Electrochemical reaction represents an essential action in fundamental chemistry that fosters wide applications. Although most electrochemical reactions involving bulk substances can be well described by the classical Marcus-Gerischer charge transfer theory, the realistic reaction character and mechanism in atomically confined systems remain unknown. Here, we report the multiparametric survey on the kinetics of lateral photooxidation in WS2 and MoS2 monolayers, where electrochemical reactions occur at the atomically thin flake edges, by quantitatively correlating its reaction rate with various crystallographic and environmental parameters, including density of lattice vacancies, humidity, temperature, and illumination fluence. In particular, we uncover an unusual non-Marcusian charge transfer mechanism in these spatially confined semiconductors due to limit in reactant supplies, where band bending played a crucial role and distinctive reaction barriers (1.4 versus 0.9 eV) are extracted from these analogous materials. These results add important knowledge into the fundamental electrochemical reaction theory.
Article
Oxidation kinetics and non-Marcusian charge transfer in spatially confined semiconductors
https://doi.org/10.21203/rs.3.rs-2542934/v1
This work is licensed under a CC BY 4.0 License
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published 10 Jul, 2023
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The development of modern science and technology benefits vastly from the quantitative understanding on natural phenomena and the acquisition of basic regularities and laws behind the world. As a matter of fact, quantitative understanding on the degradation behavior in solid materials represents an extremely challenging topic in analytical chemistry. First, it is arduous because degradation is essentially a multiparametric process that relies on a plethora of parameters1–8, such as atomic defects, energetic stimuli, and corrosion agents. Moreover, some factors, e.g. atomic defects ‒ a crucial crystallographic one affecting reaction reactivity, are hard to quantify because of their non-uniform spatial distribution within materials, making the degradation rate spatially fluctuated. More formidably, the frontal reaction boundaries constitute implicit planes that are hidden insides materials, which renders them difficult to be tracked. All pose grand challenges in quantifying the degradation kinetics in solid materials.
While two-dimensional (2D) van der Waals materials are being exploited for many emerging applications9–12, the quantitative information on their environmental stability and service expectancy remains elusive. In contrast to bulk materials, the environmental stability of 2D semiconductors is largely reduced due to reduction in dimensionality. In general, they are unusually vulnerable and are subject to degrade on short timescales when exposed in ambient conditions1,13. Hence, well formulized oxidation kinetics are not only instructive for practical reliability evaluation, corrosion protection14,15, and controllable formation of functional layers16, but also key for understanding the reaction mechanism behind. Structurally speaking, the crystalline 2D semiconductors represent a unique platform to verify the basic chemical theories that are difficult to fulfill in bulk materials17,18. A notable merit is that the density of lattice vacancies ([V]) can be readily modulated in 2D crystals, due to the full exposure of lattice atoms. In addition, the lateral reaction boundaries in 2D systems are simplified as explicit lines exposed outwards and, thus, are easy to track. Both factors facilitate the quantification of reaction kinetics therein.
To data, most studies on the degradation behavior of 2D semiconductors have been carried out via less efficient micro-zone techniques, such as atomic force microscope (AFM)4–6, transmission electron microscope (TEM)7,8, and Raman spectrum2,3,13, which are often spatially limited, time-consuming, or implicit in analysis, to unravel the long-lasting compositional or morphological changes during degradation. In addition, the tunability of environmental parameters (e.g. humidity or temperature) constitutes another requirement for full-parametric quantification. Thus, a convenient strategy that features merits including concurrent spatio-temporal resolutions, adaptive environmental compatibility, and high overall throughputs is highly sought-after.
