## 4 Discussion
These silicate ions subsequently form Si(OH)\({}_{4}\) (Equation (5)): \[\text{Si}(\text{OH})_{5}^{-}\ \rightarrow\ \text{Si}(\text{OH})_{4}+\text{ OH}^{-}\] (5) Subsequently, Si(OH)\({}_{4}\) can change into siloxane chains, as described in Equation (6): \[\text{Si}(\text{OH})_{4}\rightarrow\ (\text{HO})_{3}\text{SiOSi}(\text{OH})_{3}+ \text{ H}_{2}\text{O}\] (6) Given that the bonding interface is a confined system (interface width \(\approx\) 1 nm), the silicate compound could condense elsewhere at the interface [58]. In our context, it is conceivable that condensation is more efficient around contact points, potentially due to an increased number of binding sites, thereby resulting in higher bonding energies (see Figure 12). These contact points experience compression (approximately 100 bars [50]), which could explain the localization of condensation to mitigate elastic energy. Enlarging the contact point will reduce the compression pressure inside the asperities induced by van der Waals. This will reduce the interfacial elastic mechanical energy. Figure 11: Asperity contact model with flattened asperities through silica volume hydrolysis. However, this third model should no longer be considered. As demonstrated by [PERSON] et al. [59], certain specific molecules can boost adhesion to the same extent without etching the SiO\({}_{2}\) layer. Obviously, without silica dissolution phenomenon, no silicates condensation could appear. [PERSON] evaluated the impact of CsF, CsOH, and NaOH on bonding energy evolution during post-bonding annealing treatment. As shown in Figure 13, all three salts have the same effect on adherence, with the fluoride ion (F\({}^{-}\)) exhibiting the same impact as the hydroxide ion (OH\({}^{-}\)). However, as depicted in Figure 14, CsF does not etch silica more than deionized water (DiW), whereas NaOH shows a significantly higher etching rate. Therefore, the primary mechanism for bonding energy enhancement does not appear to depend on silica dissolution into silicates and condensation of these silicates on contact points. To differentiate between the two first models, a comparison with plasma effects at room temperature has been performed (see Figure 15). Indeed, a reactive ion etching (RIE) plasma surface treatment prior to bonding is known to increase direct bonding energy at room temperature while waiting in clean room environments [39]. As shown in Figure 15, an increase by a factor of 11 could be obtained after two months with bonding energy reaching 1.1 J/m\({}^{2}\). In contrast, the addition of DEAE at the bonding interface, without plasma pre-treatment, does not yield such a bonding energy increase at room temperature. An increase by a factor of just three is obtained, with bonding energy remaining below 400 mJ/m\({}^{2}\). Figure 12: Asperity contact model with surface hydrolysis condensation. Figure 13: Bonding energy as a function of annealing temperature for the Reference (no catalysts), NaOH, CsOH, and CsF samples for 2 h annealing [59]. Regarding the first model--silanol condensation enhancement--our silica surfaces are cleaned using chemical treatments, particularly SC1 cleaning, which, as shown by [PERSON] [49], fully hydrolyzes the silica surface, resulting in the maximum concentration of silanol groups. Neither plasma treatment nor the application of basic molecules alters the silanol density. Perhaps it could decrease this density, but it could not increase as it is already fully hydrolyzed due to the chemical SC1 precleaning. Now, if we consider that silanol condensation alone is responsible for the bonding energy enhancement, the lack of bonding improvement at room temperature with the basic molecule treatment suggests it would similarly fail with plasma treatment as both surfaces have the same silanol density. This implies that another mechanism must be responsible for the observed adherence increase. On a chemically precleaned surface, the effect of plasma treatment occurs at the subsurface level.