The work function

TABLE 5.1. Work Functions Measured from Different Crystal Faces of Tungsten, Molybdenum, and Tantalum 

Kaminsky, Atomic and Ionic Impact Phenomena on Metal Surfaces. Academic Press, New York. 1965. 

Protopopov et al. Sov. Phys. Solid State (English translation), 8 909 (1966). 

Chapter 17 of this text focuses on the interface between molecular systems and metals or semiconductors and in particular on electron exchange processes at such interfaces. Electron injection or removal processes into/from metals and semiconductors underline many other important phenomena such as contact potentials (the 

A macroscopic solid can be regarded as a very large molecule, and the situation pictured above remains in principle the same. Some differences however should be noted  

In metals, the ionization potential and the electron affinity are the same, and are given by the electron chemical potential (or the Fenni energy at T = 0) measured with respect to the vacuum energy. To be specific we write, for T = 0, 

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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... 

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,... 

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. 

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]. 

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). 

Similarly, adsorption of ions (n+) onto a metal surface leads to a heat of adsorption of Q,. Generally, Q is about 2-3 eV and is greater than Q, which itself is about 1 eV. The difference between Q, and is the energy required to ionize neutrals (n ) on a metal surface so as to give ions (n+) or vice versa. This difference, Q - Q, can be equal to, greater than, or less than the difference, I - ( ), between the ionization energy (1) of the neutral and the ease with which a metal can donate or accept an electron (the work function, ( )). Where Q, - Q, > I - ( ), the adsorbed... 

Clearly, the lower the ionization energy with respect to the work function, the greater is the proportion of ions to neutrals produced and the more sensitive the method. For this reason, the filaments used in analyses are those whose work functions provide the best yields of ions. The evaporated neutrals are lost to the vacuum system. With continued evaporation of ions and neutrals, eventually no more material remains on the filament and the ion current falls to zero. 

Schematic diagram showing how placing a thin layer of highly dispersed carbon onto the surface of a metal filament leads to an induced dipolar field having positive and negative image charges. The positive side is always on the metal, which is much less electronegative than carbon. This positive charge makes it much more difficult to remove electrons from the metal surface. The higher the value of a work function, the more difficult it is to remove an electron. Effectively, the layer of carbon increases the work function of the filament metal. Very finely divided silicon dioxide can be used in place of carbon.

Surface ionization. Takes place when an atom or molecule is ionized when it interacts with a solid surface. Ionization occurs only when the work function of the surface, the temperature of the surface, and the ionization energy of the atom or molecule have an appropriate relationship. 

Photoelectron spectroscopy involves the ejection of electrons from atoms or molecules following bombardment by monochromatic photons. The ejected electrons are called photoelectrons and were mentioned, in the context of the photoelectric effect, in Section 1.2. The effect was observed originally on surfaces of easily ionizable metals, such as the alkali metals. Bombardment of the surface with photons of tunable frequency does not produce any photoelectrons until the threshold frequency is reached (see Figure 1.2). At this frequency, v, the photon energy is just sufficient to overcome the work function

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The source requited for aes is an electron gun similar to that described above for electron microscopy. The most common electron source is thermionic in nature with a W filament which is heated to cause electrons to overcome its work function. The electron flux in these sources is generally proportional to the square of the temperature. Thermionic electron guns are routinely used, because they ate robust and tehable. An alternative choice of electron gun is the field emission source which uses a large electric field to overcome the work function barrier. Field emission sources ate typically of higher brightness than the thermionic sources, because the electron emission is concentrated to the small area of the field emission tip. Focusing in both of these sources is done by electrostatic lenses. Today s thermionic sources typically produce spot sizes on the order of 0.2—0.5 p.m with beam currents of 10 A at 10 keV. If field emission sources ate used, spot sizes down to ca 10—50 nm can be achieved. 

