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A compendium and meta-analysis of flatband potentials for TiO2, ZnO, and SnO2 semiconductors in aqueous media
Semiconductor/electrolyte interfaces are of great interest to numerous scientific fields including renewable energy, (photo)electrochemistry, and energy storage. The semiconductor flatband potential is a key parameter in locating the conduction band minimum or valence band maximum of the semiconductor material in electrolyte. Despite its importance for quantifying the energetic location of the semiconductor bands, literature reports for the same material demonstrate significant variability in the flatband potential. In this compendium and meta-analysis, reported flatband potentials of the common semiconductor materials TiO2, SnO2, and ZnO in aqueous electrolyte were compiled and assessed to quantify the spread in literature flatband potentials as well as determine the factors that lead to the significant spread. For TiO2, SnO2, and ZnO, literature flatband potentials referenced to the reversible hydrogen electrode span a range of nearly 2 V each. Flatband potential tabulations were separated by variables such as the solution pH, the crystalline polymorph, the crystal facet, the morphology, and the dimensions or combinations of these variables to assess the factors that contribute to the observed spread. Important and surprising findings from these categorizations are summarized: (1) Even for the narrowest categorizations, the spread in flatband potential is still large. (2) Flatband potentials of TiO2 and SnO2 follow the expected Nernstian dependence with solution pH. ZnO materials deviate from this Nernstian dependence. (3) In the aggregate, there is no statistically significant difference in the reported flatband potentials of anatase and rutile TiO2. Single crystal tabulations were the only distributions to have statistically significant differences in the flatband potential between anatase and rutile TiO2. (4) Anatase TiO2 materials with a nanotube morphology appear to have a +400 mV difference in mean flatband potential compared to all other morphologies, but we argue that this is likely due to widespread misuse of the Mott–Schottky analysis. Other interesting findings are revealed within the spread of literature flatband potentials, and possible explanations are provided to generate discussion. We also briefly review and discuss common techniques that were used to determine the flatband potential and the pitfalls/criticisms of these techniques. Last, we discuss some ways in which future research on the determination of the flatband potential can be performed to improve the reliability of reported values and the quality of the work. In total, the results from this meta-analysis suggest multiple factors can affect the measured flatband potential and that an abundance of caution should be applied when attempting to quantify the flatband potential of complex or nanostructured systems.
Measuring the flatband potential in 2D semiconductors: Pitfalls and a possible SECCM solution
The flatband potential (V fb ) is a critical parameter in semiconductor electrochemistry, defining the potential at which no excess charge exists at the semiconductor/electrolyte interface. It serves as a key reference for interpreting charge transfer kinetics and current–voltage behavior. However, conventional methods like Mott–Schottky analysis fail for atomically thin 2D materials due to the breakdown of the depletion approximation. This perspective examines the limitations of traditional V fb measurements for 2D semiconductors and the experimental challenges that arise. To address these issues, we propose using scanning electrochemical cell microscopy (SECCM) to spatially resolve the potential of zero charge (V pzc ), equivalent to V fb . This approach mitigates sample heterogeneity issues, such as pinholes or multilayer defects, and offers a pathway to more accurate electrochemical characterization. Ultimately, this method will enhance understanding of current–potential behavior in 2D materials, supporting the design of advanced systems for photoelectrocatalysis, energy conversion, and sensing.
