Fermi energies work function

Equally important is the observation that, as Figure 25 shows, the chemisorptive binding energy-work function behavior can be described almost quantitatively by taking into account only the electrostatic (Stark) interactions, i.e., only the through the vacuum electrostatic interactions in the double layer and neglecting the through the metal interactions, i.e., the redistribution of electron states near the Fermi level of the cluster. This is an important result as it provides... 

Fig. VIII-5. Schematic potential energy diagram for electrons in a metal with and without an applied field , work function Ep, depth of the Fermi level. (From Ref. 62.)...

Figure 9-19. Bund diagram of LPPP with hole traps and gold electrodes with Va<- vacuum level. Ec conduction band, Eva valence band. E, Fermi level. . baudgup energy. and , " trap depths. ,( ) trap distribution, X electron affmity, and All work function of the gold electrodes.

As discussed already in Chapter 2 the work function, , of a solid surface is one of the most important parameters dictating its chemisorptive and catalytic properties. The work function, (eV/atom) of a surface is the minimum energy which an electron must have to escape from the surface when the surface is electrically neutral. More precisely is defined as the energy to bring an electron from the Fermi level, EF, of the solid at a distance of a few pm outside of the surface under consideration so that image charge interactions are negligible. 

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

As previously noted the work function O is the work required to bring an electron from the Fermi level of the metal to a point outside the metal where the image forces are negligible, i.e., typically 1 to 0.1 pm outside the metal surface.9,10,16 22 The Volta potential at this point is defined so that the energy required to bring an electron from that point to an "infinite" distance from the metal surface is e. ... 

The work function is the minimum energy needed to remove an electron from a solid and take it infinitely far away at zero potential energy. The weakest bound electrons in a solid are the electrons at the Fermi level. All sp and d bands are filled... 

Consider the case of a junction between two different metals a and p. Generally, they will have different values of the Fermi energy and work function. Between the two metals, a certain Volta potential will be set up. This implies that the outer potentials at points a and b, which are just outside the two metals, are different. However, it will be preferable to count the Fermi levels or electrochemical potentials from a common point of reference. This can be either point a or point b. Since these two points are located in the same phase, the potential difference between them (the Vofta potential) can be measured. Hence, values counted from one of the points of reference are readily converted to the other point of reference when required. 

Unlike the values of values of electron work function always refer to the work of electron transfer from the metal to its own point of reference. Hence, in this case, the relation established between these two parameters by Eq. (29.1) is disturbed. The condition for electronic equilibrium between two phases is that of equal electrochemical potentials jl of the electrons in them [Eq. (2.5)]. In Eig. 29.1 the energies of the valence-band bottoms (or negative values of the Fermi energies) are plotted downward relative to this common level, in the direction of decreasing energies, while the values of the electron work functions are plotted upward. The difference in energy fevels of the valence-band bottoms (i.e., the difference in chemical potentials of the... 

It should be mentioned that one can detect two types of equilibrium in the model of charge transfer in the absorbate - adsorbent system (i) complete transition of chemisorbed particles into the charged form and (ii) flattening of Fermi level of adsorbent and energy level of chemisorbed particles. The former type takes place in the case of substantially low concentration of adsorbed particles characterized by high affinity to electron compared to the work function of semiconductor (for acceptor adsorbates) or small value of ionization potential (for donor adsorbates). The latter type can take place for sufficiently large concentration of chemisorbed particles. 

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... 

Figure 2.23 (a) The energy levels of tip and sample when connected by a wire. EF is the Fermi level, d the tip/sample separation, and s and the work functions of the sample and tip, respectively, (b) As for (a) except depicting the effect on the system of an imposed bias voltage, Vb. The bias voltage is defined as From Christensen (1992). 

Fig. 9 OMT bands for NiOEP, associated with transient reduction (1.78 V) and transient oxidation (—1.18 V). Data obtained from a single molecule in a UHV STM. The ultraviolet photoelectron spectrum is also shown, with the energy origin shifted (by the work function of the sample, as discussed in [25]) in order to allow direct comparison. The highest occupied molecular orbital, n, and the lowest unoccupied molecular orbital, %, are shown at their correct energy, relative to the Fermi level of the substrate. As in previous diagrams,

The relative position of the electronic level eo to the Fermi level depends on the electrode potential. We perform estimates for the case where there is no drop in the outer potential between the adsorbate and the metal - usually this situation is not far from the pzc. In this case we obtain for an alkali ion eo — Ep — where is the work function of the metal, and I the ionization energy of the alkali atom. For a halide ion eo — Ep = electron affinity of the atom. 

The decreased CO stretch frequencies are easily rationalized as the result of adsorption on sites with a lower work function, as explained in the Appendix. The effect of a lower work function is that all orbitals of CO shift downward with respect to the Fermi level of the substrate. This shift of the occupied CO levels to higher binding energy has been observed in UPS spectra (see Fig. 3.20), while the shift of the unoccupied part of the 2tt -derived chemisorption orbital has been observed in inverse photoemission [33, 34, 45], The overall effect is that the bond between the metal and the CO becomes stronger while at the same time the intramolecular CO bond is weakened. 

In photoemission experiments, the Fermi level shows up as a sharp edge therefore it is often chosen as a convenient zero of the energy scale. Note, however, that electrons at the Fermi level are bound to the metal. The energy necessary to disconnect them from the metal is equal to the work function (the molecular analog would be the ionization potential). This property is discussed later on. 

The second electronic property that plays an important role at surfaces is the work function. This is a kind of binding energy the work function is the minimum energy needed to remove an electron from the Fermi level to a state where it is at rest without interacting with the solid. As such it equals the energy difference... 

We consider two cases (see Fig. A.13). First, the metal has a work function that is between electron affinity (the energy of the o -level) and the ionization potential (the energy of the o-level) of the molecule. Upon adsorption, the levels broaden. However, the occupation of the adsorbate levels remains as in the free molecule. This situation represents a rather extreme case in which the intramolecular bond of the adsorbate molecule stays about as strong as in the gas phase. The other extreme occurs if both the a-level and the o -1evel fall below the Fermi level of the metal. Because the antibonding G -level is filled with electrons from the metal, the intramolecular bond breaks. This is the case for hydrogen adsorption on many metals. Thus, a low work function of the metal and a high electron affinity of the adsorbed molecule are favorable for dissociative adsorption. 

First, we describe the various system parameters, primarily adapted from Newns (1969). From the energy dispersion relation (2.32), the bulk states are distributed through a band, centered at a, and with width Wb = 4 / . The Fermi level Ef is taken to be at the center of this band, and is chosen to be the energy zero (so that Ef = a = 0, for all systems). The position of /, relative to the vacuum level, is given by the work function (j>, whence the isolated H adatom level, relative to Ef is... 

Model calculations for the Cs suboxides in comparison with elemental Cs have shown that the decrease in the work function that corresponds to an increase in the Fermi level with respect to the vacuum level can be explained semi-quantitatively with the assumption of a void metal [65], The Coulomb repulsion of the conduction electrons by the cluster centers results in an electronic confinement and a raising of the Fermi energy due to a quantum size effect. 

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