Vacuum Tubes. In the manufacture of vacuum tubes for use in polarized ion sources, vaporized cesium is used as a getter for residual gaseous impurities in the tube and as a coating to reduce the work function of the tungsten filaments or cathodes of the tube. The cesium vapor is generated by firing, at about 850°C within the sealed and evacuated tube, a cesium chromate pellet and zirconium (12) (see Vacuum technology). 

A guide to tire stabilities of inter-metallic compounds can be obtained from the semi-empirical model of Miedema et al. (loc. cit.), in which the heat of interaction between two elements is determined by a contribution arising from the difference in work functions, A0, of tire elements, which leads to an exothermic contribution, and tire difference in the electron concentration at tire periphery of the atoms, A w, which leads to an endothermic contribution. The latter term is referred to in metal physics as the concentration of electrons at the periphery of the Wigner-Seitz cell which contains the nucleus and elecUonic structure of each metal atom within the atomic volume in the metallic state. This term is also closely related to tire bulk modulus of each element. The work function difference is very similar to the electronegativity difference. The equation which is used in tire Miedema treatment to... 

Mdissociates as a positive ion. Conversely, the enhanced ion yields of the cesium ion beam can be explained using a work function model, which postulates that because the work function of a cesiated surface is drastically reduced, there are more secondary electrons excited over the surface potential barrier to result in enhanced formation of negative ions. The use of an argon primary beam does not enhance the ion yields of either positive or negative ions, and is therefore, much less frequently used in SIMS analyses. 

Electron-tunneling Model. Several models based on quantum mechanics have been introduced. One describes how an electron of the conducting band tunnels to the leaving atom, or vice versa. The probability of tunneling depends on the ionization potential of the sputtered element, the velocity of the atom (time available for the tunneling process) and on the work function of the metal (adiabatic surface ionization, Schroeer model [3.46]). 

Thermionic Emission - Because of. the nonzero temperature of the cathode, free electrons are continuously bouncing inside. Some of these have sufficient energy to overcome the work function of the material and can be found in the vicinity of the surface. The cathode may be heated to increase this emission. Also to enhance this effect, cathodes are usually made of, or coated with, a low work-function material such as thorium. 

Shottky Emission - This is also a thermionic type of emission except that in this case, the applied electric field effectively decreases the work function of the material, and more electrons can then escape. 

High Field Emission - In this case, the electric field is high enough to narrow the work-function barrier and allow electrons to escape by tunneling through the barrier. 

Photoemission - Electromagnetic radiation of energy can cause photoemission of electrons whose maximum energy is equal to or larger than the difference between the photon energy and the work function of the material. 

From such information even the inexperienced estimator can establish an approximation of the costs, provided he adequately visualizes the work functions and steps involved. From the same type of work reference, the experienced estimator can develop a realistic cost, usually expressed with certain contingencies to allow for unknown factors and changing conditions. The professional estimator wall normally develop cost charts and tables peculiar to the nature of his responsibilities and requirements of his employer. 

In a light-emitting MSM structure the two metal electrodes selected such that the work functions of the electrodes are near the edge of the valence band (VB) and the conducting band (CB) of the semiconductor, respectively, so that oppositely charge carriers are injected from the opposite electrodes. An ohmic and a rectifying contact is therefore formed in the MSM structure (see Fig. 9-22). 

Table 11-2 shows the built-in potential in metal/MEH-PPV/metal structures measured by either electroabsorption [15] or photocurrenl techniques [37] for a variety of contact metals. The uncertainty in both the work function differences and the built-in potential measurements is about 0.1 eV. For all of the structures except the Pt-Ca and Al-Sm devices there is good agreement between the metal work function difference, AW, and the built-in potential, Vhi. This indicates that for a wide range of metal contacts the Schottky energy barrier between the metal and MEH-PPV is well approximated by the ideal Schottky model and that state chaiging, which pins the Schottky energy barrier, is not significant. A built-in potential smaller than the difference between the contact work functions implies that... 

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