1. Introduction

Out of the photonic platforms currently available, only Silicon-on-insulator (SOI), InP and TriPleX are available to users through Multi-project Wafer runs [1, 2]. Here, the TriPleX is a SiN-based platform which is manufactured by Low Pressure Chemical Vapor Deposition (LPCVD) stoichiometric Si3N4 and SiO2, exhibiting ultra low-loss propagation from the visible to near-infrared wavelength range [3, 4]. Integrating tunable components, such as phase shifters, modulators and switches in the platform have been implemented using the thermo-optic effect [1,5]. State-of-the-art modulators in TriPleX exploiting the thermo-optic effect typically consume 200–500 mW power per modulator and provide 0.5–1 kHz modulation speed [5]. For applications requiring large number of modulators, such as microwave photonics, significant reduction of the power consumption to the nW level per modulator is greatly desired. For applications requiring fast modulation such as flow cytometry, biomedical imaging/biosensors, confocal florescence microscopy and so on thermo-optic modulators also pose restrictions. As a solution, Vescent Photonics [6] used liquid crystal (LC) on top of the TriPleX platform to yield phase modulators. The modulation speed in the range of 1–5 kHz and the power consumption of 30 μW were shown however, LC based modulators intrinsically cause (optical) excess loss due to the required overlap between LC region and optical mode and are thus not preferred. In this paper, it is proposed to exploit the stress-optic effect by integrating a piezoelectric layer on top of an optical waveguide structure. In this way modulation can be optimized in terms of minimal power consumption and maximal modulation speed without compromising the optical insertion loss, analogous to thermo-optic modulation.

Recently, the stress-optic effect has been investigated intensively in various photonic devices [7–15]. Active control of stress in the waveguide structure can be implemented by deposition of a thin layer of piezoelectric material on top of the structure. Among piezoelectric materials, the lead zirconate titanate (PZT) is particularly interesting because of its relatively large effective transverse piezoelectric coefficient (e_31,f = 20 C/N) and its wide use in micro-electro-mechanical systems [16–18]. The stress-optic effect has been previously used for controlling birefringence and bi-stability in the SOI platform [12, 13], but to the best of our knowledge no one has used it yet for active stress modulation in the SiN-based platform. In this work, Mach-Zehnder interferometers (MZIs) designed for visible light is used to demonstrate the functionality of the stress-optic modulator in the TriPleX platform.

2. Basic device principle

Figure 1(a) shows a schematic top view of a MZI with a stress-based phase shifter on one of the arms used in this work. The cross-sectional overview of the arm along the dashed line (c) is illustrated in Fig. 1(b). The overview consists of an optical waveguide structure with a stress-based phase shifter on top. The waveguide is designed for visible light applications for TM-polarization and shows ultra-wide band single mode characteristics in the visible range [19]. It consists of a silicon nitride strip (Si₃N₄) as core, with a thickness and width of respectively 25 nm and 4.4 μm, embedded in 8 μm thick silicon oxide (SiO₂) cladding layers as top and bottom cladding, respectively. The waveguide structure was fabricated using the standard TriPleX technology [20]. On top of the waveguide, the stress-based phase shifter consists of a uniform layer of PZT sandwiched between a uniform bottom- and a structured top electrode which were both deposited by evaporation. The bottom electrode is composed of a Ti/Pt bilayer, a known good seed layer for PZT growth on amorphous materials, of 10 nm/100 nm thickness while the top electrode is composed of a Pt/Au bilayer (Au allowing for wire- or flip-chip bonding, Pt preventing indiffusion of gold) of 100 nm/500 nm thickness. The PZT layer was deposited at wafer level using the SMP700 pulsed laser deposition system (SolMateS BV [21]). With this system the 2 μm PZT was deposited with a thickness variation below 2% on the 100 mm wafer.

 

Fig. 1 (a) Top view of a MZI with a PZT phase shifter on one of the arms. (b) Cross-section overview of the MZI active arm along the dashed line (c).

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By applying a voltage across the two electrodes a uniform vertical electric field is created in the PZT layer. As a consequence of the piezoelectric effect, the PZT layer expands and contracts respectively across the thickness and width of the active area between two electrodes. Being clamped to the waveguide, the contraction gives rise to stress in the PZT layer and the underlying waveguide structure. This stress results in changing refractive indices of both SiO2 and Si3N4 layers, which in turn is transferred into an effective refractive index change ∆n_eff of the fundamental TM-mode propagating through the waveguide structure. To calculate the stress-optical modulation, we used a commercially available software based on finite element analysis (Field Designer of PhoeniX Software) in which stress distribution and optical mode modules are included [22]. Figure 2 shows a typical example of the calculated induced stress in the waveguide structure, showing maximum effects around the edges of the top electrode. The changes in the optical indicatrix due the mechanical strain are specified by the symmetric fourth rand elasto-optic tensor. This material dependent tensor is specified in the PhoeniX software via the ”StrainOpticMatrix” material property.

