High-speed programmable photonic circuits in a cryogenically compatible, visible–near-infrared 200 mm CMOS architecture

switching on average for every 1 µ s and 6 nW hold power, operation at 700–780 nm with optical transmission up to 1,550 nm, and improved power efficiency at 5 K.

modulator for SiN (ref. 17 ). Electrostatic MEMS devices meet the power requirement (promising sub-picowatt hold power) 30,31 , but modulation timescales have thus far been limited to the microsecond regime. Figure 1b summarizes this power-modulation bandwidth trade space for SiN and Si platforms compatible with the scalability requirement mentioned earlier. For a cross-platform comparison, Fig. 1b plots the power dissipated for π-phase shifts as a function of the circuit reconfiguration rate. In the thermal regime, the power dissipated is constant up to the maximum reconfiguration bandwidth, whereas piezo-actuation contains a trade-off between faster programming speeds and power dissipated on chip. The piezo-optomechanical approach offers up to three orders of magnitude improvement in programming time with lower power consumption as that of thermal approach and three to five orders of magnitude improvement in power dissipation at the maximum thermal reconfigurability rate, showing the exceptional suitability of this technology for MZM systems. Motivated by these considerations, we advance our wafer-scale process for SiN photonic integrated circuits (PICs) (Fig. 1c) with phase-only piezo-optomechanical tuners, whose basic design and operation are shown in Fig. 1d,e, through the co-design and development of photonics, electromechanics, electrical and mechanical control systems, and driver software. We combine the best attributes of the different devices discussed in our previous work 25 into a proof-of-principle MZM architecture capable of achieving 20 ns reconfiguration time, on-chip power dissipation per modulator below 200 µW when switching on average for every 1 µs and 6 nW hold power, operation at 700-780 nm with optical transmission up to 1,550 nm, and improved power efficiency at 5 K. results Device fabrication, design and theory of operation. Our devices are designed and fabricated on a 200 mm wafer following an improved process flow based on our previous work 25 . The optical layer consists of a 300-nm-thick SiN layer in a silicon dioxide cladding, located on top of aluminium nitride (AlN) piezoelectric actuators with functionality for selective release and metal routing; Supplementary Section 1 provides additional fabrication details. This process enables high-speed and broadband active modulators. Specifically, Fig. 2a shows a full MZI with strain-actuated phase shifters both internal and external to the directional couplers, as indicated by the unfolded layout in Fig. 1d. Each arm of the internal phase shifter contains an optical-path-length-matched piezo-actuated segment (imparting a phase Θ 1,2 ) and same for the external phase shifter (imparting a phase Φ 1,2 ). Each phase shifter consists of a 400-nm-width SiN waveguide passing through an adiabatic taper, expanding to a width of 5 µm for improved strain transfer 25 , propagating for a distance of 1.1 mm, and then through a second adiabatic taper back down to a 400-nm-wide single-mode turn. This loop repeats nine times, as shown in Fig. 2b, for a total path length of ~1 cm per phase shifter. The cross section shown in Fig. 2c,d reveals a slightly undercut 10-µm-wide pillar around the oxide-clad 5-µm-wide SiN waveguide and AlN actuators. Applying a potential difference across AlN transfers strain to the waveguide (a finite element simulation is shown in Fig. 2e), imparting a shift in the refractive index predominantly due to the strain-optic effect 32 in addition to moving boundary effects 33 .
When applying a potential difference, the strain imparts phase change Δθ to the optical mode for a given length L of the phase shifter as follows: where λ is the free-space wavelength, n eff is the static effective mode index, ΔL is the strain-induced path-length change in the phase shifter and Δn eff is the total effective strain-induced change in the refractive index:  is a signed quantity depending on the direction of induced strain, meaning opposite strains produced by a negative applied voltage produce an opposite-shift effective index. This effect allows for a push-pull or differential operation 34 of the phase shifts Θ 1,2 , Φ 1,2 ∈ [-π/2, π/2] in Fig. 2a for an applied V s ∈ [-V π /2, V π /2], defined as the potential relative to ground with V π being the required voltage for a π phase shift.
