# High-Performance Electro-Optical Mach–Zehnder Modulators in a Silicon Nitride–Lithium Niobate Thin-Film Hybrid Platform

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

_{2}and Type II: unpackaged) were simulated, calculated, and optimized. The Optical parameters included the single-mode conditions, effective indices, the separation distance between the electrode edge and the Si

_{3}N

_{4}-strip-loaded edge, optical power distribution, bending loss, optical field distribution, and half-wave voltage. The radio frequency parameters included the characteristic impedance, attenuation constant, radio frequency effective index, and −3 dB modulation bandwidth. According to the numerical simulation and theoretical analysis, the half-wave voltage product and the −3 dB modulation bandwidth were, respectively, 2.85 V·cm and 0.4 THz for Type I modulator, and 2.33 V·cm and 1.26 THz for Type II modulator, with a device length of 3 mm.

## 1. Introduction

_{2}layer (lithium niobate-on-insulator (LNOI)) [1] has become commercially available. This film offers a high-refractive-index contrast between LN and SiO

_{2}, good optical confinement, and strong light guidance [2]. Due to the small size and high energy density in the waveguide, the electro-optical (E-O) and nonlinear optical effects are enhanced. Compared with traditional LN modulators, the devices based on LNOI have larger confinement for the light, resulting in smaller footprints and higher modulation efficiency [3,4]. The waveguide devices in LNOI are usually prepared using dry etching [5]. However, a waveguide that is directly etched can have a significant sidewall angle [6,7] that limits the minimum separation distance between the waveguide edge and the electrode edge, resulting in difficulties in producing devices based on strongly coupled waveguides.

_{3}N

_{4}) has widely been employed in photonic integrated circuits because it is easy to implement and process. A Si

_{3}N

_{4}ridge waveguide loading strip on an LNOI (Si

_{3}N

_{4}-strip-loaded LNOI) can effectively form a composite strip waveguide [8,9,10]. Since the process is only performed for the Si

_{3}N

_{4}layer, this prepared waveguide structure avoids the difficulty of etching the direct LN [11,12]. A Si

_{3}N

_{4}-strip-loaded LNOI structure can be designed to confine most of the energy in the LN layer [13]. Therefore, the roughness of the sidewalls of a Si

_{3}N

_{4}-strip-loaded waveguide has less effect on the transmission losses than that of an etched LN ridge waveguide [14]. More importantly, these types of hybrid structures can take advantage of the properties of different materials to form heterogeneous photonic devices. Compared with silicon, Si

_{3}N

_{4}does not suffer from two-photon absorption, and it has lower material loss [15]. Furthermore, silicon thin film is usually conductive and will screen the modulation field from x-cut LN devices with transverse electric (TE) polarization [16,17]. Si

_{3}N

_{4}-strip-loaded LNOI has been successfully demonstrated for use in E-O [10], second-harmonic generation [18], and integrated platforms [19,20,21]. However, few reports in the literature involve the systematic simulation of E-O Mach–Zehnder modulators (MZMs) in a silicon nitride–lithium niobate thin film hybrid platform. Our work has focused on E-O modulators based on a Si

_{3}N

_{4}-strip-loaded waveguide on LNOI in order to obtain low half-wave voltages and large modulation bandwidths.

_{3}N

_{4}-strip-loaded E-O MZMs in 0.5 μm thick x-cut LNOI are presented. The dimensions of the Si

_{3}N

_{4}-strip-loaded and coplanar waveguide electrode were optimized to achieve ultra-compact routing and high-performance modulation for single-mode operation with transverse electric (TE) polarization. We evaluated the performance of the analyzed modulator based on the separation distance between the electrode edge and the Si

_{3}N

_{4}-strip-loaded edge, the bending radius, the half-wave voltage product (V

_{π}·L), the characteristic impedance, the attenuation constant, the radio frequency (RF) effective index, and the modulation bandwidth. For the modulators that were packaged with 2 μm thick SiO

_{2}(Type I) and unpackaged (Type II), the half-wave voltage-length products were 2.85 and 2.33 V·cm, and the modulation bandwidths with a length of 3 mm were 0.4 and 1.26 THz, respectively. The realization of a Si

_{3}N

_{4}composite strip waveguide could have good prospects for fabricating more advanced and complicated integrated optical devices and circuits based on LNOI.

