Rafael
Almaraz‡
^{a},
Thomas
Sayer‡
^{b},
Justin
Toole‡
^{cd},
Rachelle
Austin
^{c},
Yusef
Farah
^{c},
Nicholas
Trainor
^{e},
Joan M.
Redwing
^{ef},
Amber
Krummel
^{c},
Andrés
Montoya-Castillo
^{b} and
Justin
Sambur
*^{ac}
^{a}School of Advanced Materials Discovery, Colorado State University, Fort Collins, CO 80523, USA
^{b}Department of Chemistry, University of Colorado, Boulder, Boulder, Colorado, 80309, USA
^{c}Department of Chemistry, Colorado State University, Fort Collins, Colorado, 80523, USA. E-mail: jsambur@colostate.edu
^{d}Department of Chemistry and Life Science, United States Military Academy, West Point, New York, 10996, USA
^{e}Department of Materials Science and Engineering, Penn State University, University Park, Pennsylvania 16802, USA
^{f}2D Crystal Consortium Materials Innovation Platform, Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA
First published on 16th August 2023
Hot carrier extraction occurs in 2D semiconductor photoelectrochemical cells [Austin et al., Proc. Natl. Acad. Sci. U. S. A., 2023, 120, e2220333120]. Boosting the energy efficiency of hot carrier-based photoelectrochemical cells requires maximizing the hot carrier extraction rate relative to the cooling rate. One could expect to tune the hot carrier extraction rate constant (k_{ET}) via a Marcus–Gerischer relationship, where k_{ET} depends exponentially on ΔG°′ (the standard driving force for interfacial electron transfer). ΔG°′ is defined as the energy level difference between a semiconductor's conduction/valence band (CB/VB) minima/maxima and the redox potential of reactant molecules in solution. A major challenge in the electrochemistry community is that conventional approaches to quantify ΔG°′ for bulk semiconductors (e.g., Mott–Schottky measurements) cannot be directly applied to ultrathin 2D electrodes. The specific problem is that enormous electronic bandgap changes (>0.5 eV) and CB/VB edge movement take place upon illuminating or applying a potential to a 2D semiconductor electrode. Here, we develop an in situ absorbance spectroscopy approach to quantify interfacial energetics of 2D semiconductor/electrolyte interfaces using a minimal many-body model. Our results show that band edge movement in monolayer MoS_{2} is significant (0.2–0.5 eV) over a narrow range of applied potentials (0.2–0.3 V). Such large band edge shifts could change k_{ET} by a factor of 10–100, which has important consequences for practical solar energy conversion applications. We discuss the current experimental and theoretical knowledge gaps that must be addressed to minimize the error in the proposed optical approach.
Broader contextIn the solar energy conversion process, a photo-excited electron must be extracted from a light-absorbing material. Ultrathin 2D semiconductors are attractive materials for this purpose because their small physical dimensions (e.g., 3 atom thickness in single layer MoS_{2}) minimize the distance electrons must travel to reach their destination. For solar fuel applications, the destination could be protons (H^{+}) in solution, such that two extracted electrons reduce two protons to make hydrogen fuel. One requirement for this electron transfer reaction is that the energy level of the electron in the photocatalyst material is higher than that of the acceptor species in solution. The problem with emerging 2D semiconductor photocatalysts is that their energy levels are ill-defined. Here we develop a novel approach to quantify the electron energy levels under conditions relevant to solar fuel formation. Obtaining this “interfacial energetics” knowledge is critical because it allows researchers to tune the electron transfer rates from the material to the acceptor species, perhaps by a factor of 10–100! |
ΔG°′ = E_{CB} − qE°′ | (1) |
The specific problem is the 2D semiconductor energy levels move under working photocatalytic or photoelectrochemical conditions, due to both the applied potential (E)^{11–14} and absorption of photons.^{15–19} The phenomenon called band gap renormalization (BGR) involves movement of the semiconductor band edges, resulting in a potential- or light intensity-dependent ΔG°′ that currently remains unknown or ill-defined.^{13} The magnitude of BGR effects depend on the semiconductor's carrier concentration (n), which changes with applied potential or illumination. BGR effects are enormous in 2D semiconductors (e.g., >360 meV in photo-excited ML-MoS_{2})^{17} due to strong Coulomb interactions, dielectric screening effects, and quantum confinement.^{11–13,20–25} In the context of photoelectrochemistry, BGR shifts the semiconductor band edges dramatically upon illuminating or applying a potential to the semiconductor, changing ΔG°′ (see eqn (1)). Importantly, quantifying the extent to which applied potential, BGR, and other effects, such as illumination, tune the semiconductor band energies in these low dimensional materials remains a largely open question inspiring active research.^{13,26} In addition, the large band edge movement is significant because it violates a key assumption in the field of semiconductor electrochemistry: k_{ET} is essentially independent of E because the band edges are “fixed”.^{7} This assumption means E_{CB} and E_{VB} are independent of applied potential (E) and, therefore, ΔG°′ is independent of E, too. Thus, these assumptions fail for 2D semiconductors. There is a critical need to quantify interfacial energetics of 2D semiconductor/electrolyte interfaces so we can rationally tune the electron transfer kinetics of these systems for solar energy conversion applications.
