Cite this Article
Yue Yunliang, Song Yu, Zuo Xu. First-principles investigations of proton generation in α-quartz. Chinese Physics B, 2018, 27(3): 037102  
Permissions
First-principles investigations of proton generation in α-quartz
Yue Yunliang1, Song Yu2, 3, Zuo Xu1, 4, †
College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300071, China
Microsystem and Terahertz Research Center, China Academy of Engineering Physics, Chengdu 610200, China
Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621999, China
Municipal Key Laboratory of Photo-electronic Thin Film Devices and Technology, Nankai University, Tianjin 300071, China

 

† Corresponding author. E-mail: xzuo@nankai.edu.cn

Abstract
Abstract

Proton plays a key role in the interface-trap formation that is one of the primary reliability concerns, thus learning how it behaves is key to understand the radiation response of microelectronic devices. The first-principles calculations have been applied to explore the defects and their reactions associated with the proton release in α-quartz, the well-known crystalline isomer of amorphous silica. When a high concentration of molecular hydrogen (H2) is present, the proton generation can be enhanced by cracking the H2 molecules at the positively charged oxygen vacancies in dimer configuration. If the concentration of molecular hydrogen is low, the proton generation mainly depends on the proton dissociation of the doubly-hydrogenated defects. In particular, a fully passivated center can dissociate to release a proton barrierlessly by structure relaxation once trapping a hole. This research provides a microscopic insight into the proton release in silicon dioxide, the critical step associated with the interface-trap formation under radiation in microelectronic devices.

PACS: 71.15.Mb;71.20.-b;61.72.Bb;61.80.Az
Keyword:first-principles calculation;interface trap;proton;silicon dioxide
1. Introduction

Radiation-induced silicon/silica interface traps are the dominant defects associated with the reliability of microelectronic devices.[1–4] The mechanisms leading to the interface-traps have been extensively studied, where hydrogen plays a crucial role. It has been shown that both interface and oxide charge buildups induced by radiation increase with the increasing hydrogen amount exposed during processing, indicating that hydrogen can facilitate the interface trap generation and enhance the degradation of microelectronic devices.[5–7] In fact, hydrogen can play a double role. On one hand, it can passivate or anneal the interface dangling bonds, the dominant interface traps,[8] if its concentration and form near the interface are appropriate. On the other hand, it can react with the interface dangling bonds previously passivated by hydrogen and reactivate them. The reactions giving rise to the interface dangling bond have also been intensively studied, and it has been shown by first-principles calculations that protons generated by ionization radiation can attack the Si–H bonds, the passivated dangling bonds, at the interface to reactivate the interface trap with a low reaction barrier.[9,10] The radiation-induced proton release is thus directly correlated to the interface trap reactivation. In fact, since the proton release and transportation are generally slow, they may contribute to the enhanced low dose rate sensitivity (ELDRS).[11–13]

Several mechanisms have been proposed for proton release from different sources in silica. A mechanism is the dissociation of H2 molecules at the positively charged oxygen deficiency defects,[14,15] such as and centers, which has been investigated by first-principles calculations.[16–18] It has been shown that H2 molecules react with these positively charged defects, producing protons and neutral hydrogenated defects. This mechanism tends to be dominant if there is a sufficient supply of H2 molecules, which can be the residue of hydrogen exposed in processing. Another mechanism is the dissociation of hydrogenated defects after trapping holes. It has been shown that the passively charged singly or doubly hydrogenated oxygen deficient defects can release protons and restore neutral charge state.[19] Hydrogen annealing of the interface dangling bonds can also anneal the oxygen vacancies that are abundant in silica, leading to the hydrogenated defects.