Here, we report comprehensive survey on the kinetics of photooxidation in 2D WS2 and MoS2 through environment-controlled photoluminescent (PL) imaging inside a glovebox. The ad hoc defect engineering on [V] levels and on-demand controls over the environmental factors allow us to fully access a wide parameter space for quantitative analyses. On the basis of the systematic data, we managed to formulize the lateral oxidation rate as a function of various crystallographic (i.e., [V]) and environmental [i.e., relative humidity (RH), temperature (T), and illumination fluence (F)] parameters, which thus enables an insight into the roles of lattice vacancies and absorbed aqueous oxygen during degradation. Moreover, we identify the presence of conditional boundaries [V] ~ 3×1014 cm− 2 and RH ~ 46% that determine the practical oxidation modes (i.e., peripheral or basal) and reaction mechanism (i.e., dry or wet), respectively. Most importantly, through contrastive analyses on the reaction barriers and band alignments in the two analogous 2D semiconductors (WS2 and MoS2), we unravel an unusual non-Marcusian charge transfer mechanism in these spatially confined systems due to limit in reactant supplies, which represents a correction to the classical reaction theory. Apart from the technical contributions for reliability evaluation and corrosion protection, these findings also add important scientific knowledge.
Methodology and compositional characterization
Figure 1a illustrates the schematic experimental setup for the kinetic analysis via real-time PL imaging, where the monolayer (1L) van der Waals semiconductors are globally illuminated with a beam of 455-nm wavelength below an objective lens. Hence, the compositional changes can be conveniently monitored via a real-time CCD camera (See Supplementary Movies 1 and 2). In such a setup, the temporal resolution and spatial breadth are mainly determined by the integration time of the camera and the fields of view of the objective lens, respectively, which were set as 350 ms and 400 µm.
Figure 1b,c shows the serial PL images captured at different reaction stages for two typical oxidation modes (termed as peripheral and basal), in which the local PL quenching occurs due to compositional change after degradation. As a result, the entire reaction process can be well tracked from the progressive spread of the frontal reaction boundaries inward or outward, which are recorded in images captured at planned intervals. We verified that the PL imaging enables extraction of consistent length of reaction (L1L) with AFM (Supplementary Fig. 1), constituting a high-throughput way to quantify the kinetic process. The lateral oxidation rate (r1L) can be explicitly calculated from the ratio of L1L to illumination time (t). An exemplified analysis on the serial PL images given in Fig. 1b is illustrated in Fig. 1d, where L1L exhibits linear dependence on t, revealing a roughly constant r1L at 0.16 ± 0.03 µm/min.
Figure 1e shows the AFM recorded surface morphology for a typical reacted region mixed with pristine and oxidized areas, where the locally oxidized areas evolve into random protrusions in morphology. X-ray photoelectron spectrum (XPS) was used to assess the elemental compositions and valences in the local areas. Before reaction, the pristine areas exhibit intense 2p excitations from the sulfur atoms, around 164.0 and 162.8 eV, and 2f excitations from the tungsten atoms, around 35.3 and 33.1 eV, corresponding to a valence state of + 4 for W atoms in WS2 (Fig. 1f). After reaction, two extra peaks emerge at 36.2 and 38.1 eV, which can be attributed to excitations from the highly valent W+ 6 atoms in derived oxysulfides or oxides (WSxO3−x or WO3 − y). The elemental mappings for the typical local areas after peripheral (Fig. 1g) and basal (Fig. 1h) oxidation also support above analyses on the oxidation products, where a noticeable loss (increase) of element sulfur (oxygen) can be seen, in spite of the insignificant change in tungsten content. Hence, the underlying chemical reaction equation during degradation is deduced as
where the subscripts x, y and z denote the unfixed ratios in the products.
The material crystallinity in the oxidized areas is destroyed and a full amorphous state is detected from the circular STEM diffraction patterns (top inset of Fig. 1i). In contrast, the crystallinity is well preserved in the unoxidized areas, as corroborated by the spotted diffraction patterns (bottom inset of Fig. 1i). Previous theoretical calculations19,20 revealed that the lattice atoms on the basal planes are more stable than those at edges. Thus, the basal oxidation mode is normally deactivated. Here, by appropriate engineering [V], we reproducibly activated the basal oxidation mode in WS2. Moreover, we identified the threshold [V] level ~ 3×1014 cm− 2 to activate this mode, as shown in Fig. 1c and Supplementary Fig. 2. Evidently, the full exposure of lattice atoms in 2D semiconductors represents a unique advantage to address the reaction character and mechanism.
