1. Introduction

The silicon micro-ring resonator (MRR) has gained significant attention for use in an energy-efficient and high-bandwidth photonic system and is ideally suited for both inter- and intra- data center communication [1–3]. The small footprint of the resonator (a few hundred µm²) allows multiple MRRs to be cascaded on a single bus to form an elegant and compact wavelength-division-multiplexed system [4–6]. Compared to other non-resonant modulators, the efficiency of the MRR is dramatically enhanced owing to its resonant nature. However, for the same reason, the MRR is susceptible to thermal fluctuation that can cause an undesired resonance variation due to the strong thermo-optic effect present in silicon waveguides [7]. For example, in a highly clustered system, a transient thermal load in an adjacent channel or a slow ambient temperature drift can lead to an MRR modulator failure. Therefore, resonance control is necessary to insure the stability of the MRR modulator in a real-word deployment. Several methods have been reported in the literature aimed at an integrated solution for resonance control [8–11]. The most common approach uses a power detector and an integrated heater that can form a closed-loop via proportional-integral-differential (PID) feedback [12]. Other non-PID based approaches exist such as the homodyne method reported in [13].

Figure 1 summarizes the principle of some possible feedback-control geometries. In Fig. 1(a), the feedback signal (i.e., photocurrent) is provided by a Ge photodetector at the drop-port of the MRR. For a stable single wavelength input, the photodetector monitors the power variation owing to the resonance change of the MRR. The PID feedback-control is then applied to compensate for drift using the heater power for stabilization. In Fig. 1(b), a similar control method is presented but a designated photodetector placed inside the ring is used to measure the resonant power in order to provide the feedback signal [14,15]. Figure 1(c), shows the geometry used in this work. A photocurrent is measured using the p-n junction formed during the fabrication of the modulator. This photocurrent arises due to residual lattice defects following junction formation via ion implantation and rapid-thermal-annealing [16]. It is well known that lattice defects provide efficient absorption when deliberately introduced into a silicon waveguide and the fabrication of photodetectors using such defects has been demonstrated [17–19]. High-speed detection using residual processing defects has also been demonstrated, including in a resonant structure [20,21]. In the present case, we directly measure the defect-mediated photocurrent from the p-n junction via a source-meter at the DC end of a Bias-T during high-speed operation. The advantage of this method compared to the other two geometries in Fig. 1 can be clearly seen. The p-n junction can be designed to maximally cover the ring resonator, thereby increasing the modulation efficiency for the depletion-type MRR. Further, no excess optical loss is introduced to the modulator over the intrinsic loss associated with the fabricated device. Melikyan et al. proposed a similar device geometry to that reported here in 2017 [22]. However, the mechanism for photocurrent generation in that case relies on two-photon-absorption (TPA). The drawback for TPA is that a resonator with very high Q (> 20,000 in ref [22]) together with a relatively large optical input power are required to generate sufficient photo-carriers. The high-Q requirement is particularly limiting because it leads to a maximum cavity bandwidth of approximately 9.5 GHz. Moreover, the non-linear nature of TPA results in a potentially large change in photocurrent for a small variation in input optical power. In contrast, the defect-mediated method shown here is a linear process, requires much lower optical input power, and is essentially independent of the Q-factor of the resonator. Thus, the proposed method is compatible with bandwidths of many tens of GHz. Further, the linear characteristic of this method is advantageous for compensating any variation in optical input power.

 

Fig. 1 (a) Resonance control in the MRR modulator using a drop-port tap. (b) Resonance control using a designated extrinsic defect-mediated photo-detector, integrated onto the ring resonator. (c) Proposed resonance control using the intrinsic defect-mediated photocurrent.

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In section 2, we demonstrate resonance control using the photocurrent intrinsically generated in a depletion-type p-n junction from a high-speed MRR modulator designed with a deep-notch. The dependency of the photocurrent on input power is shown to be linear in nature. In section 3, a computer-controlled digital PID loop is described and the control algorithm is discussed. High-speed measurements utilizing eye-diagrams and back-to-back bit error rate (BER) measurements are shown to verify the control capability. A solution to overcome the instability of the PID control that results from optical input power fluctuation is proposed based on the linear property of the defect-mediated photo-absorption. Consequently, we suggest that the current work described in this paper provides a route to silicon photonic circuit transmitter fabrication from which all germanium integration (most commonly used for power monitoring) can be removed.

