# Process Development of Low-Loss LPCVD Silicon Nitride Waveguides on 8-Inch Wafer
## 2 Design of Silicon Nitride Waveguide  
In silicon photonic integrated circuits, a rectangular optical waveguide is the basic component, and a single-mode waveguide is commonly used to avoid inter-mode interference and mode dispersion. In order to guarantee the single-mode condition of the Si\({}_{3}\)Nrectangular waveguide, we have simulated the mode properties of the Si\({}_{3}\)N\({}_{4}\) waveguide using the Finite Difference Eigenmode solver (FDE) in Lumerical's Mode Solution software. The structure is shown in Figure 1a; the thickness of the lower cladding layer is 3.6 \(\upmu\)m, the thickness of the core layer is 0.4 \(\upmu\)m, and the thickness of the upper cladding layer is 2.6 \(\upmu\)m.  
To determine the single mode condition, the width of the silicon nitride waveguide was scanned at a wavelength of 1550 nm, and the relationship between the waveguide width and the effective refractive index (n\({}_{\text{eff}}\)) of the waveguide is shown in Figure 2. According to the orange dashed line, the width limit of the single-mode condition is 1.0 \(\upmu\)m.  
Based on the above simulation, the critical bending radius of the waveguide with a width of 1.0 \(\upmu\)m was then simulated by the FDTD (Finite Difference Time Domain) simulation module. The relationship between the bending loss and the bending radius is shown in Figure 3. With the increasing bending radius, the bending loss decreases exponentially. When the bending radius is larger than 50 \(\upmu\)m, the bending loss of pre 90\({}^{\circ}\) bending waveguide basically remains smaller than 0.0092 dB, so we set the minimum bending radius to 50 \(\upmu\)m in the optical circuits.  
Figure 1: (**a**) Schematic cross-section of a rectangular Si\({}_{3}\)N\({}_{4}\) waveguide, (**b**) Schematic of light transmission in the waveguide.  
Figure 2: The simulation curve of the effective refractive index under different waveguide widths.  
In order to test the waveguide, an edge coupler was used for the coupling between the waveguide and the fiber in this work, considering the higher coupling efficiency, polarization independency, and wider bandwidth compared to the grating coupler [26; 27; 28]. The structure of the edge coupler is shown in Figure 3. In order to avoid damaging the coupler during the deep trench process, the coupler tip is set 2 \(\upmu\)m away from the deep trench.  
Based on the structure shown in Figure 4, we set the mode field diameter (MFD) of the light source to 2.5 \(\upmu\)m, similar to that of the lensed fiber we used in tests; the effect of the tip width (W\({}_{\text{t}aper}\)) was firstly simulated with the length (L\({}_{\text{t}aper}\)) of 100 \(\upmu\)m. The W\({}_{\text{t}aper}\) was scanned from 0.1 \(\upmu\)m to 0.4 \(\upmu\)m, and the results are shown in Figure 5a. The highest coupling efficiency of 88.1% was achieved at W\({}_{\text{t}aper}\) = 0.3 \(\upmu\)m, so we set the W\({}_{\text{t}aper}\) to 0.3 \(\upmu\)m in our design. Subsequently, the L\({}_{\text{t}aper}\) was simulated with a W\({}_{\text{t}aper}\) of 0.3 \(\upmu\)m. The L\({}_{\text{t}aper}\) was scanned from 5 \(\upmu\)m to 300 \(\upmu\)m; the results are shown in Figure 5b. In the range of 5-50 \(\upmu\)m, the condition of adiabatic coupling could not be achieved, which caused large radiation loss. The coupling efficiency was stable after 100 \(\upmu\)m, and a coupling efficiency of 88.6% was realized with a length of 200 \(\upmu\)m.  
Figure 4: Schematic of inverse tapered edge coupler.  
Figure 3: The simulation curve of the waveguide bending loss per 90\({}^{\circ}\) under different bending radii.  
The final structural parameters of the inverse tapered edge coupler are shown in Table 1. The simulation results are shown in Figure 6. It can be seen that the lightwave is transferred to the well-confined waveguide from the input fiber through the edge coupler.