Piezoelectrically driven Fano resonance in silicon photonics

A Fano resonance is observed in a system when a discrete resonance mode interferes with a continuous background, resulting in a sharp and asymmetric profile.¹ For a given quality factor of a resonator, a Fano resonance can lead to a sharper profile compared to the classical Lorentzian resonance from the standalone resonator. Owing to this distinctively sharp profile, a slight external perturbation in a Fano resonator can cause a significant amplitude and phase change in the Fano spectrum. This provides a powerful tool for ultrasensitive and power-efficient devices. In photonic integrated circuits (PICs), Fano resonances have been demonstrated primarily through waveguide-coupled microresonator systems,^2–7 photonic crystal cavities,^8–10 and plasmonic resonators^11,12 and are used in a wide range of applications such as sensing, low-power switching and modulation, slow-light devices, low-threshold lasing, and non-linear enhancement.^13,14 However, the fabrication of photonic crystal cavities remains challenging due to their reliance on strict fabrication tolerances. Plasmonic resonators have drawbacks such as optical loss and heat dissipation from their metallic components. While these Fano resonances were predominantly reported within the optical domain, the rapid growth of microwave photonics warrants the exploration of such mechanisms within the microwave domain.¹⁵ For instance, Fano resonances can be exploited to create microwave-assisted reconfigurable photonic filters, modulators, and switches with very narrow passbands and steep roll-off characteristics.¹⁶ 

In this paper, we present a novel approach to generate a Fano resonance in a Si PIC using a piezoelectrically driven mechanism. We integrate a lead zirconate titanate (PZT) thin film on a Si PIC and undercut the device to harbor the mechanical vibration into the waveguide system. The unique synergy of strong electro-optic effect,¹⁷ piezoelectric effect,¹⁸ and optical transparency¹⁹ within our PZT film allows efficient electro-optomechanical interaction into the waveguide, rendering a Fano resonance in the microwave domain. Notably, the piezoelectric effect-based operation offers an additional degree of control through the electrical input. Hence, this work demonstrates a promising approach to achieve Fano resonances in passive photonics platforms (such as Si and SiN), which could lead to the development of highly sensitive and efficient devices that can be relevant in a wide range of applications, including sensing, filtering, modulation, switching, and microwave to optical conversion for quantum information processing.^13,20

Integrated electro-optic modulators based on the Pockels effect are often implemented using a co-planar electrode design in which parallel electrodes are used to apply an electric field across the electro-optic material.²¹ The optical mode is confined partially or completely inside a linear electro-optic material such as barium titanate (BaTiO₃), lead zirconate titanate (PbZrTiO₃), or lithium niobate (LiNbO₃). When an electric field is applied across the material, the effective index of the mode changes due to the electro-optic (EO) effect. Typically, these modulators show a broadband modulation response with their bandwidth limited by RC-effects (if the modulator length is substantially shorter than the RF wavelength), where R is the contact resistance and C is the capacitance of the device.

In this work, we demonstrate an electro-optomechanical transducer (EOMT), wherein the EO device is suspended by selectively etching the SiO₂ cladding layer, as illustrated in Fig. 1. The free suspension of the device enables a large mechanical perturbation in the structure, e.g., when driven through a piezoelectric transducer, resulting in a strong phase modulation. Contrary to the electro-optic (EO) effect, this phase modulation shows a strong frequency dependence, peaking at the mechanical resonance of the suspended structure. The mechanically induced phase modulation stems from different physical effects.

The full process flow to fabricate the suspended devices is presented in Fig. 3. A silicon-on-insulator (SOI) chip with waveguide circuits was used as a starting sample. This chip was fabricated by imec in a multi-project wafer process,²⁵ where the waveguides were defined in a 220 nm thick silicon layer on top of a 2 μm buried SiO₂ layer, using deep UV (193 nm) lithography. The wafer was planarized using SiO₂ deposition and chemical mechanical polishing (CMP). Next, the wafers were diced into centimeter-scale samples.