2. Device fabrication and static characterization

The MRR modulator was fabricated using 220 nm SOI through the multi-project-wafer shuttle service at A*star, IME, Singapore. The all-pass ring resonator with a 12-µm radius has a depletion p-n junction coverage of 88% of the perimeter. The waveguide dimension is 220 nm (height) $\times$ 500 nm (width) with a 90 nm slab providing electrical contact. The nominal doping concentrations of the p-dopant and n-dopant are 5 $\times$ 10¹⁷cm⁻³ and 3 $\times$ 10¹⁸cm⁻³, respectively with a doping offset of 75 nm towards the n-doped region so that the majority of the waveguide is p-doped. The junction design provides for efficient use of the plasma dispersion effect owing to an increased overlap between the optical mode and the depletion region [23]. We note that it has been shown previously that lattice defects in p-doped silicon produce a significantly higher photo-absorption than n-type silicon due to a larger availability of the neutrally charged defects [24]. As a result, the p-n junction design in our work is beneficial in design for carrier generation. The total cavity loss due to carrier absorption in the unbiased ring was estimated to be 35 dB/cm. Heavily doped contact regions were located 800 nm away from the either side of the waveguide edge to avoid parasitic absorption of the signal within the ring. The gap between the ring and bus was 265 nm (based on FDTD simulation) to match the coupled power to the cavity loss so that the critically coupled condition was anticipated. Both the junction offset and the coupling gap were varied through multiple device designs in order to counteract fabrication variation.

The optical spectra measured using a tunable laser source under different reverse bias (ranging from 0 to −4 V) are shown in Fig. 2 for two selected modulator designs with different junction offsets and gap distances (thus different Q-factors). The notch depth (>25 dB) and DC modulation efficiency (>17 pm/V) as seen in Fig. 2(a) validate the design optimization with the realization of an almost critically coupled modulator. The full width at half maximum (FWHM) at −2 V bias for device A is approximately 0.15 nm and the Q-factor is approximately 10,000, derived from the ratio of resonance and FWHM. The free spectral range (FSR) was measured to be 8.3 nm. Thus, the finesse, defined as the ratio of FSR and FWHM, is calculated to be 55.3. As the tunable laser source was swept, a source-meter provided the junction reverse bias through a pair of DC probes and simultaneously recorded the photocurrent that results from the intrinsic sub-bandgap absorption, the results of which are also shown in Fig. 2. The photo-detection benefits from a large optical power build-up in the ring resonator. At resonance, the build-up factor (BUF) is proportional to the finesse (BUF = finesse × 2/π) [18] under the assumption of a critically coupled condition and calculated to be 36.9 for a finesse of 55.3. For a relatively low optical input power, photocurrent can be measured even in the absence of a reverse bias. The peak photocurrent increases proportionally with increases in reverse bias due to the improved carrier collection efficiency of the device. The photocurrent measured for device B (with Q-factor of approximately 7500) is lower than that measured for device A mainly due to two reasons. Firstly, lower Q-factor results in a smaller finesse that consequently reduces the BUF. Secondly, the junction offset in device B does not provide an optimal overlap between the center of the optical mode and the center of the depletion region. However, the photo-absorption mechanism, as well as the resonance control for this paper, would be applicable in both cases A and B. We selected device A for the remainder of the experimental work outlined here.

 

Fig. 2 MRR spectra under different reverse bias from 0 V to −4 V (left) and measured photocurrent (right). Intensity refers to light output from the chip and includes coupling and transmission loss. (a) Device A: MRR modulator with junction offset 75 nm and gap 265 nm. (b) Device B: MRR modulator with junction offset 0 nm and gap 235 nm.

