Energetics of a Semiconductor

Key factors in the utilization of semiconductor electrodes in electrochemical cells and devices are (a) knowledge of the relative location of the energy levels in the 

At absolute zero, the first term in equation (9.3.1) vanishes and 

A redox couple will also have a distribution of energy levels similar to semiconductors. These were first described by Gerischer (16, 17) in terms of a Gaussian-type distribution 

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PVF films may alter the electrochemical response of semiconductor electrodes in useful ways. For example, for potentials more positive than —0.8 V (SCE) only reductions are possible with single crystal or polycrystalline Ti02 in contact with a ferrocene solution (acetonitrile). However, with plasma coated with PVF, ferrocene sites are oxidized in a potential region where n-Ti02 is considered blocked to electron transfer.70 Here two factors are involved obviously the coating of the electrode with an electroactive species, but also alteration of the surface energetics of the semiconductor. 

In the mechanisms to be described in this section, one of the idealizations of electrochemistry is being portrayed. Thus, in perfectly polarizable metal electrodes, it is accepted that no charge passes when the potential is changed. However, in reality, a small current does pass across a perfectly polarizable electrode/solution interphase. In the same way, here the statement free from surface states (which has been assumed in the account given above) means in reality that the concentration of surface states in certain semiconductors is relatively small, say, less than 10 states cm. So when one refers to the low surface state case, as here, one means that the surface of the semiconductor, particularly in respect to sites energetically in the energy gap, is covered with less than the stated number per unit area. A surface absolutely free of electronic states in the surface is an idealization. (If 1012 sounds like a large number, it is in fact only about one surface site in a thousand.) A consequence of this is the location of the potential difference at the interphase of a semiconductor with a solution. As shown in Fig. 10.1(a), the potential difference is inside the semiconductor, and outside in the solution there is almost no potential difference at all. 

Figure 15 schematizes the energetics and dynamics of processes that take place after charge injection from a molecular excited state to the acceptor levels of a semiconductor. Thermalization and trapping of hot injected carriers is known to occur typically with a rate constant kth = 10 s [69-71]. Reverse transfer of a hot... 

Figure 15. Energetics of the charge recombination following electron injection (/ i) from a dye excited state S into the conduction band of a semiconductor. Thermalization and/or trapping of injected electrons (Mh) takes place prior to the interfacial electron back transfer to the dye oxidized state S (/cb). The reaction free energy associated to the latter process depends upon the population of the electronic states in the solid and can be distributed over a broad range of values. Numerical potential data shown are those of the c/s-[Ru (dcbpy)2(NCS)2] Ti02 system.

A junction of this sort can be used as a light-sensitive switch. With a reverse bias applied (extra electrons supplied to the p side), no current would flow, as described for diodes. However, if the difference in energy between the valence band and the conduction band of a semiconductor is small enough, light of visible wavelengths is energetic... 

The discussion given above has concentrated on the energetics of metal surfaces. Though we could similarly enter into a description of the energetics of ideal semiconductor surfaces, such a discussion is much less revealing since in the case of semiconductor surfaces, the driving force for structural reconstruction is so high. As a result, we find it convenient to await a discussion of semiconductor surfaces until we have introduced the next level of structural elaboration, namely, that of surface reconstructions. 

As soon as Ep - Ejjomo becomes smaller than k T, the OFET s conductance increases by several orders of magnitude due to the thermal excitation of the carriers from the localized states into the HOMO band. As a result, a conduction channel is formed at the interface between the semiconductor and the gate dielectric. Overall device operation depends, to a large extent, on the energetics of the semiconductor bands and metal contacts, and therefore studies of the electronic structure of molecular interfaces are important [58],... 

J.A. Turner, Energetics of the semiconductor-electrolyte Interface. J. Chem. Educ. 60, 327-329 (1983)... 

In the case of a semiconductor-based photoelectrochemical system, the measurement of the electrochemical admittance serves two purposes. As is explained in Sect. 2.1.3.1, it allows on the one hand the in situ determination of the energetics of the (bulk) semiconductor surface. On the other hand, it makes the dynamics of various (photo)electrochemical processes experimentally accessible. Clearly, EIS is also possible using an illuminated semiconductor, an experimental method sometimes referred to as PEIS. Finally, it should be noted that although the electrochemical admittance is determined experimentally (the applied electrode potential is used as the perturbation), the electrochemical impedance is generally plotted as the result of an EIS measurement. 

In Fig. 17(a), the energetics of a typical interfacial region between an n-type semiconductor and an electrolyte solution is shown (see also Sect. 2.1.2.2). Electronic equilibrium exists between the semiconductor and a redox system present in the solution the electrochemical potential of electrons /Xg in the solid is equal to that in the liquid phase, and does not change with the spatial coordinate x, perpendicular to the solid/liquid interface. The electrochemical potential of the electrons is also equal to the electron Fermi level, denoted as and can be written as... 

Energetic levels of a semiconductor (a) intrinsic semiconductor (b) n-type semiconductor (c) p-type semiconductor. 

The notion of energetic levels of electrons in soUds can be extended to the case of an electrolytic solution containing a redox system (Gerischer, 1970). The occupied electronic levels correspond to the energetic states of the reduced species whereas the unoccupied ones correspond to the energetic states of the oxidized species. The Fermi level of the redox couple, ii redox, corresponds to the electrochemical potential of electrons in the redox system and is equivalent to the reduction potential, Vq. In order to correlate the energetic levels of a semiconductor to those of a redox couple in an electrolyte, two different scales can be used. The first is expressed in eV, the other one in V (Fig. 6.7a). The difference between the two scales is due to the fact that in solid state physics zero is the level of the electron in vacuum, whereas in electrochemistry the reference is the potential of the normal hydrogen electrode (NHE). The correlation between the two scales can be calculated from the value of potential of NHE which is equal to -4.5 eV when it is referred to that of the electron in vacuum (Lohmann, 1967). 

The photocatalytic properties of a semiconductor depend on the position of the energetic levels, on the mobihty and mean lifetime of the photogenerated electrons and holes, on the hght absorption coefficient and on the nature of the interface. Moreover, the photoactivity depends on the methods of preparation of the powders which allows varying many physico-chemical properties of the semiconductor as the crystalline structure, the surface area and the distribution of the particle size. 

Figure 9.14 Energetics of the semiconductor-electrolyte interface, when n- and p-type semiconductors are brought in contact with the redox couple having in between the band gaps, (a and b) The situations before contact, (c and d) The situations after contact. Arrows shown in (a) and (b) show the direction of electron flow before equUibrimn is established.

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