## 2. Device Description and Methods

_{2}cladding deposited on an LN substrate [2]. The crystal orientation of the LN thin film was chosen to utilize the highest E-O coefficient of LN, r

_{33}= 31 pm/V, at λ = 1.55 µm [22], for the TE mode. To provide lateral optical confinement, a Si

_{3}N

_{4}-strip-loaded waveguide was located at the top of the LN thin film. Coplanar waveguide electrodes were configured in ground-signal-ground form, and two LN waveguides were located in two gaps between the ground and signal metals. To produce a large E-O modulation bandwidth, the coplanar waveguide electrodes were operated in a traveling wave manner and optimized for impedance matching, as well as velocity matching for the microwave and optical signals. Table 1 shows the refractive indices and dielectric constants of the materials in the simulation at a wavelength of 1.55 µm.

## 3. Results and Discussion

_{3}N

_{4}-strip-loaded dimensions based on four aspects: single-mode conditions, the effective refractive index, the separation distance between the electrode edge, and the Si

_{3}N

_{4}-strip-loaded edge, and the optical power confinement in the LN layer. The single-mode conditions were first investigated because of their advantages: (i) There was no energy transformation between modes. (ii) The signal distortion caused by several modes of transmission at different speeds could be avoided [27]. Figure 2a shows the cutoff dimension of the Si

_{3}N

_{4}-strip-loaded waveguide for the TE mode between the single- and multi-mode conditions. The cutoff width and thickness of the Si

_{3}N

_{4}-strip-loaded waveguide for the fundamental mode were both zero. No matter how small the thickness and the width of the Si

_{3}N

_{4}-strip-loaded waveguide were, there was always a waveguide mode [28]. Waveguides of all widths and thicknesses under the curves satisfied the single-mode conditions. For example, for a 0.3 μm thick Si

_{3}N

_{4}-strip-loaded Type I, the cutoff width of the achieved single-mode operation was 1.732 μm. The cutoff thickness decreased with the increase in the Si

_{3}N

_{4}-strip-loaded width. At the same Si

_{3}N

_{4}-strip-loaded thickness, the cutoff width of Type I was larger than that of Type II. Considering the single-mode conditions, the effective refractive index, and separation distance, six combinations of widths and thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguide were selected for both the Type I and Type II structures in subsequent simulations, marked in Figure 2 as circles.

_{3}N

_{4}-strip-loaded waveguides as a function of the width for different thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguides are presented in Figure 2b. The effective refractive index increased with the increasing width and thickness of the Si

_{3}N

_{4}-strip-loaded LNOI. At the same Si

_{3}N

_{4}-strip-loaded width and thickness, the effective refractive index of Type I with the single-mode operation was larger than that of Type II. To ensure that only one electric field intensity peak was supported in the Si

_{3}N

_{4}-strip-loaded waveguide, the width of the Si

_{3}N

_{4}-strip-loaded waveguides should be less than the value of the first-order mode. The hollow circles in the figure correspond to the effective refractive index of six combinations of widths and thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguide for Type I, and the solid circles correspond to the effective refractive index of six combinations of widths and thicknesses of Si

_{3}N

_{4}-strip-loaded waveguide for Type II.

_{3}N

_{4}-strip-loaded edge was selected. The target electrode-induced loss was 0.5 dB/cm in this simulation. The separation distances as a function of the width for different thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguides are shown in Figure 2c. The separation distance decreased with the increasing width and thickness of the Si

_{3}N

_{4}-strip-loaded LNOI. At the same Si

_{3}N

_{4}-strip-loaded width and thickness, the separation distance of Type I was larger than that of Type II. The hollow circles in the figure correspond to the separation distances of the six combinations of widths and thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguide for Type I, and the solid circles correspond to the separation distance of six combinations of widths and thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguide for Type II.

_{3}N

_{4}-strip-loaded LNOI was mainly divided into four parts. The layers from the top to the bottom were the SiO

_{2}layer (Type I) or air layer (Type II), the Si

_{3}N

_{4}-strip-loaded, the LN layer, and the SiO

_{2}cladding layer. As much optical power as possible is required to be concentrated in the LN layer in E-O applications. Figure 3 shows the optical power in the LN layer, with the thickness and width of the Si

_{3}N

_{4}-strip-loaded waveguide as the parameters. The optical power in the LN layer decreased with the increasing width and thickness of the Si

_{3}N

_{4}-strip-loaded waveguide. At the same Si

_{3}N

_{4}-strip-loaded width and thickness, the optical power in the LN layer of Type I was less than that of Type II. The hollow circles in the figure correspond to the optical power in the LN layer for six combinations of widths and thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguide for Type I, and the solid circles correspond to the optical power in the LN layer of six combinations of the widths and thicknesses of Si

_{3}N

_{4}-strip-loaded waveguide for Type II.

