Work function.

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 

The position of the Fermi edge thus defines the solid s work function (d ). As can be envisaged, the work function is a substrate surface and environment (modified by adsorbates) specific parameter. This generally falls within the range 2-8 eV. 

Electron Spectroscopy (AES), Energy Dispersive X-ray spectroscopy (EDX), X-ray Photo-electron Spectroscopy (XPS), and X-Ray Eluorescence (XRF). 

In essence, the work function is the first ionization potential once modified by the long-range electronic interaction occurring within a solid. The 1st ionization potential and the work function can be related (Wong et al. 2003) through the approximation  

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Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

Another potential, mentioned in the next section, is the thermionic work function, where ei gives the work necessary to remove an electron from the highest populated level in a metal to a point outside. We can write... 

B. Volta Potentials, Surface Potential Differences, and the Thermionic Work Function... 

When two dissimilar metals are connected, as illustrated in Fig. V-16, ]here is a momentary flow of electrons from the metal with the smaller work function to the other so that the electrochemical potential of the electrons becomes the same. For the two metals a and /3... 

The potential corresponding to the reversible overall process is the measurable quantity Vobs- If we know the work function for R, that is, the potential for e (in R) = e (in air), then Vobs - r is E for the process... 

While field ion microscopy has provided an effective means to visualize surface atoms and adsorbates, field emission is the preferred technique for measurement of the energetic properties of the surface. The effect of an applied field on the rate of electron emission was described by Fowler and Nordheim [65] and is shown schematically in Fig. Vlll 5. In the absence of a field, a barrier corresponding to the thermionic work function, prevents electrons from escaping from the Fermi level. An applied field, reduces this barrier to 4> - F, where the potential V decreases linearly with distance according to V = xF. Quantum-mechanical tunneling is now possible through this finite barrier, and the solufion for an electron in a finite potential box gives... 

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.)...

Measuring the electron emission intensity from a particular atom as a function of V provides the work function for that atom its change in the presence of an adsorbate can also be measured. For example, the work function for the (100) plane of tungsten decreases from 4.71 to 4.21 V on adsorption of nitrogen. For more details, see Refs. 66 and 67 and Chapter XVII. Information about the surface tensions of various crystal planes can also be obtained by observing the development of facets in field ion microscopy [68]. 

The work function across a phase boundary, discussed in Sections V-9B and VIII-2C, is strongly affected by the presence of adsorbed species. Conversely,... 

Fig. XVni-8. (a) Work function change for Pt(lU) as a function of oxygen adatom coverage. From Ref. 82. b) Same, for potassium. The corresponding sequence of LEED structures is indicated. [Reprinted with permission from R. G. Windham, M. E. Bartram, and B. E. Koel, J. Phys. Chem., 92, 2862 (1988) (Ref. 83). Copyright 1988, American Chemical Society.]...

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

When an electropositive or electronegative adsorbate adaches itself to a surface, there is usually a change in the surface dipole, which, in turn, affects the surface work ftmction. Thus, very small coverages of adsorbates can be used to modify fhe surface work ftmcfion in order to ascertain the role that the work function plays in a given process. Conversely, work ftmction measurements can be used to accurately detennine the coverage of these adsorbates. 

If two metals with different work functions are placed m contact there will be a flow of electrons from the metal with the lower work function to that with the higher work fimction. This will continue until the electrochemical potentials of the electrons in the two phases are equal. This change gives rise to a measurable potential difference between the two metals, temied the contact potential or Volta potential difference. Clearly... 

UPS UV photoelectron spectroscopy Absorption of UV light by an atom, after which a valence electron Is ejected. Chemical bonding, work function... 

The final technique addressed in this chapter is the measurement of the surface work function, the energy required to remove an electron from a solid. This is one of the oldest surface characterization methods, and certainly the oldest carried out in vacuo since it was first measured by Millikan using the photoelectric effect [4]. The observation of this effect led to the proposal of the Einstein equation ... 

Wlien an electrical coimection is made between two metal surfaces, a contact potential difference arises from the transfer of electrons from the metal of lower work function to the second metal until their Femii levels line up. The difference in contact potential between the two metals is just equal to the difference in their respective work fiinctions. In the absence of an applied emf, there is electric field between two parallel metal plates arranged as a capacitor. If a potential is applied, the field can be eliminated and at this point tire potential equals the contact potential difference of tlie two metal plates. If one plate of known work fiinction is used as a reference electrode, the work function of the second plate can be detennined by measuring tliis applied potential between the plates [ ]. One can detemiine the zero-electric-field condition between the two parallel plates by measuring directly the tendency for charge to flow through the external circuit. This is called the static capacitor method [59]. 

Swanson L W and Davis P R 1985 Work function measurements Solid State Physics Surfaces(Methods of Experimental Physics 22) cd R L Park and M G Lagally (New York Academic) chi... 

Kiena A and Wo]ciechowski 1981 Work function of metals relation between theory and experiment Prog. Surf. Sci. 11 293-338... 

The work function (p is the energy necessary to just remove an electron from the metal surface in thermoelectric or photoelectric emission. Values are dependent upon the experimental technique (vacua of 10 or torr, clean surfaces, and surface conditions including the crystal face identification). 

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