Defect engineering
A comprehensive survey was performed on the oxidation kinetics versus various parameters, including [V], RH, T, F and photon energy (Fig. 2a). In this study, ambiently stable transition metal sulfides, WS2 and MoS2, are selected as the prototypes for their balance in chemical stability and reactivity, because in their pristine states they are robust enough to avoid unintentional degradation before tests, while they can be chemically activated via ad hoc defect engineering, such as soaking in oxidants (e.g., solutions of hydrogen peroxide, H2O2, for 5‒30 min) to modulate the parameter [V]. In addition, well controlled high [V] levels enable the entire reaction process to accelerate and unfold within a short time of minutes or hours, as compared to, otherwise, months in pristine states.
Since the precise control and identification of [V] levels are essential for the quantitative characterization, we first prepared defect engineered WS2 monolayers with various [V] levels. Here, we employed an aberration-corrected STEM to estimate the generation rate of [V] versus the pretreatment time (tpt) in H2O2 soaking. Figure 2b,c displays a typical 1L WS2 on STEM grid (also Supplementary Fig. 4) and an annular dark-field (ADF) atomic image. In the ADF imaging mode, the most and adjacent less bright dots correspond to the tungsten and sulfur atoms (denoted by blue and yellow balls in Fig. 2d), respectively. The lattice vacancies, i.e., missing atoms (denoted by red arrow in Fig. 2c), would manifest themselves with a reduced brightness. This feature becomes more evident in the brightness profiling taken along the atom chains (Fig. 2e).
The generation rate of lattice vacancies is then assessed by counting the [V] levels in samples treated under different tpt conditions. Figure 2f–j shows typical STEM images for these samples, where [V] increases as tpt changes from 10 to 30 min, at a step of 5 min. Atomic images from more local regions and different samples can be found in Supplementary Figs. 7‒12. The statistical [V] distributions are all illustrated in Fig. 2k. According to the random nature of vacancy creation on lattice sites, discrete Poisson statistics were used to analyze the spatial distribution of [V]. Theoretically, in Poisson statistics the standard deviation would roughly equal the square roots of average value. We note that the large deviation of experimental [V] levels (~ 20‒30% in most cases) originates from its intrinsic nature, which is inevitable even at large sampling numbers, constituting the primary origin of overall uncertainties in experiment. As can be seen in Fig. 2k, the Poisson statistics well describe the experimental data, implying the reliability of the STEM results. The average [V] level increases linearly from 3.0×1013 (pristine) to 2.8×1014 cm− 2 (30-min-treated). Quantitative XPS analyses on the S/W atomic ratio (Supplementary Fig. 13) also show consistent result of loss of element sulfur after oxidation. Both facilities confirm the efficiency of defect engineering in modulating [V] levels. In Fig. 2l the [V]-tpt trend is plotted, which reveals a generation rate ~ 0.8×1013 cm− 2 min− 1 through soaking WS2 in the 30% H2O2 solution. Overall, this method represents a simple venue to on-demand control [V] levels for quantitative purpose.
Multiparametric quantification
The on-demand control over [V] levels allows us, for the first time, to quantify the r1L–[V] relationship from experiments. For each condition, we collected relevant r1L data at about 30‒120 locations from 3‒5 samples (See Supplementary Figs. 14 and 15 for extracting method). Figure 2m shows r1L versus [V] for 1L WS2 at T = 27℃ and RH = 60%. At low [V] levels < 1.2×1014 cm− 2, r1L is insignificant and approaches the limit of detection (~ 10− 3 µm/min), but it increases exponentially when [V] > 1.5×1014 cm− 2, indicating the existence of a threshold ~ 1.2×1014 cm− 2 to trigger fast oxidation of 1L WS2. This result represents unprecedentedly fine microscopic evidence for corrosion in 2D disulfides, which can well explain the empirical observation between the environmental stability and crystalline quality21. Further analysis extracts a characteristic coefficient \({{\alpha }}_{1\text{L}}\)= (4.0 ± 0.5)×1013 cm− 2 in the exponential correlation \({r}_{1\text{L}}\propto {\text{e}}^{\frac{\left[\text{V}\right]}{{{\alpha }}_{1\text{L}}}}\).
