## 3 Discussion  
In practical applications, it may not be easy to fabricate the air gap using a selective wet etching process due to the capillary-force action [20,21]. Therefore, a few parts of the sacrificial layer should be carefully left to avoid the collapse of the dielectric slots by controlling the etching conditions [27]. We studied the effect of the remaining sacrificial layer on optical loss and \(S\) when the horizontal etching depth was varied. In the simulation, we used the optimized PhC NB cavity with three mirror holes as shown in Figure 3b. Here, we assume that the etching speed from the sidewall is isotropic. The inset of Figure 5a shows the horizontal cut-view of the sacrificial layer (SiO\({}_{2}\)) at the center of the PhC NB cavity structure. The black and gray areas indicate the remaining SiO\({}_{2}\) layer and the air, respectively. The white lines indicate the outline of the Si dielectric slot. When the etching depth exceeds \(0.15a\), SiO\({}_{2}\) at the cavity region is completely removed. Therefore, from the simulation results, both the Q-factor and \(S\) are almost constant when the etching depth is over \(0.15a\). However, if the etching depth is less than \(0.15a\), \(S\) decreases suddenly, which is caused by the reduction of the electric field in the environment. When the air switches to SiO\({}_{2}\), the mirror strength increases due to the red-shift of the TM band edge modes. Consequently, the waveguide loss decreases and the Q-factor increases. In consideration of mechanical stability and easy fabrication, the PhC NB cavity with a SiO\({}_{2}\) layer after fine selective etching (depth \(<0.05a\)) is a good candidate for practical applications of gas sensing because of the high Q (\(>5000\)) and \(S\) (\(>800\)). Figure 4: Characteristics of the air gap cavity mode in a PhC NB cavity with various thicknesses (\(t\)) of the Si waveguide. (**a**) Q-factor, (**b**) \(S\), and (**c**) figure of merit (FOM) as functions of the thickness of the horizontal air gap (\(t_{\rm g}\)). In the simulation, the number of mirror holes is three, \(w=0.95a\), \(r_{0}=0.45a\), and \(\Delta r/r_{0}=0.10\). The circles in (**c**) indicate that the optimal conditions of each Si waveguide have a similar Q-factor (\(\sim\)1000) and \(S\) (\(\sim\)1000 nm/RIU). Figure 5: **(a)** The effect of the remaining sacrificial layer on the Q-factor and \(S\) of the air gap mode in the PhC NB cavity as a function of etching depth. The inset shows a horizontal cut-view of the structure with different etching depths. Optimization of the waveguide structure of the PhC NB cavity for refractive index sensing. (**b**) Transmitted spectra of the PhC NB cavity with different background refractive indices. The inset graph shows the magnified spectra around the resonant wavelength of the air gap mode. Finally, we studied the transmission spectra in an Si/air/Si TM waveguide system with the optimized air-slot cavity structure. In the simulation, the total number of mirror holes was set as five in order to save computational time. Figure 5b shows the transmission spectra of the PhC NB cavity with different refractive indices of the environment. The sharp peak observed near 1550 nm corresponds to the TM air gap cavity mode with \(a\) = 585 nm. Below 1550 nm, the transmitted intensity is zero owing to the PBG effect. However, modulated peaks are observed beyond 1600 nm. These are the higher order TM air gap cavity modes in the PhC NB cavity. According to the magnified spectra shown in the inset of Figure 5b, the Q-factor and \(S\) of the air gap cavity mode are 4000 and 1000 nm/RIU, respectively. We believe that this high value of Q and ultrasensitive PhC NB TM waveguide system with very small dimensions (\(\sim\)14 \(\times\) 0.5 \(\times\) 0.8 \(\upmu\)m\({}^{3}\)) can be considered promising for compact optical sensors in photonic integrated circuits composed of TM waveguide structures with low index slots filled with dielectric gain media or non-linear materials [19].