Band edges, pinning

Moderately doped diamond demonstrates almost ideal semiconductor behavior in inert background electrolytes (linear Mott -Schottky plots, photoelectrochemical properties (see below), etc.), which provides evidence for band edge pinning at the semiconductor surface. By comparison in redox electrolytes, a metal-like behavior is observed with the band edges unpinned at the surface. This phenomenon, although not yet fully understood, has been observed with numerous semiconductor electrodes (e.g. silicon, gallium arsenide, and others) [113], It must be associated with chemical interaction between semiconductor material and redox system, which results in a large and variable Helmholtz potential drop. 

Let us return to the band-bending process at the interface. For a given semiconductor, the expectation is that as the redox Fermi level is moved more positive ( down on the energy diagram), Fsc should increase concomitantly. This is the ideal (band-edge pinned ) situation. In other words [23],... 

In a system with band-edge pinning, the flatband potentials are to the potentials at which there is no band bending. 

In the following sections we consider new problems in electrochemistry and photoelectrochemistry of semiconductors proper, such as Fermi-level pinning at the surface of a semiconductor electrode (as an alternative to the more common band-edge pinning ), the quasithermodynamic description of electrode reactions—in particular the concept of quasi-Fermi level and the limits of its applicability—and so on. In these sections we also consider briefly the principles of certain of the most up-to-date practical applications of electrochemistry of semiconductors. 

Figure 4. Energy diagram of the interface with an external voltage applied illustrating the band-edge pinning (transition from a to b) or the Fermi-level pinning (transition from a to c) at the surface of a semiconductor electrode. The flatband case is chosen as the initial state.

Fermi-level pinning leads to the situation that the level F can reach the level F dox even for systems characterized by a rather positive or negative value of the equilibrium potential when the level Fredox is beyond the semiconductor band gap. Thus, in the case of Fermi-level pinning, conditions (16a) and (16b) are satisfied, which permit electrochemical reactions to proceed at a semiconductor electrode, while in the case of band-edge pinning these conditions are unattainable. ... 

Figure 14 schematically shows that various situations are possible here. The semiconductor is stable against cathodic decomposition if the electrochemical potential level of the corresponding reaction lies in the conduction band and against anodic decomposition if it lies in the valence band. In both cases, if the whole potential change occurs in the semiconductor (band edge pinning at the surface), this level is inaccessible to the Fermi level of the semiconductor.t For example, in the case of Fig. 14a, the semiconductor is absolutely stable because the levels of both decomposition reactions lie outside the forbidden band. However, more frequent are the cases where the semiconductor is stable against only one type of decomposition cathodic (Fig. 14b) or anodic (Fig. 14c). Finally, if both levels Fdec, and Fjec.p He in the forbidden band (Fig. 14d) the semiconductor can, in principle, suffer decomposition both under anodic and cathodic polarization.

Acj>H is the interfacial potential, which is constant due to the band edge pinning... 

It is worth noting that, as far as they are less than several nanometers thick, the passive films are subject to the quantum mechanical tunneling of electrons. Electron transfer at passive metal electrodes, hence, easily occurs no matter whether the passive film is an insulator or a semiconductor. By contrast, no ionic tunneling is expected to occur across the passive film even if it is extremely thin. The thin passive film is thus a barrier to the ionic transfer but not to the electronic transfer. Redox reactions involving only electron transfer are therefore allowed to occur at passive film-covered metal electrodes just like at metal electrodes with no surface film. It is also noticed, as mentioned earlier, that the interface between the passive film and the solution is equivalent to the interface between the solid metal oxide and the solution, and hence that the interfacial potential is independent of the electrode potential of the passive metal as long as the interface is in the state of band edge pinning. 

The linearity of the Mott-Schottky plot is often considered to be the evidence of the band-edge pinning.82 The measured capacitance, C, can be written as... 

The effect of CH on the Mott-Schottky plots obtained by using Eqs. (32)-(34), (37), (39), and (40) is shown in Fig. 11. The plots are linear when potential change is large but curved when (A Vsc + A VH) < ca. 0.3 V. The slope of the linear portion of the relation is almost identical whether A VH is neglected or not. Thus, the linearity of the Mott-Schottky plot does not necessarily mean the existence of band-edge pinning. 

Vsc should increase concomitantly. This is the ideal (band edge pinned ) situation. In other words [23]... 

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