# High-\(Q\) TeO\({}_{2}\)-Si Hybrid Microring Resonators
## 3 Microring Resonator Characterization
Close-up views of the under-coupled resonances for the (**d**) uncoated, (**e**) SiO2-coated, and (**f**) TeO2-coated silicon microring resonators showing an intrinsic quality factor, \(Q_{i}\), of 1.5 \(\times\) 10\({}^{6}\), corresponding to 0.42 dB/cm optical propagation loss for the TeO2-coated silicon microring resonator. We calculated the theoretical radiation loss and equivalent \(Q\) factor for the TeO\({}_{2}\)-coated silicon microring resonator structure using an FEM bent eigenmode solver, for varying bend radii, as shown in Figure 4a. The dashed lines in Figure 4a indicate the experimentally determined internal \(Q\) factors for the MRRs with different claddings. The calculated radiation-limited \(Q\) factors were measured to be 3 \(\times\) 10\({}^{8}\), 1 \(\times\) 10\({}^{8}\), and 1.7 \(\times\) 10\({}^{7}\) for the TeO\({}_{2}\)-clad, SiO\({}_{2}\)-clad, and unclad microring resonators, respectively, at a radius of 30 \(\upmu\)m, corresponding to 0.002 dB/cm, 0.007 dB/cm, and 0.04 dB/cm propagation losses. The results show that the radiation loss was low (\(Q>\) 10\({}^{7}\)) at the selected bend radius of 30 \(\upmu\)m.  
The surface scattering loss is the waveguide scattering loss per unit length and was calculated using the widely used Payne-Lacey model [34]. This model has been applied previously to 3D-SOI bent waveguides [35, 36, 37] such that  
\[\alpha_{Surface\ Scattering}=4.34\frac{\sigma^{2}}{\sqrt{2}k_{0}\left(\frac{W}{2 }\right)^{4}n_{1}}f.g.\eta \tag{1}\]  
where \(\sigma,k_{0}\), \(W\), and \(n_{1}\) are the roughness, free-space wave vector, waveguide width, and core index, respectively. The function \(f\) is determined by the correlation length (\(l_{\text{c}}\)), while g is determined by the geometry of the waveguide and accounts for ridge-type waveguide structures such as the SOI ridge rings investigated here. Both \(\sigma\) and \(l_{\text{c}}\) are typically measured via atomic force microscopy or scanning electron microscopy of a waveguide. We assumed values of 1.0 nm and 50 nm for \(\sigma\) and \(L_{\text{c}}\), respectively, based on previous measurements on SOI waveguides [35, 36, 37, 38]. We also assumed the roughness of the TeO\({}_{2}\) coating can be neglected based on previous AFM roughness measurements showing <1 nm root mean square (RMS) surface roughness on low-loss sputtered thin films [38]. Details of the expressions g and f can be found in the Payne-Lacey model [34]. The Payne-Lacey model was modified for bent waveguides and rings by adding a correction factor \(\eta\)[35] which allows us to accurately predict the loss of bent waveguides or resonators given the value of the sidewall roughness. The correction factor \(\eta\) is defined as the ratio of the mode overlap between bent and straight waveguides using an FEM simulation. In the Payne-Lacey bending model, \(\eta\) is considered 1 in the straight waveguide. We plot the sidewall scattering loss as a function of the wavelength in Figure 4b. The experimental loss obtained from the quality factor measurements of the MRRs follows the same trend as the Payne-Lacey model, which indicates that the losses in the different MRRs are largely  
Figure 4: (**a**) Calculated internal Q factor of uncoated-, SiO\({}_{2}\)-coated, and TeO\({}_{2}\)-coated silicon resonator waveguides versus bend radius. (**b**) Calculated scattering loss as a function of wavelength for microring resonators with air, SiO\({}_{2}\), and TeO\({}_{2}\) claddings based on the 3D Payne–Lacey model. influenced by the core cladding refractive index contrast and sidewall roughness [23]. These results show that the application of a high-refractive-index TeO\({}_{2}\) top cladding can be considered promising for low-loss passive components as well as active devices such as monolithic amplifiers and lasers with improved performance on the SOI platform [32].