Image-potential states

Grimes, C.C. and Brown, T.R. (1974). Direct spectroscopic observation of electrons in image-potential states outside liquid helium, Phys. Rev. Lett. 32, 280-283. 

Steinmann, W. (1989) Spectroscopy of image-potential states by 2-photon photoemission. Appl. Phys. A, 49, 365-377. 

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.

Liipke, G., Bottomley D., and van Driel, H. (1994). Resonant second-harmonic generation on Cu(lll) by a surface-state to image-potential-state transition. Phys. Rev. 8,49 17303-17306. 

As discussed in Section 5.2, the very origin of this behavior is the electron-electron interaction. Zo denotes the position of the image plane. The precise position of Zo is not known a priori, although it is clear that it is located quite close to the surface. Attempts have been made to derive its position from the spectroscopy of surface states, which - as we will see - exist for such a long-range potential in addition to the Shockley states discussed before and the Tamm states discussed in Section 5.3.6 the image-potential states (see also Chapter 3.2.4). 

Electron transfer. This mechanism is not related to energy relaxation processes, but it describes the contribution from the energy-conserving resonant electron transfer from an excited electron state to bulk and/or surface states. The electron-transfer mechanism is important for resonance surface and image-potential states on clean or adlayer-covered surfaces. Defects may also lead to a charge transfer between bulk and surface electronic states. 

Most calculations that have been performed to date of the lifetimes of electrons and holes for surface and image-potential states use the so-caUed random phase approximation (RPA). In this approximation, the exchange and correlation kernel is omitted from both Eqs. (6.7) and (6.8). Inclusion of exchange and correlation effects in the screened interaction (Eq. (6.7)) and in the screening (Eq. (6.8)) act in opposite directions as the evaluation of the lifetimes is concerned [5]. 

Figure 6.8 Adsorbate-induced scattering of the Cu(lOO) image-potential state electrons. The figure shows the energy of the image-potential states (dashed lines) as a function of the electron momentum parallel to the surface, (cy. The shaded area represents the 3D bulk states. The intraband and interband scattering processes, which...

As an example of scattering by adsorbates of an electron in image-potential states. Figure 6.9 shows the adsorbate-induced decay rate of the n = 1 and n = 2 image-potential states on a Cu(lOO) surface with Cs adsorbates [15]. The decay rate is given for a Cs coverage of the surface equal to 1 Cs adsorbate per 1000 Cu surface atoms. 

Figure 6.11 Decay rates for the image-potential states as a function of binding energy for Cu(lll) (squares), Cu(117) (circles), and Cu(OOl) (diamonds). The dashed lines indicate an dependence.

So far, we have discussed the electron dynamics mainly for image-potential states. Owing to their relatively long lifetimes, they serve as a model system to study electron scattering processes at surfaces by time-resolved 2-PPE. Studies on other systems are relatively scarce because the overlap of adsorbate or surface states with bulk bands is usually relatively large and the lifetime is below the attainable time resolution. Figure 6.15 shows time-resolved data for the lowest unoccupied molecular orbital (LUMO) of C Fg on Cu(lll) [89[. The population dynamics is... 

The image-potential states on (001) surface of copper have been studied by several groups in considerable detail. The inelastic decay rates for the image-potential states on Cu(OOl) are given in the first two rows of Table 6.5. The agreement between experiment [84, 120] and calculations [73, 82, 121] is almost perfect. This holds for the various scattering rates F at ky = 0 as weU as for the increase with energy denoted by the slope dF /dE. 

Table 6.5 Inelastic and elastic scattering rates for image-potential states on clean and Cu-adatom-covered Cu(OOl) [84, 120] compared with theoretical calculations [73, 82, 121]. The inelastic scattering rates P are given in milli-electronvolts and the elastic scattering rates y are given in millielectronvolts per 0.01 monolayers."...

Figure 6.26 Decay rate at the n = 1,2, and 3 image-potential states on Cu(lOO) as a function of Cu adatom coverage. Adapted from Ref. [121].

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