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We show enhanced optical bistability induced by free carrier absorption from junction doping in substrate-removed silicon ring modulators. Such linear thermal effects dominate the loss in high-speed depletion silicon ring modulators. Optical bistability was observed with about 100 μW of input optical power. We further show that such thermal interactions causes data-dependent ring resonance shifts, and consequently severely degrade the data modulation quality at low speeds. The frequency response of this effect was measured to be about 100~200 kHz.
©2012 Optical Society of America
1. Introduction
Silicon photonic WDM links are viewed as a promising improvement to chip-to-chip communications in future processors and computing systems that require interconnects with high energy efficiency and bandwidth density [1,2]. Among many potential candidates, the silicon microring resonator has emerged as a key building block to enable such scalable WDM interconnects efficient in both area and power consumption [3]. Many of the recently proposed intra/inter-chip interconnect network architectures are based on ring resonator devices. High-index contrast silicon waveguides with low loss allow the fabrication of ultra-compact ring resonators with high Q. Many different types of devices have been demonstrated based on ring resonators [4–8], among which the microring modulator is a very critical component in dense and efficient silicon photonic WDM links and networks [9–11].
Silicon, as an indirect band gap material, has a very weak electro-optic effect. However, strong transverse confinement of light in submicron silicon waveguide can be further enhanced using resonator structures such as ring resonators. High-speed voltage modulation across a reverse-biased PN junction embedded in the ring waveguide, therefore, allows for fast, low-voltage modulators with low capacitance [10,11]. Such ring modulators are hence better suited for low power, dense WDM photonic links [12,13]. Such strong light confinement can, inadvertently, also lead to nonlinear effects in silicon waveguide at relatively low power levels. Both thermal effects [14] and carrier [15] induced optical bistability have been reported in silicon ring resonators with total input optical power of larger than 200 μW and 3 mW, respectively. Special waveguide design and device thermal impedance control can even balance the two photo absorption (TPA) induced thermal resonance shift and blue shift from free carrier dispersion [16]. A detailed study on an undoped high Q (62500) ring resonator [17,18] further showed that thermal contributions arise from surface state absorption, two photon absorption(TPA) and free-carrier absorption (FCA) from carriers excited by TPA with input power of 0.3 mW. A general model for the thermal broadening of the cavity linewidth was also described in [18]. Such nonlinear behavior leads to distortions that can degrade the performance of the modulators.
In a reverse-biased depletion ring modulator, FCA from the doped P and N area dominates the ring loss. The absorption leads to phonon creation, resulting in heating and consequently a thermal refractive index change in the waveguide. In this work, we experimentally demonstrate optical bistability dominated by FCA in doped microrings at relatively low power levels. We further demonstrate that such optical bistability is enhanced in a ring modulator with local substrate removal designed for high tuning efficiency. This self-heating from FCA causes resonance run-away and also interacts with ring modulator data modulation, the impact of which is experimentally studied. Potential solutions to mitigate such link impairments are discussed.
2. Optical bistability induced by self-heating from FCA in a depletion ring modulator
2.1High-speed tunable depletion ring modulator
A high-speed depletion ring modulator with good performance requires careful design of both the ring waveguide and the embedded PN junction [12]. Our ring modulator design was based on the Luxtera/Freescale 130nm SOI CMOS process. A ring radius of 7.5 μm was chosen in order to achieve a free spectral range (FSR) of ~12.8 nm to enable a 200GHz-spacing synthetic resonant comb structure uniformly covering the entire C-band [19]. We optimized ring waveguide structure to enable a small ring size with low bending loss. The ring waveguide is designed with 380 nm width, 220 nm etch depth and 80nm Si slab thickness, as shown in Fig. 1(a) .
Fig. 1 A tunable high-speed depletion silicon ring modulator. (a) Cross-section diagram of the ring waveguide high-speed section. (b) Photograph of the ring modulator.
A symmetric lateral PN junction is employed in the high-speed modulation waveguide. The doping density design is critical for modulator performance. The PN junction doping determines the depletion width and overlaps with the center of the optical mode. Hence, it has significant impact to the modulation depth and optical loss. The optical loss, in turn, determines the quality factor of the ring and the photon-lifetime-limited modulation bandwidth. Under the critical coupling condition, the photon-lifetime-limited modulator bandwidth is proportional to the waveguide loss, fO = cα/(πng), where c is the light speed in vacuum, α = αdop + αother is the effective waveguide loss, and ng~4.0 is the optical group index. αother introduced by waveguide bending, scattering, etc., is estimated to be about 6dB/cm for the waveguide we designed. Hence to achieve a desired photon-lifetime-limited modulation bandwidth, an appropriate junction doping density has to be selected to introduce the right amount of αdop. For photon-lifetime-limited modulation bandwidths of 10, 15 and 25 GHz, doping losses of about 12, 21, and 39 dB/cm are repectively required. For instance, a doping density of 3x1018 cm−3 was chosen for a 25Gigabits/s ring modulator design [20].
