Nanophotonic Pockels modulators on a silicon nitride platform

Silicon nitride (SiN) is emerging as a competitive platform for CMOS-compatible integrated photonics. However, active devices such as modulators are scarce and still lack in performance. Ideally, such a modulator should have a high bandwidth, good modulation efficiency, low loss, and cover a wide wavelength range. Here, we demonstrate the first electro-optic modulators based on ferroelectric lead zirconate titanate (PZT) films on SiN, in both the O- and the C-band. Bias-free operation, bandwidths beyond 33 GHz and data rates of 40 Gbps are shown, as well as low propagation losses ($\alpha\approx 1$ dB/cm). A $V_\pi L\approx$ 3.2 Vcm is measured. Simulations indicate that values below 2 Vcm are achievable. This approach offers a much-anticipated route towards high-performance phase modulators on SiN.

The paper mainly highlights the results on C-band ring resonator modulators. However, more device types have been fabricated and characterized. Apart from the C-band rings, this section provides more details on O-band (1260 nm -1360 nm) ring modulators and a C-band Mach-Zehnder type modulator. Fig. 1 gives an overview: Supplementary  Fig. 1a-c show respectively the top-view, cross section and a detailed cross section of the C-band device described in the paper, whereas Supplementary Figs. 1d-f and 1g-i do the same for an O-band ring and a C-band Mach-Zehnder Interferometer (MZI). The O-band ring has a Q-factor of 1820 and a free-spectral range ∆λ FSR of 3.27 nm. The ring radius is 40 μm, with a phase shifter length L of 195 μm. The MZI modulator electrodes have a length of 1 mm. Note the differences between the cross-sections of the devices, the waveguides in Supplementary Fig. 1c and 1i were planarized trough back-etching of the top (≈ 1 μm thick) oxide using a combination of reactive ion etching (RIE) and wet etching (HF), variations in top oxide thickness, etch rates and exact etch times can lead to relatively large steps ( Supplementary Fig. 1c). Moreover, the etch rates of the deposited oxide depend on the exact nitride structures underneath, even in the case of a seemingly planar surface ( Supplementary Fig. 1i), trenches of several tens of nanometers arise next to the waveguide (see inset in Supplementary Fig. 1i). On Supplementary Figs. 1d-f however, a device planarized using chemical mechanical polishing (CMP) is shown. A buffer layer of 50-100 nm of oxide is left on top of the nitride waveguide, so the obtained surface is much smoother. This leads to much smaller propagation losses (see   1g-i), the transmission spectrum for different voltages applied across the PZT and the electro-optic phase shift (with respect to 0 V) as a function of voltage. The voltage is applied to only one of the MZI arms. From this, we can estimate the V π (voltage needed to induce a π phase shift, or a shift of the sinusoidal transmission pattern over half a period) to be 47.6 V, corresponding to a V π L of 4.76 Vcm. This corresponds to an r eff of the PZT-layer of about 70 pm V −1 .
Variations in the measured V π L values are mainly due to variations in the waveguide cross-sections, electrode spacings and the used wavelengths (C-band versus O-band), see Eq.
(2). Extracted electro-optic coefficients r eff also vary somewhat, differences can in part be due to variations in film quality on different samples, but mainly stem from small uncertainties on the exact cross-section dimensions.
In Supplementary Fig. 3 the loss measurements on different types of PZT-covered waveguides without metallic contacts are summarized. For the C-band measurements, chips were planarized using a combination of reactive ion etching (RIE) and wet hydrogen fluoride (HF) etching. Typically resulting in steps and trenches of several tens of nanometers in the vicinity of the waveguide (see Supplementary Note 1 and Supplementary Fig. 1c, i). Supplementary Figs. 3a-c summarize loss measurements on such waveguides, for a set of rib waveguide spirals (blue line on Supplementary Fig. 3a and Supplementary Fig. 3b) and a set of wire waveguide spirals (green line on Supplementary Fig. 3a and Supplementary Fig. 3c). The PZT-covered wire waveguides, resembling the ones used in the C-band modulators, have an estimated loss of 5 to 6 dB cm −1 . The rib waveguides were defined using a partial etch of 220 nm next to the waveguide core, the influence of this on the propagation loss is only expected to be minor, as is demonstrated by the measurements. Note that before PZT deposition, the waveguide loss can be as low as 0.5 dB cm −1 . For the O-band measurements, the planarization of the waveguides was done by chemical-mechanical polishing (CMP), resulting in a waveguide cross-section as shown in Supplementary Fig. 1f, with a residual oxide layer of 50 to 100 nm on top of the waveguide (see Supplementary Note 1). Supplementary Figs. 3d-e show the loss measurements of such waveguides for 3 test samples. The smoother surface for the PZT deposition can result in losses below 1 dB cm −1 . The simulated confinement factor in the PZT layer for the C-and O-band waveguides used in the loss measurements are respectively ≈ 0.23 (for both rib and wire waveguides) and ≈ 0.3. Based on the measured eye diagrams, the Q-factors of the eyes and corresponding bit error rates (BER) can be estimated (Ref. [31] of the main text). The results of this analysis are plotted in Supplementary Fig. 4. As can be seen on the plot, the estimated BER remains below the hard-decision forward error coding (HD-FEC) limit with 7% overhead of 3.8 · 10 −3 for all used bitrates (a common limit, see for example Refs. [32,33] of the main text).

Supplementary Note 4. Extinction ratio measurement
The eye diagram shown in Supplementary Fig. 5 was obtained using a DC-coupled Tectronix 80 C02-CR optical receiver with a sampling oscilloscope (Tektronix CSA 8000), applying a peak-to-peak voltage of 4.2 V at 10 Gbps (same as for Fig. 2c). Since the measured voltage scales with the total optical power, we can estimate the extinction ratio to be about 10 · log 10 (P max /P min ) dB ≈ log 10 (23.8/11.6) dB = 3.12 dB. This corresponds well with a simple ball-park estimate based on the observed transmission spectrum and static e), since the extinction ratio in DC can be estimated as ∆T ≈ | dT dλ max · dλ dV · V pp | ≈ 60 dB nm −1 · 13.5 pm V −1 · 4.2 V = 3.4 dB, where T is the transmission expressed in dB.
11.6 mV 23.8 mV Supplementary Figure 5: Extinction ratio measurement. Eye diagram of a C-band ring modulator, measured with a 10 Gbps non-return-to-zero scheme and a peak-to-peak voltage of 4.2 V (same as in Fig. 2c). Obtained using a DC-coupled optical receiver.
In the simulations in Fig. 4, a sweep of the electrode spacing and PZT thickness was performed, since these can be easily tailored in post-processing. This was done for a fixed waveguide width of 1.2 μm. The waveguide width can however also be designed, an optimization is given here. At each width, a sweep of V π Lα as a function of PZT thickness and electrode gap of the kind described in the main text and shown in Fig. 4 was performed. Supplementary  Fig. 6a shows the optimal (smallest) value min(V π Lα) and the V π L at that optimum. Supplementary Fig. 6b shows the PZT thickness and electrode spacing of this optimum. The light blue area shows the waveguide width/PZT thickness combinations for which the waveguide only supports a single TE mode. In the main text, a width of 1.2 μm was chosen in order to minimize min(V π Lα) whilst still having single-mode behavior at the optimal point. 500 1, 000 1, 500 2, 000