Firstly, the defects in a-SiO₂/Si(100) interface are briefly introduced to facilitate the subsequent simulation of its reaction with H₂O. There are two different types of defects in a-SiO₂/Si(100) interface, namely P _b0 and P _b1 defects. Among them, P _b0 defect is located in the second unoxidized silicon atomic layer adjacent to the interface transition zone, and it is constructed by removing one of the Si atoms from the unoxidized top layer on the silicon side, which can be represented as ∙Si-(-Si)₃, as shown by the blue Si defect atom in Figure 1A. The dangling bond of it lies along the [111] direction (54.74°) (Li et al., 2019b), and the remaining dangling bonds of three defect atoms (silicon atoms 1, 2 and 3 in Figure 1A) can be passivated by hydrogen atoms into the form of Si-H, which has no effect on the defect model due to the lack of electrical activity.

In addition to P _b0 defect, the a-SiO₂/Si(100) interface also involves another dangling bond defect, whose defect density is lower than that of P _b0 , which is called P _b1 defect. Different from P _b0 defect, P _b1 is created by removing one of the oxygen atoms from a-SiO₂/Si(100) interface, resulting in it being located on the top layer of bulk silicon and the dangling bond is roughly along the [112] direction (30–36°) (Li et al., 2019b), which is not consistent with any chemical bond orientation. A more intuitive schematic diagram of the location of P _b0 and P _b1 defects in a-SiO₂/Si(100) is shown in Supplementary Figure S2. Moreover, P _b1 defect is extremely sensitive to the local structure deformation. Depending on the different positions of the defect, it can be divided into dimer, bridge and AOD (asymmetric oxidized dimer) models, and the latter has been verified to be superior to the former two in terms of Fermi contact value and dangling bond orientation (Poindexter et al., 1981) (more details in Supplementary Figure S3). Considering that the interface transition region of the amorphous model is more complicated than that of the crystal model, the atomic configuration around the defects of a-SiO₂/Si(100) interface will significantly influence the simulation results. In order to make the results more convincing, we simulated the reaction process between P _b1 defect with AOD configuration at three random positions (as shown in Figures 1B–D) and H₂O, and compared the reaction results to obtain a more reliable conclusion.

Here, we will simulate the interaction of H₂O and P _b0 defect concretely. First, place a H₂O at an appropriate position around the defect atom (Si89), and make sure that it does not bond with other atoms near the defect, so the initial state 00 for the reaction of P _b0 defect and H₂O is constructed, as shown in Figure 2A. For the final state 05, one hydrogen atom (H39) in H₂O is attached to the nearest neighboring oxygen atom (O18) with a form of proton, while the remaining hydroxyl group is bonded with Si89 to passivate the dangling bond defect, so that the system can reach a stable structure. Furthermore, we have subtracted an electron from the initial state to ensure the conservation of the electron numbers before and after the reaction, whose equation can be expressed as: P b 0 + + H 2 O → P b 0 − OH + H + (1)

After determining the initial and final state of the reaction, the CI-NEB method based on first-principles calculation is employed to simulate the reaction process of H₂O and P _b0 defect in a-SiO₂/Si(100) interface, as shown in Figure 2A. Compared with Si89, H₂O is closer to the silicon atom (Si36) passivated by H atom (2.500 Å), thereby the oxygen atom (O129) in H₂O prefers to connect with Si36 in the initial stage. This step can cause Si36 to change from a quadruple to a quintuple coordination, which will further increase the energy of the system, as shown in Figure 2B. Next, H39 in H₂O detaches from its parent and gradually approaches the position of O18 until after connection with it, thus reaching the saddle point 02 of the reaction. As the reaction continues, the distance between H₂O and Si89 gradually becomes smaller, so that they are linked to each other, and the energy of the system begins to show a downward trend. Moreover, the increase in the distance between H₂O and Si36 passivated by hydrogen atom leads to the cleavage of the Si36-O129 bond, then Si36 is also restored to a stable quadruple coordination from the preceding quintuple coordination. Finally, H39 in H₂O is bonded with O18 (1.006 Å) in a form of proton, while the remaining hydroxyl group is bonded with Si89 (1.685 Å) in order to passivate the dangling bond defect, so that the system reaches the most stable state. As shown in Figure 2B, the forward and reverse reaction barriers are 0.73 and 1.58 eV, respectively. In the whole reaction, the variation of interatomic bond length around the defect is shown in Table 1.