The processing of the sample starts with ∼ 400 nm PZT thin film deposition using the chemical solution deposition method as described in Ref. 26. This thickness was chosen based on our previous success in fabricating and demonstrating piezoelectric micro-electromechanical system (MEMS) actuation with a similar PZT film.²⁷ Due to the high permittivity of the PZT, it was difficult to image the high-resolution alignment markers on the chip within the e-beam lithography tool. Therefore, the PZT film was partially etched in several regions that had e-beam markers defined in the silicon layer underneath. An optimized PZT reactive ion etching (RIE) recipe involving CHF₃, SF₆, Ar, and O₂ as reactant gases was used. Next, the electrodes were defined using e-beam lithography (to maintain high alignment accuracy), followed by Al deposition and a lift-off process. The contact pads were then patterned with optical lithography, followed by Al deposition and a lift-off process. In the next step, a 50 nm Al₂O₃ thin film was deposited on the sample using atomic layer deposition (ALD). This thin film was employed as a protection layer against the HF vapor used in the next step. In this sample, a layer of Ti35 was spin-coated, and the under-etch windows were defined using UV lithography. After hard-baking the sample, first the Al₂O₃ thin film was etched with a diluted 1% (by volume) buffered hydrogen fluoride (BHF) solution, followed by dry etching the PZT layer. Subsequently, the Ti35 hard mask was dissolved with AZ 100 k remover at 70 °C, and the sample was cleaned in O₂ plasma. Finally, the sample was dehydrated and loaded in HF vapor phase etcher (Idonus VPE100) to expose the sample to an HF vapor at a substrate temperature of 40 °C. The SiO₂ etching process was monitored by looking through the microscope, and the process was carried on until the device looked fully suspended. Figure 4(a) shows an optical image of a fully suspended device. The length of the modulator region is 100 μm.

To verify that the device is fully suspended, a cross section of one of the devices on the chip was made using a focused ion beam (FIB). The scanning electron microscope (SEM) image of the cross section is shown in Fig. 4(b), which confirms the waveguide is fully underetched as ∼2 μm of SiO₂ is removed. However, a ∼280 nm thick layer of SiO₂ still seems to be present under the PZT and surrounding the Si waveguide. Even after another exposure to HF vapor for about 5 min, this residue remained.

A heterodyne setup was used to measure the optical phase modulation²⁸ from the EOMT. A continuous wave (CW) laser at 1590 nm with an output power of 14 dBm was used to couple the light into the chip through a grating coupler. When the phase of the light into the chip is modulated, the output optical spectrum shows sidebands around the reference acousto-optic modulator (AOM) driving frequency. The strength of the phase modulation was measured in terms of modulation efficiency given by η² = 10 × log₁₀(P_sideband/P_AOM). Here, P_sideband is the peak power of the sideband, and P_AOM is the peak power of the AOM signal. For a detailed description of the measurement technique, see Ref. 28.

Figure 5(a) shows the modulation efficiency η² measured on the device EOMT1, driven with a 12 dBm RF driving signal (P_RF), before and after poling the PZT film. EOMT1 parameters are described in Table I. Before poling, the as-deposited PZT shows four main peaks labeled B₀, B₁, B₂, and B₃. These peaks possibly originate from shear mode actuation through the transverse electric field (in-plane) with respect to the PZT domains, which are oriented out-of-plane after deposition.^26–28 Moreover, the transverse electric field generates a weak EO effect. This is manifested through the low broadband (non-resonance) modulation response. The weak EO response furthermore explains the absence of any Fano response, as explained in Fig. 2. Next, the PZT film was poled to align its domain polarization along the applied in-plane electric field. For the poling process, a DC voltage (40 V) was applied to the electrodes at room temperature for about 40–60 min.

After the poling process, EOMT1 shows several Fano-like (asymmetric) resonances. The Fano resonance peaks are labeled A₀ (∼220 MHz), A₁ (∼570 MHz), A₂ (∼4.4 GHz), and A₃ (∼6.73 GHz). As explained above, these Fano resonances appear due to the interference between the broadband EO response and a narrowband mechanical mode excitation. Since the strongest Fano resonance was observed around 220 MHz, an additional measurement was carried out to collect more data points around this resonance (A₀). These measured data were then fitted with Eq. (5). Both the data and the fit are presented in Fig. 5(b). We can clearly see that the dip of the Fano curve goes to the noise floor, with an extinction ratio and slope of ∼41 dB and 1.194 × 10⁻³ rad/MHz, respectively. The higher frequency Fano resonance (A₃) has an extinction ratio and slope of ∼21 dB and 0.035 3 × 10⁻³ rad/MHz, respectively.