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An integrated resistive heater located above the ring waveguide provided a local heating mechanism. To obtain the heater efficiency, optical spectra with zero electrical bias on the p-n junction were obtained for a range of heater powers, with the results plotted in Fig. 3(a). The resonance shift versus heater power was extracted and through a linear fit as shown in Fig. 3(b), the heater efficiency (defined as resonance shift per mW) was determined to be 56.8 pm/mW. This calculation includes the parasitic resistance associated with the wire bonding of the integrated heater to a carrier PCB.

 

Fig. 3 (a) Measured MRR spectra for different heater powers. (b) Extracted resonance shift with respect to the applied heater power using a linear fit.

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In order to study the linearity of the photo-absorption mechanism described here (and thus to provide evidence for its origin), the photocurrent was first measured against a range of on-chip (optical) power. The laser wavelength was fixed at 1554 nm (red-side of the resonance indicated by Fig. 3(a)) so that addition or removal of a bias to the heater could produce a red or blue shift respectively. A sub-mounted temperature controller (TEC) maintained the temperature of the chip at 25 °C. The photocurrent was recorded at the DC port of the Bias-T when the heater power was increased from 0 mW to 60 mW to ensure that the laser wavelength could scan across the entire resonance notch. The laser power was varied from 0.2 mW to 2.4 mW in steps of 0.2 mW. Furthermore, we observed that the insertion losses (defined as the laser power at off-resonance wavelength minus the received optical power at off-resonance wavelength) obtained for different laser powers were essentially constant (17.5 dB), indicating any TPA effect was negligible in the bus waveguide and the on-chip power was in fact linearly varied. The photocurrent versus reverse bias is shown in Fig. 4(a). Values for the on-chip power were calculated by subtracting the input grating coupler loss and the propagation loss from the laser output power. In Fig. 4(b), a 2^nd-order polynomial fit of the photocurrent curve at a reverse bias of −4 V is performed, and used to separate the photocurrent into the linear term and the quadratic term (i.e. those resulting from the defect-mediated photo-absorption and TPA-induced photo-absorption, respectively). The responsivity of the linear photo-detection for this specific bias (−4 V) is extracted to be 0.17 mA/W. In Fig. 4(c), the ratio of the linear term and the quadratic term is shown, allowing us to deduce that the defect-mediated photo-absorption (linear) should be the dominant detection mechanism when the on-chip power is lower than 0.46 mW. As the on-chip power increases, TPA-induced photo-absorption begins to dominate. In the work that follows regarding resonance control, we maintain on-chip power to a level that ensures the photo-detection is dominated by the linear absorption component.

 

Fig. 4 (a) Measured photocurrent versus the on-chip power estimated at the ring resonator input for different reverse bias (ranging from −1 V to −6 V). (b) A 2nd-order polynomial fit of the photocurrent curve at reverse bias −4 V, separating the photocurrent components that result from the linear-absorption and non-linear-absorption. (c) Ratio of the linear term (0.17P) and quadratic term (0.37P²) for different on-chip power. (d) Measured photocurrent versus the heater power for two data rates: 7.5 Gb/s and 12.5 Gb/s RF signals with 2 V peak-to-peak voltage and −2 V DC offset.

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The high-speed performance for the MRR modulator under test is similar to that demonstrated for a 10 Gb/s intensity-modulated system previously reported by us [25]. The Bias-T was used to combine the RF signal and DC bias and the modulated electrical signal was delivered to the ground-signal-ground pads of the device through a high-speed RF probe. The measured photocurrent at the DC port of the Bias-T should correspond only to the DC-level intensity in the ring regardless of the bit rate. To confirm this, we conducted an experiment to study the influence of the RF drive on the generated photocurrent. The peak-to-peak voltage for the RF signal was set to 2 V and the reverse bias was maintained at −2 V to insure the junction remained in a reverse bias condition during operation. The measured photocurrent when the heater power was increased from 0 mW to 60 mW for a range of on-chip input powers is shown in Fig. 4(d) for 7.5 Gb/s and 12.5 Gb/s non-return-to-zero (NRZ) signals. The measured photocurrents are almost identical, indicating that there is no discernable influence from the RF drive signal, a consequence of good electrical isolation between the DC and RF ports of the Bias-T.

