Defects in two-dimensional crystals often introduce unique properties that are absent in pristine materials 1–3. For example, tuning the defect states in two-dimensional (2D) MoS2 can sharply increase its quantum yield from 0.6% to over 95%, rendering it a promising material for next-generation light-emitting diodes 4. Controlling the defect states in MoS2 can also enhance its hydrogen generation performance 5,6. Defect engineering requires detailed knowledge of the defect states and of the evolution of the electronic structure of a material during physicochemical processes. Currently, experimental methods for characterizing electronic structures lack the flexibility necessary for monitoring electronic structure evolution under real operating conditions. Typically, the density of states (DOS) and corresponding defect states are characterized using scanning tunneling spectroscopy (STS) 7,8 and photoemission spectroscopy (PES) 9,10. Previous STS results have shown that sulfur vacancies in monolayer (1-L) MoS2 introduce a peak appearing in the gap region of the DOS, indicating these defects create in-gap states that enhance the catalytic activity of the material for the hydrogen evolution reaction (HER) 35. In another study, PES was used to provide experimental evidence for the indirect-to-direct bandgap transition that occurs in the 1-L limit of MoS2 10. While the utility of these techniques is clear, combining STS and PES measurements to obtain high-quality data for the electronic properties of 2D materials is often challenging because each technique has stringent requirements for high-quality samples. STS usually requires a clean and atomically flat substrate with adequate conductivity, while PES needs large single-crystalline domains with high uniformity. Additionally, both measurements require either ultra-high vacuum or low temperatures to gather high-quality data. The requirements of high-quality samples, ultra-high vacuum, and/or low temperatures make it difficult to characterize and understand these 2D semiconducting materials for practical applications.
Here we report an alternative approach for obtaining close-to-theoretical resolution characterization of the DOS of 2D materials under ambient conditions, which does not suffer from stringent requirements on the domain size of the samples. The central idea of the approach is that the intrinsic electrochemical capacitance of a 2D material is proportional to its density of states. The quantum capacitance of 2D materials can be directly measured if the electrochemical capacitance contribution of the electrolyte is negligibly small compared to that of the 2D material. The total electrochemical capacitance (Ctotal) of an electrochemical cell has two components; the first is the interfacial capacitance of the working electrode (CWE), and the second is the interfacial capacitance of the counter electrode (CCE). This relationship can be represented quantitatively as the sum of two capacitors in series, where 1/Ctotal = 1/CWE + 1/CCE. When CCE ≫ CWE, Ctotal ≈ CWE. Similarly, the inverse electrochemical capacitance (1/CWE) can be considered as the sum of two additive contributions 11–13. One contribution originates from the double-layer capacitance of the interfacial electrolyte (CDL). The other contribution encompasses the capacitance of the solid electrode (CE). If the solid electrode is made of a semiconductor or 2D material, the electrode capacitance is proportional to its DOS and CE becomes CQ, the quantum capacitance 14,15. The total electrochemical capacitance is related to the double-layer and electrode contributions as 1/Ctotal = 1/CDL + 1/CQ. Thereby, Ctotal ≈ CQ when CDL ≫ CQ and the measurable Ctotal is proportional to the DOS of the 2D material. The critical step in implementing this concept is identifying electrolytes with (i) a high areal capacitance much larger than Ce and (ii) an electrochemical stability window sufficiently broad to cover the conduction band minimum (CBM) and valence band maximum (VBM) of 2D materials. This is summarized in Fig. 1e.
This work uses monolayer MoS2 as the working electrode and the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), which meets the above requirements of high capacitance and a wide electrochemical window of ~ 3.5 V 16,17, as the electrolyte. The choice of MoS2 as the electrode material was based on its wide application in electronic systems and the availability of a substantial body of experimental 18–20 and theoretical data 21 on its electronic structure. This data facilitates cross-comparison with the electrochemical capacitance spectra. A schematic of the devices used for the electrochemical measurements is shown in Fig. 1a. For the strain measurements, the device construction is identical, except the substrate is changed to PET (Fig. 1b.). PMMA is used to insulate the conductive components of the device from the electrolyte, and a window in the insulating layer is fabricated to isolate the electrochemical signal from the desired area of the monolayer MoS2 flake. The window has clear boundaries, allowing the current density and areal capacitance to be calculated (Fig. 1c.). An AFM image of the MoS2 lattice is obtained within the PMMA window, indicating that the pristine crystal structure is maintained throughout the device fabrication process (Fig. 1d.).
