are designed for operation with ~1.3 μm light, use a push-pull two-electrode design, and an active PN-junction length of 2.8 mm per MZM arm. However, the two MZMs have different PN-junction electro-optic phase shifter designs. In Fig. 2(a) the modulator losses were measured using wafer scale testing of ~40 modulators on each wafer. The rise-fall time measurements in Fig. 2(b) were made with an Anritsu MP1800A pattern generator/error detector using a ‘00001111’ bit sequence driven at 25 Gb/s, which were taken on specific devices. For high speed measurements the MZMs were terminated with a GGB 40 Gb/s probe having a nominal ~25 Ω termination, created by placing a chip resistor in the probe in parallel with a 50 Ω termination cap on the probe input. This resistor termination value was lower than the ~35 to 42 Ω characteristic impedance of the MZM electrodes over the frequency range of interest, but this termination provided higher quality PRBS eyes than a 50 Ω termination. The rise-fall time measurements from the Anritsu pattern generator were found to be in good agreement with bandwidth measurements from these devices that were made on an Agilent N4375B Lightwave Component Analyzer using 1.31 μm light. The Anritsu pattern generator was limited to a ~1 V_{pp} output drive on each MZM arm. For larger drive amplitude we used a Centellax N4951B driver head with a SSB16000 controller to achieve drive signals as large as 3 V_{pp} on each MZM arm. The Centellax drive was not used for rise-fall time measurements because the de-convolved results from this driver did not agree as well with the MZM bandwidth measurements. Visual inspection of the Centellax drive waveform showed signal distortion in its ‘00001111’ output pattern, which we attributed as the root cause of the poor correlation between Centellax rise-fall time measurements and the MZM bandwidths. The extinction ratio measurements in Fig. 2(c) were all taken at 10 Gb/s, since both MZMs gave high quality eye diagrams at this bit rate. The ROMA results in Fig. 2(d) were calculated from the insertion loss and extinction ratio data in Figs. 2(b) and 2(c).

Inspection of Figs. 2(a)-2(d) show that MZM1 has a larger optical insertion loss and faster response time than MZM2. We also note that MZM1 tends to give a slightly larger extinction ratio when larger V_{pp} drives are used as compared to MZM2 These differences in MZM loss, extinction ratio, and response time are a result of having different PN-junction profiles, and also different doping levels within each PN-junction electro-optic phase shifter. These types of tradeoffs can often arise in plasma-dispersion modulators, and so it is instructive to contrast these two specific designs using an appropriate M-FOM.

## 4. Mach-Zehnder modulator link sensitivity measurements

To compare the relative performance of the two modulators, back-to-back link sensitivity measurements at 10 Gb/s and 25 Gb/s, with 1 Vpp, 2 Vpp, and 3 Vpp drive signals, and also at 28 Gb/s with 2Vpp and 3Vpp signals were taken, as shown in Fig. 3(a). The link performance with the two MZMs was measured with a 1.31 μm Eudyna FLD3F7CZ laser diode, the Centellax pattern generator in conjunction with a 40 Gb/s Discovery R402(a)PD receiver, and an Anritsu error rate tester. We were limited to a maximum data rate of 28 Gb/s for our BER testing due to our BER tester. We could not get sufficiently low BER counts with MZM2 using a 28 Gb/s 1 Vpp drive, and so this data was not included. Bit error ratio curves versus the average received optical power for the various drive conditions are shown in Fig. 3(a) for the two MZMs. Although this data is a good indicator of the relative performance of each MZM under the given drive conditions, we note that the two MZMs have different optical insertion losses and this aspect of performance is not conveyed in the data presented in Fig. 3(a). Therefore, to incorporate the differences in MZM insertion loss into the data set, and display the results in a straight forward manner, we subtract theMZM insertion loss (in dB) from the received average optical power (in dBm). Then we normalize all the results relative to error-free-performance (BER = 1 x 10^{−12}) for MZM1. Once this is done, the error-free-performance x-axis value shown by the BER curve for MZM2 directly indicates the change in continuous wave (CW) optical power launched into MZM2 required to achieve the same error free operation as was seen in MZM1, which we call the change in relative transmitter launch power as shown in Fig. 3(b). By plotting the data this way we directly show the required change in continuous wave (CW) optical launch power needed for MZM2 to maintain similar link performance relative to MZM1. Therefore, the curves in Fig. 3(b) represent the relative link penalty between the two MZMs. These results are more easily visualized by simply plotting the differences in TX launch power between the two BER curves from each plot in Fig. 3(b) at a BER of 1x10^{−12}, as a function of drive voltage and bit rate as shown in Fig. 4. Therefore, the error free data (defined as a BER of 1x10^{−12}) displayed in all the plots within Fig. 3(b) are shown in a more concise manner in Fig. 4, which gives the change in optical launch power needed to realize error free operation in MZM2 relative to MZM1 with a back-to-back receiver.

