## 4 Results
### Non-Vertical Sidewalls  
During the fabrication of slot-waveguides, silicon deep etching is applied in order to form the slot region. While doing so, it is often not possible to obtain perfectly vertical sidewalls. Therefore, the sidewalls will be tilted by an angle \(\theta\) after etching. This obviously affects the modal-field distribution of the structure, visible in Figure 5. To take these manufacturing tolerances into account, we calculated the impact on the effective refractive index \(n_{\text{eff}}\). A linear shift can be observed, increasing with the tilt angle \(\theta\). We defined the percentage of effective refractive index shift at a given tilt angle with respect to perfectly straight sidewalls by  
\[\eta(\theta)=\frac{n_{\text{eff}}(\theta)}{n_{\text{eff}}(\theta=0^{\circ})} \cdot 100\%. \tag{4}\]  
The change \(\eta(\theta)\) ranges from 1.6% to 7.9%, as shown in Figure 6. With increasing slot width \(s\), the influence of the tilt angle \(\theta\) becomes less pronounced, due to the relative large distance between the two silicon wires. Comparing Figure 6a,b shows that the difference between both concentration is negligible and, hence, the tilt angle \(\theta\) has a more dominant effect on the effective refractive index.  
Figure 4: Enlarged section of the slot-waveguide’s design and denotation of its parameters. A large tilt angle \(\theta=9^{\circ}\) has been used for better visibility.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Parameter** & **Standard Value** \\ \hline \(\theta\) & tilt angle & \(0^{\circ}\) \\ \(w\) & waveguide width & 180 nm \\ \(y\) & waveguide height & 220 nm \\ \(h\) & slab height & 30 nm \\ \(s\) & slot width & variable \\ \(\lambda\) & wavelength & 1550 nm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Slot-waveguide parameters and their standard values.  
The difference in the effective refractive index between the two concentrations \(C_{1}=0\,\mathrm{wt}\%\) and \(C_{2}=10\,\mathrm{wt}\%\) is given by  
\[\Delta n_{\mathrm{eff}}=n_{\mathrm{eff}}(C_{2})-n_{\mathrm{eff}}(C_{1}). \tag{5}\]  
The results of our simulation study is shown in Figure 7a. There is a clear maximum at \(s=60\,\mathrm{nm}\) and \(\theta=0^{\circ}\) of \(\Delta n_{\mathrm{eff}}=0.0187\), while at an increasing tilt angle the behavior follows a linearly decreasing trend down to \(\Delta n_{\mathrm{eff}}=0.0157\). For the confinement factor within the slot region \(\Gamma_{\mathrm{slot}}\), we find that it has a maximum of \(\Gamma_{\mathrm{slot}}=0.181\) at \(s=60\,\mathrm{nm}\) and \(\theta=0^{\circ}\), from where it linearly decreases with \(s\). However, considering the very low change of \(\Delta\Gamma_{\mathrm{slot}}=0.005\) at its maximum and even negative values below \(s=70\,\mathrm{nm}\), the influence of the tilt angle on the confinement factor appears negligible in Figure 7b.  
Figure 5: Influence of sidewall tilt angle \(\theta\) on the modal properties. It becomes visible that confinement of the optical mode decreases with larger angle.  
Figure 6: Percentual shift in effective refractive index \(\eta(\theta)\) over the tilt angle \(\theta\) of both concentrations, with slot width \(s\) as parameter.