Interpretation Of Scanning Tunneling Microscopy Images Research Articles

Interpretation of STM images of graphite with an atomic vacancy via density-functional calculations of electronic structure

This paper is devoted to the interpretation of scanning tunneling microscopy (STM) images of a single atomic vacancy on single and double graphene sheets as a model for the (0001) surface of graphite. We first selected a one-layer model which would allow us to run periodic density-functional theory calculations without destroying the charge density waves that form in the vicinity of the vacancy. We assigned the main features of STM images [bright spots in the vicinity of the defect, $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ modulation of the local electronic density near the Fermi level, third-order symmetry structure] to the electronic band structure of the defective graphite surface. We further analyzed a more extended crystal working cell model to ensure convergence toward the isolated atomic vacancy. The interlayer interaction plays a crucial role in the interpretation of STM images. A double-layer model was subsequently considered and the impact of the interlayer interaction analyzed. We produce the local density of state for the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ vacancies which may be differentiated. Our calculations reproduce the main features of STM images and the results we get are in good agreement with experimental observations.

Structure and apparent topography ofTiO2(110)surfaces

We present self-consistent ab-initio total-energy and electronic-structure calculations on stoichiometric and non-stoichiometric TiO2 (110) surfaces. Scanning tunneling microscopy (STM) topographs are simulated by calculating the local electronic density of states over an energy window appropriate for the experimental positive-bias conditions. We find that under these conditions the STM tends to image the undercoordinated Ti atoms, in spite of the physical protrusion of the O atoms, giving an apparent reversal of topographic contrast on the stoichiometric 1x1 or missing-row 2x1 surface. We also show that both the interpretation of STM images and the direct comparison of surface energies favor an added-row structure over the missing-row structure for the oxygen-deficient 2x1 surface.

Imaging of the Cu(111) surface state in scanning tunneling microscopy.

Scanning-tunneling-microscopy (STM) data for the Cu(111) surface have been calculated theoretically, based on Bardeen's approximation and a layer-Korringa-Kohn-Rostoker-like approach to describe the sample. The onset of the surface state gives rise to a steplike increase in the conductivity in very good agreement with recent experimental data, which demonstrates the ability of Bardeen's approximation to describe surface states in spite of its failure regarding surface states in one dimension. The STM conductivity can be approximated in terms of the local density of states (LDOS) of the sample at the voltage V, plus a background term which involves states at all energies, and which is frequently neglected in the interpretation of STM images. In the presence of a step edge, the LDOS of the Cu(111) surface state displays standing wave oscillations. In this case, the background term shows oscillations of the Friedel type which drop as ${\mathit{J}}_{1}$(2kx)/kx for a two-dimensional electron gas. This has important implications for determining the surface state dispersion relation and for the interpretation of standing wave patterns in terms of the LDOS.

Generalized expression for the tunneling current in scanning tunneling microscopy.

We present an analytical method for treating the tunneling current between a tip and a sample in scanning tunneling microscopy (STM) that goes beyond the independent-electrode (Bardeen) approximation and is valid for smaller tip-to-surface separations. The extremity of the tip is represented by a single spherical potential well. This well is strongly coupled to neighboring tip atoms, as well as the sample electrode, both of which we leave in a general form. The wave function for the entire system is obtained by a matching procedure, from which the total current is determined. If the current is associated with s-derived tip orbitals, the result is comparable in simplicity with that of J. Tersoff and D. Hamann [Phys. Rev. B 31, 805 (1985)]. The low-bias tunnel conductance is proportional to the local density of states (LDOS) of the surface, but renormalized to include multiple reflections to all orders: \ensuremath{\sigma}\ensuremath{\propto}${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$(${\mathbf{r}}_{0}$,${\mathit{E}}_{\mathit{F}}$)/D, where D depends on both the tip and sample electronic structures and on the tip position ${\mathbf{r}}_{0}$. This effect includes the modification of the surface LDOS due to the presence of the tip. A compact expression is also obtained for orbitals of higher angular momenta: p and d states. The current then depends on the gradients of the surface spectral density, and not on the LDOS, and also has a characteristic denominator. We discuss the significance of this effect, both in the interpretation of STM images and related spectroscopies.

Beyond Tersoff and Hamann: A generalized expression for the tunneling current

We present an analytical method for treating the tunneling current between a probe tip and a sample in scanning tunneling microscopy (STM). The choice of a highly idealized tip permits a direct calculation of the tunnel current without resorting to perturbation theory (Bardeen approximation). In our model, the tip is a semi-infinite chain of spherical potential wells oriented orthogonal to the sample surface. The sample surface, however, is arbitrary. The wavefunction for the entire system is obtained by a matching procedure, from which the total current is determined. For small bias voltage the result is comparable in simplicity with that of Tersoff and Hamann [Phys. Rev. B 31, 805 (1985)]. We find that the tunnel conductance is proportional to the local density of states (LDOS) of the surface, but renormalized to include multiple reflections to all orders: σ∝ρL(r0,EF)/D, where D depends on both the tip and sample electronic structure, and the tip position r0. As the tip-surface separation increases D approaches unity, and we recover the result of TH. We find that D can be smaller or greater than unity, leading to a relative reduction or enhancement of the current. This effect which can be significant, both in the interpretation of STM images and in related spectroscopies, depends on the particular surface electronic structure.