Although the proton release reactions in amorphous silica (a-SiO2) have been investigated by first-principles calculations, the calculated reaction curves depend on the local environments, which are different site-by-site. Thus, the reaction barriers and energies calculated using a-SiO2 models are usually scattered, leading to uncertainties in further numerical simulations based on drift-diffusion equations, where they are the fixed parameters. The calculations using a crystalline isomer of SiO2 can detour this difficulty. In fact, all the defect centers involved in the proton release reactions in a-SiO2 have their counterparts in quartz, the well-studied crystalline SiO2. For example, the center in a-SiO2 corresponds to the center in quartz, and the singly hydrogenated oxygen vacancy in a-SiO2 can be mapped to the or in quartz. More than that, the microscopic structures of these centers have been reliably specified by the electron paramagnetic resonance (EPR) measurements.[20–23] We thus take α-quartz to model the proton release reactions in a-SiO2.[24]

In this work, the first-principles calculations are taken to investigate the defects and reactions associated with two proton release mechanisms, the dissociation of molecular hydrogen at a positively charged defect and that of a hydrogenated defect after trapping a hole. The structures, density of states (DOS), and spin densities are calculated for the defects, and also the Fermi contacts for the EPR-active ones. The reaction barriers and energies, the key parameters in further numerical simulations based on drift-diffusion equations, are extracted from the calculated reactions curves. The crystalline structure of quartz significantly reduces the uncertainty of the calculation due to the randomness of a-SiO2, which is helpful to identify and characterize atomic scale mechanisms for radiation-induced proton release.

2. Methods

The calculations have been performed in the framework of density functional theory (DFT) with the projected augmented wave method implemented in the Vienna ab initio simulation package (VASP).[25–27] The Perdew–Burke–Ernzerhof (PBE) parameterization of general gradient approximation (GGA) is chosen for the exchange–correlation functional.[28] The cut-off energy of plane wave expansion is set to be 520 eV. The experimental lattice parameters,[29] a=4.916 Å and c=5.4054 Å, are set for the initial quartz unit cell. The 2×2×3 supercells including 108 atoms are constructed for the calculations. The Brillouin zone integration is taken only at the -point. The structure optimization will continue until the total energy difference between consecutive cycles is less than 10−4 eV and the force on each atom is less than 0.05 eV/Å. The partial occupancies are determined by using the Gaussian smearing scheme with a smearing width of 0.1 eV. The climbing image nudged elastic band (CI-NEB) method that couples a series of DFT calculations is applied to calculate the reaction curves.[30] Images are inserted to search for the minimum-energy path and the saddle point between the initial state (IS) and the final state (FS), and the spring constant is set to be 5.0 eV/Å2 between adjacent images. The (forward) reaction barrier is defined by , where and are the total energies of transient and initial states, respectively. The reaction energy is defined by , where and are the total energies of final and initial states, respectively. To reproduce the bandgap underestimated by the exchange-correlations based on local density approximation including GGA, the electronic structures of the defects are specially calculated by using the unscreened hybrid functional where the Hartree–Fock exchange is mixed with PBE at 35%.[31] Spin-polarization is enabled in all calculations to describe the unpaired electrons properly.

3. Results and discussion

Holes play a crucial role in the mechanisms of radiation-induced proton release. They are induced as electron–hole pairs in the oxide by ionization radiation, and then transport with a rather low mobility compared to electrons, since they tend to trap themselves by distorting the lattice. The holes that survive from the initial recombination may be trapped by neutral oxygen vacancies, the most abundant defect in oxygen deficiency silica. This leads to the positively charged configurations, such as dimer ( ) and puckered ( ) configurations in a-SiO2, which may react with H2 molecules to give rise to protons.[32] This mechanism however requires a sufficient supply of H2, which can also be radiolytic. The holes may also be trapped by the hydrogenated defects, and then the positively charged hydrogenated defects dissociate to give protons. This mechanism requires pre-existing hydrogenated defects, which can be generated in the hydrogen annealing of interface traps.