Apart from the crystallographic parameter [V], the influences of environmental factors (i.e., RH, F, and T) on r1L are also quantitatively understood (Fig. 2n–p). Figure 2n shows the dependence of r1L on RH at different Ts from 20 to 26 ˚C, while Fig. 2o depicts the linear trend of r1L versus F up to 6 W/cm2. The r1L‒RH results are quite informative. An important finding is the identification of a general humidity threshold 
46 ± 4% to trigger appreciable reaction, below which r1L is insignificant at all tested T values from 20 to 26 ˚C. This implies that the 2D disulfides would sustain greatly reduced degradation in surroundings with RH below 46%, constituting useful guidance for corrosion protection. In the broad range covered, we also accessed other linear and nonlinear response regimes, respectively. A linear relation \({r}_{1\text{L}}\propto (\text{R}\text{H}-{\text{R}\text{H}}_{0})\) is present in the intermediate RH regime, while r1L becomes saturated at high RH levels. We attribute the deviation of the linear trend at high RH levels to the excessive supply of water molecules, which leads to the saturation of reactants (e.g., the aqueous superoxide anions O2−).
To rationalize r1L completely, we further consider the effect of T. At first, we exclude the possibility of remarkable T rise induced by photothermal effect. The T rise under typical F levels is simulated to be less than 0.1 K (Supplementary Note 11 and Fig. 16). According to the Arrhenius relation, r1L is plotted versus 1/T in Fig. 2p to extract the effective reaction activation energy (Ea). Its magnitude is found closely associated with absolute humidity (AH), which divides the inset of Fig. 2p into two regions: I) dry oxidation; II) wet oxidation. In dry oxidation region, with AH spanning from 9 to 11 g/m3, \({E}_{\text{a}}\) gradually drops from 2.5 to 1.8 eV, whereas it keeps almost constant at \(1.4\pm 0.3\) eV in the wet oxidation region (AH ranging from 11 to 14 g/m3). This behavior implies the existence of distinct reaction paths/mechanisms that are relevant to environmental humidity.
The extensive data enable us to formulize the oxidation kinetics of 1L WS2 in a quantitative form. By fitting the data in the linear RH regime, we derived
$${r}_{1\text{L}}=\text{A}·F·\beta ·(\text{R}\text{H}-{\text{R}\text{H}}_{0}){{·\text{e}}^{\frac{\left[\text{V}\right]}{{\alpha }_{1\text{L}}}} \text{e}}^{-\frac{{E}_{\text{a}}}{kT}}$$
1
where \(\text{A}={\text{e}}^{22\pm 1}\)m4∙s2∙(kg)−2 is a prefactor accounting for parameters not addressed explicitly, \(\beta =\) 2.17 g∙K∙J−1∙es(T)∙T−1 is inserted for the algebraic conversion from RH to AH, and es(T) is the T dependent saturation vapor pressure, in unit of Pa. The former exponential term reflects the crucial role of chalcogen vacancies in the degradation process. The latter is a natural result of the Arrhenius plot to reflect \({E}_{\text{a}}\). This semi-empirical equation can be used as guidance for evaluating reliability and service expectancy in electronic devices (Supplementary Fig. 17) and for exploiting strategies of corrosion protection in these 2D semiconductors.
Reaction paths and energy landscapes
To further shed light on the underlying reaction mechanisms3,13, we further looked into the threshold of photon energy (Ephoton) for oxidation reaction. In Fig. 3a, we identify the threshold ~ 1.94 eV to trigger fast oxidation with appreciable r1L, because the oxidation is inactive at Ephoton below 1.91 eV (i.e. above 650 nm, see also Supplementary Fig. 18) and is active when Ephoton equals or exceeds 1.94 eV. We note that this threshold is rather close to the optical gap (~ 2 eV) of 1L WS2 from the absorption spectrum (upper red line, Fig. 3a), confirming the photochemical reaction mechanism3,22. In detail, the role of illumination is to excite electrons from the valence (EV) to conduction band (EC) in WS2; the excited electrons are then transferred to the aqueous oxygen via electrochemical paths to produce superoxide ions O2− as the active oxidant (Fig. 3b,c). In addition to illumination, oxygen and humidity were also found crucial elements to trigger fast degradation. Even illuminated, the samples would behave inactively in surroundings with low oxygen and humidity levels (Supplementary Fig. 19).
