Jellium work functions

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

Figure 6.13. The electron distribution in the model metal jellium gives rise to an electric double layer at the surface, which forms the origin of the surface contribution to the work function. The electron wave function reaches...

Figure 9.10 Up work function of alkali-promoted metals as a function of alkali coverage (see also Table 9.2). Down electrostatic potential around a single alkali atom adsorbed on jellium. The effective local work function at each position is the sum of the substrate work function and the value of the electrostatic potential in the figure (from Lang el at. [39]).

To explain where the surface contribution to the work function comes from, we need a model for the electron distribution in the surface region of a metal. One of the simplest is the jellium model [18]. 

The resonant level model readily explains the change in work function associated with chemisorption. It is well known that alkali atoms such as potassium lower the work function of the substrate, whereas electronegative atoms such as chlorine increase the work function [2,8,19]. Figure A. 10 indicates that potassium charges positively and chlorine negatively when adsorbed on jellium. Remember that the surface contribution to the work function is caused by... 

The intimate relationship between double layer emersion and parameters fundamental to electrochemical interfaces is shown. The surface dipole layer (xs) of 80SS sat. KC1 electrolyte is measured as the difference in outer potentials of an emersed oxide-coated Au electrode and the electrolyte. The value of +0.050 V compares favorably with previous determinations of g. Emersion of Au is discussed in terms of UHV work function measurements and the relationship between emersed electrodes and absolute half-cell potentials. Results show that either the accepted work function value of Hg in N2 is off by 0.4 eV, or the dipole contribution to the double layer (perhaps the "jellium" surface dipole layer of noble metal electrodes) changes by 0.4 V between solution and UHV. 

Kg. 2-11. Work function, 4>, observed and calculated by using the jellium model as a function of Wigner-Seitz radius, rs, for various metals rs = 3 / (4 n n, = electron... 

The simplest model of a metal surface is the jellium model, which is a Sommerfeld metal with an abrupt boundary. In provides a useful semiquanti-tative description of the work function and the surface potential (Bardeen, 1936). It validates the independent-electron picture of surface electronic structure Essentially all the quantum mechanical many-body effects can be represented by the classical image force, which has been discussed briefly in Section... 

Table 4.1. Measured work functions and predictions from the jellium model. First three rows are experimental values for different materials and crystallographic orientations, from Handbook of Chemistry and Physics, 69th edition, CRC Press (1988) the last row is the predictions of the jellium model, from Smith (1968)...

An early application of the jellium model is to estimate the work function (Bardeen, 1936 Smith, 1968). In the jellium model, there is only one parameter G. The work function is then a function of r, only. In reality, the work function depends not only on the material, but also on the crystallographic orientation of the surface. For most metals used in STM, the work function predicted by the jellium model is 1-2 eV smaller than the experimentally observed values, as shown in Table 4.1. 

As shown, the jellium model gives inaccurate predictions for the work functions. The work functions predicted by first-principles calculations (see Section 4.7) are much more accurate. 

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... 

One of the earliest treatments of a metal surface was based upon a jellium model (Bardeen, 19.36). If the electron gas terminated abruptly at the surface of the jellium there would be no net potential to contain the electrons in the metal. Therefore the electron gas extends beyond the metal, giving a dipole layer, as illustrated in Fig. 17-5. Bardeen attempted the self-consistent calculation of the resulting potential. It should be mentioned that the Fermi-Thomas approximation is not adequate for this task and was not used by Bardeen it is not difficult to see that it would predict the Fermi energy to be at the vacuum level, corresponding to a vanishing work function. 

Two other jellium calculations are of interest. One (27) is a study of the local density of states in the spill-out region. It has been found that the farther out from the surface, the larger the contribution of electrons at the Fermi level to the total charge density (Fig. 6). The latter quantity decreases with distance it decreases exponentially, with a characteristic length that is inversely proportional to the square root of the work function. The other... 

The PZC is an important point of reference in discussing the properties of a polarizable interface. Its location depends on the nature of all of the components which are at the interface, that is, on the metal, on the solvent used for the electrolyte solution, and on the nature and concentration of the solute components in this solution. Its importance was first pointed out by Frumkin [G3] who was able to carry out the first experiments at polarizable electrodes other than mercury. He showed that there is a fairly simple relationship between the PZC and the work function of the metal for a given solution composition and reference electrode. In this section the relationship is derived and its consequences illustrated with experimental data. Then a model which describes the role of the metal in interfacial properties, namely, the jellium model, is presented. 

The role of the metal in double layer properties can be understood in greater detail when the system is examined on the basis of the jellium model. This model was developed to describe the electron gas within sp metals. It can be used to estimate several properties of interest, including the chemical potential of an electron in the metal, the extent of electron overspill, and the work function of the metal. More recently, it has been extended to describe metal surfaces in contact with polar solvents [26]. In its simplest form, the metal atoms in the metal are modeled as a uniform positive background for the electron gas, no consideration being given to their discrete nature and position in the metal lattice. The most important property of the system is the average electron density, N ), which depends on the number of metal atoms per unit volume and the number of valence electrons per atom, n. Thus, if pjj, is the mass density of the metal, and M, its atomic mass... 

---