Existing approaches and measurement techniques for quantifying interfacial energetics of bulk semiconductors cannot be directly applied to ultrathin 2D electrode materials. Hankin and co-workers discussed and compared popular methods: (1) Mott–Schottky (MS) analysis of differential capacitance versus potential data, (2) Gärtner–Butler (GB) analysis of photocurrent–potential data, and (3) determination of the transition potential between anodic and cathodic photocurrents under chopped illumination.^{27–30} Each method involves key assumptions to extract band edge positions. Those assumptions often fail even for bulk single crystal electrode materials and likely fail for 2D electrode materials as the material thickness becomes much thinner than the charge carrier depletion region thickness. For example, MS and GB analyses assume the applied potential manifests as a potential drop within the semiconductor's depletion region while the band edges remain fixed. As discussed above, large band edge movement is inherent to 2D semiconductor electrodes. The transition potential method between cathodic and anodic photocurrents interprets the transition potential as the flatband condition, where the band bending in the semiconductor is zero. Interpreting this potential as the flatband condition is problematic for 2D semiconductors because they have large (500 meV)^{11,31} exciton binding energies, and it is unclear how much additional electric field strength (i.e., applied potential) is required to overcome the binding energy and induce current flow near the zero-field condition. Another complicating factor is the exciton binding energies renormalize upon applying a potential to the 2D semiconductor. Extracting the electronic band gap (E_{g}) with optical measurements alone is problematic because we cannot assume the optical band gap and E_{g} renormalize equivalently in an electrolyte environment.^{32} Another practical experimental challenge for MS measurements is making defect-free 2D semiconductor/substrate contacts so the underlying metallic substrate does not contribute to the capacitance measurement. In summary, the methods for quantifying interfacial energetics of bulk semiconductor/electrolyte interfaces will most likely not be valid for 2D semiconductor electrodes.
Here we propose a new measurement approach to quantify the band edge movement of 2D semiconductor electrodes. Our optical approach involves the following steps: (1) measure potential-dependent absorbance spectra; (2) correlate carrier concentration (n) by matching the phenomenology of a many-body model to its predicted spectra; (3) interpolate the potential-dependent band gap energy based on first-principles-based effective-mass model calculations of the 2D semiconductor;^{33} and (4) construct an energy level diagram that quantifies BGR as a function of applied potential. The novel aspect of the approach is how it quantifies n via an easily accessible absorbance measurement (the 2D materials community routinely performs spatially resolved absorbance measurements).^{34} The Discussion section describes critical assumptions in steps 2–4 that currently limit the method to the model ML-MoS_{2} system, and pinpoints needed developments in experiment and theory to validate the approach for a wide range of 2D materials.