3.1. Positively charged oxygen deficiency defects

It is necessary to specify the structure and other properties of the positively charged oxygen deficiency defects in quartz before the simulation of H2 dissociation at the defects.[24,33] Since both quartz and a-SiO2 are networks of SiO4 building blocks, it is reasonable to assume that the most prevalent positively charged oxygen deficiency defects in quartz are analogous to those in a-SiO2. Two configurations of positively charged oxygen vacancies in quartz are considered in the calculations. One is the dimer configuration, analogous to the center in a-SiO2, and the other is the well-known center,[34] corresponding to the center in a-SiO2. The and centers are characterized by the puckered configuration, where a Si atom adjacent to the oxygen vacancy relaxes backward through its basal oxygen plane and bonds to a back oxygen atom, leading to a Si dangling bond and a three-coordinated oxygen.

The dimer configuration can be obtained by optimizing the initial structure, where the oxygen vacancy is induced by removing an oxygen atom and the hole-trapping is simulated by removing an electron. A perturbation to the initial structure is however required to obtain the puckered configuration, since there is an energy barrier between the initial structure and the puckered configuration. In spite of the barrier, the puckered configuration is energetically more stable than the dimer by 133 meV.

The atomic structure of the dimer configuration is presented in the inset of Fig. 1(a). The Si–Si bond over the vacancy in the dimer configuration is 2.95 Å, which is longer than that in a neutral oxygen vacancy and in good accordance with the previous report.[35] The total magnetic moment is 1.0 , and the spin density asymmetrically distributes between the two Si atoms adjacent to the vacancy. The asymmetry of the spin density is confirmed by the calculated Fermi contacts on the two Si atoms, which are −10.54 mT and −8.20 mT, respectively. The asymmetry is associated with the quartz structure, where the two bonds of each oxygen atom are unequal. The calculated DOS shows that there is an occupied shallow state in the spin-up channel at 0.26 eV above the valence band maximum (VBM) and an unoccupied deep state in the spin-down channel at 4.67 eV above the VBM. The calculated DOS implies that the dimer configurations are not deep hole traps, and may exchange the captured holes with the lattice.

Fig. 1. (color online) The calculated DOS of (a) the dimer configuration and (b) the puckered configuration ( ) of the positively charged oxygen vacancy in α-quartz, where the structures and spin densities are shown in the insets, respectively.

The structure of the puckered configuration ( ) is presented in the inset of Fig. 1(b). The puckering significantly increases the Si–Si distance over the vacancy to 4.29 Å, which is much larger than the Si–Si bond length in the neutral oxygen vacancy. The total magnetic moment is 1.0 , and the spin density is almost entirely localized on the three-coordinated Si atom. A large Fermi contact of −42.04 mT on the three-coordinated Si atom is consistent with the spin density and in excellent agreement with the electron spin resonance measurements in α-quartz.[36] The calculated DOS shows that the occupied and unoccupied states are at 2.46 eV and 7.64 eV above the VBM, respectively, implying that the puckered configuration is a deep hole trap.

3.2. Reactions between H2 and the dimer or puckered configuration

The dissociation of H2 at the dimer configuration is investigated by the NEB calculations, which gives the reaction curve connecting the initial and final states and the transition state associated with the energy barrier (Fig. 2). The reaction starts from the initial state where the H2 molecule stands by at a local energy minimum. When the H2 molecule moves toward one moiety of the dimer, the reaction curve goes up in energy and reaches its maximum at the transition state, where the H2 molecule splits and the two H atoms bond to a Si atom adjacent to the vacancy and one back oxygen atom of the Si atom, respectively. It should be noted that there are a three-coordinated oxygen and a five-coordinated silicon simultaneously in the transition state. It has been shown by first-principles calculations that protons (H+) tend to attach to oxygen bridges in silica, leading to three-coordinated oxygen atoms, and that ions tend to attach to silicon atoms, leading to five-coordinated silicon atoms.[37] The negatively-charged five-coordinated Si atom is unstable due to the positively-charged Si–Si bond adjacent to it, and then the transition state further relaxes to the final state where a Si dangling bond is projecting toward a H–Si group. By this reaction, a proton is released and a Si dangling bond is also created, which can be correlated to the fact that both oxide and interface traps may increase with the increasing hydrogen exposure.[6] It should be noted that the released proton attaches to one oxygen bonded to the dangling bond Si, which lowers the total energy as shown by first-principles calculations.[16]

Fig. 2. (color online) The reaction curve of H2 dissociating at the dimer configuration. The structures of the initial, transition, and final states are illustrated in the insets.

