Fermi surfaces

The surface Fermi level, Cp, which depends on the surface state, is not the same as the interior Fermi level, ep, which is determined by the bulk impurity and its concentration. As electron transfer equilibrium is established, the two Fermi levels are equilibrated each other (ep = ep) and the band level bends downward or upward near the surface forming a space charge layer as shown in Fig. 2-31. 

Fig. 2-81. Surface degeneracy caused by Fermi level pinning at a surface state of high state density (a) in flat band state (Ep ep), G>) in electron equilibrium (cp = cp). cp = surface Fermi level = surface ccmduction band edge level.

The semiconductor surface where the Fermi level is pinned at a surface state of high density (Fig. 2-31) is in the state of degeneracy of electron levels, because of the high electron state density at the surface Fermi level. Similarly, the surface degeneracy is also established when the band bending becomes so great that the Fermi level is pinned either in the conduction band or in the valence band as shown in Fig. 2-32. 

Since the electron state density near the Fermi level at the degenerated surface (Fermi level pinning) is so high as to be comparable with that of metals, the Fermi level pinning at the surface state, at the conduction band, or at the valence band, is often called the quasi-metallization of semiconductor surfaces. As is described in Chap. 8, the quasi-metallized surface occasionally plays an important role in semiconductor electrode reactions. 

On surfaces of some d band metals, the 4= states dominated the surface Fermi-level LDOS. Therefore, the corrugation of charge density near the Fermi level is much higher than that of free-electron metals. This fact has been verified by helium-beam diffraction experiments and theoretical calculations (Drakova, Doyen, and Trentini, 1985). If the tip state is also a d state, the corrugation amplitude can be two orders of magnitude greater than the predictions of the 4-wave tip theory, Eq. (1.27) (Tersoff and Hamann, 1985). The maximum enhancement factor, when both the surface and the tip have d- states, can be calculated from the last row of Table 6.2. For Pt(lll), the lattice constant is 2.79 A, and b = 2.60 A . The value of the work function is c() w 4 cV, and k 1.02 A . From Eq. (6.54), y 3.31 A . The enhancement factor is... 

On the contrary, the Fourier transform of an image such as shown in Fig. 6 contains an internal calibration, because the distance separating the lattice spots in the Fourier transform is related to the lateral lattice parameter of Cu(lll). In this case one can determine with high precision the size of the surface Fermi wave vector, which turns out to be kp = 0.205 0.02 A, i.e. a Fermi wavelength of 30 3 A for Cu(lll), in nice agreement with... 

In addition, the presence of surface charges leads to band bending at the semiconductor-metal interface. For /(-type semiconductors, these states are acceptor-like and the semiconductor at equilibrium may exhibit upward (negative) band bending as the surface Fermi level moves towards the charged... 

From a conceptual point of view, it appears that polymer quantum chemistry is an ideal field for cooperation between condensed matter physicists and molecular quantum chemists. There exists a common interpretation in the discussions concerning orbital energies, orbital symmetry, and gross charges by chemists and solid-state physicists. These physicists use terms less familiar to the chemist, such as first Brillouin zone, dependence of wave function with respect to wave vector k (the one-electron wave function is called an orbital by the chemist), Fermi surfaces, Fermi contours, and density of states (DOS). 

The various spectra have been recorded under a square-wave modulation of the potential between the two values indicated below the curves. They represent the change in absorbance when the potential is changed from the lower to the higher value. The change in shape is consistent with a broad distribution of interface states through the gap. It is associated with the increasing energy of the surface Fermi level (increased... 

The Fermi level in the electrolyte has been left undefined since it depends on the initial relative concentrations of H2 and O2 in solution. Figure 3b shows the situation at equilibrium in the dark once the semiconductor and the metal are brought into contact with the electrolyte and a depletion layer is formed near the semiconductor surface. Fermi levels of the three phases equilibrate, giving rise to a band bending in the semiconductor. When the semiconductor is irradiated with photons of energy corresponding to the band gap, electron-hole pairs are created and the Fermi level in the semiconductor is raised towards the flat band potential Vfb by an amount Fph which is the photopotential generated. The maximum value the... 

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