Fig. 1 (A) Cartoon illustration of the experimental setup (see main text and ESI† for detailed description). (B) Representative 10× bright field transmission image of the sample showing predominantly ML-MoS_{2} and some macroscopic defects. (C) 60× image of the sample edge. The yellow and red polygons show I_{0} and I ROIs for (λ) = log_{10}(I_{0}(λ)/I(λ)) calculations. |
To ensure our optical data stems from ML-MoS_{2} only, we spatially select regions of interest (ROIs) within each image that represent pristine ML-MoS_{2} and ITO (see Fig. 1C), and calculate A(l) = log_{10}(I_{0}(l)/I(l)), where I_{0}(l) and I(l) are the monochromatic light intensities transmitted through the ITO substrate and ML-MoS_{2}, respectively. In this way, we acquire spatially resolved in situ absorbance (A) data as a function of applied potential (E (V) vs. a calibrated Ag wire quasi-reference electrode (QRE), where E (V vs. Ag QRE) = E (V vs. NHE) − 0.498 V, see ESI† for calibration details). Crucially, this procedure removes the contributions from macroscopic defects in the sample. The uncertainty in A is <0.003 for measurements (see Fig. S3 in absorbance error analysis section in ESI†).
Fig. 2A shows representative absorbance spectra of ML-MoS_{2} from the hyperspectral imaging technique. Fig. S4 (ESI†) shows additional experimental data from multiple samples and for multiple potential cycles. We did not observe changes in Raman or absorbance spectra before or after experiments that would indicate significant chemical or structural transformation of the 2D electrode material (such as the 2H to 1T transition), in agreement with literature.^{13} However, in situ Raman spectroscopy measurements indicate the applied potential imparts a structural change in ML-MoS_{2} due to uniaxial tensile strain.^{13} The structural changes are apparently reversible, as evidenced by repeated Raman spectroscopy measurements. Regardless of the sample, the number of cycles, and the scan direction, we observed the following potential-dependent trends. First, the absorbance spectra at more positive potentials (light yellow trace in Fig. 2A) shows three distinct peaks at 655, 610, and 425 nm, which are attributed to the A, B, and C excitons, respectively.^{35} The A and B exciton peak intensities decrease and broaden with more negative potential (dark blue trace in Fig. 2A). On the other hand, the C exciton absorbance feature is essentially potential-independent (Fig. 2A-inset). Control experiments with bulk MoS_{2} material do not exhibit these dramatic spectral changes under the same electrochemical conditions (Fig. S5, ESI†).
The potential-dependent trends in Fig. 2A agree with literature spectroelectrochemistry data for thin films of few-layer MoS_{2} nanosheets and colloidal film electrodes.^{13,26} However, little attention has been paid to the potential-dependent A-exciton lineshape for ML-MoS_{2} in liquid electrolyte. Fig. 2B shows potential-dependent spectra of the A-exciton peak for another ML-MoS_{2} sample using identical experimental conditions as Fig. 2A. Two distinct resonances contribute to this convoluted absorption feature.^{36} The neutral A-exciton absorbance (A^{0}) dominates at more positive potentials. While at more negative potentials, the negatively charged trion (A^{−}) dominates, resulting in a shoulder feature at 670 nm (see Fig. 2B). The spectral changes in Fig. 2 also occur in aqueous electrolyte and in potential regimes that are relevant to electrocatalytic hydrogen evolution (Fig. S6, ESI†). In the section that follows, we describe an approach to quantitatively link the measured absorbance spectrum to carrier concentration using a many-body model of minimal complexity to describe trion formation in ML transition metal dichalcogenides (TMDs) such as MoS_{2}.^{37,38}
The MND model considers the MoS_{2} sample is an n-doped 2D semiconductor,^{40,41} where the majority carriers are conduction band electrons. In the experiment, the external power supply modulates the carrier population. For an unbiased sample at T = 0 K, the model assumes the Fermi level is below the conduction band minimum and the A-exciton absorbance saturates. Consistent with this expectation, we observe A^{0} absorbance saturation at positive applied potentials (e.g., E > 0.7 V, Fig. S4, ESI†). At this undoped condition (Fig. 3A), the MND model predicts two peaks for the A^{0} and A^{−} transitions (dashed and dotted lines in Fig. 3A and B). The oscillator strength is mostly associated with the higher energy A^{0} transition, as indicated by the thick black line in Fig. 3A. After convolving the calculated A^{0} and A^{−} linewidths to account for Gaussian broadening and the instrument response, we obtain a single broad peak at 1.894 eV (solid line in Fig. 3B). The key point here is that the experimentalist observes a single absorbance peak at positive potentials because the oscillator strength is mostly associated with A^{0} at lower n.