In the above reaction, we noticed that when the hydroxyl group in H₂O passivates the dangling bond, the position of O129 is closer to Si36 passivated by hydrogen atom than Si89. As a result, the hydroxyl group in H₂O is easier to interact with Si36, which makes Si36 vary from quadruple to quintuple coordination, resulting in an overall increase of the energy. In order to avoid this situation from adversely affecting the reaction, we adjusted the spatial position of Si36 accordingly. At the same time, the direction of the dangling bond passivated by hydrogen atom is also changed from the original [ 1 ¯ 11 ] to [ 1 1 ¯ 1 ¯ ] , thereby expanding the space where H₂O exists.

As shown in Figure 3A, we reconstructed the initial and final state of the reaction according to Eq. 1. On this occasion, H₂O first moves towards the position of Si89 and bonds with it to achieve the expected purpose of passivating dangling bond, which results the energy of intermediate states 01 and 02 being lower than initial state 00 of the system, as shown in Figure 3B. Subsequently, the distance between O129 in H₂O and Si89 gradually decreases, and H39 in H₂O also combines with O18 in a form of proton, which makes the reaction reach the saddle point 03. Finally, with the continuous optimization of the positions about the hydroxyl group and proton, the energy of the system is also reduced to a minimum. In the entire reaction, the variation of interatomic bond length around the defect is shown in Table 2. Remarkably, the hydroxyl group used to passivate the dangling bond in the reaction is no longer interfered by Si36, which also proves that our adjustment to P _b0 defect model is more conducive to simulate the real reaction of H₂O and P _b0 defect in a-SiO₂/Si(100).

In addition, we can observe from Figure 3B that the energy of the intermediate state 02 is about 0.33 eV lower than that of the initial state 00. Taking into account that the structure of the intermediate state 02 can also meet the requirement of Eq. 1 for the reactants. Therefore, the intermediate state 02 is subsequently selected as the initial state structure of the reaction between H₂O and P _b0 defect, but the final state structure remains unchanged. In the following simulation, we directly choose the model with a lower energy as the initial state of the reaction, which enables H₂O to passivate the dangling bond defect rather than existing in a free form.

In Figure 4A, the slight movement of H₂O towards Si89 leads to a decrease in the distance between H39 and O18, which in turn increases the energy of the system by 0.11 eV. When the absorbed energy reaches 0.44 eV, H39 in H₂O breaks with the oxygen atom connected to it, and combines with O18 in a form of proton to reach the highest energy state, which is the saddle point of the reaction. After that, with the continuous optimization of the positions about the hydroxyl group and proton, the system finally reaches an equilibrium state. In the whole reaction, the variation of interatomic bond length around the defect is shown in Table 3. Also, Figure 4B shows that, the forward and reverse reaction barriers are approximately the same, 0.44 and 0.46 eV, respectively. It is worth noting that the energy of the final state 05 is lower than that of the initial state 00 in all three cases, which indicates that the passivation of dangling bond defect by hydroxyl group is more stable than that by H₂O for the interaction of H₂O and P _b0 defect in a-SiO₂/Si(100) interface.

Now, we perform computational simulations on the interaction of H₂O and P _b1 defects at three random locations. According to the analysis in the last section, the initial state 00 of this part adopts the form of bonding between H₂O and triple coordinated silicon defect atom (Si84). In addition, in order to ensure the conservation of the number of electrons in the system before and after the reaction, we have subtracted an electron from the structural model of the initial state 00. The reaction equation can be written as: P b 1 + + H 2 O → P b 1 − OH + H + (2)

For the reaction of H₂O and P _b1 defect with AOD configuration at random position 1, two oxygen atoms with different coordinates are selected to establish the final state, where the length of O-H bond is 1.502 Å and 1.907 Å, respectively. The relaxation results show that the hydrogen atom in H₂O cannot combine with the nearest oxygen atom in a form of proton, and it still appears that H₂O is intactly attached to the triple coordinated Si84. Our solution is to specify an oxygen atom (O89) that is relatively far away (3.153 Å) from the hydrogen atom (H37) in H₂O and bond with it as the final state 05 of the reaction. Hereby, we speculate that it is relatively stable to passivate the dangling bond defect with H₂O for the reaction of H₂O and P _b1 defect with AOD configuration at random position 1.