Although a ring resonator has periodic resonances, it is a narrow-band device with its resonance locations very sensitive to manufacturing tolerances and ambient temperature change. We integrated a doped silicon resistor directly onto the ring waveguide for efficient modulator wavelength thermal tuning. Two-thirds of the ring is made as a PN diode for high-speed modulation, while the upper-right 25% is N-type doped as a Si resistor for thermal tuning. The remaining 8% is undoped and used for isolation between the PN junction section and the doped resistor section.
A picture of a fabricated tunable depletion ring modulator is shown in Fig. 1(b). It demonstrated good performances in close agreement with the design targets. Figure 2(a) shows the spectra of one of its resonances around 1549 nm with good extinction ratio, from which we measured a loaded Q of about 8000. As expected, the modulator works at high-speed up to 25 Gbps. A clean open optical “eye” diagram for PRBS 231-1 data at 20 Gbps is shown in Fig. 2(b) with a measured dynamic extinction ratio of >7 dB.
Fig. 2 25G depletion ring modulator performance. (a) Spectra of one measured resonance of the ring modulator, indicating a Q of about 8000; (b) Optical “eye” diagram of the modulator for 20 Gbps PRBS 231-1 data modulation.
The thermal tuning efficiency of the microring resonator has been tested by applying tuning power to the integrated Si resistor. The Si resistor has a resistance of about 750Ω. The resonant wavelength versus tuning power is plotted as diamonds with solid blue line in Fig. 3(a) , showing a tuning efficiency of 0.17nm/mW. With a backside local substrate-removal technique [21,22], its tuning efficiency can be improved by an order of magnitude. Figure 3(a) shows an improved tuning efficiency of ~1.02 nm/mW (6x) for a ring modulator with ~105μm × 105μm backside pit opening. A picture of the locally substrate-removed device with an etch pit window size of about 105μm × 105μm is shown in Fig. 3(b), taken from the substrate side of the chip through the buried oxide (BOX) layer.
Fig. 3 Wavelength tuning efficiency improvement using back side substrate removal technique. (a) Tuning efficiency before (diamonds, blue line) and after (squares, pink line) substrate removal; (b) A picture of substrate removed tunable ring modulator taken from the substrate side with an etch pit window size of about 105μm × 105μm, seeing through the BOX layer.
2.2 Optical bistability induced by self-heating from FCA
As discussed above, the FCA loss from PN junction doping dominates the total round trip loss in a high-speed depletion-mode ring modulator. The absorbed optical power creates heat and results in a thermally-induced ring waveguide refractive index change. Because the optical field circulating inside a ring resonator is significantly enhanced due to resonance, the index change can be substantial. At resonance, the field enhancement factor (FE), defined as the ratio of field intensity inside of the ring and in the input bus waveguide, is about 1/κ, where κ is the coupling coefficient between the bus waveguide and the ring waveguide. Figure 4(a) shows the plot of the corresponding resonator Q and resonance power enhancement factor in the ring versus targeted photon-lifetime-limited bandwidth.
Fig. 4 (a) Q (blue line) and corresponding power enhancement factor (red line) in photon-life-time-limited rings; (b) Maximum heat power generated from junction doping FCA for ring modulators with different photon-lifetime-limited bandwidth at 1mW of input optical power.
Assuming 1 mW of power is input to the ring modulator, and all absorbed optical power is converted to heat, Fig. 4(b) plots the heating power due to absorption in a doped ring modulator with different photon-lifetime-limited bandwidth. As explained above, the photon-lifetime-limited modulator bandwidth is proportional to the waveguide loss. Higher ring modulation speed requires a lower Q, and consequently higher effective loss. Due to limited waveguide loss, a higher junction doping density, therefore, has to be selected to achieve the desired total loss. At the same input power of 1 mW, we observe a monotonic increase of heating power in the ring modulator with respect to photon-lifetime-limited bandwidth. The figure also indicates that a heating power comparable to the input optical power can be generated from the doping absorption. For comparison, one can also calculate the TPA loss and the free carrier density generated by TPA under the same conditions. Using a TPA coefficient of 7.9 × 10−12 m/W [23], we obtained a nonlinear absorption coefficient in the ring of less than 0.2 dB/cm for 10GHz to 30GHz depletion ring modulator designs with 1 mW of input optical power, which is orders of magnitude smaller than the linear FCA. Consequently, the carrier density produced by TPA would be lower than 1 × 1014cm−3. Hence, the nonlinear absorptions in such high-speed depletion ring modulators are negligible.