The situation changes as n increases. The MND model predicts oscillator strength transfers from A^{0} to A^{−}, as indicated by thicker lines for the A^{−} transition in Fig. 3EversusFig. 3A and C. The oscillator strength shift changes the A^{0}:A^{−} intensity ratio and the peak energy shifts complicate the observed spectrum. As the applied potential shifts from positive to negative, the experimentalist observes a “super peak” split into two discernable peaks (see convolved spectrum in Fig. 3D). A key point of Fig. 3A–F is that the MND model predicts how and why the “super peak” absorbance feature at low n (positive potentials) transitions to two separate peaks at high n (negative potentials).
Having summarized the general predictions of the model, we can now discuss the general fitting procedure to determine n at each E for the experimental data in Fig. 2. Our previous work provides complete MND model calculation details.^{38} Briefly, the model quantitatively links the experimental observable (absorbance spectrum) to n via the Fermi doping energy parameter ε_{F}, defined as an energy level position at or above the conduction band minimum.^{37,42} First, we obtain model parameters, the undoped A^{0} peak (i.e., energy, width, and height), using data acquired at E = +1.00 V and account for phenomenological peak broadening by convolving the simulated peak with a Gaussian. Then, for all other more negative E values (i.e., higher ε_{F} conditions), we make an initial guess at the parameters for both A^{0} and A^{−} and perform a 5-step procedure to determine ε_{F} for every E (see ESI† for details). The rationale of the steps is to model the data globally at the level of the MND peak lineshape outputs instead of guessing at the correct Hamiltonian. We can infer an effective doping density from the ratio of peak heights in the experimental absorbance data based on the series of spectra predicted from the MND model.
Fig. 3G shows the results of the fitting procedure applied to the absorbance spectra in Fig. 2B. The model captures all potential-dependent features of the A-exciton region, specifically how the A^{0} and A^{−} peak intensities, positions, and widths change with applied potential. A key point of Fig. 3G is we obtain a single ε_{F} value that best describes each measured spectrum. Minor disagreement between the MND model and experimental data, such as the high energy tail region, is likely because the MND model only considers the pristine ML-MoS_{2} sample in vacuum and does not consider the possible screening effects from the substrate and liquid electrolyte. Disagreement between the theory and experiment may also be due to non-Gaussian sources of broadening that we do not consider, as well as the simple background subtraction method that does not accurately remove contributions from the B exciton and B trion,^{43} which the model does not consider.
Having determined ε_{F} for each E, we then calculate n. Chang and Reichman applied the MND Hamiltonian to ML-MoS_{2} to calculate n (in units of cm^{−2}) assuming a parabolic band structure:
(2) |
Fig. 4 shows calculated n values versus E. n remains low for E > +0.50 V. Then, n abruptly increases by an order of magnitude over a narrow range (0.30 to 0.50 V). n steadily increases with increasingly negative potentials (E < 0.20 V). For comparison, we also calculated n values using the approach of Carroll et al.,^{13} who adapted Wannier–Mott (WM) effective mass theory for 2D quantum wells^{44,45} to calculate n for 2D materials (see WM model calculations section in ESI† for details). Notably, the WM model does not consider the potential-dependent A^{−} feature and, therefore, the A-exciton region of the absorbance spectrum is fitted with a single component Gaussian. The n values in Fig. 4 differ by an order of magnitude but show qualitatively similar behavior. The n values calculated from the MND model are likely lower because the approach ignores thermal contributions to n and, therefore, likely underestimates the true concentration of conduction band electrons. On the other hand, the n values calculated from the Wannier–Mott model sensitively depend on the exciton Bohr radius (n ∝ a_{0}^{−2}), which linearly depends on m_{e}.^{46} Varying a_{0} (or m_{e}) by a factor of 3 results in nearly an order of magnitude change in n (Fig. S7, ESI†). While it is difficult to know at this stage what the true n values are, the remarkable qualitative agreement using two different approaches indicate that the n–E trends observed in Fig. 4 are robust.