 

Fig. 2 Induced stress distribution, (a) the horizontal direction σ_xx and (b) the vertical direction σ_yy, in waveguide structure after applying an electric field of 10 V/μm across top and bottom electrodes. The PZT layer including electrodes is marked in blue in the picture. Clearly, the dominating induced stress contribution in the waveguide region is formed by the horizontal component σ_xx.

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3. Modulator optimization

To maximize the stress-optic effect in the waveguide structure shown in Figure 1(b), simulations are performed using TM polarization at 640 nm wavelength. Two parameters are varied, being the thickness of the PZT layer (with a maximum of 2 μm for practical reasons) and the width of the top electrode. The mechanical and optical properties of the layers used in the simulation are described elsewhere [16, 20]; the most important mechanical parameter is the Youngs modulus, which is 95, 160, 70, and 130 GPa for PZT, Si3N4, SiO2, and Si, respectively. For simplicity, the e_31,f is assumed to be independent upon applied electric field in these simulations, with a value of 20 C/N. In Fig. 3 the results are plotted. The graphs show the effective index change δn_eff of the waveguide while applying electric field 1 V/μm across the PZT layers. Two trends are clearly visible. Firstly, the modulation effect increases with increasing PZT thickness: as thicker PZT means stronger mechanical effects. Secondly, each PZT thickness corresponds to an optimal top electrode width, which value also increases at increasing PZT layer thickness: this can be understood in view of the typical stress distribution, mainly originating at the edges of the top electrode, see Fig. 2. The structure with respectively PZT thickness and width of 2 μm and 30 μm results in the highest δn_eff = 5.164 × 10⁻⁶.

 

Fig. 3 The induced change in effective refractive index of waveguide under applied electric field of 1 V/μm.

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4. Experimental validation and discussion

To demonstrate experimentally the modulation caused by the stress-optic effect, the MZI structure as shown in Fig. 1(a) has been manufactured and validated for TM polarization. Here, the PZT thickness value is fixed to 2 μm, while the top electrode width is varied from 10, 20, 30 to 40 μm. The top electrode length is fixed to 10 mm. To elaborate the simulations with more realistic conditions, the value of e_31,f varying under applied electric field instead of constant value are used in simulation of these waveguide configurations. The red dashed line in Fig. 4 illustrates the variation of e_31,f measured using the Aix4PB (Aixacct Systems GmbH) on a sample prepared from a reference wafer without waveguides with the PZT thickness of 1 μm. Using the e_31,f shown in Fig. 4 in the simulations, a linear modulation response under applying electric field of above 2.5 V/μm are observed, shown with marked lines in Fig. 4. A linear fit was added to the simulated ∆n_eff omitting values smaller than 2.5 V/μm (since the e31 value is not constant in that region), which results in an accurate fit equals to χ² = 0.998. In order to compare the simulation results, the slope of the corresponding fitted relation are extracted, shown above the figure. Comparing the extracted slope, the configuration with 30 μm gives rise to the optimal modulation effect with the value of the slope of 5.259 × 10⁻⁶. At this value for the slope, it is also expected to experimentally observe a linear performance of the PZT modulators, in case an electric field larger than 2.5 V/μm is applied.

 

Fig. 4 Red dashed line is the measured e_31,f responses to applied electric field for a 1 μm thick PZT layer. The marked lines are the simulation results for waveguide structures with 10, 20, 30 and 40 μm top electrode widths and a fixed PZT thickness of 2 μm.

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To characterize the performance of our MZI modulators shown in Fig. 1(a), we measured the optical output intensity as a function of the driving electric field for TM polarization. Figure 5 shows the measured and calculated optical transmission versus applied electric field for a MZI device having a 30 μm top electrode width. The red markers and blue solid line are experimentally measured- and calculated output intensities. The applied electric field is increased until the slope of the modulated optical signal changed sign (the minimum optical transmission is reached), as illustrated in Fig. 5. The measured data was normalized to the maximum output intensity. The MZI modulators typically show an extinction ratio of 25 dB when the optical output intensity of the MZI reached its minimum value. Based on the simulation results shown in Fig. 4, a linear relation between the effective refractive index change and electric field is assumed (∆n_eff = δn_eff E) for electric field values larger than 2.5 V/μm. Therefore, the MZI transmission relation (T_MZI) is modelled to the measured output intensity to extract δn_eff. In a MZI with 3-dB splitting ratio, the transmission is calculated by T_MZI = Cos(∆ϕ/2)² where ∆ϕ is the phase difference between two arms [5, 23]. The phase difference is related to the applied voltage through ∆ϕ = (2πδn_eff E/λ)L where λ is the wavelength of light in free space and L is the active length of the phase shifter (equal to 10 mm). The red dashed line in Fig. 5 is the modelled MZI relation to the measured data. By excluding the measured data below 2.5 V/μm (the red circles in Fig. 5) a very good agreement between measurements and model is observed. δn_eff of the other of configurations are determined in the same procedure. This exclusion is done since the e₃₁ value is not linear for values below 2.5 V/μm while a linear fit is applied to the data. The reason for this nonlinearity at low field strengths is not known, and will be further investigated in future research. Figure 6 shows the simulated (solid blue line) and measured δn_eff (blue circles). As a figure of merit, the product V_πL, the applied voltage needed along the active area to induce π phase shift, is determined from the simulated- and extracted δn_eff, shown respectively by the red dashed line and squares in Fig. 6. A reasonable good agreement between the simulation and measured data can be seen. Both simulated and measured data follow the same trends and show that the top electrode width of 30 μm provides the best performance.