An electrochemical method known as staircase potentio electrochemical impedance spectroscopy (SPEIS) is employed to measure Ctotal and the electrochemical tunneling current. Two scan frequencies, 5 and 100 Hz, are selected to investigate the DOS of the basal plane of MoS2. At low frequency, the capacitance of the interfacial [BMIM][BF4] layer is equal to 61.7 µF/cm2 (Fig. 2a), which is significantly higher than Ce (~ 4 µF/cm2) at the CBM of the monolayer MoS2 22. Under these conditions, the positions of the VBM and CBM are clearly captured in the electrochemical capacitance measurement, with a measured bandgap of 1.79 ± 0.147 eV (Fig. 2b, Figure S1). In addition to the apparent CBM position at 0.1 V vs. Ag/AgCl (4.83 eV vs. vacuum), another threshold occurs around − 0.3 V vs. Ag/AgCl. This threshold matches very well with the STS results at low temperatures 18,23,24 and the calculated features of the conduction band of a single-layer MoS2 (Fig. 2c). The electrochemical tunneling spectrum and corresponding dI/dV-V spectrum (Figure S2) further verify the CBM and VBM positions of monolayer MoS2 at 0.1 V and 1.9 V vs. Ag/AgCl, respectively. We note that DFT simulations predict the appearance of the shoulder associated with 4d atomic orbitals of Mo (Mo 4d) at the top of the valence band. This shoulder is not observed in the measurements of the electrochemical capacitance spectra. Its absence is likely due to the insufficient resolution of fine features of the DOS in electrochemical measurements. The calculated bandgap of 1.73 eV is about 9% smaller than the direct bandgap of 1.90 eV measured using optical spectroscopy 25. The difference is expected due to the systematic underestimation of the bandgap by the generalized gradient approximation with the PBE exchange-correlation functional 25,26. When the frequency is increased from 5 to 100 Hz, Cion decreases sharply to 0.8 µF/cm2 and becomes lower than the Ce at the CBM of the monolayer MoS2. Thereby, no apparent threshold is observed in the electrochemical capacitance spectrum (the black line in Fig. 2b).
Electrochemical capacitance measurements are further employed to investigate defect states in monolayer MoS2. Defect states at the zigzag edge and armchair edge of MoS2 are studied separately. MoS2 edge types are determined using second-harmonic generation spectroscopy (Figs. 3a, b) 28. To investigate defect states at the MoS2 zigzag edge, the sample is covered with a PMMA insulating layer with the zigzag edge exposed to the ionic liquid (Figs. 3c, d). The PMMA layer contributes little capacitance compared to MoS2 (Figure S3). Hence the measured capacitance is primarily associated with the MoS2 zigzag edge. Compared with the MoS2 basal plane, there are two significant changes in the electrochemical capacitance spectrum (Fig. 3e). First, four new peaks appear on the MoS2 capacitance curve. One method of peak assignment is comparing features on the experimental capacitance curve with theoretical simulations of the DOS of MoS2 zigzag ribbons with stoichiometric structure and with vacancies at the edges or in the basal plane (Fig. 3g and Figures S4 – S6). The main peak at 1.6 eV vs. Ag/AgCl can be identified as the signal of occupied Mo 4d atomic orbitals just below the Fermi level. The smaller peak at about 1 eV vs. Ag/AgCl corresponds to unoccupied states of undercoordinated Mo atoms at the edge, consistent with the theoretical prediction that the Mo-edge is the energetically favored termination compared to the S-edge 29,30 (Fig. 3e, inset). Second, the shape of the conduction band changes and, the shoulder at the CBM is no longer observed. Instead, a new peak appears at 0.3 eV vs. Ag/AgCl. Simulations suggest that these two features are associated with the formation of S vacancies in the basal plane (Figure S4). The observed CBM and VBM shift toward more negative potentials vs. Ag/AgCl. It implies that edges and point defects can modulate the absolute positions of the CBM and VBM of semiconductors, highlighting new opportunities to optimize material performance through defect engineering. The defect-tuned band edge positions and bandgap are also observed in the MoS2 with an armchair edge exposed (Figs. 3f, h, Figure S7). The peak associated with the edge S atoms and S-defects in the basal plane (0.7 V vs. Ag/AgCl) is more significant than the peak associated with edge Mo-vacancies and Mo atoms at the MoS2 armchair edge, which can be attributed to the lower formation energy of S-vacancies than Mo-vacancies 31. Unfortunately, AFM images of the edge structure were unable to be obtained owing to the inherent limitations of the tip geometry and radius of our probes, which are further elucidated in the Supplementary Information section on AFM methodologies. However, our proposed edge structures agree with those imaged by STEM in other work 32.