_{eff}) of the TE mode of a single waveguide was the difference between the effective refractive index with and without the voltage. Figure 4 shows the effective refractive index change for six combinations of the Si

_{3}N

_{4}-strip-loaded widths and thicknesses for the unit voltage. For an increasing Si

_{3}N

_{4}-strip-loaded thickness and a decreasing Si

_{3}N

_{4}-strip-loaded width combination, the Δn

_{eff}/V increased at first but then decreased after reaching the peak at a thickness of 0.3 μm. For the combination of the same thickness of Si

_{3}N

_{4}-strip-loaded waveguide, the Δn

_{eff}/V of Type I was smaller than that of Type II. The selection of these parameters was insensitive of Δn

_{eff}/V.

_{eff}/V enabled an ultra-compact, high-efficiency, and low-loss E-O MZM. Considering the above factors in the subsequent simulations, the thicknesses and widths of the Si

_{3}N

_{4}-strip-loaded waveguides and the separation distance in Type I and Type II structures are shown in Table 2.

_{3}N

_{4}-strip-loaded waveguide for Type I and Type II were 121,103 and 127,997 V/m, respectively. The electric field in the LN layer of Type I was less than that of Type II.

_{eff}[29,30].

_{eff}, and V is the change in applied voltage. The phase shift is given by the following equation:

_{π}is the half-wave voltage. For the Type I and Type II devices, when the thickness of the Si

_{3}N

_{4}-strip-loaded combination was 0.3 µm, the Δn

_{eff}/V values were 1.36 × 10

^{−5}and 1.66 × 10

^{−5}V

^{−1}, and the half-wave voltage-length products were calculated as 2.85 and 2.33 V·cm.

_{2}was larger than that of air. Then, for each combination of the width and height of the signal electrode, the RF effective mode index and the RF attenuation of the electrodes were further analyzed, as shown in Figure 7b,c. For the RF attenuation, thick and narrow signal electrode combination facilitated the low-loss RF signal. When the electrode thickness was larger than 0.8 µm, the decrease in the RF attenuation was saturated, which was also the preferred region for metal thickness in order to achieve the ultimate performance. The group effective indices of the Si

_{3}N

_{4}-strip-loaded LNOI waveguide for the optical mode are marked in Figure 7c. The group effective index was obviously smaller than the RF effective index for Type I, and the propagation speed of the optical and RF signals was well-matched for Type II. This was because the dielectric constant of the SiO

_{2}was much higher than that of air, so the RF effective index of Type I was significantly higher than that of Type II. In subsequent simulations, considering the RF attenuation and velocity-matching between the RF signal and the optical mode, the signal electrode height was set at 1.8 μm, and the electrode widths for Type I and Type II were set to 4.4 and 4.8 μm, respectively.

_{L}and R

_{G}are the load and generator resistances, respectively. In the expression, Z

_{in}is the modulator input impedance:

_{G}and Z

_{L}are the generator and load impedances, Z

_{0}is the characteristic impedance, $F({u}_{\pm})=(1-{e}^{{u}_{\pm}})/{u}_{\pm}$, where ${u}_{\pm}=\pm {\alpha}_{m}L+j\omega (\pm {n}_{m}-{n}_{g})L/{c}_{0}$, and ${\gamma}_{m}={\alpha}_{m}+j\omega {n}_{m}/{c}_{0}$ is the propagation constant. In this expression, n

_{m}and α

_{m}are the RF effective mode index and RF attenuation. The units of α

_{m}are Np/cm, with 1 Np/cm equal to 8.68 dB/cm. c

_{0}is the speed of light in a vacuum. We assumed R

_{L}= R

_{G}= Z

_{G}= Z

_{L}= 50 Ω.

## 4. Conclusions

_{3}N

_{4}-strip-loaded 0.5 μm thick x-cut LNOI. The widths and thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguides of Type I and Type II were optimized. The optimized values of V

_{π}·L for Type I and Type II were calculated to be 2.85 and 2.33 V·cm, respectively. The widths and heights of the coplanar waveguide electrodes for Type I and Type II were optimized. The −3 dB E-O modulation bandwidths for Type I and Type II with a device length of 3 mm were calculated to be 0.4 and 1.26 THz, respectively. The process of this design, which did not require etching or sawing of LN, was based on a current silicon nitride ultra-low-loss passive optical waveguide.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic of the Si

_{3}N

_{4}-strip-loaded MZM in LNOI. The cross-section schematics of the MZMs of (

**b**) Type I (packaged with 2 µm thick SiO

_{2}) and (

**c**) Type II (unpackaged).

**Figure 2.**(

**a**) Cutoff dimensions for TE mode between the single- and multi-mode conditions; (

**b**) effective indices of the TE fundamental mode and (

**c**) separation distance between the electrode edge and the Si

_{3}N

_{4}-strip-loaded edge as a function of the width for different thicknesses of the Si

_{3}N

_{4}-strip-loaded waveguides. The modes were calculated at λ = 1.55 µm.

