Surface state bands

L. S. O. Johansson, R. I. G. Uhrberg, P. Martensson and G. V. Hansson, Surface-state band structure of the Si(100)2 x 1 surface studied with polarization-dependent angle-resolved photoemission on single domain surfaces, Phys. Rev. B 42, 1305 (1990). 

The required 2D nearly free electron gas is realized in Shockley type surface states of close-packed surfaces of noble metals. These states are located in narrow band gaps in the center of the first Brillouin zone of the (lll)-projected bulk band structure. The fact that their occupied bands are entirely in bulk band gaps separates the electrons in the 2D surface state from those in the underlying bulk. Only at structural defects, such as steps or adsorbates, is there an overlap of the wave functions, opening a finite transmission between the 2D and the 3D system. The fact that the surface state band is narrow implies extremely small Fermi wave vectors and consequently the Friedel oscillations of the surface state have a significantly larger wave length than those of bulk states. 

The example of Ce/Ag demonstrates that the surface state electron mediated adsorbate-adsorbate interactions may well be employed for the creation of ordered atomic and possibly also molecular superlattices. In principle the lattice constant can be adjusted by the surface state band structure. 

The surface state bands are shown in fig. 30 for GaAs(llO), band As corresponding to an occupied dangling bond localized mainly on the surface As, and C3 to an unoccupied dangling bond on the surface Ga. These bands are pushed out of the fundamental gap (except at the C3 band minimum at A) by the relaxation (Alves et al., 1991 Schmeits et al., 1983). 

For the 7x7 reconstructed surface, two occupied surface state bands near the valence band maximum have been identified by angle-integrated UPS [155—158, 161]. This contrasts with the single structure on the 2x1 surface. The dominant feature is about 1 eV below the Fermi level and, in addition, there is a metallic edge-like structure at EF. ... 

The surfaces of metal oxides and their H2 chemisorption characteristics have been far less studied than the surfaces of elemental metals and semiconductors [113,133]. Cation surface states are formed on ideal oxide surfaces at about 2 eV below the bottom ofthe conduction band. The charge of the surface ions is found to be reduced compared with that of the bulk ions and this leads to an enhanced co valency at the surface. The reduction amounts to less than 10 % for oxides of simple metals such as MgO and to 20-30% for transition metal oxides. Cluster and slab calculations reveal that special surface state bands with metallic character can be formed on polar surfaces by charge compensation effects. To what extent the metallic band accounts for special catalytic activity is not yet known [114]. 

Fig. 5.2-33 Theoretical surface state bands (full lines) and resonances (dashed lines) for a relaxed jr-bonded chain model of diamond(l 11)2x1. Comparison with experimental results (open circles) obtained by ARUPS along the TJ line [2.51,52]...

Subsequently, a number of experiments have proved that Ob is not given by Schottky s equation, and that it does not depend upon the metal properties. Such a result may be found if the Fermi level is pinned by a surface state band (Bardeen, 1947), in which case Ob is equal to the energy difference between the bottom of the conduction band and the surface state. The same is true in the presence of defect states or of high MIGS densities, such as those seen at the interfaces between metals and covalent semi-conductors (Rhoderick, 1978 Schluter, 1982 Brillson, 1982 Flores and Tejedor, 1987). 

As a first example, we examine the occupied surface state found close to Bf at the Y point of the Cu(llO) and Ag(llO) surfaces [37]. The surface state occurs in the L21 — Li band gap (see Figure 5.16 for the position of the surface-state band in the projected bulk band gap at Y and Figure 5.17 for the location of the Y point with respect to the bulk Brillouin zone). Energetically, the surface state lies very close to the L2/ point of the bulk band structure. Thus, we can consider it as a state split from the L2/ bulk band. The orbital composition of the L2/ band can be found in tabulations, for example, in Ref. [38], and is given as 1/V (x + y + z). This function is a representation of a p orbital oriented in the [111] direction. Note that the coordinates refer to the orientation of the bulk Brillouin zone as shown in Figure 5.17. We can transform these coordinates into surface coordinates for the (110) surface Zs = l/v (x + y) is oriented in the [110] direction, Xj = l/-s/2 (—x + y) in the [110] direction, and yj = z in the [001] direction. This yields the orbital character of the L2/ band in terms of the surface coordinates 1/V3 (y + V2zs). 

Figure 5.25 Na-induced shift of the occupied Shockley surface-state band of Cu(llO) at Y for adsorption at lOOK and after annealing to 370 K. (From Ref [44].)...

If surface states are (partially) occupied, that is, if the surface-state bands extend to below the Fermi level, they contribute to the electron density at the surface and may thus directly influence the properties of and the processes on the surface. Inspection... 

Figure 6.2 Projected bulk band structure (shaded areas) for the Cu(lll) and Cu(lOO) surfaces with intrinsic Shock-ley surface-state bands (n = 0) and image-potential bands (n > 1). Arrows indicate possible electron-electron (ee), electron-phonon (ep), and defect (def) scattering processes.

Discrete localized surface states below Ep Continuous distribution of surface states at Ep Surface state band below i... 

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