In Fig. 3b,c we further analyze the possible reaction paths under four combined conditions, in terms with lattice defects (perfect or defective lattices) and humidity (dry or wet conditions), and related activation energies for the reconfiguration of atomic structures between oxygen and WS2 lattices, based on the first-principle calculations. Under dry and wet conditions, the realistic oxidants are molecular O2 and highly active O2−, respectively. Combined with two crystallographic conditions, the reaction barriers are calculated to be 2.89, 2.3, 1.66, and 0.92 eV in the four paths. Evidently, the magnitude of barrier is strongly associated with the crystallographic and environmental conditions, which determine the exact oxidant and reaction path followed. By comparing the values of barriers, we confirm, at high RH levels, the path of defective lattice plus O2− as the most reasonable one, where the reaction barrier is minimized; the other three paths all features higher values than the experimental Ea. Detailed discussion can be found in Supplementary Note 18.
Apart from the reaction paths, we also investigate the charge transfer process responsible for the photochemical reactions. To this end, the actual energy levels of sulfides were analyzed by ultraviolet photoelectron spectroscopy (UPS). The verification of the accuracy of UPS can be found in Supplementary Figs. 21 and 22. Figure 3d shows the UPS spectrum for a p-doped 1L WS2. We extracted a spectral width W = 15.44 eV, which determines the positions of Ev ~ 5.8 eV and Ec ~ 3.8 eV below the vacuum energy level (Evac) after considering the ~ 2 eV energy gap. These derived positions of band edges agree with the theoretical calculations23. At the Fermi edge, the UPS spectra features a characteristic energy of 0.83 eV, giving rise to a Fermi level (EF) at -4.95 eV.
In the classical Marcus-Gerischer theory, an assumption of weak interaction (i.e., a simplified flat band model) is often adopted when discussing the charge transfer process in the electrochemical reactions22–25, that is, the energy levels of reactants are assumed virtually isolated and the rule of band equilibrium between reactants is rarely considered, though being a standard rule used in semiconductor physics. Following this theory, the additional energy barrier is only 0.06 eV for charge transfer from WS2 to absorbed aqueous oxygen, which is too small to interpret the experimental barrier (~ 1.4 eV).
Given the positions of energy levels and ~ 1.4 eV Ea value, we propose a strong interaction model, that is, the band equilibrium between reactants and resultant band bending should be considered. In Fig. 3e, we plot the actual band alignment during oxidation. Before interaction (Supplementary Fig. 23), the EF of WS2 lies at -4.95 eV, which is ca. 0.35 eV higher than the redox potential of aqueous oxygen (EF,redox ~ -5.3 eV22 ). Hence, an upward band bending of 0.35 eV arises for WS2 at the reaction interface, due to the equilibrium of chemical potentials. Accordingly, the photo-excited electrons at Ec need to overcome an extra transfer barrier, Δ, of 0.35 eV to produce the active O2− ions. As such, the ion concentration \(\left[{\text{O}}_{2}^{-}\right]\propto {\text{e}}^{-\frac{\varDelta }{kT}}\). We further deduced that the two reaction steps are both limited in reactant supplies because of the spatially confined nature. Accordingly, the overall reaction rate \({r}_{1\text{L}}\propto \left[{\text{O}}_{2}^{-}\right]\bullet \left[\text{T}\text{S}\right]\propto {\text{e}}^{-\frac{\varDelta }{kT}}\bullet {\text{e}}^{-\frac{0.92 \text{e}\text{V}}{kT}}\), where [TS] denotes the density of transition reaction states for atomic reconfiguration. Hence, the effective Ea = Δ + 0.92 eV = 1.27 eV, which reasonably agree with the experimental value (1.4 ± 0.3 eV). This analysis unravels the crucial roles of potential equilibrium and band bending in understanding the reaction chemistry in spatially confined systems.
