Fermi Levels Doped Semiconductors

The Fermi level represents in a way the pressure of electrons and is rather similar to the redox potential of an electrode. 

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A semiconductor laser takes advantage of the properties of a junction between a p-type and an n-type semiconductor made from the same host material. Such an n-p combination is called a semiconductor diode. Doping concentrations are quite high and, as a result, the conduction and valence band energies of the host are shifted in the two semiconductors, as shown in Figure 9.10(a). Bands are filled up to the Fermi level with energy E. ... 

Degeneracy can be introduced not only by heavy doping, but also by high density of surface states in a semiconductor electrode (pinning of the Fermi level by surface states) or by polarizing a semiconductor electrode to extreme potentials, when the bands are bent into the Fermi level region. 

Schematic representation of how doping can lead to (a) w-type and (b) / -type semiconductors. Note that the exact position of the Fermi level is temperature-dependent.

Electrical cells based on semiconductors that produce electricity from sunlight and deliver the electrical energy to an external load are known as photovoltaic cells. At present most commercial solar cells consist of silicon doped with small levels of controlled impurity elements, which increase the conductivity because either the CB is partly filled with electrons (n-type doping) or the VB is partly filled with holes (p-type doping). The electrons have, on average, a potential energy known as the Fermi level, which is just below that of the CB in n-type semiconductors and just above that of the VB in p-type semiconductors (Figure 11.2). 

Figure 11.2 Energy diagram for various semiconductors. Shown are examples for pure (intrinsic) and doped (extrinsic) n- and p-types. In each case the Fermi level is shown as a dotted line...

By varying the impurity concentration in the semiconductor, one may regulate not only the activity of the catalyst but its selectivity as well. Indeed, if the reaction proceeds along two parallel paths, one of which is of the acceptor type and the other of the donor type, then upon the monotonic displacement of the Fermi level (i.e., upon the monotonic change of Z) the reaction will be accelerated on one path and retarded on the other, as appears, e.g., from a comparison of Figs. 19a and 19b. Doping of the crystal may accelerate the reaction on one path and retard it on the other. 

As shown in Fig. 3.6, for intrinsic (undoped) semiconductors the number of holes equals the number of electrons and the Fermi energy level > lies in the middle of the band gap. Impurity doped semiconductors in which the majority charge carriers are electrons and holes, respectively, are referred to as n-type and p-type semiconductors. For n-type semiconductors the Fermi level lies just below the conduction band, whereas for p-type semiconductors it lies just above the valence band. In an intrinsic semiconductor tbe equilibrium electron and bole concentrations, no and po respectively, in tbe conduction and valence bands are given by ... 

Conversely, doping Ge with As introduces an extra electron that cannot be accommodated in the tetracovalent network (valence band), and this creates a narrow band of occupied donor levels, just below the conduction band in energy. The Fermi level is now located between the donor band and the conduction band, and electrons in the donor band can be readily excited thermally into the conduction band (Fig. 5.5). Thus, a negative or n-type semiconductor is created. Semiconductors can exhibit electrical conductivities in the range 10-3 to 104 S m 1, as compared to 103 to 107 S m 1 for metals. 

The Fermi level is a theoretical energy of electrons in a semiconductor, such that the probability of occupation of the VB and CB is 50%. In an intrinsic semiconductor this Fermi level is about half-way between the VB and the CB, but it can be displaced substantially in doped semiconductors. An intrinsic semiconductor would be for example a crystal of pure Si or Ge, all tetravalent atoms being linked together in a three-dimensional array. In a doped semiconductor of n -type some of the Si atoms are replaced by pentavalent atoms such as As, and these will release electrons into the CB. A p -type semiconductor, however, contains some trivalent atoms like A1 which are electron deficient. The Fermi level moves closer to the CB in the n-doped semiconductor, while it comes closer to the VB in the p-type semiconductor (Figure 3.46). 

The hypothesis can be tested if the catalytic activity of a metal can be modified by a controlled shift of the Fermi level of the support. With semiconducting supports such a shift is readily achieved by doping additions of cations of higher charge than that of the matrix cations produces quasi-free electrons and/or removes defect electrons and raises the Fermi level addition of lower charged cations has the opposite effect. This calls for investigation of metal catalysts on doped semiconductors as supports. 

In a metal, the Fermi level is located within the conduction band. In a semiconductor, this level usually is found in the forbidden gap between the valence band and the conductivity band by doping it can be shifted up or down relative to the band edges. The activation energy of a catalyzed reaction depends on the distance of the Fermi level from the band edges for acceptor reactions it is related to the distance from the conduction band, for donor reactions to the distance from the valence band. The exact theory will not be presented here it has been given by Hauffe (6) and by Steinbach (9). 

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