# Improvement of Porous GaN-Based UV Photodetector with Graphene Cladding
## 4 Discussions  
The formation of porous morphology on GaN through PEC can be ascribed to the following chemical reaction [21]:  
\[2\text{GaN}+6\text{h}^{+}\ \rightarrow\ 2\text{Ga}^{3+}+\text{N}_{2} \tag{4}\]  
where GaN underwent dissolution in an acidic medium in the presence of photogenerated carriers due to UV light illumination. This electrochemical process occurred preferentially towards the doped region, hence leading to the formation of a porous network. The average pore diameter as determined from the histogram was 35 nm, and with densely packed pores distributed throughout the porous GaN surface, this led to higher surface area that promoted greater sensing compared to that of the as-received GaN. GaN in general possessed a hexagonal wurtzite structure, with a space group of \(\text{C}^{4}_{\text{6V}}\). Under group theory, a total of eight sets of phonon modes were predicted measured from \(\Gamma=0\) in the Brillouin zone. These modes were categorized in this manner: 2E\({}_{2}\), 2A\({}_{1}\), 2E\({}_{1}\), and 2B\({}_{1}\). From there, one of the A\({}_{1}\) and E\({}_{1}\) modes was Raman active, while all of the B\({}_{1}\) modes were silent [46]. In Figure 4a, the as-received GaN was comprised of two notable peaks that were ascribed to E\({}_{2}\)(HI) and A\({}_{1}\)(LO). When correlated to the Raman configuration of \(z(x\), unpolarized)\(\overline{z}\), it is discernible that the as-received GaN was \(c\)-oriented. Due to the dissolution of GaN through PEC etching, other facets have been exposed, and as light scattering occurred along the pore channels, modes that were deemed forbidden under the aforementioned Raman configuration such as E\({}_{1}\)(TO) and A\({}_{1}\)(TO) would be shown. The differences among Raman spectra, seen in Figure 4b,c, have provided some insights into the interaction between graphene and the porous GaN surface. Prior to that, the characteristics of the graphene film need to be studied. Through studying the Raman spectra in Figure 4b, it can be seen that CVD-grown graphene possessed higher I\({}_{\text{D}}\)/I\({}_{\text{G}}\) than that of EC-exfoliated graphene. This is largely attributed to the growth mechanism of CVD graphene employing heptane as a precursor. For typical CVD graphene, hydrocarbon precursors, such as methane, underwent stepwise decomposition under hydrogen ambient, subsequently condensed on the copper surface. Due to the poor solubility of carbon towards copper, additionally being the mono carbon atom, the condensed carbon atoms would have more room for crystallization, which resulted in larger grains. In contrast to the use of heptane (heptane contained seven carbon atoms), the decomposition of a longer hydrocarbon chain would be less efficient, hence resulting in smaller crystallites being formed. The I\({}_{\text{D}}\)/I\({}_{\text{G}}\) ratio can be further used to determine the average crystallite size (I\({}_{\text{a}}\)) and average distance between defects (L\({}_{\text{D}}\)) by employing the Tuinstra-Koenig relation [47]:  
\[(\text{L}_{\text{D}})^{2}\Big{(}\text{nm}^{2}\Big{)}=\Big{(}1.8\ \times\ 10^{-9} \Big{)}\times\lambda^{4}\ \times\ \Big{(}\frac{\text{I}_{\text{D}}}{\text{I}_{\text{G}}}\Big{)}^{-1} \tag{5}\]  
\[\text{L}_{\text{a}}(\text{nm})=\Big{(}2.4\ \times\ 10^{-10}\Big{)}\ \times\lambda^{4}\ \times\ \Big{(}\frac{\text{I}_{\text{D}}}{\text{I}_{\text{G}}}\Big{)}^{-1} \tag{6}\]  
where \(\lambda\) is the wavelength of the incident Raman laser, which is 514.5 nm in this work. The L\({}_{\text{a}}\) for EC- and CVD graphene were 17.5 and 11.6 nm, while those of L\({}_{\text{D}}\) were 11.5 and 9.3 nm. The comparable L\({}_{\text{a}}\) to L\({}_{\text{D}}\) infer that defects would be located at the edges of graphene crystallites. This leaves the in-plane domains having available \(\pi\)-bonds that would interact with the porous GaN surface. Figure 4c shows the Raman spectra of graphene cladding on the porous GaN surface.