Universality of reaction scenario
To verify the applicability of the above reaction scenario, we also adopted MoS2 as the second prototype. Figure 4a − e shows the corresponding r1L data of MoS2 with respect to the same five factors as above, including [V], photon energy, F, RH and T. By and large, the oxidation characters of MoS2 are quite similar to WS2 (See also Supplementary Fig. 25‒27). In particular, its oxidation rate exhibits similar dependence as WS2 for most parameters and can basically share a same analytical formula as Eq. (1), though the relevant coefficients would differ. Surprisingly, both materials share a close humidity boundary at RH0 ~ 46 ± 2% that determines the practical dry or wet reaction mechanism (Fig. 3c).
Few discrepancies are also observed between the two. In general, r1L in MoS2 is much higher than in WS2 (Fig. 4a − e), implying a reduced Ea in MoS2. For this reason, the slope of \({r}_{1\text{L}}\) to RH is too large to access the linear response within our experimental accuracy; only a step-like transition is recorded in \({r}_{1\text{L}}\) as RH crosses the 46% boundary (Fig. 4d). Therefore, the formulized relationship for MoS2 is slightly modified as
$${r}_{1\text{L}}=\text{A}·F·\text{H}\left({\text{R}\text{H}-\text{R}\text{H}}_{0}\right){{·\text{e}}^{\frac{\left[\text{V}\right]}{{\alpha }_{1\text{L}}}} \text{e}}^{-\frac{{E}_{\text{a}}}{kT}}$$
2
where H() denotes the Heaviside step function, used to describe its quick saturation behavior. In this case, the prefactor \(\text{A}={\text{e}}^{4.2\pm 0.3}\)Pa−1, the characteristic vacancy factor \({{\alpha }}_{1\text{L}}\)= 3.7×1013 cm−2, and the activation energy Ea = 0.9 ± 0.2 eV.
Bringing together the data from the two analogous 2D materials, we then have the chance to further verify the proposed strong interaction model, by discussing the origin of Ea difference (1.4 versus 0.9 eV) between them. It is well known that the WS2 and MoS2 monolayers share several physical features, such as lattice structure and bandgap (~ 2.0 eV)23. Following the UPS characterization for WS2, we also determined the energy levels for MoS2 (Fig. 4f) and determined Ev ~ 6.02 eV and EF ~ 5.20 eV below Evac. We found that there would be hardly solutions to explain the Ea difference between WS2 and MoS2, if the rule of band bending is not applied. For comparison with Fig. 3e, we further depict in Fig. 4g the band alignment for MoS2. One can find the most remarkable difference between the two materials lies in the EF positions, which are ~-4.95 for WS2 and ~-5.20 eV for MoS2. Because the EF position of MoS2 (-5.20 eV) is very close to the EF,redox of aqueous oxygen (-5.3 eV), a lower barrier forms in MoS2 than in WS2 as charges transfer to surfacial aqueous oxygen. Hence, higher charge transfer capacity and faster oxidation rates are thus observed in MoS2. This contrastive study emphasizes the role of band equilibrium in the electrochemical reaction, and adds important corrections to the classical reaction model.
We performed systematic survey on the fundamental photo-oxidation kinetics in 2D transition-metal disulfides, with providing quantitative understanding on the oxidation rate of the atomically thin edges with various crystallographic and environmental parameters. We identified the different conditional boundaries in vacancy level and humidity to trigger fast electrochemical oxidation. Also, the microscopic reaction mechanisms were extensively discussed, in terms of the involved reaction paths and energy landscapes. By comparing the actual reaction barriers between WS2 and MoS2, we depicted the realistic charge transfer scenario in the electrochemical process. In particular, we unraveled non-Marcusian charge-transfer mechanism in the spatially confined systems and clarified the crucial roles of potential equilibrium and band bending in quantitative understanding the reaction barriers, which adds an important correction to the classical Marcus-Gerischer charge transfer theory. Overall, the profound knowledge provides insightful understanding on the fundamental reaction chemistry in low-dimensional materials, as well as instructive guidance for corrosion protection, reliability prediction, and stability evaluation.
