Surface band structure

We emphasize two natural limitations of the finite cluster model. It does not allow to make a statement about the dependence of essential parameters such as adsorption and transition energies on the level of surface coverage, and it does not account adequately for charge delocalization or surface relaxation phenomena. Further, it excludes by definition any information about the modification of the surface band structure as a consequence of the organic molecule adsorption. The following case study of 1-propanol on Si(001) - (2 x 1) is intended to clarify how these elements can be consistently incorporated into the description of the Si surface interaction with organic species. 

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...

Fig. 3. Stopping power as a function of the distance to the top-most layer for V = 1 a.u. protons traveling parallel to the Cu (111) surface. The solid line is the result of the model in which the surface band structure of the target is considered, the short-dashed line is obtained neglecting the surface state in the calculation, the long-dashed line is the result of using the jellium model and constructing XoCG, z, z , within the RPA using the self-consistent solutions for a finite step potential (see text), and the dot-dashed line is obtained in the jellium model within the SRM.

In this work we have reviewed some recent developments in the energy loss of ions scattered off solid surfaces. In the weak-coupling regime (Zj/v 1) linear response theory allows one to calculate the distance-dependent stopping power. In this respect, we have shown that a linear approach with the SRM is capable to reproduce the measured energy losses of fast protons reflected at metal surfaces. Additionally, in this weak-coupling limit we have seen that in the case of metal targets details of the surface band structure do... 

Figure 5.26 Comparison of surface band structures for bulk diamond and nanodiamond. The extra levels result from additional surface states (refer to the text). For...

Fig. 1. The fundamental interactions between the frontier orbitals of an adsorbate and a metal surface band structure that occur upon chemisorption.

Many physical and chemical properties of surfaces can be associated with the electronic nature of the surface. This electronic character is determined largely by the concentration of mobile charge carriers (electrons, holes, and diffusing ions). Their concentration is dependent on both the inherent electronic structure of the bulk and the unique environment of the surface. Band structure theory has been used successfully to describe many electronic properties of the bulk solid. Here the discussion of electronic properties is restricted to those associated with the presence of the surface. 

The optical properties of a Au(lOO) surface in its reconstructed state differ markedly because of the participation of electronic surface states in the optical excitation these states depend on the crystallographic surface structure [95]. Surface band structure calculations have revealed the existence of empty surface states [96]. These surface states can be shifted in their energy by the electrode potential (Stark shift) [97]. Optical transitions into these states thus become potential dependent. 

The truncation of the lattice and/or the reconstruction and relaxation cause the electronic states at the surface or in the uppermost layers to be distinctly different from those of the bulk. Such new states are called surface states. Their wave functions decay exponentially on both sides of the surface. Since their k is imaginary, the surface band structure is defined in the surface Brillouin zone (SBZ), which is the projection of the 3-D Brillouin zone onto the surface plane. The projection of the bulk bands onto the SBZ is called the projected band structure. When the energy of a surface state is localized in a gap of the projected bulk structure (either an absolute gapp, i. e. one that extends throughout the whole SBZ, or a partial gap), one speaks of a true (or bona fide) surface state. When there is degeneracy (both in energy... 

Fig. 5.2-36 Surface band structure of Si( 111 )2 x 1. Comparison between theoretical structure based on pseudopotential calculations for the jr-bonded chain model (see Sect. 5.2.2.3, Fig. 5.2-11) and experimental results from ARUPS. Photoemission from the excited surface states (around the B point in the figure) is obtained by using highly doped samples. Arrows indicate optical transitions observed in SDR and EELS (see Figs. 5.2-41 and 5.2-43) [2.56,57] ...

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]...

The surface electronic structure, or surface band structure, of a finite lattice is defined by the characteristic property of their eigenfunctions that these be attenuated in the surface normal direction. Thus they are a subset of the entire... 

It is necessary to probe both filled and empty surface states to obtain a complete sampling of the surface band structure. Filled surface states are most conveniently probed with conventional The process is illustrated in... 

InSb and InAs) and it has been possible to establish some features of the surface band structure common to all these materials. 

The volume and surface densities of states Dy(E) and Dg(E), respectively, typical of compound semiconductors are illustrated in Fig. 10a. It is evident from PES, PYPES and EELS that compound semiconductors have a surface band structure with a bandgap separating a low-lying filled valence surface band from a higher-lying empty surface conduction band. l It is further observed that the surface valence band maximum consistently lies below the bulk valence band maximum and that... 

Recently, a tight binding calculation of the surface band structure of GaAs has been reported (at this summer school by Dr. C. Calandra ) that reproduces the observed density of states quite accurately. The calculation used sp -hydridized orbitals to construct the band structure in lattice layers parallel to the surface and then considers the interaction of the lattice layers in the tight binding sense. This computation is patterned after that of Levine and Freeman who used s and p-orbitals located on neighboring M- and X-ions to simulate ionic binding rather than the sp-hybridized orbitals used by Calandra. This is not the place to go into the details. 

Figure 21 shows the calculated surface band structure for the fully relaxed Pandey chain model. Experimental angle-resolved photoemission data are shown for comparison. The dispersion of the calculated surface band is in good agreement with experiment. However, the calculated band is too high by a rigid shift of eV. 

The calculated surface band structure for H on site C is shown in Fig. 25. The H adatoms induce extensive changes in the surface electronic structure of the clean Pd (111) indicating a strong surface chemical bond. The two most striking H-induced features are the narrow H-Pd bonding adsorbate band which appears about 2 eV below the Pd bulk d bands, and the 4 eV wide anti-bonding H-Pd band just above Ej, in a gap in the projected band structure... 

An examination of the charge distribution of the H-Pd adsorbate states shows that the wavefunctions of these states are almost completely localized on the H atoms and the first Pd layer (Fig. 28). The strong bonding at the surface, is predominantly from the interaction between the Pd 4d and the H Is orbitals. The highly localized nature of the H-substrate interaction explains the virtually identical surface band structures for the sites B and C. 

Fig. 7. The experimental surface band structure of an ordered Gd(OOOl) film on W(110) from T-M of the surface Brillouin zone. The data were reduced from fig. 6 and taken from Dongqi Li et al. (1991a). The increasing density of bulk band states near M is evident from the width of the d-band states near the Fermi energy as a function of Aj, as plotted in the top panel.

Figure 19. Schematic representation of the formation of surface banded structure in PAA/HPC...

Cottineau, T., M. Morin, and D. Belanger. Surface band structure of aryl-diazonium modified p-Si electrodes determined by X-ray photoelectron spectroscopy and electrochemical measurements. RSCAdv. 3, 2013 23649-23657. 

Fig. 5.2-3ir Theoretical surface band structure of Si (100)2 X1, obtained with the asymmetric dimer model (see Sect. 5.2.2.3, Fig. 5.2-7). Ddown and Dup refer to the DB bands at the down and up atoms. The bands labeled Si - S5 and Bi -B5 are back-bond states (modified by the surface) [2.53]...

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