**Figure 3.**Optical power distributions in the LN layer of the TE fundamental mode as a function of width for different Si

_{3}N

_{4}-strip-loaded thicknesses. The modes were calculated at λ = 1.55 µm.

**Figure 4.**Effective refractive index change for six combinations of the Si

_{3}N

_{4}-strip-loaded widths and thicknesses for unit voltage. The modes were calculated at λ = 1.55 µm.

**Figure 5.**Dependence of the bending loss on the radius of the bending waveguide. The modes were calculated at λ = 1.55 µm.

**Figure 6.**Optical field distribution of (

**a**) Type I and (

**c**) Type II. Electrostatic field distribution of (

**b**) Type I and (

**d**) Type II after a 1 V voltage was applied to the electrodes.

**Figure 7.**The relationship between the signal electrode height and (

**a**) width, (

**b**) RF attenuation, and (

**c**) RF effective mode index of the coplanar waveguide electrode. The real part of the characteristic impedance was kept at 50 Ω.

**Figure 8.**(

**a**) Characteristic impedance, (

**b**) RF attenuation, (

**c**) RF effective mode index n

_{m}, and (

**d**) modulation response variation as RF frequency.

Material | Refractive Index | Dielectric Constant | |
---|---|---|---|

Ordinary Refractive Index (n _{o}) | Extraordinary Refractive Index (n _{e}) | ||

LN [22] | 2.211 | 2.138 | 28.4 |

SiO_{2} | 1.445 | 3.9 | |

Si_{3}N_{4} | 1.989 | 7.5 |

**Table 2.**The parameters of the dimensions of the Si

_{3}N

_{4}-strip-loaded waveguides and the separation distance.

Type | Thickness (µm) | Width (µm) | Separation Distance (µm) |
---|---|---|---|

Type I | 0.3 | 1.532 | 2.629 |

Type II | 0.3 | 1.46 | 2.336 |

Structure | Experimental or Theoretical | Interaction Length (mm) | V_{π}·L(V·cm) | Bandwidth (GHz) | References |
---|---|---|---|---|---|

SiN_{x}-LNOI | Experimental | 12 | 3 | 8 | [10] |

SiN-LNOI | Experimental | 8 | 3.1 | 33 | [34] |

Si_{3}N_{4}-LNOI | Experimental | 7.8 | 2.24 | 80 | [35] |

SiN-LNOI | Theoretical | 3 | 3.6 | 420 | [36] |

LNOI-SiN_{x} | Experimental | 5 | 6.67 | 30.6 | [37] |

LN ridge | Experimental | 10 | 2.3 | 80 | [3] |

LN ridge | Experimental | 3 | 2.2 | >70 | [33] |

Si-LNOI | Experimental | 5 | 6.7 | >100 | [38] |

Si-LNOI | Theoretical | 5 | 1.76 | 350 | [30] |

Si_{3}N_{4}-LNOI (Type I) | Theoretical | 3 | 2.85 | 400 | This work |

Si_{3}N_{4}-LNOI (Type I) | Theoretical | 10 | 2.85 | 83 | This work |

Si_{3}N_{4}-LNOI (Type II) | Theoretical | 3 | 2.33 | 1260 | This work |

Si_{3}N_{4}-LNOI (Type II) | 10 | 2.33 | 230 | This work |

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## Share and Cite

**MDPI and ACS Style**

Han, H.; Yang, F.; Liu, C.; Wang, Z.; Jiang, Y.; Chai, G.; Ruan, S.; Xiang, B.
High-Performance Electro-Optical Mach–Zehnder Modulators in a Silicon Nitride–Lithium Niobate Thin-Film Hybrid Platform. *Photonics* **2022**, *9*, 500.
https://doi.org/10.3390/photonics9070500

**AMA Style**

Han H, Yang F, Liu C, Wang Z, Jiang Y, Chai G, Ruan S, Xiang B.
High-Performance Electro-Optical Mach–Zehnder Modulators in a Silicon Nitride–Lithium Niobate Thin-Film Hybrid Platform. *Photonics*. 2022; 9(7):500.
https://doi.org/10.3390/photonics9070500

**Chicago/Turabian Style**

Han, Huangpu, Fan Yang, Chenghao Liu, Zhengfang Wang, Yunpeng Jiang, Guangyue Chai, Shuangchen Ruan, and Bingxi Xiang.
2022. "High-Performance Electro-Optical Mach–Zehnder Modulators in a Silicon Nitride–Lithium Niobate Thin-Film Hybrid Platform" *Photonics* 9, no. 7: 500.
https://doi.org/10.3390/photonics9070500