Room-temperature operation. Figure 3 summarizes the modulator performance at room temperature (300 K). Figure 3a,b shows the operation across a broadband range of wavelengths (700-780 nm). The plots shown here take advantage of the push-pull operation for optical loss balance (typical insertion loss of −3.5 dB at 737 nm; Supplementary Section 2 provides the loss characterization details) of the phase shifters by applying opposite-polarity voltages to each arm. We estimate V π L from the sinusoidal fits, yielding values from 50 V ⋅cm (700 nm) to 65 V ⋅cm (780 nm) in the push-pull configuration or a corresponding V π L in the range of 100-130 V cm per phase shifter. We attribute the variance in V π L to material and waveguide dispersion. From Fig. 3a, we observe an inherent static phase shift in our MZIs. This shift does not highly depend on the wavelength and is a result of local stress and refractive-index differences seen by the two arms of the MZI due to fabrication. We note that the peak of the MZI's cross-port transmission (Fig. 3a) depends on the splitting ratios of our passive directional couplers and decreases as the wavelength increases, thus moving further away from the 50:50 point. An improved 2 × 2 × 2 MZI design 35,36 in conjunction with wavelength-tolerant directional couplers 37 would enable full tunability across the range of wavelengths tested. Time-resolved measurements shown in Fig. 3c-e indicate short rise and fall times of ~5 ns. Figure 3c plots the transmission when averaging over 16 square-wave voltage pulses applied through an arbitrary waveform generator (AWG), indicating a fall time of 5 ns. As shown in Fig. 3d, the modulator follows a Gaussian pulse with a full-width at half-maximum of 15 ns. We do not observe substantial hysteresis during active modulation, estimating a <1% deviation from single-shot traces limited by detector noise and stability of our measurement setup. Figure 3f plots the small-signal frequency-resolved modulator response, indicating a −3 dB cutoff at ν 3dB = 120 MHz. This cutoff is consistent with the RC time constant during measurement, consisting of the device capacitance of 17 pF and series resistance of ~80 Ω arising from the voltage source and on-chip routing metal. We attribute the peak at 241 MHz to the fundamental mechanical resonance, which is 253 MHz as per our finite element model (Fig. 2e). The shape of the peak exhibits a characteristic resonance and anti-resonance feature typical of mechanical resonators 38,39 . We note that the AWG used for these tests does not produce the full 20 V swing across its entire bandwidth (500 MHz), which accounts for the distorted Gaussian envelope and atypical falling edge shown in Fig. 3d,e, respectively. The contrast in these measurements is low, as this device is optimized for cryogenic operation, as described later.
Cryogenic operation at 5 K. We performed the cryogenic characterization in a 4 K closed-cycle cryostat (Montana Instruments). Using a fibre array and radio-frequency probe mounted on nanopositioners inside the cryostat (Supplementary Section 5), we applied various voltage waveforms. The transmission curves in Fig. 4 show no degradation in the switching operation, with an overall similar performance at a base temperature of 5 K (Fig. 4a,b) compared with room temperature. Figure 4c indicates an extinction of approximately 30 dB. We remark that compared with Fig. 3a, the static phase offset shown in Fig. 4c shifts due to differences in thermal contraction and stress-optic effects in the two MZI arms at cryogenic temperatures. Figure 4d  on the timescale of minutes. The corresponding hold power of 2 nW is nearly eight orders of magnitude smaller than the cooling power (90 mW) of the Montana cryostat. This low power consumption is a critical benefit, as even state-of-the-art thermal SiN waveguide modulators (Fig. 1b) would easily overwhelm the cryostat's cooling power. We note that the actual extinction ratio of the modulator is larger than 30 dB; however, limited volume in the cryostat prevented the use of differential driving (as demonstrated at room temperature) and limited the phase change to approximately π/2 rather than π.