It is worthwhile to point out that the reaction details revealed by this work are very different from those given in Ref. [17]. According to Ref. [17], the H2 molecule first hydrogenates the dimer configuration in SiO2, leading to the transition state in which two adjacent H–Si groups share a positive charge, and then one of the H–Si bonds dissociates to give a proton, which migrates and attaches to a nearby oxygen bridge. It is obvious that the reaction in a-SiO2 can be divided into three major steps corresponding to the three peaks in the reaction curve. However, the reaction in quartz is one-step, and then there is only one peak in the reaction curve.

The forward reaction barrier in quartz is 0.79 eV, slightly higher than that in a-SiO2. The rate constant of the reaction estimated from the barrier is approximately 0.3 s−1 at room temperature (300 K), implying that the reaction takes place rather quickly, possibly in seconds. More than that, while the reaction in a-SiO2 is shown to be endothermic by first-principles calculations,[17] the reaction in quartz is exothermic, and the final-state energy is lower than the initial state energy by 0.74 eV. This implies that the reaction tends to generate protons in quartz instead of annihilating them in a-SiO2.

The dissociation of H2 molecules at the puckered centers is also investigated, and the reaction curve is plotted in Fig. 3. The reaction starts from the initial state where the H2 molecule is approaching the Si dangling bond of the puckered configuration. When the reaction goes up, the H2 molecule gradually interacts with the dangling bond and dissociates. At the transition state, one of the H atoms passivates the Si dangling bond and the other is neutral and free in the interstitial space. The neutral free H atom then attaches to one oxygen atom of the puckered moiety of the center, and triggers the collapse of the puckered moiety with a charge transfer. At the final state, the bond between the puckered Si atom and its back oxygen is broken, and the hole trapped at the three-coordinated oxygen in the puckered moiety transfers to the oxygen attached to the H atom. By this reaction, a proton is released and a Si dangling bond is also created. In addition, the released proton attaches to one oxygen atom bonded to the dangling bond Si atom. In fact, the final state of the reaction at the puckered configuration is almost identical to that at the dimer, except that the dangling bond is projecting forward the H–Si group in the former but backward in the latter.

Fig. 3. (color online) The reaction curve of molecular hydrogen dissociating at the puckered configuration of the positively charged oxygen vacancy. The structures of the initial, transition, and final states are illustrated in the insets.

It should be noted that the details of the reaction simulated by this work are quite different from those given in Ref. [17]. According to Ref. [17], the H2 molecule is split by an sp2 hybridized Si atom and an oxygen atom, leading to the final state in which the released proton is attached to one oxygen not bonded to the dangling bond Si atom.

The forward barrier of the reaction in quartz is 1.00 eV, about twice that in a-SiO2. The rate constant estimated from the forward reaction barrier is approximately at 300 K, implying that the reaction takes place rather slowly. Given the concentration of the puckered configuration is about a tenth that of the dimer,[38–40] it can be estimated that the proton production rate at puckered configurations is lower than that at dimers by four orders of magnitude. The final state is lower than the initial state by 0.12 eV, so the reaction is exothermic. This implies that the reaction at puckered configurations tends to release protons instead of annihilating them. From the reaction energies at dimer and puckered configurations and the fact that the concentration of puckered configuration is about a tenth that of dimer, it can however be estimated that the proton concentration associated with the H2 dissociation at puckered configurations is lower than that at dimers by five orders of magnitude at equilibrium at 300 K. This implies that the H2 dissociation at dimers can be the dominant reaction that generates protons from H2 molecules.