Bonds over Electrons: Proton Coupled Electron Transfer at Solid–Solution Interfaces
This Perspective argues that most redox reactions of materials at an interface with a protic solution involve net proton-coupled electron transfer (PCET) (or other cation-coupled ET). This view contrasts with the traditional electron-transferfocused view of redox reactions at semiconductors, but redox processes at metal surfaces are often described as PCET. Taking a thermodynamic perspective, transfer of an electron is typically accompanied by a stoichiometric proton, much as the chemistry of lithium-ion batteries involves coupled transfers of e – and Li + . The PCET viewpoint implicates the surface–H bond dissociation free energy (BDFE) as the preeminent energetic parameter and its conceptual equivalents, the electrochemical ne – /nH + potential versus the reversible hydrogen electrode (RHE) and the free energy of hydrogenation, ΔG° H . These parameters capture the thermochemistry of PCET at interfaces better than electronic parameters such as Fermi energies, electron chemical potentials, flatband potentials, or band-edge energies. A unified picture of PCET at metal and semiconductor surfaces is presented. Exceptions, limitations, implications, and future directions motivated by this approach are described.
Energetic Tug-of-War between Pt and Leaky TiO 2 : Positive and Negative Effects on the Function of Molecularly-Modified p -Si(111)|TiO 2 |Pt Photocathodes
Photoelectrochemical solar energy conversion to chemical products is a promising avenue towards renewable fuels, and TiO 2 deposition on semiconductor photocathodes is a widespread surface protection strategy. However, the electronic, thermodynamic, and kinetic effects of protection layers on interfacial energetics remains poorly understood. Here, electrochemical data (photocurrent onset and flatband potentials) of p-Si(111)|TiO 2 |Pt is collected in contact with an outer-sphere redox couple. We find that onset potentials shift negatively as a function of increasing oxide thickness, but this effect is not reflected in the flatband potentials. This reveals the mechanism of these shifts is kinetic rather than thermodynamic,and suggests that hole leakage through the TiO 2 is responsible. When Pt nanoparticles are deposited onto the TiO 2 , positive shifts in both the onset and flatband potentials are observed, revealing Pt catalysts are beneficial for more than just increased catalytic rates. These results highlight the importance of understanding the effects of surface modifications on the energetics at the interface in both catalytic and simple electron transfer systems.
A contactless in situ EFISH method for measuring electrostatic potential profile of semiconductor/electrolyte junctions
In photoelectrochemical cells, promising devices for directly converting solar energy into storable chemical fuels, the spatial variation of the electrostatic potential across the semiconductor–electrolyte junction is the key parameter that determines the cell performance. In principle, electric field induced second harmonic generation (EFISH) provides a contactless in situ spectroscopic tool to measure the spatial variation of electrostatic potential. However, the total second harmonic generation (SHG) signal contains the contributions of the EFISH signals of semiconductor space charge layer and the electric double layer, in addition to the SHG signal of the electrode surface. The interference of these complex quantities hinders their analysis. In this work, to understand and deconvolute their contributions to the total SHG signals, bias-dependent SHG measurements are performed on the rutile TiO2(100)–electrolyte junction as a function of light polarization and crystal azimuthal angle (angle of the incident plane relative to the crystal [001] axis). A quadratic response between SHG intensity and the applied potential is observed in both the accumulation and depletion regions of TiO2. The relative phase difference and amplitude ratio are extracted at selected azimuthal angles and light polarizations. At 0° azimuthal angle and s-in–p-out polarization, the SHG intensity minimum has the best match with the TiO2 flatband potential due to the orthogonal relative phase difference between bias-dependent and bias-independent SHG terms. We further measure the pH-dependent flatband potential and probe the photovoltage under open circuit conditions using the EFISH technique, demonstrating the capability of this contactless method for measuring electrostatic potential at semiconductor–electrolyte junctions.
Determining the Point of Zero Zeta Potential in Solid Samples
Technique for measuring pzzp in solid samples incorporates sample in photochemical cell and measures temperature dependence of flatband potential. Pzzp is obtained from slope of best straight line through measured points. Tests agree well with expected values. In technique sample does not have to be in powder form.
