LDOS, surface

The surface charge density of Al(lll) has been well characterized by first-principles calculations as well as helium scattering experiments. The asymptote of the corrugation amplitude Az of equal-LDOS surface contours follows an exponential law, as obtained from a first-principles calculation of the electronic structure of the Al(l 11) surface (Mednick and Kleinman, 1980) ... 

The presence of a defect in the lattice (impurity, surface, vacancy...) breaks the symmetry and induces perturbations of the electronic structure in its vicinity. Thus it is convenient to introduce the concept of local density of states (LDOS) at site i ... 

The LDOS have been calculated using 10 exact levels in the continued fraction expansion of the Green functions. For clean surfaces the quantities A Vi are the same for all atoms in the same plane they have been determined up to p = 2, 4, 6 for the (110), (100) and (111) surfaces, respectively, and neglected beyond. The cluster C includes the atoms located at the site occupied by the impurity and at al the neighbouring sites up to the fourth nearest neighbour. 

Changes in electronic properties, such as Fermi level shifts and changes in the DOS, which still have to be confirmed experimentally. For example, Yano and co-workers used Pt NMR to probe possible changes in electronic properties induced by particle size [Yano et al., 2006]. They concluded that the surface Knight shifts as well as Ep-LDOS of surface Pt atoms showed no noticeable size dependence in the particle size range from 4.8 down to 1.6 nm hence, electronic properties are independent of size in this interval. 

In order to ameliorate the sharply sloping background obtained in an STS spectrum, the data are often presented as di,/dFh vs. Vb, i.e. the data are either numerically differentiated after collection or Vb has a small modulation applied on top of the ramp, and the differential di,/d Vb is measured directly as a function of Vb. The ripples due to the presence of LDOS are now manifest as clear peaks in the differential plot. dt,/dFb vs. Vb curves are often referred to as conductance plots and directly reflect the spatial distribution of the surface electronic states they may be used to identify the energy of a state and its associated width. If V is the bias potential at which the onset of a ripple in the ijV plot occurs, or the onset of the corresponding peak in the dt/dF plot, then the energy of the localised surface state is e0 x F. Some caution must be exercised in interpreting the differential plots, however, since... 

Plots of the LDOS at the surface (n = 1) site of a 100-atom chain are presented in Fig. 7.3 for various field strengths. For no field, F = 0 (Fig. 7.3(a)), the LDOS exhibits a discretized version of the semi-elliptical shape, familiar for a surface DOS. For small field strength (Fig. 7.3(b)), an almost-linear region appears in the lower end of the quasi-band. As the field strength increases (Fig. 7.3(c) and (d)), the region spreads across the band, with increasing intensities. In addition, there is a rigid shift in the structure to... 

The scanning tunneling microscope uses an atomically sharp probe tip to map contours of the local density of electronic states on the surface. This is accomplished by monitoring quantum transmission of electrons between the tip and substrate while piezoelectric devices raster the tip relative to the substrate, as shown schematically in Fig. 1 [38]. The remarkable vertical resolution of the device arises from the exponential dependence of the electron tunneling process on the tip-substrate separation, d. In the simplest approximation, the tunneling current, 1, can be simply written in terms of the local density of states (LDOS), ps(z,E), at the Fermi level (E = Ep) of the sample, where V is the bias voltage between the tip and substrate... 

The study of adsorbates on metal surfaces is a particularly fruitful area, which has received much attention. Experimentally, atomic adsorbates are known to yield very different images ranging from bumps [S on Pt(l 11)] to depression [O on Ni(lOO)] depending on the nature of the interaction with the LDOS of the metal surface [58,70,71]. The phenomenon has been analyzed in terms of the impact of the adsorbate on the local density of states at the substrate Fermi level [57,71-75]. Importantly, even... 

FIG. 10. Theoretical calculations reveal that in the case of adsorption of Xe on Ni the resonance associated with Xe(6s) state is broadened significantly with a long tail that extends to the Ni Fermi level. STM images are determined by the LDOS at the Fermi level. Although the contribution of Xe to the LDOS is small, it significantly extends the spatial distribution of the electronic wave function further away from the surface thereby acting as the central channel for quantum transmission to the probe tip. (From Ref. 71.)... 

For simple metal surfaces with fundamental periodicity a, the corrugation amplitude of the Fermi-level LDOS as a function of tip-sample distance can be estimated with reasonable accuracy (Tersoff and Hamann, 1985) ... 

An early systematic experimental study on the imaging mechanism was conducted on Al(lll) (Wintterlin et al., 1989). The observed corrugation amplitude was more than one order of magnitude larger than the Fermi-level LDOS corrugation. Aluminum is a textbook example of simple metals. The electronic states on the AI(lll) surface have been studied thoroughly. 

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. 

Table 4.2 is a summary of the Fermi-level LDOS for three commonly used tip materials Pt, Ir, and W. At the Fermi level, the d states dominate the bulk DOS. Therefore, on surfaces of Pt, Ir, and W, the wavefunctions as tails of bulk states are also dominated by d states. 

If available, the LDOS at different energy levels, for the tip and the sample, is very useful information for predicting STM images. Several examples of surface electronic structures from first-principles calculations are reproduced as illustrations. 

The corrugation amplitude of the Fermi-level LDOS for a metal surface with one-dimensional corrugation can be obtained using Equations (5.7) and (5.18),... 

Fig. 5.5. Geometrical structure of a close-packed metal surface. Left, the second-layer atoms (circles) and third-layer atoms (small dots) have little influence on the surface charge density, which is dominated by the top-layer atoms (large dots). The top layer exhibits sixfold symmetry, which is invariant with respect to the plane group p6mm (that is, point group Q, together with the translational symmetry.). Right, the corresponding surface Brillouin zone. The lowest nontrivial Fourier components of the LDOS arise from Bloch functions near the T and K points. (The symbols for plane groups are explained in Appendix E.)...

The STM images of large superstructures on metal surfaces exhibit a very simple form. As shown first time by Tersoff and Hamann (1983, 1985), at the low-bias limit, the STM images of large superstructures on metal surfaces are independent of tip electronic states, and an STM image is simply a contour of an important quantity of the sample surface only the Fermi-level local density of states (LDOS), taken at the center of curvature of the tip. An attempt was also made to interpret the observed atom-resolved images of semiconductors... 

In the original papers of Tersoff and Hamann (1983, 1985), the result of the s-wave approximation was compared with the STM images of the superstructure profiles of the reconstructed Au(llO) surfaces. By assuming the center of the i-wave is approximately 15 A from the top-layer nuclei of the gold surface, the Fermi-level LDOS contour approximately matches the measured image of Au(110)-2X1 and Au(110)-3X1 surfaces. For Au(110)-3xl, 0.25A" , and Vk wO.I. For small I, the Tersoff-Hamann condition, Eq. (5.63), is approximately satisfied, and the STM images are approximately independent of tip electronic states. 

Similar to the. y-wave model, the Na-atom-tip model predicts a poor resolution. The agreement of the Na-atom-tip model with the y-wave-tip model does not mean that the s-wave-tip model describes the actual experimental condition in STM. According to the analysis of Tersoff and Lang (1990), real tips are neither Na or Ca, but rather transition metals, probably contaminated with atoms from the surface (for example. Si and C are common sample materials). For a Si-atom tip, the p state dominates the Fermi-level LDOS of the tip. For a Mo-atom tip, while the p contribution is reduced, this is more than compensated by the large contribution from states of d like symmetry. The STM images from a Si, C, or Mo tip, as predicted by Tersoff and... 

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