## 3 Results and Discussion  
### SiOC Layer Properties  
SEM cross-section image of the SiOC film deposited on SiO\({}_{2}\)/Si wafer under the optimized sputter process is displayed in Figure 3. The thickness of the SiOC layer is determined to be 400 nm. The deposited SiOC film shows dense columnar structure with pillars perpendicular to the plane of film. The columnar structure of the film provides a basis for anisotropy investigation and is taken into consideration during the optical characterization of SiOC film. The columnar structure is a typical feature in sputtered SiOC films that were deposited under different conditions, however the films were amorphous to XRD [14]. Figure 3: SEM cross-section image of SiOC deposited layer on SiO\({}_{2}\)/Si wafer. Figure 2: (**a**) Schematic of optical bench setup used for SiOC waveguides characterizations, (**b**) the measurement setup showing alignment of SiOC chip with small core optical fibers. Figure 4a shows 3D topographical image of the SiOC film scanned with AFM in contact mode over an area of 100 \(\upmu\)m\({}^{2}\). The scans were performed at five different locations on the four-inch wafer and the rms roughness is estimated to be 0.88 nm, sufficiently smooth for the realization of optical waveguides. In Figure 4b, 1D measured profile of the AFM image is given showing peak-to-valley roughness that is in-line with surface roughness estimated with ellipsometry. The optical properties of the deposited SiOC film were characterized with variable angle spectroscopic ellipsometry in the infrared wavelength region from 1200 nm to 1600 nm. The measurement angles were 65\({}^{\circ}\), 70\({}^{\circ}\), and 75\({}^{\circ}\) which are around the Brewster's angle of Si substrate. Prior to SiOC film, the SiO\({}_{2}\)/Si wafer was characterized with ellipsometry to obtain the thickness and accurate optical constants of SiO\({}_{2}\). The refractive index of SiO\({}_{2}\) was determined as 1.444 at \(\lambda\) = 1550 nm. The tabulated optical constants of crystalline Si substrate were used from the WVASE32 database [17]. Since ellipsometry is sensitive to film roughness conditions, surface roughness (SR) layer [16] was added to simulate roughness on SiOC film which improved fit and MSE. The SR layer that is the ellipsometry equivalent of AFM is estimated around 2 nm and agrees well with the AFM data. The ellipsometric \(\psi\) and \(\Delta\) data acquired at different angles and their respective model curves are given in Figure 5.  
The four-layer anisotropic optical model discussed in Section 2 was used to fit the experimental data (green curves) and the calculated model data (red curves) matches well over the entire spectral range. Material anisotropy is expected from the columnar structure present in the sputtered SiOC film as shown in SEM image (see Figure 3). Our measurements indicate that the out-of-plane refractive index (n\({}_{\text{e}}\)) is higher than the in-plane index (n\({}_{\text{o}}\)) by 0.02438. These results agree with the studies reporting anisotropy in different material thin films with columnar structure where the in-plane refractive index is smaller than out-of-plane refractive index [18; 19; 20]. Therefore, the origin of the anisotropy is attributed to the columnar structure oriented normal to the plane of SiOC film. The anisotropy exhibited by SiOC film is on the order of 10\({}^{-2}\), the optical waveguides are sensitive to even this level of anisotropy because the two polarizations (TE and TM) will see a different index of refraction and propagate with different effective indices. Figure 4: (a) 3D AFM topography scan of SiOC film surface (color scale from -5 nm to +5 nm); (b) 1D measured profile of AFM image: a peak-to-valley roughness of about 2 nm is observed that agrees well with surface roughness estimated with spectroscopic ellipsometry.