Work function, simple metals

The simple picture of the MOS capacitor presented in the last section is compHcated by two factors, work function differences between the metal and semiconductor and excess charge in the oxide. The difference in work functions, the energies required to remove an electron from a metal or semiconductor, is = —25 meV for an aluminum metal plate over a 50-nm thermally grown oxide on n-ty e siUcon with n = 10 cm . This work... 

This simple empirical model for predicting the I.S. shift of a Mossbauer nucleus placed in a metallic system (alloys, as well as intermetallic compounds), uses differences in the tabulated macroscopic work functions and bulk moduli to model differences in the microscopic electronegativities and electron densities at... 

Hackerman and Lee (83) have also used the simple vibrating electrode to examine the effect of O2 and other gases on evaporated metal films of Fe, Ni, Cr, Al, and Pb. Employing a Pt plate as a reference electrode, they found that the work function increased when the transition metals were exposed to O2 later it decreased as the chemisorbed O2 was converted to an oxide layer. With Al and Pb, however, the work function steadily decreased... 

The explanation for the apparent correlation between catalytic activity and electron affinity of metals cannot be as simple as that which has been advanced for the homogeneous catalysts. This is because chemisorption on metals (unlike the splitting of hydrogen by metal ions in solution ) is an exothermic process and, hence, as shown earlier, catalytic activity depends not only on a low activation energy of adsorption but also on a low heat of adsorption. The interpretation applied earlier to homogeneous catalysts can account for an inverse dependence of Ea on the work function, but does not suggest any obvious reason why Q should show a similar dependence. 

The connection between electronic work function and catalytic activity was shown some time ago, especially by Suhrmann (1-4) and Czesch (1), who found a simple relation between the changes of the work functions of different metal surfaces upon adsorption of H atoms, and the catalytic activities of such surfaces for the recombination of H atoms. 

A simple model is the diode circuit with two metals with known work functions, as in fig. 16 in VI.9. The whole is in thermal equilibrium at temperature T ( Alkemade s diode ) ). The charge Q on the condenser obeys the phenomenological equation... 

The volcano curve is based on the performance of simple metals, and the heat of adsorption is the factor which turns out to be responsible for the change in activity from metal to metal. However, the difficult issue from a theoretical point of view is the identification of the properties of metals which govern the magnitude of the adsorption heat. A number of correlations have been proposed, based on different electronic or structural properties of metals [56-65]. The aim has been to establish a reactivity scale from which predictions on the behaviour of unknown materials could be made. It appears that the correlation between the electron work function and the activity of metals for hydrogen evolution is very likely to be the most reliable [54,66], since it has been verified several times by different authors independently [57,62,67],... 

Although the availability of d electrons will certainly influence the ease of formation and the strength of the covalent bonds in chemisorption phenomena on metals, we may not expect a simple relationship between the heat of chemisorption and some more or less simple property which is related to the d electrons. There will certainly be other properties of the metals which play a role. In expression (32) the last term containing the electronegativities has some relation to the availability of electrons from the metal, and it must be said that the order in which the heats of chemisorption fall (Sec. V,8,b) is nearly the same as that in which the work function of the metals rises. In the formation of the dipoles between the adsorbed atoms and the metal, work has to be done against the work function we may expect that less work will be necessary to form these dipoles and that the dipole moment will be larger, the smaller the work function. 

Among the devices with characteristics sensitive to the metal work function, the most simple structure is the Schottky barrier. Nevertheless, the Pd/a-Si H structure does not show any sensitivity to H2. This behavior is analogous to that described by other authors (Fonash et al, 1982 Shivaraman et al., 1976 Keramati and Zemel, 1982), for Schottky barriers on... 

Lennard-Jones and Goodwin2 have, however, shown that the adsorbed atoms can be activated by collisions with the free electrons in the underlying metal there is no reason to expect a simple connexion between activation and the thermionic work function. 

Once the structure of the stable chemisorbed species has been established, it is important to analyze the nature of the chemisorption bond, with special emphasis on the CO2-K interaction. Using the projection operator technique, the net charge on CO2, K and Pti6 are about -0.9 e, 0.7 e, and 0.2 e, respectively. This is a strong indication that K is the main donor agent. However, a point that remains unclear is whether the donation from K to CO2 is direct or indirect and mediated by the metal surface. It may be claimed that the effect of K is simply to reduce the work function of the substrate, thus enhancing the charge donation to CO2 which is activated without a direct K-CO2 interaction. A simple theoretical experiment shows... 

The transition from the atom to the cluster to the bulk metal can best be understood in the alkali metals. For example, the ionization potential (IP) (and also the electron affinity (EA)) of sodium clusters Na must approach the metallic sodium work function in the limit N - . We previously displayed this (1) by showing these values from the beautiful experiments by Schumacher et al. (36, 37) (also described in this volume 38)) plotted versus N". The electron affinity values also shown are from (39), (40) and (34) for N = 1,2 and 3, respectively. A better plot still is versus the radius R of the N-mer, equivalent to a plot versus as shown in Figure 1. The slopes of the lines labelled "metal sphere" are slightly uncertain those shown are 4/3 times the slope of Wood ( j ) and assume a simple cubic lattice relation of R and N. It is clear that reasonably accurate interpolation between the bulk work function and the IP and EA values for small clusters is now possible. There are, of course, important quantum and statistical effects for small N, e.g. the trimer has an anomalously low IP and high EA, which can be readily understood in terms of molecular orbital theory (, ). The positive trimer ions may in fact be "ionization sinks" in alkali vapor discharges a possible explanation for the "violet bands" seen in sodium vapor (20) is the radiative recombination of Na. Csj may be the hypothetical negative ion corresponding to EA == 1.2 eV... 

Two problems with this simple picture are immediately apparent. First, typical refractory metals have work functions exceeding 4 ev. Polycrystalline tungsten, for example, has a work function of 4.6 ev. To obtain a current density of 1 1 amp /cm with this material would require an operating temperature of 2600 K. Second, electron space charge effects would limit current flow in a vacuum diode to less than a mllllampere with a typical Interelectrode gap of 254 ym (10 mils). 

A last practical question how can one easily measure the absolute potential of a support The answer is simple by simply depositing a metal (any metal) electrode on it and measuring the work function of the backspillover-modified electrode [140]. 

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