Combined Experimental and Theoretical Investigations of n-Type BiFeO 3 for Use as a Photoanode in a Photoelectrochemical Cell
Combined experimental and theoretical investigations were performed to evaluate the potential of n-type BiFeO 3 as a photoanode. While previous experimental and theoretical studies on BiFeO 3 mainly focused on its ferroelectric properties, several studies have reported the advantages of BiFeO 3 as a photoelectrode for solar water splitting (e.g. bandgap energy and band edge positions relative to water reduction and oxidation potentials). However, the photoelectrochemical properties of n-type BiFeO 3 have not yet been thoroughly investigated. In our experimental investigation, we developed an electrodeposition-based synthesis to prepare uniform n-type BiFeO 3 thin-film electrodes. Furthermore, using a heat treatment under a N 2 environment, we intentionally introduced additional oxygen vacancies into the pristine n-type BiFeO 3 electrodes to increase the majority carrier density. The bandgaps, flatband potentials, photocurrent onset potentials, photocurrent generation, and photoelectrochemical stabilities of the pristine and N 2 -treated BiFeO 3 photoanodes were investigated comparatively to improve our understanding of BiFeO 3 photoanodes and to examine the effect of oxygen vacancies on the photoelectrochemical properties of BiFeO 3 . In our theoretical investigation, we performed first-principles calculations and demonstrated the formation of a small polaron when an extra electron was introduced into the BiFeO 3 lattice. Changes in electronic states cause by the small polaron formation were carefully investigated. We also examined the effects of oxygen vacancies on electron polaron formation and carrier concentration in BiFeO 3 . Using charge formation energy calculations and referencing charge transition levels to the free electron polaron level instead of to the conduction band minimum, we showed that the oxygen vacancy is capable of serving as a donor to enhance the carrier concentration of BiFeO 3 . Furthermore, our theoretical results agree well with our experimental findings. Together, the new experimental and theoretical results and discussion provided in this study have considerably improved our understanding of n-type BiFeO 3 as a photoanode.
Effect of counterions on the formation of ohmic contact between p-Si and poly(pyrrole) film - An ac impedance analysis
Conditions under which poly(pyrrole) (PP) films form ohmic contact with single-crystal p-Si are described. Counterions affect both the conductivity and flatband potential, V(FB), values of poly(pyrrole). While paratoluene-sulfonate-doped PP acts like a switch, the impedance behavior of PP films doped with ClO4(-), BF4(-), or PF6(-) allows evaluation of the V(FB) of these films. The formation of 'quasi-ohmic' and 'nonohmic' contacts, respectively, of PP (ClO4) and PP films doped with other counterions, with p-Si, are explained in terms of conductivity of these films and V(FB) of PP films with respect to that of p-Si. PP film seems to passivate or block intrinsic surface states present on p-Si surface.
Coherent phonon flatband generated in GaAs/AlAs superlattices via layer-selective optical pumping
Flatbands, characterized by their dispersionless energy levels in electronic, magnetic, and phononic systems, hold substantial potential for advancements in electronics and quantum information processing. Most flatbands exist in thermal equilibrium and cannot be easily created or annihilated externally, limiting their flexibility as switchable knobs for use in microelectronics and quantum applications. In our work, we demonstrate the generation of a coherent phonon flatband in a GaAs/AlAs superlattice using 800 nm femtosecond laser pulses. This coherent phonon flatband does not correspond to a phonon eigenmode at equilibrium and exhibits strong coupling with two branches of coherently excited longitudinal phonon modes. With molecular dynamics simulations, we show more generally that the coherent phonon flatband can be induced by coherently and spatially modulated optical excitations of superlattice structures. Our results highlight a pathway for coherent phonon flatband creation in the time domain that can be generalized to various superlattice systems, potentially inspiring the realization of coherent flatband generation of other quasiparticles.
