Surfaces density of states

The shape of the density of states reveals the peculiarities of the hybridization between anion and cation orbitals, which depend upon three parameters the values of the resonance integrals the coordination number of the surface atoms and the energy separation between the relevant atomic levels. In the absence of relaxation, rumpling or reconstructions, the resonance integrals have the same values as in the bulk. The surface atom coordination numbers and the level separation, on the other hand, are smaller than in the bulk and they decrease as the surface becomes more open. We will first discuss how these modifications are reflected in the gross features of the local densities of states at the surface and, more specifically, in their second moments. Then we will focus on the details of the band shapes and on the possible occurrence of localized states in the gap. 

Moments of the density of states Within the assumption that electron delocalization takes place only between first neighbours, the second moment of the local density of states on an anion is related to its coordination number Za, to the effective anion-cation resonance integral / , to the anion atomic energies e x and to the degeneracy of the outer levels (Equation (1.4.40) in Chapter 1)  

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Suppose an atom adsorbs on the surface. Which bands of the fee (100) surface are candidates to be involved in chemisorption bonds Most likely the coordina-tively unsaturated orbitals dxy, dxz, dx%2 and s. We will come back to this later on and return for the moment to the surface density of states. 

Thus, the charge transfer probability can be related to the surface density of states. 

Recently, we have studied the effect of the surface density of states on the charge-transfer probability, in the case where the surface possesses localized states created by surface perturbations or the presence of adatoms. For the tight-binding linear chain these perturbations or adatoms are taken into account by changing the electronic energy of the end atom of the chain to a, which differs from the energy a of the other atoms in the chain. This difference can lead to the formation of a localized surface state, whose energy is... 

The surface states observed by field-emission spectroscopy have a direct relation to the process in STM. As we have discussed in the Introduction, field emission is a tunneling phenomenon. The Bardeen theory of tunneling (1960) is also applicable (Penn and Plummer, 1974). Because the outgoing wave is a structureless plane wave, as a direct consequence of the Bardeen theory, the tunneling current is proportional to the density of states near the emitter surface. The observed enhancement factor on W(IOO), W(110), and Mo(IOO) over the free-electron Fermi-gas behavior implies that at those surfaces, near the Fermi level, the LDOS at the surface is dominated by surface states. In other words, most of the surface densities of states are from the surface states rather than from the bulk wavefunctions. This point is further verified by photoemission experiments and first-principles calculations of the electronic structure of these surfaces. 

Slow ionized atoms, usually He+, strike a surface, where they are neutralized in a two - electron process that can eject a surface -electron -a process similar to Auger emission from the valence band. The ejected electrons are detected as a function of energy, and the surface density of states can be determined from the energy distribution. The interpretation is more complicated than for SPI or UPS. 

Atomic force microscopy has been up to now only scarcely used by the plasma processing community. Results mainly concern low-resolution measurements, that is modification of the surface roughness induced by the plasma [43,44], Micro masking effects have been observed when processing Si with a SF6 plasma beam at low temperature (Fig. 11) and correlated to the multi-layer adsorption of plasma species as observed by XPS [45], Further development of vacuum techniques should allow high resolution surface probe microscopy measurements on plasma-treated samples, and possibly lead to complementary information on adsorption kinetics, surface density of states. 

The simplest electrochemical reaction is an outer sphere electron transfer where the interactions with the electrode are weak. Hence, the details of the band structure are not important we can ignore the k dependence of the coupling constants and replace them by a single effective value. The sum over k in Eq. (16) then reduces to the surface density of states corresponding to the electrode and the chemisorption function h.(e) can be taken as constant. It corresponds to the interaction with a wide, stractureless band on the electrode. In this approximation" " the chemisorption K(s) functions vanishes (see Fig. 8a) ... 

Here G /" denotes the retarted or advanced Green s function of the central region, while r depends on the surface density of states of the leads and the molecule-lead coupling. Both terms are directly amenable to a first principles evaluation using effective single-particle theories like Hartree-Fock or density functional theory (DFT). In this way the actual electronic structure of the device is accounted for, without the need to resort to few level models for the molecule or empirical wide band approximations for the leads. 

Fig. 1. Surface density of states with K 0 on Al(OOl) (Inglesfteld and Benesh, 1988). Full curve, top layer of atoms broken curve, second layer. The densities of states are calculated with an imaginary part of the energy = 0.001 a.u., which broadens the discrete surface state bv this amount.

The Singh-Krakauer calculation does not rule out Fermi surface effects as an additional effect, and these still offer the most plausible explanation for the long periodic reconstruction of Mo(001). The peak in the surface density of states — the main driving force — does come from a large region of the Brillouin zone, but the Fermi surface may be in there somewhere. 

Fig. 9. Calculated surface density of states for two Si l00 2 X 1 models compared with photoelectron density after subtraction of secondaries (after Appelbaum et al. [126]).

Although it has been given little attention, excess energy at the transition state may be transferred to surface electronic excitation, instead of surface vibrations. The surface density of states has a small band gap of about 7 kcal/mol, with the main tt - tt transition at 18 kcal/mol [106]. Thus, a single surface electronic excitation can account for the excess energy in the transition state. In other words, the majority of molecules may desorb on a potential surface corresponding to an excited surface electronic state. This proposal has several implications ... 

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