As can be seen from Fig. 4 MZM2 provides a better link budget at 10 Gb/s, since this modulator has lower optical loss, and its rise-fall time is more than adequate for this bit rate. At 25 Gb/s with a 3 V_{pp} drive the two modulators give comparable link performance, which indicates MZM2 creates ~1 dB of link penalty due to its limited bandwidth, but this penalty is compensated for by its larger ROMA. Also, inspection of the 25 Gb/s and 28 Gb/s results in Fig. 4 show that as the Vpp drive increases the performance of MZM2 improves relative to MZM1. This is because the rise-fall time of MZM2 improves at a faster rate than MZM1 as the DC bias is increased from −0.5 V to −1.5 V (see Fig. 2(b)), which helps mitigate the significant negative impact MZM2 has at higher bit rates due to its relatively slow rise-fall time at lower DC biases. Figure 4 also indicates that the faster rise-fall time of MZM1 more than compensates for its higher optical insertion loss for NRZ applications above 28 Gb/s, and so provides better link budget performance. The cross over point, where the two MZMs provide comparable link budget performance is for a ~25 Gb/s data rate with a ~2.5 V_{pp} drive, or a 28 Gb/s data rate with a ~3 V_{pp} drive, which corresponds to when the M-FOM-ratio ~0 dB. These results demonstrate how the trade off in penalties between MZM loss, rise-fall time, and VπL sensitivity can manifest as a function of bit rate and V_{pp} drive.

## 5. Scaling M-FOM with Transmitter-Bandwidth-Related Link Penalty

In considering the applicability of an M-FOM for comparing these two modulators we note that the low-loss slow modulator MZM2 is more appropriate for lower bit rate applications, whereas the higher-loss faster modulator MZM1 is more appropriate for higher bit rate applications. However, the M-FOM given in Eqs. (6 – 8) have no dependence on the targeted bit rate of operation. Since plasma dispersion modulators can show tradeoffs between ROMA and response time, incorporating a bit rate dependence into the M-FOM can significantly improve its utility. One way to achieve this is to replace the linear response time term, τ, in Eq. (6) with a low pass filter function as shown below:

_{BitRate}is defined as the transmitter rise-fall time that creates an additional 3 dB of back-to-back link penalty as compared to a transmitter with optimal rise-fall characteristics for the targeted bit rate and transmission format. The ‘FilterOrder’ term in Eq. (9) is related to how quickly the link budget degrades as a function of the transmitter rise-fall time characteristics. We note that, to the best of our knowledge, the approach of incorporating a low pass filter function into the M-FOM is novel. We suggest this approach to enhance the utility of the M-FOM metric. We also note, it may be possible to use filter functions other than the low pass function as defined in Eq. (9) for this purpose. However, we found the use of the filter function in Eq. (9) gave excellent agreement with our experimental results, as will be further discussed in section 6. For our current example, we choose a transmitter 20%-80% rise-fall time of 40% of the bit-rate bit-period to be that which creates an additional 3 dB of link penalty. Therefore, τ

_{BitRate}= 40 ps for a 10 Gb/s line rate, which has a 100 ps bit period. For reference, 10 Gb/s, 25 Gb/s and 32 Gb/s eye diagrams are shown for the two MZMs with a 2Vpp drive and −1 V DC bias in Figs. 5(a)-5(f). 32 Gb/s was the fastest data rate of operation for our Centellax pattern generator. The inter-symbol interference created by the slower response of MZM2 can be most clearly seen by comparing Figs. 5(c) and 5(f).

To determine which filter order should be used to best fit our experimental results, we empirically tried 2^{nd}, 3^{rd}, and 4^{th} order filter functions within our M-FOM, and we found the 3rd order filter function gave the best results. As previously discussed, we took rise/fall time and bandwidth measurements from each MZM, and found consistent agreement between these device metrics such that MZM-Bandwidth ~{220/(rise-fall time)}, where the MZM-Bandwidth is given in GHz and the rise-fall time is given in picoseconds. When taking these measurements, the MZM bandwidths were acquired with a small signal drive waveform, whereas the rise-fall times were taken with a larger signal drive waveform, and we attribute the good correlation between these measurement techniques as an indication the MZMs were providing high-quality output waveforms when using a large signal drive. We expect the 3^{rd} order filter function will give a good fit to NRZ data given this relation between the (small signal) MZM-bandwidth and (large signal) rise-fall time is well preserved, regardless of what type of modulator is being considered. We use a third order filter function for our non-return to zero (NRZ) M-FOM, with τ_{Bitrate} = 0.4*(bit-period) as previously discussed, due to the good agreement this gave with our experimental results. In this case the M-FOM becomes:

_{BitRate}factor, and filter function order, can be adjusted to reflect how sensitive a given transmission format is to transmitter rise-fall time or bandwidth. For example, it is instructive to compare the channel bandwidth and baud rate requirements for NRZ, duobinary, and pulse amplitude modulated (PAM) transmission formats at the same bit rate [42]. An NRZ signal has a baud rate that is equal to its bit rate, and a relatively large channel bandwidth. Whereas, a duobinary signal has the same bit and baud rate as NRZ, but with about half the channel bandwidth. In contrast, a PAM4 transmission has a baud rate that is half that of NRZ and duobinary, and a channel bandwidth similar to that of duobinary at the same bit rate [43, 44]. Therefore, τ

_{BitRate}will need to be adjusted accordingly for each of these formats. In addition, the filter order required to accurately reflect the degradation in link budget as a function of transmitter bandwidth may also need to be modified if this M-FOM is applied to different transmission formats. While a complete exploration of transmission formats other than NRZ is beyond the scope of this paper, the ability to tailor a given M-FOM to different transmission formats will become increasingly important as advanced transmission formats become more main stream in this application space.

One aspect of system function not yet represented in this M-FOM is the power required to stabilize and control the modulator, which we will refer to as ‘thermo-optic power’ (TOP), since local heaters are often used for this purpose. However, this aspect of modulator power consumption can be incorporated into the M-FOM by adding the maximum modulator control and stabilization power needs to the V_{pp}^{2}/50Ω or ¼*C* V_{pp}^{2} term, as shown below:

## 6. Modulator Figure of Merit Comparison to Measurements

We note that the data shown in Figs. 3(a), 3(b), and 4 represent a ‘special case’ circumstance for our M-FOM, where we compare two MZMs when they are being driven with the same V_{pp} drive conditions. Also, the M-FOM given in Eq. (10) is constructed such that its value at a BER of 1x10^{−12} is proportional to the required laser power input into the MZM for error-free back-to-back link operation, which is the same performance metric used to plot the data shown in Fig. 4. To better illustrate this point we calculate the ratio of the M-FOMs in decibels for the two modulators used in Fig. 4. To make this comparison the M-FOM-ratio = 10*log_{10}{(MZM1_{_}FOM)/(MZM2_FOM)} is calculated at the various data rate and drive voltage conditions investigated. This also enables us to investigate the utility of our derived M-FOM for predicting the measured relative MZM performance shown in Fig. 4. A direct comparison of the M-FOM-ratio calculations to the measured relative link penalty data is presented in Fig. 6, and shows that the two scale quite closely. This result is significant because it indicates that our novel approach based on this M-FOM not only gives a qualitative indication of which modulator is more appropriate for a given application, but also gives a direct quantitative estimation of how much relative link penalty would result if either MZM were used. This stands in distinct contrast to the traditional LiNbO_{3} MZM FOM, which only provides a general qualitative indication of which modulator is better. This adds a new level of utility to our M-FOM, changing its use from just a qualitative indicator of relative modulator performance into a quantitative tool that system engineers can use to quickly estimate how much link penalty/benefit will result from a given modulator choice.

## 7. Discussion

We note that when the two MZMs are driven with the same V_{pp} drive, then the V_{pp} term cancels when the ratio of M-FOMs is taken, as shown below in decibels:

Our proposed M-FOM can also be used to compare modulators with different V_{pp} drives. In this case, the M-FOM-ratio becomes a general indication of changes in transmitter power consumption, but is no longer directly relatable to changes in CW laser power requirements for a given link budget. We have proposed the M-FOM forms given in Eq. (10) and Eq. (11) since it makes the M-FOM scale with link laser power needs under these conditions, which is useful insight for system design.

## 8. Summary

We have presented an M-FOM that allows one to compare different types of MZM transmitters using metrics that are most significant to system performance for CMOS compatible modulators in short reach links with no optical amplification. We introduced a bit-rate dependent aspect to the M-FOM calculation, which helps highlight basic trade-offs often encountered with plasma dispersion MZMs, and how drive conditions and data rate can influence what MZM type may be preferred for a specific application. We presented a novel approach of using the ratio of M-FOMs from two different modulators, using the same V_{pp} drive conditions, to get a direct quantitative indication of the resulting changes in required CW laser power for a given optical link if either MZM were used. In addition, we have suggested an M-FOM form that, for the first time, allows a direct comparison of ring modulators to MZMs. Finally, we have proposed a bit rate dependence to the M-FOM that allows tailoring for different transmission formats, which will be of increasing relevance as advanced transmission formats become more main stream in this application space.

## Acknowledgments

The authors acknowledge Jon Proesel, Tymon Barwicz, Marwan Khater, Jens Hofrichter, Folkert Horst, Carol Reinholm, Frederick Anderson, Michael Nicewicz, Yan Ding, Kate McLean, Michel Paradis, Crystal Hedges, Doris Viens, Robert Leidy, Bruce Porth, Chip Whiting, Andrew Stricker, Bert Offrein, Mounir Meghelli, Ken Giewont, Natalie Feilchenfeld, Wilfried Haensch and the rest of the IBM Research and GlobalFoundries Microelectronics Division teams for their important contributions to this work, and the CMOS9WG Silicon Photonics technology development program.

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