Energy Diagram of Semiconductor/Electrolyte Junctions.

I electrochemistry and photoelectrochemistry, it is most common to refer the voltage to a reference electrode (RE) or in a two-electrode cell with respect to a counterelectrode (CE). However, in a semiconductor film that is composed of several junctions, as in semiconductor nanoheterostructures including catalytic layers, it is convenient to use the energy scale with reference to the vacuum level (VL). This type of reference in the energy diagram allows one to track the local variations of energy, electrostatic potential, and Fermi energy inside the solid, and it is the standard representation in solidstate electronics as well as in materials characterization involving ultraviolet photoelectron spectroscopy (UPS) measurements. In contrast, the measurement with respect to RE only takes the voltage at a point on the surface of the solid. Therefore, the relationship between the two pictures can lead to some confusion. In this Guest Commentary, we provide a consistent set of definitions and a diagram that allow one to combine both types of conventions. It is far from the scope of this paper to define the physical meaning of all quantities involved, but we do provide a set of mathematical relationships that allow us to relate the different expressions of voltage and energies such as the flatband potential and the energy (or potential) of the semiconductor conduction band at the surface. The energy diagram of an n-type semiconductor electrode in contact with electrolyte is shown in Figure 1a. In the scheme, the vertical direction indicates increasing electron energy. The arrow indicates the convention of sign for a given quantity. The arrow for A, joining levels B (base of the arrow) and C (tip of the arrow), means that the defined quantity is A = C − B. We consider the general definitions (see also Table 1): (a) V is a voltage in volt units (V). In the diagram, it is given in energy units as −qV, q being the positive elementary charge. A voltage in the diagram is positive if the arrow in the diagram points downward. Vr is measured with respect to the RE. Vapp is measured with respect to an equilibrium situation (as EFn = Eredox). The sign for Vsc, VH, and other internal voltage drops is specified by the arrow as noted above. (b) φ is an electrostatic potential (volts) that is given (in energy units as −qφ) as the local vacuum level (LVL) with respect to the reference level at which φ = 0. (c) E is an energy level, or electrochemical potential level, in units of electronvolts (eV). It is measured with respect to the LVL. Note that a usual reference for the absolute electron energies is the energy of the electron at rest in vacuum just outside of the surface of interest. In Figure 1a, the VL in the electrolyte, Evac el , is taken as the reference of absolute energies scale. The dipole at the electrolyte/vacuum interface is not represented in Figure 1a. Because a change of local φ moves the LVL, all energies in the semiconductor shift accordingly. Material properties such as χ and ζnb are defined positive. An arrow pointing downward in the diagram indicates a negative energy difference. (d) Subindex s is for a surface quantity, and subindex b is for a bulk semiconductor quantity. The doped n-type semiconductor has a uniform distribution of donor ions ND that are balanced by the same quantity of free electrons n0 = ND in the neutral region, where the band edge is flat. The following quantity indicates the amount of doping