Bulk band structure

At a surface, not only can the atomic structure differ from the bulk, but electronic energy levels are present that do not exist in the bulk band structure. These are referred to as surface states . If the states are occupied, they can easily be measured with photoelectron spectroscopy (described in section A 1.7.5.1 and section Bl.25.2). If the states are unoccupied, a teclmique such as inverse photoemission or x-ray absorption is required [22, 23]. Also, note that STM has been used to measure surface states by monitoring the tunnelling current as a fiinction of the bias voltage [24] (see section BT20). This is sometimes called scamiing tuimelling spectroscopy (STS). 

In many cases there are electronic states with a strong weight in the surface layer, but which are not located in a gap of the projected bulk band structure. The electrons in these states can decay into bulk states much faster than those occupying pure surface states. These states are known as surface resonances. One of these cases occur in the Ru(0001) surface. 

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 surface Wave function is determined from the bulk band structure of the solid. 

Figure 14-7. Surface band structures for the configurations 1-1,1-2, F-l and F-2 at 0.125 ML. The shaded areas represent the projected bulk band structure, while surface states are shown as solid lines...

Hinkel, V., H. Haak, C. Mariani, L. Sarba, K. Horn, and N. E. Christensen (1989). Investigation of the bulk band structure of IV-VI compound semiconductors PbSe, PbTe. Phys. Rev. B40, 5549-56. 

The band structure of oxides is very important for their behavior as electrocatalysts through the role of surface states and chemisorption of intermediates at their surfaces. When a crystalline solid is terminated by a surface, a new set of electronic states appears associated with the surface which are a continuation from the bulk band structure of the solid. These surface states are d-band surface states on transition metal oxides, which play a vital role... 

All the TB models discussed so far are based on the nearest neighbor interactions. Recently, Sapra et al. proposed [73] the sp d tight-binding model with cation-anion nearest neighbor and anion-anion next nearest neighbor (NNN) interactions for the A B semiconductor compounds with A = Zn, Cd, Hg and B = S, Se, Te. The model was chosen after a careful analysis of the bulk band structures of these compounds obtained from the linearized muffin tin orbital (LMTO) method as described earlier in this section. These calculations were car-... 

With increasing film thickness the electronic structure of the adsorbate overlayer becomes undistinguishable to that of the bulk material this will be demonstrated for Fe evaporated on W(llO) [13]. In the following it will be shown that a thickness of 20 layers is already sufficient to map the transitions in the spin resolved bulk band structure of Fe(llO). The analogous behavior was found for Co(OOOl) films on W(llO) [14]. 

Where possible, a comparison with theoretical results and the projected bulk band structure has been presented. 

Fig. 5.2-39 Surface band structure of GaAs(l 10). Comparison between theoretical structure (continous brown line) and experimental determinations KRIPES filled and open circles), ARUPS dashed line), and two-step photoemission triangles). It can be noticed that the surface states nearly coincide with the band edges of the projected bulk band structure [2.63-67]...

As can be seen from table 1, most of the band structure calculations are for the bulk (for reviews of the bulk electronic structure see Barrett 1992 and Liu 1978). Often these calculations are along the F-A direction of the bulk Brillouin zone (as indicated in the diagram of the surface and bulk Brillouin zone in fig. 3). There are a few calculations that do consider the electronic structure of the surface. Of particular interest are surface states states that occur in a gap of the bulk band structure when projected on to the surface Brillouin zone. Surface resonances, i.e. states where there is considerable weight... 

Fig. 5. Photoemission spectra of an ordered Gd(OOOl) film deposited on W(llO) showing the Gd 5d surface state (S) and bulk bands (B). The spectra were taken along the T-A direction of the bulk band structure. Data taken from Dongqi Li et al. (1991a). The solid lines indicate the energy distribution curves taken for bulk gadolinium, adapted from Himpsel and Reihl (1983).

The combination of photoemission and inverse photoemission provides a general picture of the 5d/6s gadolinium band structure along the F-A direction of bulk Brillouin zone, as is summarized in fig. 10. As previously pointed out, fig. 10 makes clear that the surface states fall into a gap of the projected bulk band structure. Note that while the... 

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