3.3. Hydrogenated oxygen vacancies

The H2 dissociation mechanism can generate protons efficiently, as long as there is a sufficient supply of H2 molecules. However, radiation can still induce interface traps, even if excess H2 is absent in the oxide.[5] This can be partly attributed to the radiolytic hydrogen molecules from hydroxyl groups,[41] and partly to other mechanisms of proton release, such as the dissociation of hydrogenated oxygen vacancies. Before exploring these reactions, we specify the structures and properties of these defects in neural charge state.

When an oxygen vacancy is singly hydrogenated, there are two different resulting structures depending on the projection of the Si dangling bond. In the so-called centers, the Si dangling bond is projected backward to the H–Si group as shown in the inset of Fig. 4(a), where the spin-density is well localized on the dangling bond Si atom except that a small amount diffuses on the three oxygen atoms bonded to the Si atom and one nonbonding back oxygen. The back-projected Si dangling bond will be well isolated if there is no back oxygen atom close to the dangling bond in a-SiO2. This structure is thus proposed for the observed in EPR.[42–44] In the so-called centers, the Si dangling bond is however projected toward the H–Si group as shown in the inset of Fig. 4(b), where two Si atoms and one H atom are bonded by two electrons and asymmetrically share one extra spin. The calculated DOS shows that the occupied defect states are 3.34 eV and 4.20 eV above the VBM in the and centers, respectively. It should be noted that H2 dissociations at dimers and puckered configurations lead to the and centers, respectively.

Fig. 4. (color online) The calculated DOS of (a) the center, (b) the center, (c) the doubly hydrogenated oxygen vacancy derived from the center, and (d) the doubly hydrogenated oxygen vacancy derived from the center. The structure and spin density of the centers are illustrated in the insets, respectively.

Two doubly-hydrogenated oxygen vacancies are obtained by further passivating the and centers (Fig. 4(c) and 4(d)). They are nonmagnetic and silent in EPR measurements. The calculated DOS shows that the occupied defect states of the and centers induce shallow defect states in the bandgap, which lie at 0.24 eV and 0.52 eV above the valence band, respectively.

3.4. Proton release reactions of hydrogenated oxygen vacancies

The hydrogenated oxygen vacancies may dissociate to give protons once positively charged. These reactions are simulated by the NEB calculations, and the initial states are given by the structure optimizations of the positively charged hydrogenated centers. We first consider the dissociations of the positively charged and centers. Although the neutral and centers have different structures, the positively charged centers both relax to the hydrogen bridge configuration , which is the initial state of the dissociation (Fig. 5). The forward reaction barrier is as high as 2.25 eV, corresponding to a rate constant of at room temperature, which implies that the dissociation is almost impossible. The high barrier is due to the strong three-center bond that stabilizes the initial state, the configuration. In fact, the configuration can be obtained by removing the extra spin on the nonbonding orbital from the neutral center. It can thus be estimated from the calculated DOS of the center that the configuration is lower than the neutral center in energy by about 4 eV. The strong three-center bond is interrupted in the transition state, and then the H atom moves from the middle of the H configuration to one side of the vacancy, which leads to the high forward reaction barrier. The final state however is rather low in energy because of the hydronium-like structure associated with the released proton and the neutral Si–Si bond over the vacancy, but is higher than the initial state by about 0.27 eV. The dissociation is thus an endothermic reaction, which is more likely to trap protons instead of freeing them.

Fig. 5. (color online) The reaction curve of the proton liberated from the positively charged configuration. The structures of the initial, transition, and final states are illustrated in the insets.

In addition to the configuration, there is another possible configuration for the singly hydrogenated oxygen vacancy in the positive charge state, that is, the singly hydrogenated configuration. In this configuration, the dangling bond in the puckered configuration is passivated by hydrogen, and the puckered moiety stays untouched (Fig. 6). Taking this configuration as the initial state, the dissociation takes place in two major steps. The singly hydrogenated configuration first converts to the configuration by overcoming a low barrier of 0.5 eV associated with the transition state, where the puckered moiety collapses to give a three-coordinated Si atom with sp2 hybridization. The intermediate configuration then dissociates to give a proton with a high barrier. It should however be noted that the reverse barrier of the first step is as low as 0.25 eV, and the singly hydrogenated configuration is lower than the configuration in energy by about 0.25 eV. This implies that the configurations, generated from the and centers, should dominantly take the reverse reaction and convert to the singly hydrogenated configurations, instead of releasing protons.

