Band-edge energies

Fig. 1. Band-edge energy diagram where the energy of electrons is higher in the conduction band than in the valence band (a) an undoped semiconductor having a thermally excited carrier (b) n-ty e doped semiconductor having shallow donors and (c) a -type doped semiconductor having shallow acceptors.

Flood R, Enright B, Allen M, Barry S, Dalton A, Doyle H, Tynan D, Eitzmaurice D (1995) Determination of band edge energies for transparent nanocrystaUine TiOa-CdS sandwich electrodes prepared by electrodeposition. Sol Energy Mater Sol Cells 39 83-98... 

The situation where the excess electric charge in the bulk of the semiconductor is zero has a particular importance because this can often be obtained experimentally. This state is called flat band situation and the respective electrode potential, flat band potential because in the absence of electric fields inside the semiconductor the position of the band edge energies runs flat from the interior to the surface 20>. This energy pattern at the semiconductor-electrolyte contact is shown in Fig. 10 for the flat band situation, i. e. an anodic and a cathodic... 

Fig. 8.6 Ca— PPV interfacial barriers. The figures are drawn with alignment to the vacuum level of energy, so that the band edge energies can be seen. In this illustration, the electro-chemical potential is not a constant throughout the sample. The band edge values used for the polymer are for MEHPPV.

It is often convenient to refer the Fermi level to reference levels that are close to the band edge energies. If we were to fill up the conduction band with electrons to a value equal to the effective density of states in the conduction band, N, then the Fermi level would shift until it was exactly equal to the energy of the bottom of the conduction band, E b- Our new reference level would then be the energy of the Fermi level at the bottom of the conduction band, that is, E = E h-That is. 

Figure 1.7 Dye-sensitised solar cell (a) cell architecture (b) electronic energy levels. The placement of the semiconductor band-edge energy and the solution Fermi levels S/S, S /S and 1713 on the same scale, the vacuum scale of electronic energy, is explained in Appendix lA at the end of this chapter.

The SHE and SCE scales do not allow electrode potentials to be directly compared with the electronic energy levels (such as the band-edge energies of a semiconductor) in the electrode. To do this, we need a scale of electrode potential based, not on a reference electrode, but on a reference electronic energy level. A good choice, which allows different electrodes to be compared in the same solvent, is the local vacuum level of the... 

Figure 4.25 shows the relevant densities-of-states functions, again for the example of an n-type electrode. On the solution side, the density-of-states functions DofE) and of the Rd, Ox couple have the usual gaussian form (and we again assume these to be independent of electrode potential). On the semiconductor side, the density DfE) of states in the conduction band increases parabohcally from the band-edge energy E. The occupancy functionpfE) has the same Fermi-Dirac form as for a metal electrode but only its tail lies in the conduction band, where the Boltzmann approximation usually suffices. 

Notations used in this review are in accord with the lUPAC electrochemical nomenclature, but only with the exception that the electrode potential is denoted by (p instead of F, because, in semiconductor physics, the symbol E conventionally denotes the energy characteristics (such as, for example, the band-edge energies and F , and the band gap Eg). 

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