× programmable interferometer.
Having characterized the MZIs, we now consider a proof-of-principle SU(4) programmable unitary transformation, which consists of N(N − 1)/2 = 6 MZIs. The MZM is fully programmable, where all the phase shifters are computer controlled (Supplementary Section 3). Figure 5 summarizes the MZM characterization. After a basic voltage calibration, we run voltage sweeps across all the six MZIs, producing internal phase-shifter transmissions as shown in Fig.  5d. The optical input and output combinations (Fig. 5c) here for each plotted MZI show maximum power differences on actuation; a full dataset of all the 12 phase shifters is shown in Supplementary Section 4. Figure 5d plots the transmission of output port 3 on actuating 'MZI3' , which indicates an optical extinction ratio in excess of 40 dB. The total loss through the MZM ranges from −14 to −21 dB at 737 nm, depending on the optical path taken, primarily due to waveguide bending losses in the phase shifters, which could be completely eliminated with an unfolded implementation or larger-radii waveguide bends. We confirm that our MZM maintains the 100 MHz bandwidth as demonstrated in single MZI devices by applying a 10 V, 100 MHz sinusoid to the internal phase shifter of MZI2 and monitor the optical outputs 5 and 6 with a laser coupled through optical input 3. We utilize a lock-in detection scheme on the output photodiodes to extract the signal at 100 MHz (Fig. 5e,f) for both channels and a relative phase offset of 0.59π; the small deviation from π/2 is likely due to the 125 MHz bandwidth of the photodiode being close to the driving frequency.
Although the results shown in Fig. 5 demonstrate the programmability of our MZM as a single packaged device, voltage-handling limitations of our on-chip vias (see Discussion below) currently prevent accessing the full scope of SU(4) operations and thus the use of certain calibration procedures 34,40,41 to discern 4 × 4 matrices or unitary fidelities produced by the chip. However, with expected improvements in overall loss, loss balance between MZIs, and a full 2π-phase actuation (enabled by a combination of better via design, fabrication processes, and control electronic systems), we will explore such measurements in future experiments.

Discussion
We have demonstrated a four-mode programmable interferometer in a 200 mm CMOS foundry. The MZM comprises cryogenically compatible, piezo-optomechanical phase shifters with >100 MHz bandwidth operating in the visible-NIR wavelengths, which should be immediately applicable to many hybrid photonic architectures 16 , quantum protocols 8,42 and machine-learning algorithms 6 .
Although the devices presented here show promise for universal linear-optic programmable photonics in new performance regimes and application spaces, there are still some non-idealities that will be improved in future work. First, the dominant source of loss in all devices presented is the bends induced by waveguide meanders and directional couplers, measured to be −2.7 dB of the −3.5 dB MZI insertion loss (Supplementary Section 2). Waveguide propagation losses (−0.39 dB cm -1 ) and adiabatic taper losses of −0.022 ± 0.038 dB per taper account for the remaining loss of −0.8 dB. We estimate that implementing less tightly folded versions of the same devices that have fewer bends and tapers would allow us to achieve MZI insertion losses substantially lower than −1 dB. Second, in these particular devices, small voids in AlN in the vicinity of electrical vias produced metal filamentation that degraded the device breakdown voltage and prevented the application of voltages above V s = 25 V. Although we found individual vias in the test structures on the same wafer that allowed V s > 90 V, the yield was insufficient for an MZI comprising 90 vias. After a systematic failure analysis and cross-sectional imaging, the process yield improved greatly so that full SU(N) devices appear likely with maximum V s > 90 V (Supplementary Section 6). Besides the electrical vias, we have not observed any causes of systematic failure (such as mechanical failure or fatigue) in our devices, likely attributed to the relatively low strain and stress values under operation.
In addition to device performance improvements, design variations and prospects for large-scale photonics remain to be explored. With our current technology and SU(2) device footprint (approximately 1.3 mm × 0.6 mm), we can conceivably fit >500 components on a single die without any lithographic modifications (such as stitching between reticle fields), enough to make an SU(32) device. Simply lengthening the phase shifters would also allow them to operate at CMOS-level voltages at the cost of actuation bandwidth due to increased device capacitance (a 10-cm-length phase shifter would potentially have V π ≈ 5-10 V and ν 3dB ≈ 12 MHz). Alternatively, strain-concentrating structures or mechanical resonance effects would help shrink our current device size by reducing the required driving voltage. Moreover, high-scandium-concentration Sc (1-x) Al x N has shown a fivefold increase in piezoelectric responsivity 43 , promising a further five times reduction in V π or device length. Finally, the layer stack of our PIC (Supplementary Table 1 and Fig. 2c), which places the optical layers on top, enables many extensions to the platform. The optical layer-on top of all the metal and piezoelectric layers-allows for alternative optical layers to expand the transparency window into the ultraviolet regime [44][45][46] . Moreover, heterogeneously integrated thin films for either photon generation 14,47,48 and detection 13 or nonlinear interactions [49][50][51][52] could be placed directly on top of the optical layer with photons coupling evanescently to the rest of the integrated photonics. The AlN-actuator-based photonic platform is also entirely post-CMOS compatible and therefore can be directly fabricated on fully formed CMOS integrated circuits 53 for direct biasing or control of hybrid systems [54][55][56] ; thus, the architecture presented here can be scaled to both very large photonic circuit sizes and very small photonic circuit pitches without electrical control bottlenecks.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41566-021-00903-x.