Fig. 4 Potential-dependent carrier concentration values calculated via the MND (black diamonds) and WM model (red circles). |
Fig. 5 shows the resulting band energy diagrams of ML-MoS_{2} as a function of applied voltage using n-dependent E_{g} values interpolated from Gao et al.^{33} Note, we constructed two energy level diagrams using n values obtained from the MND and WM models. At positive potentials, E_{g} approaches the value predicted for “undoped” ML-MoS_{2} (see Fig. 5 inset). E_{g} decreases with increasingly negative E, causing the VB minimum to shift by over 200 meV over a narrow E range. The E_{g} decrease (and upward VB shift) is greater for larger values of n, such as those predicted by the WM model (see red circles in Fig. 5). Note, the WM model does not consider the unique many body physics of 2D semiconductors (e.g., bandgap renormalization, trion formation, screening of quasiparticle binding energies). Fig. S9 (ESI†) shows an additional band energy diagram using experimental E_{g} values obtained from TR-ARPES measurements;^{17} the quantitative values differ slightly, but the qualitative trends hold. The key point of Fig. 5 is that BGR effects cause significant band edge movement (0.2–0.5 eV) and should be given consideration when designing 2D electrodes for electrochemical applications, as will be discussed more below. Importantly, the majority of the BGR shown here occurs over a remarkably narrow range of applied potentials.
Fig. 5 Band energy diagram of ML-MoS_{2} as a function of E in a 0.25 M [Bu_{4}N][PF_{6}] acetonitrile electrolyte. The inset shows the band gap energy as a function of E. |
We now discuss key assumptions in the proposed approach and point out clear next steps to make this approach more robust with future advances in experiment and theory. First, our experimental method does not directly measure band edge positions. We assumed a potential-independent CB minimum value for this model ML-MoS_{2} system, which may not be valid for all 2D materials and those that have yet to be discovered. New in situ methods are needed to determine band edge positions of the 2D electrode. Direct measurement of CB and VB edges yield E_{g}, which could be compared to the E_{g} values we extract from in situ absorbance measurements.
Second, we quantify band edge movement by interpolating E_{g} values as a function of n. The first problem with this strategy is the accuracy of n values obtained using either the MND or WM models. We calculate n from the ε_{F} parameter in the MND model using eqn (2), which considers the pristine semiconductor at 0 K. Aside from ignoring the thermally excited carriers, the MND model does not consider the electrolyte, underlying substrate, spin–orbit coupling to treat the B-exciton and B-trion,^{43} and defects that could serve as extrinsic dopants in the 2D material. A growing body of evidence has shown that defect concentrations and types,^{49,50} substrate materials,^{31,51} solvent,^{52,53} and surrounding chemical environment^{54} all influence n. Current theory does not consider many practical materials and electrochemical factors. Future theory development is needed to accurately determine n using in situ spectroelectrochemistry (e.g., absorbance/reflectance, Raman, or PL spectroscopy). The second problem with the optical spectroscopy strategy proposed herein is it relies also on the accuracy of E_{g} values as a function of n. Experimentally measured E_{g} values^{17} show similar BGR trends as the theoretical calculations,^{33,55} but the absolute values can differ by as much as 0.2 eV. The disagreement could be due to the fact the models do not consider defects and substrate/environmental doping effects. Despite the current difficulty in precisely assigning n and E_{g}, we believe in situ absorbance measurements, modelled by many-body theory instead of the WM model, represent a viable approach to quantify interfacial energetics because there is a robust theoretical framework connecting the observed spectrum to critical parameters relevant to semiconductor energy levels (n and E_{g}).
One clear advantage of our proposed approach is experimental simplicity. Commercially available UV-vis spectrophotometers have absorbance resolution ≤0.001, which is an order of magnitude lower than exciton absorbance peak values of ultrathin TMD semiconductors (Fig. 2). However, large area, defect-free samples are required for benchtop absorbance measurements. Ensemble-average measurements in a benchtop instrument report on the average behaviour of the entire sample in the light path, which could include defects and pinholes in the material as shown in Fig. 1 and Fig. S2 (ESI†). We argue the advantages and disadvantages of the optical approach proposed herein are similar to the popular Mott–Schottky method for bulk semiconductor/electrolyte interfaces; Mott–Schottky data is easy to acquire but can be difficult to interpret.^{27} The current approach (modelling absorbance data using many body theory) can be rapidly applied to any 2D semiconductor in the TMD family.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ee01165h |
‡ These authors contributed equally to this work. |
This journal is © The Royal Society of Chemistry 2023 |