Fermi surface definition

The linearized dispersion equation (27) leads to the same definition of the Fermi surface E(k) = EF as that of Eq. (26) provided that f x t lta, with vF 2ata. We have neglected the dispersion along the c direction of very weak coupling. 

Metals and semiconductors have positive and negative slopes in their electrical resistivity p) vs. temperature (T) curves as schematically shown in (109) and (110), respectively. By definition, the Fermi surface disappears when a band gap opens at the Fermi level. If the Fermi surface nesting is complete, all the Fermi surface is removed by the appropriate orbital mixing. However, if the Fermi surface nesting is incomplete, only the nested portion of the surface is removed by orbital mixing. The unnested portion is left as small Fermi surface pockets. The system will thus retain its metallic properties although the number of carriers (i.e. those electrons at the Fermi level) will be... 

This definition, although commonly adopted, can sometimes be ambiguous and misleading. In fact, the notion of metal versus nonmetal is not obvious in clusters, because the standard definitions in terms of conductivity, Fermi surface, etc. do not apply for finite systems. 

One point of extrapolation is clear. The possibility that there be circular electron orbits in a solid has not been covered by the discussion in the text. However, since the Fermi surface, by definition, is a surface of equal energy, it is evident that, as required by the discussion in Section 9.3, there is no energetic barrier to such circular orbits. 

The resistivity of a polycrystalline sample of CaVOs showed a typical metallic temperature dependence, p(T) T, but it became higher above room temperature than is calculated on the basis of itinerant-electron scattering with a mean-free-path as short as one V—0—V distance, which makes CaVOs a bad metal. The resistivity also showed an unusually strong decrease with pressure as might be expected if pressure transfers charge carriers from a lower Hubbard band to the Fermi surface of a Fermi liquid. Pressure would increase not only Wb, but also coq, of Eq. (3), thereby broadening W. However, resistivity data on a polycrystalline sample may not be considered definitive, and they do not provide a measure of m. ... 

Cu, Ag, and Au are sd-metals (the d-band is complete but its top is not far from the Fermi level, with a possible influence on surface bond formation) and belong to the same group (I B) of the periodic table. Their scattered positions definitely rule out the possibility of making correlations within a group rather than within a period. Their AX values vary in the sequence Au < Ag < Cu and are quantitatively closer to that for Ga than for the sp-metals. This is especially the case ofCu. The values of AX have not been included in Table 27 since they will be discussed in connection with single-crystal faces. 

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... 

For electrons in a metal the work function is defined as the minimum work required to take an electron from inside the metal to a place just outside (c.f. the preceding definition of the outer potential). In taking the electron across the metal surface, work is done against the surface dipole potential x So the work function contains a surface term, and it may hence be different for different surfaces of a single crystal. The work function is the negative of the Fermi level, provided the reference point for the latter is chosen just outside the metal surface. If the reference point for the Fermi level is taken to be the vacuum level instead, then Ep = —, since an extra work —eoV> is required to take the electron from the vacuum level to the surface of the metal. The relations of the electrochemical potential to the work function and the Fermi level are important because one may want to relate electrochemical and solid-state properties. 

According to a proposed definition, the electron work function

Fermi level of the metal across a surface carrying no net charge, and to transfer it to infinity in a vacuum. The work function for polycrystalline metals cannot be precisely determined because it depends on the surface structure it is different for smooth and rough surfaces, and for different... 

Suppose we have a slab of semiconductor of thickness L placed in an external homogeneous transverse electric field. In this case the electron concentration on one of the surfaces will be increased as compared with the case of no field i.e., the Fermi level will be raised. On the opposite surface, on the contrary, the electron concentration will be reduced i.e., the Fermi level will be lowered. This is illustrated in Fig. 25, where the continuous lines indicate the band edges in the absence of the field, and the dashed lines indicate the band edges in the presence of the field. (To be definite, the surfaces are assumed to be negatively charged the field in Fig. 25 is directed from left to right.)... 

Fermi-level DOS 115 Jellium model 92—97 failures 97 schematic 94 surface energy 96 surface potential 93 work function 96 Johnson noise 252 Kohn-Sham equations 113 Kronig-Penney model 99 Laplace transforms 261, 262, 377 and feedback circuits 262 definition 261 short table 377 Lateral resolution... 

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. 

---