Intrinsic Fermi level

Figure 13. Energy band diagrams and charge distributions of an ideal MOS capacitor using p-type Si (a) accumulation, (b) depletion, and (c) inversion. Ef denotes the intrinsic Fermi level. (Reproduced mth permission from reference 8. Copyright 1985 Wiley.)...

The most important point is that the intrinsic Fermi level of silicon, fi, is not affected by the environment, because the bulk of silicon is well protected by the silicon dioxide and silicon nitride layers and provides the stable and reproducible... 

Fig. C.4 Bend bending at the surface of a p-type semiconductor. The zero potential is in the bulk of the semiconductor and is referred to the intrinsic Fermi level E. The surface potential yrsis shown as positive (Sze, 1981)...

Fig. 12. Dependence of the intrinsic Fermi level, calculated as - (EA + Eel2) where EA is the electron affinity (i.e. the energy of the conduction band edge, which can be obtained from the flat-band potential) and Eg the bandgap, on the mean electronegativity of A and B, (xaXb)112 for semiconductors A B, where Xa< Xb are Pauling electronegativities.

The actual value of the flat-band potential depends on the energies of the valence and conduction bands in the material and can be deary related to the vacuum level provided that the reference electrode can also be so referenced [41 44]. If we can relate x(SC) to the intrinsic Fermi level E , then the electron affinity of a semiconductor can be written... 

If we take into account the fact that n = p stemming from the intrinsic property, then the intrinsic Fermi level Ep = Ei is given by ... 

If the effective mass of the integral electronic density nio is equal to that of the holes mv, then Nc = Nv and the intrinsic Fermi level Ei is located at the middle of the forbidden band (see Figure 3.8a) ... 

For clarification of the type of junctions formed at the semiconductor-electrolyte, let us take an example of n-type semiconductor. In addition to possessing free electrons (referred to as the majority carrier), n-type semiconductor also possesses holes (referred to as the minority carrier). The concentration of holes is temperature-dependent and is equivalent to the intrinsic concentration of the carrier (which is related to the concentration of Frankel defects). It can be shown mathematically that the Fermi level of minority carrier hes at almost half the band gap position. On the other hand, the concentration of majority carriers as well as the Fermi level depends on doping concentration. Thus, the Fermi level of the majority carrier can he anywhere between the conduction hand edge and the intrinsic Fermi level that is situated at i g. 

Let us imagine a situation where an -type semiconductor is brought in contact with a redox electrolyte (Fig. 4a). Let us also assume that the electrochemical potential, that is, its redox potential, is almost equal to the intrinsic Fermi level of the semiconductor. This situation forces the electrons (majority carriers) to flow from the semiconductor to the electrolyte. This migration continues until the two Fermi levels achieve an equilibrium position (Fig. 4b). At this condition, no further migration of electron occurs and a dynamic equflibrium is established. In this situation, instead of electrochemically reacting with the redox electrolyte, these majority carriers accumulate at the interface of semiconductor-electrolyte to maintain neutrahty of the material. 

What would be the magnitude of potential developed between the charges accumulated at the interface (x = 0) and at plane X = —Wn (or for p-type semiconductor at X = —Wp) The driving force for these carriers depends on the magnitude of the potential difference between the Fermi level of the semiconductor and the redox potential of the electrolyte (i.e. Ey — F(redox))-This potential is known as the contact potential [6). Can we fabricate a PEC cell, which gives a contact potential equal to the band gap value of the semiconductor In other words, can we form a PEC cell with a semiconductor (whose Ec Ef) and redox electrolyte (whose / redox v). such that the contact potential (9) = g The approximate Fermi level of the semiconductor (i.e. the intrinsic semiconductor) is approximately equal to half the band gap of the semiconductor (i.e. jfg). Therefore, redox electrolyte cannot lower the Fermi level of -type semiconductor beyond jEg. This condition puts a restriction to the maximum achievable contact potential 6), and is equal to jEg value. This also suggests that for a given semiconductor, the most suitable electrolyte would be the one that has a redox potential that is almost equal to the intrinsic Fermi level of the semiconductor. 

A particular feature of the band structure of HOPG is that around the intrinsic Fermi level, the DOS is low (Figure 2.6b) [88], about 0.0022 states atom" eV" [2, 3]. This contrasts with metals such as Au, for which the DOS is around 0.28 states atom eV and more or less constant for a wide range of energies [100]. An important - and still open - general question in electrochemistry is whether (and when) the DOS of metal (and metal-like) electrodes is important in determining... 

Ei(z) is the intrinsic level, this level runs parallel to the band edges and coincides, in the bulk, with the intrinsic Fermi level E h. ... 

Now let us see if we can describe this process analytically. From Equation 20.18 we can see that adding Nu donor states will raise the Fermi level above the intrinsic Fermi level in the -material by... 

Similarly, adding acceptor states lowers the Fermi level below the intrinsic Fermi level in the p-material by... 

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