To estimate the energy resolution of electrochemical capacitance spectroscopy at room temperature, we calculated the full width at half maximum (FWHM) of the 25 peaks in the 5 electrochemical capacitance spectra obtained in this study (Figure S9). The highest energy resolution, i.e. the lowest FWHM, approaches 116 meV, close to the thermal Fermi function broadening at room temperature (3.5 kBT = 91 meV) 33.
The EQCS method can not only track the defect states in 2D materials, but also the DOS around the conduction/valence band edge. This multifaceted tracking allowed us to investigate how to manipulate the conduction band of MoS2 with mechanical strain and how band structure influences electrochemical reactions. To study these effects, monolayer MoS2 flakes were exfoliated on a polyethylene terephthalate (PET) substrate and subsequently mounted onto a PET plastic cross-shaped support. Biaxial tensile strain was applied to the PET substrate and monolayer MoS2 flakes by anchoring the plastic cross support on dome-shaped glass (Fig. 4a). The applied strain varies with changes in the glass curvature, and curvatures were chosen to apply approximately 1 and 2% biaxial strain. The actual strain felt by monolayer MoS2 flake is extracted from Raman spectra and is plotted in Fig. 4f. The intermediate strain value was found to be 0.6%, while the high strain value was 1.0%. The discrepancy in the curvature-derived and measured strain likely arises from the difference in Young’s moduli between the armchair and zigzag direction of MoS2, which will result in less efficient strain-transfer between the substrate and MoS2 flake in the zigzag direction41. This smaller than expected strain makes the observed enhancement of the catalytic current even more profound. We use the HER as a model for this study as it is a well-investigated electrochemical reaction. As shown in Fig. 4b, two uncommon phenomena are observed after applying strain on the monolayer MoS2. (1) A clear 3-zone polarization curve forms, which is unusual for the HER in 0.5 M H2SO4, and (2) at -0.3 V vs. SCE, the current density at 1% strain is 5-times higher than without strain.
EQCS was employed to relate the electronic structure to the main features of the polarization curves (Fig. 4c). The electrochemical capacitance spectrum has a plateau between 3.90–4.25 eV, slightly higher than the conduction band minimum (CBM) of MoS2. The width of the plateau is consistent with 0.3 eV energy difference of the CBM at the K-point the energy at Q-point 34. Three regions are evident in the spectra, which are bound by points d1-d4.
A similar 3-zone electrocatalytic curve is observed in the unstrained monolayer MoS2, rendering it a common feature of the Tafel plots for 0%, 0.6%, and 1% strained monolayer MoS2 (Fig. 4e inset). One interesting phenomenon is that the Tafel slope in Zone 1 monotonically decreases with an increase in tensile strain, while the Tafel slope in Zone 2 changes little (Fig. 4e). The decreased Tafel slope in Zone 1 indicates a higher efficiency of HER on strained MoS2 than on the unstrained monolayer. This conclusion is also supported by the strain dependence of the shape of polarization curves (Fig. 4b) and electrochemical capacitance spectra (Fig. 4c). At -0.3 V vs. RHE, a 5-time higher current density is captured in the 1% strained MoS2 compared to the unstrained flake. The result is in line with recent observations of strain effects on the catalytic activity of MoS2 35. The study demonstrated that, assuming the kinetics of HER can be described by a one-electron Volmer process, strain affects the electron transfer rate between MoS2 and H+. Fitting the observed Tafel slopes for strained and unstrained MoS2 monolayers using Butler-Volmer formalism revealed a more than 4-time increase in the electron transfer rate in 1% strained monolayer compared to 0% strained MoS2 35.