Metal image-potential surface states

Similar to the failures of the free-electron model of metals (Ashcroft and Mermin, 1985, Chapter 3), the fundamental deficiency of the jellium model consists in its total neglect of the atomic structure of the solids. Furthermore, because the jellium model does not have band structure, it does not support the concept of surface states. Regarding STM, the jellium model predicts the correct surface potential (the image force), and is useful for interpreting the distance dependence of tunneling current. However, it is inapplicable for describing STM images with atomic resolution. 

First of all, the existence of the surface establishes a certain correlation between different electronic states, particularly between incident and reflected electrons. In addition there are electron density variations both within the surface and along the surface normal. Since the screening radius increases with decreasing electron density, it is obviously unrealistic to third of a spherical potential hole accompanying its electron in the immediate surface region, where the electron density drops very rapidly to zero. At the very lowest densities, in particular, the potential must somehow go over in continuous fashion into the classical image potential applying far away from the metal surface. Finally, from the dynamic nature of these interactions it follows that the problem must be dealt with self-consistently each electron contributes to the holes of all the other electrons in a manner dependent on the detailed features of its own potential hole. 

Marchf et al. have applied image potential arguments to predict the orientation of a diatomic molecule of H2 type adsorbed in a precursor slate with respect to a metal surface. Their arguments are illustrated in Fig.(2.60). They use the valence bond picture of chemical bonding in H2 that we discussed in section 2.2. Bonding in H2 is considered to be the interaction of a covalent neutral state 0 nd the two... 

Amongst the optical techniques there are also the more traditional methods such as the ellipsometry, electroreflectance and particularly, surface plasmons, where experimental and theoretical advances have made it possible to offer a picture of the surface electronic states of the metal in some selected cases, such as the silver (111) phase. We should mention here the measurement of image potential induced surface states by electroreflectance spectroscopy. In this case, besides the normal surface... 

Atomic hydrogen is small and adsorbs near to the surface. H modes can directly couple to surface states and resonances, such as image potential states, that may overlap in the near-surface region. An empirical verification of this phenomenon, observed on several metals (Pd, Pt, Rh, Ru) is the enhancement of surface resonances by adsorbed H, and the enhancement of H vibrational modes at primary energies which correspond to the population of the surface resonance with electrons from the incident HREELS beam. In Figure 17, the reflectivities of the Pd(lll) and (100) surface with and without adsorbed hydrogen are shown. The relative intensities of the H frustrated translation and rotation (perpendicular and parallel) modes are shown in Figure 18. 

Figures 17 Surface reflectivity of Pd(111) and Pd(IOO) with and without adsorbed H. The reflectivity is on log scale. The addition of hydrogen shifts and intensifies the lowest energy surface resonance on Pd(111) (5.5 eV). The sharp drop in reflectivity at 8 eV corresponds to the emergence of a surface diffraction beam, and opens a new channel for electron interaction with the surface. The image potential states are just below this emergence threshold. On Pd(IOO) the curves are similar, but the energy scale is reduced due to the different crystal structure of the surface and different-sized surface Brillouin Zone. Reprinted from Surface Science, 178, M.E. Kordesch, Surface resonances in vibrational spectroscopy of hydrogen on transition metal surfaces Pd(IOO) and Pd(111), 578-588, 1986, with permission from Elsevier Science.

If the tunneling current is from the surface to the tip, the STM images the density of occupied states. If the potential is reversed, the current flows in the other direction, and one images the unoccupied density of states, as the reader can easily understand from Fig. 7.19. This figure also illustrates a necessary condition for STM there must be levels within an energy e-V from the Fermi level on both sides of the tunneling gap, from and to which electrons can tunnel In metals, such levels are practically always available, but when dealing with semiconductors or with adsorbed molecules, this condition may be a limitation. A second condition is that the sample possesses conductivity perfect electrical insulators cannot be measured with STM. 

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