## 4 Discussion  
From the seven recipes of Table 1, we find the highest refractive indices in recipes 2 and 6. In both recipes, RF power is introduced into the process. This produces an increase in the refractive index, the deposition rate, the compressive stress, and the roughness of the thin film. This last parameter, the roughness, makes these thin films inappropriate to be used for the DBR deposition due to the high number of defects that it creates, even if the stress characteristics and the extinction coefficient fit our objectives. These changes occur because the RF power potentiates the attraction of the plasma generated in the ICP coils to the substrate during deposition creating a denser plasma at the sample surface [3; 9; 23]. Further options not considered here would have been to increase the SiH\({}_{4}\)-N\({}_{2}\) ratio providing higher refractive index, but also the absorption in the 1550 region rises and depending on the pressure, this can lead to stress gradients out of the MEMS requirements. This can, to a certain degree, be compensated with the chamber pressure to obtain a balance between  
Figure 4: Cavity length \(L_{cav}\) vs. \(E\cdot W\), showing an almost perfect quadratic dependence (red line fit, \(L_{cav}=a\cdot\left(EW\right)^{2}+h_{0}\)) with an offset \(h_{0}=350\) nm due to the step caused by the chromium sacrificial layer (c.f. Figure 1). The curvature is \(a=7.44536\cdot 10^{-5}\) nm\(/\left(\text{GPa}\cdot\upmu\right)^{2}\). Figure 5: Transmission spectra for different tuning currents of a FP-filter with and arm width of W = 33 \(\upmu\)m and a length L = 23 \(\upmu\)m.  
refractive index and stress gradient as demonstrated in refs [1; 3; 24]. Further alternative recipes demonstrated in the literature use NH\({}_{3}\) as precursor gas, and dilution with Argon for generating a more uniform heat distribution in the chamber. The use of NH\({}_{3}\), however, results in N-H dangling bonds with absorption in the C-band and thus disqualifies for low loss DBR membranes at telecom wavelengths. But it is a viable option for low loss material in the 300 nm to 1100 nm range [25] where our recipe is lossy. Argon could help for a more uniform distribution; however, it caused plasma instabilities in our system. This led us to choose recipe 4 to be employed for the DBRs that form the FP filter. It provides a much higher refractive index as compared to stoichiometric Si\({}_{3}\)N\({}_{4}\) (\(n\)-1.95) and sufficiently low extinction coefficient while keeping its stress inside the required parameters that allow functional MEMS. Other studies have achieved higher refractive index with the same deposition temperature and precursor gases as in [2] where the refractive index has a maximum value of 2.6. Nevertheless, this study used low pressures that are not achievable with the PECVD machine employed in our study, and RF power that as already mentioned causes excessive film roughness, incompatible with DBR deposition. Figure 3 shows the reflectivity band of the FP-filter's top DBR, that covers two important wavelength ranges, namely, 1310 and 1550 nm. Using the matrix method, the theoretical reflectivity and stopband of this DBR is of 0.997 and 510 nm, respectively, under vertical incidence. The ellipsometric measurements shows inferior results, this is because of the angle at which ellipsometry was performed makes the reflectivity band less broad than it would be at 0\({}^{\circ}\) measurement and the incidence angle causes a shift in the centre wavelength towards shorter wavelengths as described in [26]. This effect can be noticed when comparing the 40\({}^{\circ}\) reflection bands plotted in the figure with the simulation at vertical incidence. A similar work on DBR was performed by [9] though with different reflectance band centre. This study used PECVD at 75 \({}^{\circ}\)C with no RF power obtaining values of stress that flows from compressive to tensile with a refractive index in the 1550 nm range of about 2 using the same precursor gases that were applied in our depositions.