Fig. 6. (color online) The reaction curve from the initial state (IS), the singly hydrogenated configuration, to the final state (FS), the neutral oxygen vacancy with the proton dissociated and attached to a nearby oxygen atom like hydronium, via the intermediate state (IM), the configuration.

Although the singly hydrogenated configuration is lower than the configuration in energy, its generation does depend on the back oxygen atom, which is guaranteed to be there in quartz by the crystal structure but might not be there in a-SiO2 due to amorphousness. Thus, some singly hydrogenated oxygen vacancies may convert to and stay at the configurations after trapping holes. The hydrogen atom in the H defect is located asymmetrically between the two Si atoms with the Si–H bond lengths of 1.64 Å and 1.69 Å, respectively, and the Si–H–Si bond angle is 148.41°, in agreement with the previous calculations.[35] The configuration induces a series of unoccupied defect states close to the conduction band minimum (CBM) of quartz, the lowest of which is 7.61 eV above the quartz VBM (Fig. 7). Assuming that the Si VBM is aligned at 4.5 eV above the SiO2 VBM, it can be estimated that the defect states are above the Si CBM. The configuration is thus stable for a technically meaningful Fermi level, and can be a deep hole trap in a-SiO2.[45]

Fig. 7. (color online) The atomic and electronic structure of the positive hydrogen bridge ( ) configuration.

The dissociations of the doubly hydrogenated oxygen vacancies are investigated in addition to those of the singly hydrogenated ones. The reaction curve of the doubly hydrogenated vacancy derived from the center is plotted in Fig. 8, where there is no barrier. This implies that the vacancy can readily release a proton by structure relaxation after trapping a hole. In this reaction, the hydrogen atom on the silane group pointing outward from the vacancy gets close and then bonds to one back oxygen atom, forming a hydronium-like structure, and captures the positive charge on the three-coordination oxygen atom. Facilitated by the back oxygen, the dissociation is barrierless and exothermic with a reaction energy of −0.60 eV. Both the barrierless and exothermic characters strongly recommend that this reaction can serve as the dominant mechanism of proton release when the concentration of H2 molecules is low. A caution however should be taken that the back oxygen might not be there in a-SiO2 due to amorphousness.

Fig. 8. (color online) The reaction curve of the dissociation of doubly hydrogenated oxygen vacancy derived from the center that releases a proton.

The dissociation of the doubly hydrogenated oxygen vacancy derived from the center is also simulated in Fig. 9, and there is an obvious barrier in the reaction curve unlike the case of doubly hydrogenated vacancy derived from the center. In the initial state, the vacancy is positively charged, resulting in a smaller distance between two hydrogen atoms than that in the neutral charge state. The reaction curve goes up in energy when one hydrogen atom is dissociating from a silane group, and reaches the peak associated with the transition state, where the proton is completely freed and a Si dangling bond is created. The freed proton then moves toward and finally attaches to one oxygen atom bonded to the dangling bond Si atom, which is a specific low-energy in quartz.[16] It is noted that the hydrogen atom that initially passivates one of the Si atoms surrounding the vacancy finally turns to forming a Si–H bond with the other Si atom through experiencing the Si–H–Si configuration. The forward reaction barrier of the dissociation is 0.81 eV, from which the rate constant is estimated to be 0.15 s−1 at room temperature. This implies that the dissociation can take place rather quickly, within seconds. The reaction however is endothermic with a reaction energy of 0.12 eV, from which it can be estimated that the product concentration is about one percent of the reactant concentration at equilibrium at room temperature. In fact, the reverse reaction is more likely to take place, by which a free proton is captured and fixed into a silane group.