Figure 6 shows the electrical measurement on EOMT1 with a VNA. The Smith plot shown in Fig. 6(a) confirms the capacitive behavior of the device and electromechanical actuation at certain frequencies. The curve representing the magnitude of the reflection scattering parameter S₁₁ presented in Fig. 6(b) shows five main transduction dips: V₀ (∼229 MHz), V₁ (∼600 MHz), V₂ (∼2.50 GHz), V₃ (∼3.31 GHz), and V₄ (∼6.76 GHz). The dips V₀, V₁, V₃, and V₄ correspond to the resonance peaks A₀, A₁, A₂, and A₃ from EOMT1, as presented in Fig. 5(a).

Since P_sideband/P_AOM = α(L)²/4, as discussed in Refs. 28, α(L) can be extracted from the measured η² as α(L) = $2×10(η2/20)$⁠. From this, the voltage required for a π-phase shift can be calculated as V_π = π V_p/α(L), where V_p is the voltage applied to the device. In several works,^24,28,29 V_πL is presented as a figure of merit for a resonance based modulator (e.g., an acousto-optic modulator). Often, while calculating the voltage V_p corresponding to an applied RF power, the load impedance (Z_L) is conveniently taken as 50 Ω, which may not be correct, as the actual Z_L depends on the device and its material properties. For example, the Z_L of a typical EO modulator is frequency-dependent due to its capacitive nature. Moreover, Z_L can sharply change at the mechanical resonance due to the electromechanical coupling. Hence, to estimate the actual Z_L of our device, a vector network analyzer (VNA) measurement was carried out. From this Z_L, the actual load voltage was calculated as V_L = V_p = |Z_L/(Z_L + Z_S)|× V_S, where Z_S = 50 Ω is the source impedance and V_S is the source voltage. For a detailed discussion of the electrical characterization, see  Appendix A. Now, using the data from both electrical and optical measurements, the figure of merit for EOMT1 was calculated, as presented in Table II. The table illustrates that $Vπ′L$ calculated taking into account the actual load impedance Z_L is higher than V_πL calculated using 50 Ω as the load impedance. This is because our capacitive device has a higher impedance at lower frequencies.

Figure 7(a) shows the modulation efficiency η² measured for EOMT2, driven with 14 dBm P_RF. EOMT2 parameters are described in Table I. This measurement was taken after poling the PZT film. Here, we see several Lorentzian peaks, Fano peaks, and dips. We believe this might be due to a stronger perturbation in the wider Si waveguide. Figure 7(b) shows a detail around the primary mode (A₀) of EOMT2 and a fit to the Fano curve. We notice that the Fano curve has an opposite polarity compared to that of the similar mode from EOMT1.

Here, p_ij is the photoelastic coefficient of the material. For the in-plane poled PZT, p_ij = p₃₃ and sign(p₃₃) = “ + .” Whereas, for Si, p_ij = p₁₁ and sign(p₁₁) = “ − ”.^30,31 The expression for Γ_SOxx is similar to $ΔneffPE$ except for the value of p_ij. The p_ij values were omitted for both layers as the accurate value for PZT is not known. In Fig. 8, we see that the strain-optic overlap (Γ_SOxx) from the two layers is in opposite polarity due to the opposite signs of their p_ij. This indicates that the net polarity of the PE modulation depends on which layer is dominating. In addition, as expected, we observe that Γ_SOxx in Si increases when the waveguide width is increased. We believe this trade-off between the PE contribution from the Si and PZT layers could be the reason for the opposite polarity of EOMT2 compared to that of EOMT1.

We presented piezoelectrically driven Fano resonances in a Si PIC by integrating a photonic-compatible PZT thin film and underetching the device. The resulting suspended structure, when subjected to microwave excitation at its resonance frequency, exhibits strong mechanical oscillations. The interference between the mechanical resonance-induced modulation and the broadband modulation from the electro-optic effect results in a Fano-like response in the modulation spectrum. At the primary mechanical mode, we obtained a very high modulation extinction of 41 dB. We also observed Fano resonances at frequencies up to 6.7 GHz, but with a lower extinction of 21 dB. Our results demonstrate an efficient generation of Fano resonances in PICs, opening up new possibilities for the development of highly sensitive and energy-efficient devices for a range of applications, including sensing, filtering, and modulation.

