Corrugated metal surfaces

Wahnstrdm G, Lee A B and Strdmquist J 1996 Motion of hot oxygen adatoms on corrugated metal surfaces J. Chem. 

Wahnstrom, G. Role of phonons and electron-hole pairs in hydrogen diffusion on a corrugated metal surface, Chem. Phys. Lett. 1989,163,401. 

Common roof materials for houses include shingles made from asphalt or wood shakes, corrugated metal surfaces, and tile. 

Leung, P. and George, T. (1989). Molecular spectroscopy at corrugated metal surfaces. Spectroscopy, 4 35 -41. 

Fig. 1.23. Free-electron-metal model of STM resolution. The sample is modeled as a corrugated free-electron-metal surface. The tip is modeled as a curved free-electron-metal surface with radius r, at the closest approach to the sample surface. (After Stoll, 1984.)...

Some interesting features of the Stoll formula are worth noting. First, only the sum R + d) appears in the formula. Therefore, only the distance of the center of curvature of the tip to the sample surface matters. The radius R becomes irrelevant. Second, the STM corrugation decays exponentially with tip-sample separation. By extrapolating the formula to (/ +1/) = 0, the corrugation coincides with that of the metal surface. These features are also found to be consistent with experimental results and with the results of the Tersoff-Hamann theory, as described below. 

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) ... 

Fig. 1.30. Origin of atomic resolution on metal surfaces. According to the reciprocity principle, the image taken with a d,- tip state (which exists on a W tip) on a free-electron-metal surface is equivalent to an image taken with a point tip on a fictitious sample surface with a d state on each top-layer atom, which obviously has a strong corrugation. (Reproduced from Chen, 1990, with permission.)...

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),... 

The corrugation of the charge density on metal surfaces can be obtained from first-principles calculations or helium scattering experiments. The theory and the experiments match very well. A helium atom can reach to about 2.5-3 A from the top-layer nuclei. At that distance, the repulsive force between the helium atom and the surface is already strong. The corrugation at that distance is about 0.03 A, from both theory and experiments. For STM,... 

The enhancement for the tunneling matrix element is shown in Fig. 5.2. The enhancement factor for the corrugation amplitude, Cl + (3iyV2K-)T, could be substantial. For example, on most closc-packcd metal surfaces, a= 2.5 A,... 

A straightforward calculation using the tunneling matrix elements listed in Table 3.2 shows that the state results in a large but inverted corrugation amplitude on metal surface, because the tunneling matrix element for the sample wavefunction at the F point vanishes. The role of this state and the state in the inverted corrugation will be discussed in Section 5.5. 

The corrugation inversion due to tip states is a universal phenomenon in the STM imaging of low-Miller-index metal surfaces. For most metals (except several alkali and alkaline earth metals, which have rarely been imaged by STM), the nearest-neighbor atomic distance a 3 A. Consequently, the numerical coefficients on Eq. (5.61) are very close to those for Au(lll). 

Fig. 6.9. Corrugation amplitudes of a hexagonal close-packed surface. Solid curve, theoretical corrugation amplitude for an s and a d,- tip state, on a close-packed metal surface with a=2.88 A and 4>=3.5 eV. The orbitals on each metal atom on the sample is assumed to be 1 i-type. Measured STM corrugation amplitudes are from the data of Wintterlin et al. (1989). The first-principle calculation of Al(lll) is taken from Mednick and Kleinman (1980). The corrugation amplitude for a 4-wave tip state is more than one order of magnitude smaller then the experimental corrugation. (Reproduced from Chen, 1991, with permission.)...

The modification of an x-wave sample state due to the existence of the tip is similar to the case of the hydrogen molecule ion. For nearly free-electron metals, the surface electron density can be considered as the superposition of the x-wave electron densities of individual atoms. In the presence of an exotic atom, the tip, the electron density of each atom is multiplied by a numerical constant, 4/e 1.472. Therefore, the total density of the valence electron of the metal surface in the gap is multiplied by the same constant, 1.472. Consequently, the corrugation amplitude remains unchanged. 

Tip-state effects 19—20, 126, 297 atomic resolution, and 32 corrugation enhancement 125 corrugation inversion, and 137 graphite, and 146 layered materials, on 20 metal surfaces, on 19 scanning tunneling spectroscopy, and 24, 308 Tip-sample distance 53... 

Fig. 2. The effect of chemical interactions in STM scans on three close-packed metal surfaces (a) Au(lll), (b) Cu(lll), (c) Al(lll). The left frames show a constant current contour without corrections due to chemical interactions, current and corrugation values, while the right frames show constant current contours with the corrections.

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