Fermi energy, definition

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

Adsorption related charging of surface naturally affects the value of the thermoelectron work function of semiconductor [4, 92]. According to definition the thermoelectron work function is equal to the difference in energy of a free (on the vacuum level) electron and electron in the volume of the solid state having the Fermi energy (see Fig. 1.5). In this case the calculation of adsorption change in the work function Aiqp) in... 

This is schematically illustrated in Figure 6.3. Per definition, the Fermi energy is a true bulk property and independent from the specific surface conditions. EF and 6(r) are however influenced by external means, such as a connection to a voltage source with respect to 0 V. The work function , however, is not influenced by such external means, but depends on the other hand strongly on the surface conditions. 

The sign of the thermopower is negative for electrons and positive for holes and its measurement provides a definitive identification of the type of conduction. When conduction is by a single type of carrier (either electrons or holes) far from the Fermi energy in a homogeneous material, the thermopower is... 

The distribution of the electron levels, g E), for a gas of independent and free electrons was calculated in the foregoing section. At 0 K, all energy levels up to the Fermi-energy level are occupied with one electron. (The spin degeneracy was accounted for in the density g E).) From the definition of chemical potential given... 

Figure 4. Densities of states (DOS) for La2Cu04 and LaBaCu04. The total DOS is shown in the upper panels, and the site-decomposed muffin-tin coo onents are shown in the remaining panels. The Fermi energy is 0.0. Refer to Figure 1 for site definitions.

In metals the Fami energy is the enetgy of the highest occupied energy level (at T = 0 K). In an intrinsic semiconductor the Fermi energy is per definition midway between the valence and conduction bands. Therefore, the Fermi energy for an intrinsic semiconductor is... 

The sum of these values yields the free energy of reaction for the standard hydrogen electrode. By definition, E° and therefore AG° are zero thus the electrochemical potential of the electrons (equal to the Fermi energy) is equal to ... 

Using the same change of variables as above (see equation [1.84]), and if we introduce the definition [1.87] of the Fermi energy, we find that ... 

The chemical potential p of the electron assembly, otherwise known as the Fermi energy, is found by differentiation with respect to a L, the actual number of electrons distributed among the sites. Here, because of our somewhat imusual specification of site occupancies, one encounters a common factor of 2 throughout, that may be absorbed in the definition for p (recall that the bonds with two termini actually refer to single electron spin states), so that... 

In connection with Fig. 23.5, it is worth pointing out that the reference level, i.e., the Fermi level of the spectrometer, is determined by performing a UPS measurement on a metallic specimen in equilibrium with the spectrometer, taking Au as in the example here. The Fermi level of the metal, by definition, lines up with the Fermi level of the spectrometer. Since, in equilibrium, the position of the Fermi energy is constant throughout the thickness of the thin films under discussion in this chapter, the position of the Fermi energy on the UPS... 

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