The detailed reaction process is shown in Figure 5A. At first, H37 in H₂O gradually approaches the position of O89 and the reaction can reach the saddle point 02 when the distance between these two atoms is reduced to 2.083 Å. After that, the distance between H37 and O89 in H₂O keeps the trend of decreasing and eventually connects to each other (1.069 Å) after continuous optimization of the intermediate states. Intriguingly, the structural difference between any of the intermediate states (01, 02, 03 or 04) and the initial state 00 is only reflected in the bond length, as shown in Table 4. It also demonstrates that the passivation of dangling bond defect by H₂O is more stable than that by hydroxyl group for the reaction of H₂O and P _b1 defect with AOD configuration at random position 1. Figure 5B shows the variation of the energy fluctuation during the whole reaction process, it can be seen that the forward reaction barrier of this reaction is 0.29 eV. In addition, the energy of the final state 00 is nearly 0.26 eV higher than that of the initial state 00, which again proves the stability of passivating P _b1 defect with H₂O.

Next, for the reaction of H₂O and P _b1 defect with AOD configuration at random position 2, we conventionally choose an oxygen atom (O53) that is relatively far away (2.820 Å) from the hydrogen atom (H36) in H₂O and combine with it as the final state 04. In this reaction, the distance between O53 and H36 in H₂O gradually decreases, and the saddle point 01 can be attained when the distance between these two atoms is minished to 2.406 Å, as shown in Figure 6A. Since then, the position of H36 is getting closer and closer to that of O53, and finally bonds with it in a form of proton (1.099 Å), thus reaching the final state 04 of the reaction. As in the previous case, the structural difference between any of the intermediate states (01, 02 or 03) and the initial state 00 is only embodied in the bond length, as shown in Table 5.

Figure 6B displays the change of the energy with different reaction coordinates in the interaction of H₂O and P _b1 defect with AOD configuration at random position 2. It can be seen that the forward reaction barrier of this reaction is only 0.02 eV. What’s more, the energy of the final state 04 has a smaller raise (∼0.08 eV) compared with that of the intermediate state 03, which verifies that the passivation of dangling bond defect by H₂O is more stable than that by hydroxyl group for the reaction of H₂O and P _b1 defect with AOD configuration at random position 2.

Finally, we simulated and analyzed the reaction of H₂O and P _b1 defect with AOD configuration at random position 3. Based on the above experience in constructing the final state, we still opt for an oxygen atom (O12) that is relatively far away (2.694 Å) from the hydrogen atom (H36) in H₂O and combine with it as the final state 04. As shown in Figure 7A, the movement of H36 in H₂O towards O12 leads to an increase in the bond length of O130 and H36. As the reaction proceeds, H36 in H₂O firstly breaks with O130 attached to it, and then combines with O12 in a form of proton (1.056 Å), thereby reaching the saddle point 03 of the reaction. Afterwards, with the continuous optimization of the positions about the hydroxyl group connected to Si84 and the proton bonded to O12, the system finally reaches the final state 04. The variation of interatomic bond length around the defect in the whole reaction is shown in Table 6.

In Figure 7B, we can see from the energy change curve that the forward reaction barrier of this reaction is 0.31 eV. Besides, the energy of the final state 04 is only inferior to that of the saddle point 03, which is 0.30 eV higher than that of the initial state 00. It further indicates that the passivation of dangling bond defect by H₂O is more stable than that by hydroxyl group for the reaction of H₂O and P _b1 defect with AOD configuration at random position 3.