Ideally, initial conditions such as the reverse bias and the on-chip input power should remain unchanged during high-speed operation so that the measured defect-mediated photocurrent, such as those shown in Fig. 4(d), will relate to the optical transfer of the MRR modulator. Resonance locking is achieved by maintaining the defect-mediated photocurrent intensity via feedback control (such as a PID loop) to a set-point current that corresponds to a specific resonance detuning. Figure 5 gives an example of the measured photocurrent with 0.32 mW on-chip power and different optical eye-diagrams with 2 V peak-to peak voltage obtained while the resonance was locked such as to provide different photocurrents. The chip temperature was stabilized by the sub-mounted TEC and the set-point current was tuned manually via the integrated heater. Modulation can either occur at the blue-side or the red-side of the resonance, which will result (among other outcomes) in an opposite chirp. However, it should be noted that the red-side modulation would suffer more from self-heating effects that can be readily seen by the skew appearing in the photocurrent plot in Fig. 4(d); further these effects would become more dramatic as the input optical power increases. The drawback of an excessive self-heating effect is that the resonance is more difficult to stabilize (partially also due to a sharper slope of the transfer), thereby leading to a certain amount of relative eye-closure (compared to blue-side modulation) as demonstrated in Fig. 5.

 

Fig. 5 Modulation regimes for the MRR and eye-diagrams at different photocurrents for a 12.5 Gb/s NRZ modulation.

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3. Resonance control algorithm and BER measurement

Figure 6 shows the experimental setup for control measurement and the computerized control algorithm. The source-meter and heater power supply formed a closed feedback loop, controlled by a computer. The experimental conditions were the same as those used to generate the data in Fig. 5. In addition, an off-chip optical power meter was used to tap a small portion (10%) of the output optical power to insure that the on-chip input power remained constant. In our set-up, the primary causes for a change of the on-chip input power is fiber drift from the optimum coupling location. During operation, we typically observe a 1 dB variation in on-chip power for experiments that require many minutes of operation.

 

Fig. 6 Resonance control experimental measurement setup and algorithm.

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To implement the control algorithm, the program first sweeps the heater power from a pre-defined minimum P_min (0 mW) to a maximum P_max (60 mW) to record a defect-mediated photocurrent such as the one shown in Fig. 5. Then, a set-point current I_sp is chosen for a desired modulation condition, which depends on the slope (blue or red) of the ring transfer to be modulated. The heater power is coarsely tuned either from P_min to P_max for red-side modulation or from P_max to P_min for blue-side modulation. Once the measured photocurrent approaches I_sp, the PID loop is turned on for fine tuning and eventually locks the resonance at I_sp. The period for the control-loop cycle is 1 ms, limited (in our case) by the communication delay between the computer and the control apparatus.

Confirmation of the slope type (red or blue) is achieved by providing a very small power change to the heater and measuring the resulting current change in the detector (for example, if the modulation is on the blue side, increasing the heater power will reduce the photocurrent). Maintenance of the optical input on one or other of the slopes during operation is essential to avoid an unstable system (and thus thermal runaway). In addition, the off-chip tap power is used to monitor the variation of the input power. If this is larger than 2 dB (assuming the losses at input coupling and output coupling are similar), the control loop is forced to halt to prevent a situation where the photocurrent is lower than I_sp.

Bit-Error-Rate (BER) measurements were used to evaluate the control algorithm. Several BER curves for a 12.5 Gb/s signal under different operating conditions are plotted for comparison in Fig. 7(a). I_sp was set to 180 nA on the blue-side of resonance to avoid excessive self-heating, while other driving conditions remained the same as those used to generate the data for Fig. 5. We first tested the BER when either the sub-mounted TEC control or the on-chip control was disabled. The difference between the two BER curves is very small, meaning that the on-chip PID control is as stable as the sub-mounted TEC control (which of course is also a PID control). We then obtained the BER when both controls were disabled. The measured BER was significantly degraded, resulting from an uncontrolled MRR modulator exposed to the variable lab environment. Lastly, we intentionally created a slow temperature variation of ± 1°C on the sub-mount using the TEC and measured the BER with the on-chip control on or off. Eye-diagrams were captured at random times with each eye-diagram based on 50 sweeps. With the on-chip control disabled, the eye-diagrams were completely distorted because of the large resonance drifting, leading to an immeasurable BER. However, when the on-chip control was implemented, the eye-diagram maintained the shape at the set point relatively faithfully due to successful locking. The BER curve exhibited a small power penalty of around 1 dB compared to a condition of TEC enabled thermal stabilization. The degradation was related to variation of the fiber-to-chip coupling (observed via our off-chip tap) when the sub-mount was heated and cooled.

