## 4 Discussion  
The lattice parameter of the (001) silicon surface is 0.543 nm with two atoms per lattice cell, resulting in a silicon surface density of about 7 atoms/nm\({}^{2}\). A fully hydrophilic silicon dioxide has, according to [PERSON], a maximum silanol concentration of 5 to 8 nm\({}^{-2}\)[49]. Even with the highest surface concentrations of molecules or cations, the wafer surface is covered by less than 1/10 of a monolayer of DEAE or NaOH. A small quantity of active molecules significantly enhances the bonding energy, suggesting that molecules act more as catalysts than directly participating to the adherence mechanism. Three mechanisms can be proposed to elucidate the bonding energy enhancement. 1. According to the model of [PERSON] et al., direct bonding relies heavily on the contact of asperities [50]. For hydrophilic bonding, at room temperature, wafer adhesion primarily results from capillary bridges, hydrogen bonds and van der Waals forces [6]. Even at room temperature, occasional covalent bonds may also form at contact points (asperity summits), accounting for the observed increase in bonding energy under specific circumstances at room temperature [39]. OH\({}^{-}\) ions are known to speed up the dynamics of siloxane bond formation by condensation of silanols, as observed e.g., in silica gel formation processes [49]. In silanol condensation, OH\({}^{-}\) play the role of nucleophilic agent. Increasing the pH will then increase the silanol condensation kinetics. It is indeed widely recognized that OH\({}^{-}\) ions can initiate nucleophilic attacks on surface Si atoms, resulting in the formation of siloxane bonds [51], as shown in Equations (2) and (3). \[\text{SiOH}+\text{ OH}^{-}\rightarrow\text{ SiO}^{-}+\text{H}_{2}\text{O}\] (2) In presence of SiO\({}^{-}\), the formation of siloxanes bonds is favored (Equation (6)). \[\text{SiOH}+\text{ SiO}^{-}\rightarrow\text{ SiOSi}+\text{OH}^{-}\] (3) As obvious from the equilibrium between Equations (5) and (6), OH\({}^{-}\) ions directly catalyze the condensation reaction of silanols into covalent siloxane bonds, resulting in a bonding energy increase. 2. Based on the mechanism proposed by [PERSON] et al. [39], during annealing, water molecules trapped at the bonding interface hydrolyze silicon dioxide asperities. As the annealing progresses, water molecules infiltrate the oxide asperities volume and break certain silanol bonds. Consequently, asperities become more viscoplastic and are flattened, enabling the formation of new interfacial covalent bonds and thereby increasing the bonding energy (see Figure 11). Extensive research has been conducted on the exacerbation of silica and quartz hydrolysis under alkaline conditions [52; 53]. Hydrolysis even intensifies with higher temperatures. The incorporation of basic molecules, which change the pH of interfacial water, increases hydrolysis mechanism described above and explains the bonding energy enhancement. This influence becomes even more pronounced during post-bonding anneals. Notably, the impact of alkaline ions on silica hydrolysis has also been extensively explored [54; 55]. In addition to pH influence, Na\({}^{+}\) ions could also enhance the silica hydrolysis. However, as shown by [PERSON] et al. [56], the influence of a high pH (\(\geq\)10) predominates over the type of cation influence. The cation influence might then be neglected for the moment. 3. Another mechanism could be proposed suggesting that bonding energy enhancement can be attributed to silica dissolution and immediate condensation on the bonded asperity surface. It is well-established that OH\({}^{-}\) ions attack and dissolve silica surface, as described in Equation (4) [57]: \[\text{SiO}_{2}+\text{ OH}^{-}+2\text{H}_{2}\text{O}\ \rightarrow\ \text{Si}(\text{OH})_{5}^{-}\] (4) A portion of the silica is dissolved increasing Si(OH)\({}_{5}^{-}\) species in the interfacial water.