Fig. 9. (color online) The reaction curve of the dissociation of the doubly hydrogenated oxygen vacancy derived from the center that releases a proton.

Summarizing the dissociations of the hydrogenated oxygen vacancies in quartz, there is only one reaction, the dissociation of the doubly hydrogenated oxygen vacancy derived from the center that is characterized of low activation barrier and exothermicity. In addition, the doubly-hydrogenated defects are expected to be present in concentrations ten times larger than the singly-hydrogenated defects.[19] Therefore, the doubly hydrogenated oxygen vacancies derived from the centers may serve as the dominant proton sources in quartz. A caution however should be raised, that the back oxygen facilitating the dissociation might not be there in a-SiO2 due to the amorphousness.

4. Conclusion

The first-principles calculations have been performed to investigate the reactions that probably release protons in α-quartz. The dissociations of H2 at the dimer and puckered configurations are simulated for the situation that the concentration of molecular hydrogen is sufficiently high. The calculated reaction curves show that the dissociation at the dimer configuration has a lower reaction barrier and a larger exothermic reaction energy than that at the puckered configuration. Given that the concentration of the dimer configuration is about ten times that of the puckered configuration, we conclude that the dissociation of H2 molecules at the dimer configurations should be the dominant mechanism accounting for proton production when there is plenty of molecular hydrogen. The dissociations of the hydrogenated oxygen vacancies have also been studied for the situation that molecular hydrogen is absent. The calculated reaction curve shows that the singly hydrogenated vacancies need to climb over a high energy barrier to give protons, and that the reaction is endothermic because of the low energy of the positive hydrogen bridge configuration in the initial state. In addition, the positive hydrogen bridge can further lower its energy by puckering. The dissociations of the doubly hydrogenated vacancies however sensitively depend on the projections of the silane groups. The hydrogen atom can dissociate without an energy barrier from the silane group projecting toward the back oxygen atom in the vacancy derived from the center. The dissociation of the vacancy derived from the center has a moderately high barrier and is endothermic, because both silane groups are projecting toward the center of the vacancy. The reactions investigated here can be associated with the proton generation at high and low concentrations of molecular hydrogen. The specific details of these reactions are revealed, providing an insight to proton release mechanism in silicon dioxide, the most widely applied oxide in microelectronics.