Three-dimensional higher-order saddle-point-induced flatbands in Co-based kagome metals
The saddle point (Van Hove singularity) exhibits a divergent density of states in two-dimensional systems, leading to fascinating phenomena such as strong correlations and unconventional superconductivity, yet it is seldom observed in three-dimensional (3D) systems. In this work we find two types of 3D higher-order saddle points (HOSPs) in emerging 3D kagome metals YbCo 6 Ge 6 and MgCo 6 Ge 6 . Both HOSPs exhibit a singularity in their density of states, which is significantly enhanced compared to the ordinary saddle point. The HOSP near the Fermi energy generates a flatband extending a large area in the Brillouin zone, potentially amplifying the correlation effect and fostering electronic instabilities. Two types of HOSPs exhibit distinct robustness upon element substitution and lattice distortions in these kagome compounds. Our work paves the way for engineering exotic band structures, such as saddle points and flatbands, and exploring interesting phenomena in Co-based kagome materials.
WKB Estimate of Bilayer Graphene’s Magic Twist Angles
We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.
Model for thickness dependence of radiation charging in MOS structures
The model considers charge buildup in MOS structures due to hole trapping in the oxide and the creation of sheet charge at the silicon interface. The contribution of hole trapping causes the flatband voltage to increase with thickness in a manner in which square and cube dependences are limiting cases. Experimental measurements on samples covering a 200 - 1000 A range of oxide thickness are consistent with the model, using independently obtained values of hole-trapping parameters. An important finding of our experimental results is that a negative interface charge contribution due to surface states created during irradiation compensates most of the positive charge in the oxide at flatband. The tendency of the surface states to 'track' the positive charge buildup in the oxide, for all thicknesses, applies both in creation during irradiation and in annihilation during annealing. An explanation is proposed based on the common defect origin of hole traps and potential surface states.
A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells
A numerical model that describes the transport of mobile ionic species in metal–insulator–semiconductor (MIS) and photovoltaic (PV) devices subject to temperature and voltage stress is presented. The finite element method (FEM) is used to solve the Nernst–Planck equation while imposing Poisson's equation self-consistently as a restriction for the electrostatic potential. This allows the contribution of the ionic species to the potential to be taken into account. Using a variational formulation eases the implementation of diverse boundary conditions, including the incorporation of segregation kinetics at the device interfaces. Segregation across the dielectric–semiconductor interface is relevant to modeling the electronic device degradation in systems where contamination reaches the semiconductor. The model in closed systems with no-flux boundary conditions is validated first. In the limiting case of low contamination levels with respect to the gate bias, the FEM solution matches analytically derived approximations. Then, the implementation is broadened to include an open boundary at the dielectric–semiconductor interface to account for leakage of ions. The predicted time dependence of the flatband voltage in Na-contaminated MIS test structures agrees well with measurements. This model successfully captures the role of long-range ion transport at concentrations of relevance to electronic and PV device instability and neuromorphic computing.
First Principles Determination of the Potential-of-Zero-Charge in an Alumina-Coated Aluminum/Water Interface Model for Corrosion Applications
The surfaces of most metals immersed in aqueous electrolytes have a several-nanometer-thick oxide/hydroxide surface layer. This gives rise to the existence of both metal|oxide and oxide|liquid electrotlyte interfaces, and makes it challenging to correlate atomic length-scale structures with electrochemical properties such the potential-of-zero-charge (PZC). The PZC has been shown to be correlated the onset potential for pitting corrosion. Here, we conduct large-scale Density Functional Theory and ab initio molecular dynamics to calculate the PZC of a Al(111)| γ -Al 2 O 3 (110)| water double-interface model within the context of aluminum corrosion. By partitioning the multiple interfaces involved into binary components with additive contributions to the overall work function and voltage, we predict the PZC to be -1.53 V vs SHE for this model. Furthermore, we calculate the orbital energy levels of defects like oxygen vacancies in the oxide, which are critical parameters in theories associated with pitting corrosion. We predict that the Fermi level at the PZC lies above the impurity defect levels of the oxygen vacancies, which are therefore uncharged at the PZC. From the PZC estimate, we predict the voltage needed to create oxygen vacancies with net positive charges within a flatband approximation.