The thermal refractive index change from heating induced by the doping absorption will cause a red-shift in the ring resonance wavelength. This effect was clearly observed when we used a tunable laser to scan through one resonance of a 25G ring modulator with different powers, as plotted in Fig. 5(a) . With an input optical power of −9.8dBm to −3.8dBm, we observed a ring resonance shift of 68 pm, and a slight resonance distortion.
Fig. 5 Measured ring resonance shift induced by junction doping absorption for a 25G depletion ring modulator with input power from −9.8dBm to −3.8dBm before substrate removal (a), and from −13.8dBm to −8.8dBm after substrate removal (b). Optical bistability observed at 100 μW input power from substrate removed ring modulator.
Local substrate removal techniques improve ring tuning efficiency. Effectively, more resonance wavelength shift can be achieved with less heating power. This enhancement also applies to the heating due to absorption because of increased ring thermal resistance. Figure 5(b) shows the self-heating enhancement from the same ring modulator with substrate removed, measured by wavelength scan using a tunable laser at different input power levels ranging from −13.8dBm to −8.8dBm. A maximum resonance shift of 102 pm was observed with significantly reduced input power. The measured enhancement compared to Fig. 5(a) is about 6x which agrees very well with the tuning efficiency improvement shown in Fig. 3(a). Both the on-resonance output power (Fig. 6(a) ) and resonance shift (Fig. 6b) shows linear correlation to the input power, as depicted in Fig. 6, confirming the dominance of the self-heating from FCA.
Fig. 6 Both on-resonance output power (a) and resonance wavelength (b) show linear correlation to the input optical power.
The distortion in resonance shown in Fig. 5(b) represents evidence of optical bistability [14–18] that could permit easy access to all-optical functionalities such as switching, memory, etc. Enhanced by substrate removal, such optical bistability appears with only about 100 μW of input power, while typical silicon photonic WDM links would require 1mW or more input optical power.
More direct evidence of ring bistability is the observation of a hysteresis loop in the transfer function (output power versus input power) of the ring resonator [14,15]. We experimentally verified such hysteresis by modulating the input laser power at a fixed wavelength while simultaneously monitoring the output power from the ring using a real time oscilloscope. The measurement results are shown in Fig. 7 , where the top green waveform X represents the input light modulation from about 30μW to 300μW, the bottom yellow waveform Y is the ring output power measured using a receiver whose output is reversed in sign, and the middle is X versus Y. The left graph is a screen shot of the waveforms when the laser wavelength is tuned to the right side away from the ring resonance, as A position shown in Fig. 2(a), while the right graph is for B position with laser wavelength close to the ring resonance. When the laser wavelength is positioned away from the ring resonance, the ring interacts little with the input laser. We observed clear linear correlation between the input signal and the ring output signal. When the laser wavelength is set closer to the ring resonance, as in B, the ring interacts strongly with the input laser light. The ring resonance is no longer stable because it depends on the amount of optical power circulating inside of the ring as discussed above. We observed a clear hysteresis loop of the ring output as we moved the input laser power up and down, indicating an optical bistability effect.
Fig. 7 Hysteresis loop (right graph) due to optical bistability observed when laser wavelength approach ring resonance. Top green waveform X represents the input light modulation; the bottom yellow waveform Y is the ring output power measured using a receiver whose output is reversed in sign; and the middle is X versus Y.
3. Impact to high-speed digital data transmission
As discussed above, the optical field circulating inside the ring affects the ring resonance due to FCA from PN junction doping. Hence, when using ring modulators for intensity modulation, the optical data itself will cause additional ring resonance shift on top of the shift from the applied electrical modulation signal. This data-dependent ring response could severely impair the quality of data modulation with symptoms like unstable “1” and “0” levels, and significantly reduced ER, especially for substrate-removed ring modulators with enhanced thermal tuning efficiency. Fortunately, it’s a thermal effect. Although the absorption happens instantly, it takes time for the absorbed energy to heat up the waveguide and change its refractive index. It has little impact to data modulation faster than the ring thermal response.