This work was partially supported by the EU Commission through Grant Agreement No. 732894 (FET proactive HOT) and UGent Grant No. BOFGOA2020000103. Hannes Rijckaert and Gilles F. Feutmba acknowledge the support and funding from the Research Foundation-Flanders (FWO), under Grant Nos. 1273621N and 1S68218N, as a postdoctoral fellow and an SB-Ph.D. fellow, respectively. Thanks to Laurens Bogaert, Joris Van Kerrebrouck, Geert Morthier, and Xin Yin for the discussion on the transmission line.

The authors have no conflicts to disclose.

I. Ansari: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (supporting); Investigation (lead); Methodology (lead); Project administration (equal); Resources (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). G. F. Feutmba: Investigation (supporting); Methodology (supporting); Resources (supporting); Validation (supporting); Writing – review & editing (supporting). J. P. George: Methodology (supporting); Resources (supporting); Writing – review & editing (supporting). H. Rijckaert: Investigation (supporting); Resources (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). J. Beeckman: Funding acquisition (equal); Investigation (supporting); Methodology (supporting); Project administration (equal); Resources (supporting); Supervision (equal); Validation (equal); Writing – original draft (supporting); Writing – review & editing (equal). D. Van Thourhout: Conceptualization (supporting); Funding acquisition (equal); Investigation (equal); Methodology (supporting); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (supporting); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We used COMSOL, a finite element method (FEM) based solver, to simulate the piezoelectric actuation of our EOMT. We defined the geometry of the cross section of the device as shown in Fig. 10. The thickness of the layers was set as t_AlO = 50 nm, t_Al = 100 nm, t_PZT = 400 nm, t_Si = 220 nm, and t_SiO = 280 nm. The width of the structures was set as w_el = 1 μm, w_Si = 450. The separation between the electrodes was set at 4 μm, and the total width of the device (w_beam) was taken at 6.5 μm. These geometrical values were estimated based on the optical microscope image and the SEM image, as shown in Fig. 4.

In the first step of the electromechanical simulation, an electrostatic solver was used to calculate the electric field from a voltage applied to the electrodes. The PZT domain polarization was then set along these electric field lines. This was done to account for the process whereby the PZT film was poled by a sufficiently high voltage applied to the electrodes. In the second step, an RF input signal (amplitude 1 V) was applied to the electrodes, and the piezoelectric actuation was simulated in the frequency domain. We opted for a generalized plane strain model for the solid mechanics interface to calculate the steady state solution in the frequency domain.³⁴ This model assumes that the suspended structure is not strictly restrained in the out-of-simulation plane direction (which was the case in our EOMT due to the extra underetching), the strains are independent of the out-of-plane coordinate, and the length of the structure (out-of-simulation plane direction) is much larger than the cross section area (in-plane). Finally, a mode solver was used to simulate the TE mode profile of the EOMT at 1550 nm.

Figure 10(b) illustrates the simulated x-displacement of an EOMT at a mechanical resonance of 288 MHz. The arrows show the direction of the electric field from the voltage applied to the electrodes. The PZT material properties used in the electromechanical simulation were taken from the PZT-5A,³⁵ and the refractive index used in the optical simulation was n_PZT = 2.4.¹⁷ For other materials, standard values were taken from the literature.

When a suspended structure is actuated with the piezoelectric effect, it can experience a change in the effective refractive index (Δn_eff) through the following mechanisms:

In Fig. 11(a), $ΔneffMB$ calculated from the different interfaces of the EOMT1 are shown. For this calculation, only the interfaces closer to the mode profile were selected, as other interfaces had negligible effect. Here, we observe that the strongest contribution comes from the Si–PZT interface. This is because of the strong index contrast and the optical field density, as can be seen from the mode profile in Fig. 8(a). On the other hand, the outer-most SiO₂–air interface has a weaker MB effect as both the index contrast and the optical field are comparatively lower at this interface.

For the Si crystal orientation [110], a rotational transformation was applied to the photoelastic tensor of Si taken,³¹ resulting in the following coefficients: p₁₁ = −0.090, p₁₂ = 0.013, p₂₁ = p₁₂, and p₂₂ = p₁₁. For SiO₂, p₁₁ = 0.121, p₁₂ = 0.270 were taken from.³⁹ Now, using these coefficients and the simulation results, $ΔneffPE$ was calculated for each layer as shown in Fig. 11(b). Here, we observe that $ΔneffPE$ from Si has opposite polarity compared to the rest of the layers. This is because the strongest photoelastic coefficient for Si, p₁₁, has a negative sign.