Preparation of few-layer disulfides. Except for the CVD samples used in XPS characterization, all the other WS2 and MoS2 flakes were mechanically exfoliated from synthesized crystals using viscoelastic poly(dimethylsiloxane) (PDMS) as supports. The use of viscoelastic supports helps to achieve large-area and atomically thin flakes with high yields. The ample supplies of 1L disulfide flakes laid the material foundation for this study where a huge quantity of samples were required. To avoid possible contamination, the freshly exfoliated flakes attached on the PDMS supports were directly used for defect engineering and oxidation tests without further transfer.
HR-STEM imaging. The top-view STEM samples for atomic imaging were prepared by transfer of pristine or H2O2-pretreated WS2 monolayers from silicon substrates onto 300-mesh copper STEM grids through polymer poly(methylmethacrylate) (PMMA) as transfer medium (Supplementary Figs. 3 and 4). High-resolution ADF-STEM images were acquired on a double spherical aberration-corrected FEI Titan Cubed G2 60–300 S/TEM. To identify the atomic vacancies while minimizing the adverse bombardment damage (Supplementary Fig. 5) on the fragile monolayers, the STEM was operated under a low acceleration voltage of 60 kV and a probe current of 56 pA. To enhance the contrast of the sulfur sublattices, a medium-range ADF mode was selected by adjusting the camera length properly. The experimental images used for statistics on vacancy density shown were all processed through the Wiener filtering and average background subtracting. More information can be found in Supplementary Fig. 6.
For samples pretreated under each condition, 25 independent local regions of an area of 4×4 nm2 were adopted for [V] statistics (Supplementary Figs. 7‒12). The independent regions were randomly selected from clean portions free of polymer residues on samples, due to supporting medium PMMA introduced during transfer to TEM grids, and the spatial distance of the regions ranges from 100 nm to 10 µm, dependent on the surface condition and imaging quality of the samples. On average, 2‒5 samples were used for each condition to ensure experimental reproducibility.
Computational Methods. Density functional theory (DFT) calculations were performed by using the VASP package, to gain insight into the energy landscapes for the possible reaction paths. The electron-ion interactions were evaluated by using the projector-augmented wave (PAW) pseudopotential.26,27 Exchange-correlation interactions were considered in the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) and Heyd-Scuseria-Ernzerhof (HSE). The van der Waals (vdW) interactions were described by using the DFT + D2 scheme. The climbing image nudged elastic band (CI-NEB) method was used to find minimum energy paths. To obtain an ionic pseudopotential for a superoxide anion, we used the configuration 1s1.52s22p4.5, in which a “half” electron from the 1s shell was placed in the valence shell 2p of each oxygen atom by an ionic PAW pseudopotential approach. A Monkhorst-Pack k-mesh of 3 × 3 × 1 grid was used to sample the Brillouin zone, and the plane-wave cut-off energy was set to be 450 eV. All the structures were fully relaxed until the force on each atom was less than 0.02 eV/Å and the convergence criterion for the electronic structure iteration was set to be 10− 4 V. The vacuum space was set to be 16 Å in the z-direction, which was large enough to avoid the interactions between two periodic units.
Funding: The activity in Nanjing was supported by the National Key R&D Program of China (2021YFA1202903), the National Natural Science Foundation of China (92264202, 61974060 and 616740800). The activity in Strasbourg was supported by the EC through the ERC project SUPRA2DMAT (GA-833707) and the Graphene Flagship Core 3 project (GA-881603) as well as the Labex project CSC (ANR-10LABX-0026 CSC) within the Investissement d’Avenir program ANR-10-IDEX-0002-02 and the International Center for Frontier Research in Chemistry.
Author contributions: S.L. conceived the experiments. N.X. performed the degradation experiments and electronic measurements. L.S and J.W. performed the theoretical calculations. X.P, W.Z. and P.W. performed the STEM characterization. J.C. performed the EBL operation. N.X., S.L., Z.H., and Y.S. analyzed the data and discussed the results. S.L. and P.S. co-wrote the paper.
Competing interests: The authors declare no competing interests.
Data and materials availability: The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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