 

Fig. 7 (a) Measured BER of a 12.5 Gb/s rate for several conditions (b) Recorded error currents. Associated eye-diagrams are also plotted.

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We also recorded the error current (I(kΔt)-I_sp) in the PID loop at each discrete time kΔt in order to evaluate the previous analysis. A series of error currents recorded within 2 minutes for different conditions are plotted in Fig. 7(b). When the on-chip control is enabled (green and red lines), the error current is centered at the zero level (shown as the black line) over time, which indicates a functional and stable PID loop that maintains the set-point current. When both controls are disabled (purple line), the error current simply reflects a temporal change of the photocurrent and in fact the error current slowly walks off the zero level, indicating a resonance change that was not compensated. When the temperature variation was induced and the on-chip control is off (black line), the error current records how large the deviation is without a feedback control. We can estimate the peak current variation with ± 1°C temperature fluctuation to be 40 nA. The maximum thermal tuning power required to stabilize the resonance at the set-point current (180 nA) is approximately 0.5 mW, which is deduced from Fig. 5. The heater resistor is 1400 Ω, thereby giving the maximum thermal voltage swing to be 60 mV. We note that the intentional temperature variation in our experiment is modest. In our case, the experimental set-up limits it such that increasing the variation beyond ± 1°C would cause an unacceptable misalignment of the input fiber and the chip. However, there is no fundamental reason as to why the technique shown here could not be applied to compensate more considerable variation for a packaged system with permanent fiber attached.

A disadvantage associated with resonance locking via PID control is that the set-point current depends on the on-chip power; whereas a true resonance-locking scheme is required to maintain the detuning between the resonance and the laser wavelength. The on-chip input power can readily vary due to unavoidable performance degradation (such as a laser power change or laser to chip coupling efficiency change) over time. A subsequent calibration for the photocurrent could find a new set-point current that relates to the same detuning, but a re-calibration is disruptive to the operation and thus is undesired. We thus suggest a method to alleviate this problem. The set-point current is multiplied by a normalization factor, β, mathematically defined as P(kΔt)/P(0) where P(kΔt) is the measured on-chip input power at each discrete time step kΔt in the PID loop and P(0) is the initial on-chip input power in the PID loop. In this way, the influence of the input power variation can be negated by the normalized set-point current that always corresponds to the same detuning. This is only true when the on-chip input power and the photocurrent have a linear dependency, which is the case for the detection mechanism described in this paper. This method requires a means to measure the on-chip power, likely prior to the modulator, via a tap-port terminated with an integrated detector. In order to maintain our Ge-free process, the detector could be formed through an extrinsic defect mediated detection mechanism [8] as previously reported by us and other groups.

4. Conclusion

In this paper, we have proposed and experimentally demonstrated a ring resonator control method using the intrinsic defect-mediated photocurrent of a p-n junction as a feedback signal. The generated photocurrent from the reverse-biased junction negates the need for a ring drop port and germanium photodetector or for sacrificing a portion of the ring resonator circumference to make an extrinsic defect-mediated photodetector. The MRR modulator used in this work was optimized to provide a critically coupled condition that provides a large power build-up in the ring. The digital PID loop was designed and evaluated by BER measurements for a 12.5 Gb/s signal, and included functional blocks in order to prevent catastrophic failure. The BER results were obtained as essentially error free when the on-chip feedback control was enabled, even under an intentionally induced temperature fluctuation. The proposed method can be transferred into an integrated solution with the capability to achieve a tap-free resonance control.