 

Fig. 5 Modelling MZI transmission relation (the red dashed line) to the measured optical transmission from the MZI with the PZT thickness of 2 μm and 30 μm top electrode (red squares). Modelling was done with a constant e₃₁ value. The measured data showed by red circles excluded from modelling. The blue solid line shows the calculated results for the corresponding structure.

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Fig. 6 The simulated (blue solid line) and measured (red circles) slopes δn_eff of waveguides under applied electric field for MZI devices with the PZT thickness of 2 μm and varying the top electrode. The red squares and dashed line show the corresponding V_πL.

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The frequency response of our MZI modulator with the active area of the PZT thickness, top electrode width and length of respectively 2, 30 μm and 10 mm measured under application of a 12 V square wave with a rise time of 30 ns from a signal generator to one of the arms. The voltage response of the PZT structure and the optical output intensity were recorded using an oscilloscope, see Fig. 7. In order to find the rise time of both the voltage and the optical response, the device is modelled as a simple parallel plate capacitor. The relation used to find rise time τ is α(1 − e^{−(t−β)/τ}) where α can either be the maximum of applied voltage or the optical intensity output [24, 25]. The relation modelled to the measured data is depicted by the solid and dashed black line in Fig. 7. The measured rise time of both the voltage and the optical response are respectively 287 ns and 253 ns, corresponding to a 3-dB bandwidth of 554.5 and 629.1 kHz, respectively. Using an LCR meter (Inductance (L), Capacitance (C), and Resistance (R)) the capacitance of the PZT capacitor is measured to be 3 nF. A coaxial cable is used to connect the electronic signal generator, the oscilloscope and the MZI device. To avoid electrical reflections, both the electronic signal generator and oscilloscope are put on 50 Ω mode. The top and bottom electrode resistance is measured to be 30 Ω. Based on these inputs, both voltage and optical rise time are estimated to be 240 ns, which are in good agreement with the measured rise time. A small discrepancy can be caused by an accidental parasitic resistance or inductance in our electronic setup and pins. Using the relation CV²/2 for the energy dissipation of the parallel plate capacitor, where C is the capacitance and V is the applied voltage, a power dissipation of 300 nW per π phase shift for quasi-DC operation and the energy consumption of 430 nJ per one bit can be estimated. This means an improvement of the power consumption by a factor of one million for quasi-DC operation compared to thermo-optic modulators. In addition, the modulation speed is improved by a factor of a thousand compared to regular thermo-optic modulation.

 

Fig. 7 Modulation speed measurement. The red and blue marker are electronic and optic response of the device and the black dashed and solid line are the turn-on transient relation for parallel plate capacitor modelled to data.

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5. Conclusion

We have demonstrated the feasibility of a stress-optic phase modulator in the SiN-based TriPleX platform using a PZT layer deposited on top of a waveguide structure. To measure the phase shift, MZI devices designed for operation at 640 nm have been used and measured. The measured phase shift for four devices with top electrode width of 10, 20, 30, 40 μm show a good agreement with theory. Compared to the state-of-the-art phase modulators in TriPleX, we have achieved a one million time reduction in the power consumption for quasi-DC operation (resulting in 300 nW per π -phase shift) and 430 nJ per one bit and a thousand times increase in modulation speed (a rise time of 253 ns). The modulator performance currently still requires a long electrode length (8–10 mm) which makes existing modulator principles in other material systems (such as InP and LiNbO3) more than competitive with the bare modulator performance of this work. The modulator can be further improved by optimizing the stress distribution in the waveguide structure. This should lead to a thinner PZT layer with a consequently smaller capacitance and therefore an increased tuning speed. This stress-induced low-power tuning mechanism is especially applicable to low-loss SiN-waveguides. It results in a strongly reduced power consumption and a significantly faster response time compared to currently existing thermo-optic based modulation in application areas such as Micro Wave Photonics (MWP) and (bio)sensing.