Nature PhotoNics
Methods Hold-power consumption and reconfiguration energy calculations. We first calculate the device capacitance C and on-chip routing metal resistance R chip based on the measured RC roll-off in our frequency response curve, yielding C = 17 pF and R chip = 30 Ω in addition to a series voltage source resistance of 50 Ω. The device leakage resistance based on previous measurements 25 is estimated to be 500 MΩ and 200 GΩ at 300 and 5 K, respectively. The hold power P = IV, where I and V are the leakage current and applied voltage across the device, respectively, is found for two phase shifters holding 25 V to maintain a phase shift of π. The reconfiguration energy dissipated on chip is calculated using the formula E = (R chip /R tot )CV 2 , where R tot is the total series resistance of the circuit including external resistors in the AWG and V s = 50 V. This equation accounts for two phase shifters with a 50 V swing and represents energy dissipated from on-chip resistances from vias and routing metal lines. To reduce on-chip energy dissipation for slower reconfiguration rates, R tot is adjusted such that the corner frequency 1/(2πR tot C) matches the current reconfiguration frequency (which is done off chip at the voltage source). This minimizes the on-chip energy dissipation as well as maintaining the necessary reconfiguration rate. The total power dissipated (Fig. 1b) is simply the hold power plus the reconfiguration energy times the reconfiguration rate.
Device characterization. We characterize individual MZI modulators both at room temperature and cryogenic temperature with a 250-µm-pitch optical fibre array that is coupled through gratings to the on-chip waveguides. We use a 150-µm-pitch radio-frequency probe (in the ground-signal-ground-signalground configuration at room temperature and ground-signal-ground at cryogenic temperature) to apply high-frequency electrical signals.

Digital lock-in amplifier.
A time trace of output channels 5 and 6 of the MZM is directly digitized by a high-speed oscilloscope. The time traces are digitally integrated (for 4 ms) with sinusoids of varying frequencies and phases, whose resulting amplitudes form the data for the plots in Fig. 5e,f. The two photodiodes used for both channels have bandwidths of 125 and 600 MHz. Please see Supplementary Information for more detailed experimental methods.

Data availability
The data that support the plots and findings within this paper are available from the corresponding authors upon reasonable request.