Reference
[1] Fleetwood D M Pantelides S T Schrimpf R D 2008 Defects in Microelectronic Materials and Devices Boca Raton CRC Press pp. 215–238
[2] Pacchioni G Skuja L Griscom D L 2000 Defects in SiO2 and Related Dielectrics: Science and Technology New York Springer Science & Business Media pp. 529–556
[3] Devine R A 1988 The Physics and Technology of Amorphous SiO2 New York Plenum Press pp. 259–265
[4] Deal B E Helms C R 1993 The Physics and Chemistry of SiO2 and the Si-SiO2 Interface New York Springer Science & Business Media pp. 455–457
[5] Pease R L Dunham G W Seiler J E Platteter D G Mcclure S S 2007 IEEE Trans. Nucl. Sci. 54 1049
[6] Chen X J Barnaby H J Vermeire B Holbert K Wright D Pease R L Dunham G Platteter D G Seiler J McClure S Adell P 2007 IEEE Trans. Nucl. Sci. 54 1913
[7] Batyrev I G Hughart D Durand R Bounasser M Tuttle B R Fleetwood D M Schrimpf R D Rashkeev S N Dunham G W Law M Pantelides S T 2008 IEEE Trans. Nucl. Sci. 55 3039
[8] Rashkeev S N Fleetwood D M Schrimpf R D Pantelides S T 2004 IEEE Trans. Nucl. Sci. 51 3158
[9] Oldham T R McLean F B 2003 IEEE Trans. Nucl. Sci. 50 483
[10] Rashkeev S N Fleetwood D M Schrimpf R D Pantelides S T 2001 Phys. Rev. Lett. 87 165506
[11] Pease R L Adell P C Rax B G Chen X J Barnaby H J Holbert K E Hjalmarson H P 2008 IEEE Trans. Nucl. Sci. 55 3169
[12] Fleetwood D M Schrimpf R D Pantelides S T Pease R L Dunham G W 2008 IEEE Trans. Nucl. Sci. 55 2986
[13] Pantelides S T Tsetseris L Rashkeev S N Zhou X J Fleetwood D M Schrimpf R D 2007 Microelectron. Reliab. 47 903
[14] Conley J F Lenahan P M 1993 IEEE Trans. Nucl. Sci. 40 1335
[15] Conley J F Lenahan P M 1993 Appl. Phys. Lett. 62 40
[16] Van Ginhoven R M Hjalmarson H P Edwards A H Tuttle B R 2006 Nucl. Instrum. Methods Phys. Res. Sect. 250 274
[17] Tuttle B R Hughart D R Schrimpf R D Fleetwood D M Pantelides S T 2010 IEEE Trans. Nucl. Sci. 57 3046
[18] Shen X Puzyrev Y S Fleetwood D M Schrimpf R D Pantelides S T 2015 IEEE Trans. Nucl. Sci. 62 2169
[19] Rowsey N L Law M E Schrimpf R D Fleetwood D M Tuttle B R Pantelides S T 2011 IEEE Trans. Nucl. Sci. 58 2937
[20] Silsbee R H 1961 J. Appl. Phys. 32 1459
[21] Jani M G Bossoli R B Halliburton L E 1983 Phys. Rev. 27 2285
[22] Rudra J K Fowler W B Feigl F J 1985 Phys. Rev. Lett. 55 2614
[23] Isoya J Weil J Halliburton L 1981 J. Chem. Phys. 74 5436
[24] Vitiello M Lopez N Illas F Pacchioni G 2000 J. Phys. Chem. 104 4674
[25] Kresse G Furthmüller J 1996 Comput. Mater. Sci. 6 15
[26] Kresse G Joubert D 1999 Phys. Rev. 59 1758
[27] Blöchl P E 1994 Phys. Rev. 50 17953
[28] Perdew J P Burke K Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[29] Levien L Prewitt C T Weidner D J 1980 Am. Mineral. 65 920
[30] Henkelman G Uberuaga B P Jónsson H 2000 J. Chem. Phys. 113 9901
[31] Alkauskas A Broqvist P Devynck F Pasquarello A 2008 Phys. Rev. Lett. 101 106802
[32] Stahlbush R E Mrstik B J Lawrence R K 1990 IEEE Trans. Nucl. Sci. 37 1641
[33] Stahlbush R E Edwards A H Griscom D L Mrstik B J 1993 J. Appl. Phys. 73 658
[34] Snyder K C Fowler W B 1993 Phys. Rev. 48 13238
[35] Blöchl P E 2000 Phys. Rev. 62 6158
[36] Boero M Pasquarello A Sarnthein J Car R 1997 Phys. Rev. Lett. 78 887
[37] Godet J Pasquarello A 2005 Microelectron. Eng. 80 288
[38] Sushko P V Mukhopadhyay S Mysovsky A S Sulimov V B Taga A Shluger A L 2005 J. Phys.: Condens. Matter 17 S2115
[39] Girard S Richard N Ouerdane Y Origlio G Boukenter A Martin-Samos L Paillet P Meunier J P Baggio J Cannas M 2008 IEEE Trans. Nucl. Sci. 55 3508
[40] Lu Z Y Nicklaw C J Fleetwood D M Schrimpf R D Pantelides S T 2002 Phys. Rev. Lett. 89 285505
[41] Griscom D L 1985 J. Appl. Phys. 58 2524
[42] Griscom D L 1985 J. Non-Cryst. Solids 73 51
[43] Griscom D L 1991 J. Ceram. Soc. Jpn. 99 923
[44] Griscom D L 1984 Nucl. Instrum. Methods Phys. Res. Sect. 1 481
[45] Godet J Giustino F Pasquarello A 2007 Phys. Rev. Lett. 99 126102