The thermal response time measurement of a substrate-removed microring modulator indicated a 10-90% rise time of about 3 μs, and fall time of about 2 μs, as shown in Fig. 8(a) . The estimated 3dB bandwidth for ring thermal response is about 100~200 kHz. When modulated at data rates much higher than the 3dB thermal bandwidth, the ring modulator showed no degradation in modulation. Figure 8(b) is an optical “eye” diagram at 20Gbps for 231-1 PRBS data from the 25G local substrate removed ring modulator with 0.5mW input optical power. It’s a clean open “eye” as good as the one shown in Fig. 2(b). We further reduced the data rate down to 622 Mbps. Still no obvious degradation was observed, as the eye shows in Fig. 8(c) measured using a 1G optical receiver. As in the PRBS 231-1 data, the longest run length of 31 “1s” or 31 “0s” last only about 50 ns, which is still much faster than the ring’s thermal response time. We then applied a custom pattern at 622 Mbps data rate with 5 repeating patterns of 2048 “1s” and 2048 “0s”, plus 10240 “10s” to have both the shortest “1” of “0” state of 1.6 ns and the longest “1” of “0” state of 3.3 μs. The latter obviously gives the ring enough time to be impacted within the ring’s thermal time constant by data dependent heating. As a result, we observed severe “eye” closure with this artificial data pattern as shown in Fig. 8(d). Although such patterns are not likely to naturally occur in typical encoded data, it is imperative to ensure that the link is protected against errors in case such patterns should occur. This can be done at the physical layer, at the link layer, and at higher levels in the protocol stack.
Fig. 8 (a) Thermal response time measurement for a substrate removed ring modulator. Rise time of ~3μs, and fall time of ~2μs were measured. (b) Optical “eye” diagram of the substrate removed ring modulator for 20Gbps PRBS 231-1 data modulation with no observable degradation. (c) “Eye” diagram of the substrate removed ring modulator for 622 Mbps PRBS 231-1 data modulation. (d) Severely closed “eye” for an artificial data pattern with low frequency content within the ring thermal response bandwidth.
4. Discussion and conclusions
The plasma dispersion effect is the most common method of achieving high-speed optical modulation in silicon devices in which the concentration of free carriers changes the refractive index of silicon [20]. Both the real part and imaginary part of the refractive index changes due to such effect. Mechanisms such as carrier injection, depletion, and accumulation have been exploited. Carrier induced absorption exists in all these mechanisms.
FCA from junction doping dominates the loss in high-speed depletion ring modulators. The heat generated from junction doping FCA could be significant due to the field enhancement inside a ring resonator. Because a high-speed ring modulator bandwidth is photon-lifetime-limited, the resonator Qs are limited to 20000~8000 for photon-lifetime-limited bandwidth of 10~25GHz, which in turn limits the power enhancement factor inside the ring to 70~30. With such limited enhancement factors, effects from other nonlinear absorptions in high-speed depletion ring modulator are much smaller in magnitude in the input power range for a photonic link of interest. But the absorbed thermal power can be comparable to the input optical power depending on the bias point and voltage swing used, which can introduce large enough thermal refractive index changes to cause substantial input power and wavelength dependent ring resonance shifts.
FCA from doping in PIN carrier injection ring modulators can be smaller because the optical mode largely overlaps with the undoped intrinsic silicon waveguide. However, absorption from the injected carriers could be significant. We, therefore, expect to see a similar effect in forward-biased carrier injection ring modulators.
The ring resonance shifts in response to the self-heating from FCA, which causes nonlinear behavior and/or optical bistability. Such effects can be significantly enhanced in microring resonators with their local substrates removed in direct relation to their thermal tuning efficiency improvements. We demonstrated optical bistability with only 100 μW of optical input power.
The ring resonance shift induced by self-heating from FCA further affects the data modulation of a depletion ring modulator. It causes unstable “1” and ”0” signal levels, as well as inconsistent and reduced ER. It is, however, a relatively low-speed effect due to its thermal nature. Measurements and experiments confirmed that it only affected low frequency data contents, <1 MHz, in high-speed data transmission. In general, data dependent interaction complicates the control loop and makes it harder to stabilize. Since closed-loop control will likely be needed to stabilize the ring resonance in practice, it may also be used to correct for data dependent self-heating. Another approach would be to use data encoding to reduce or eliminate low-frequency content within the ring thermal bandwidth. We will explore both techniques in future work. In addition, link-level error detection can be used with relatively low energy costs [24], particularly for tightly coupled systems, to further boost link integrity.
Acknowledgements
This material is based upon work supported, in part, by DARPA under Agreement HR0011-08-9-0001. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. The authors thank Dr. Jagdeep Shah of DARPA MTO for his inspiration and support of this program. Approved for Public Release, Distribution Unlimited.
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