Structure and spectroscopy of surface defects from scanning force spectroscopy: theoetical predictions

A possibility to study surface defects by combining noncontact scanning force microscopy (SFM) imaging with atomically resolved optical spectroscopy is demonstrated by modeling an impurity Cr3+ ion at the MgO(001) surface with a SFM tip. Using a combination of the atomistic simulation and the ab initio electronic structure calculations, we predict a topographic noncontact SFM image of the defect and show that its optical transitions can be either enhanced or suppressed depending on the tip atomistic structure and its position relative to the defect. These effects should allow identification of certain impurity species through competition between radiative and nonradiative transitions

Electrostatic energy calculation for the interpretation of scanning probe microscopy experiments

We discuss the correct expression for the classical electrostatic energy used while analysing scanning probe microscopy (SPM) experiments if either a conducting tip or a substrate or both are used in the experiment. For this purpose a general system consisting of an arbitrary arrangement of finite metallic conductors at fixed potentials (maintained by external sources) and a distribution of point charges in free space are considered using classical electrostatics. We stress the crucial importance of incorporating into the energy the contribution coming from the external sources (the `battery'). Using the Green function of the Laplace equation, we show in a very general case that the potential energy of point charges which are far away from metals is equally shared by their direct interaction and the polarization interaction due to charge induced in metals by the remote charges (the image interaction). When the charges are located close to the metals, there is an additional negative term in the energy entirely due to image interaction. The exact Hamiltonian of a quantum system interacting classically with polarized metal conductors is derived and its application in the Hartree-Fock and the density functional theories is briefly discussed. As an illustration of the theory, we consider an interaction of several point charges with a metal plane and a spherical tip, based on the set-up of a real SPM experiment. We show the significance of the image interaction for the force imposed on the tip

The prediction of metastable impact electronic spectra (MIES): perfect and defective MgO(001) surfaces by state-of-the-art methods

We re-examine the theory of metastable impact electron spectroscopy (MIES) in its application to insulating surfaces. This suggests a quantitative approach which takes advantage of recent developments in highly efficient many-electron computational techniques. It gives a basis to the interpretation of experimental MIES spectra for perfect and defective surfaces. Our method is based on a static approach to predicting Auger de-excitation (AD) rates of He*(1s2s) projectiles. A key quantity is the surface density of states (DOS) projected on the Is orbital of the He* atom, which is calculated along its trajectory. We use density functional theory within both supercell geometry and embedded cluster models to calculate MIES spectra for the perfect MgO surface and for an MgO surface with different concentrations of adsorbed oxygen atoms. First we calculate the Auger de-excitation rates at various positions of the projectile above the surface. To predict MIES spectra, we integrate over projectile trajectories, with a subsequent weighted averaging with respect to various lateral positions of He* above the MgO surface unit cell. It is important to examine final-state effects for a correct comparison between theory and experiment, especially when there are localised defect states. (C) 2000 Elsevier Science B.V. All rights reserved

Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence

We discuss a relation between the Kantorovich-Wasserstein (KW) metric and the Kullback-Leibler (KL) divergence. The former is defined using the optimal transport problem (OTP) in the Kantorovich formulation. The latter is used to define entropy and mutual information, which appear in variational problems to find optimal channel (OCP) from the rate distortion and the value of information theories. We show that OTP is equivalent to OCP with one additional constraint fixing the output measure, and therefore OCP with constraints on the KL-divergence gives a lower bound on the KW-metric. The dual formulation of OTP allows us to explore the relation between the KL-divergence and the KW-metric using decomposition of the former based on the law of cosines. This way we show the link between two divergences using the variational and geometric principles

General theory of microscopic dynamical response in surface probe microscopy: from imaging to dissipation.

We present a general theory of atomistic dynamical response in surface probe microscopy when two solid surfaces move with respect to each other in close proximity, when atomic instabilities are likely to occur. These instabilities result in a bistable potential energy surface, leading to temperature dependent atomic scale topography and damping (dissipation) images. The theory is illustrated on noncontact atomic force microscopy and enables us to calculate, on the same footing, both the frequency shift and the excitation signal amplitude for tip oscillations. We show, using atomistic simulations, how dissipation occurs through reversible jumps of a surface atom between the minima when a tip is close to the surface, resulting in dissipated energies of 1.6 eV. We also demonstrate that atomic instabilities lead to jumps in the frequency shift that are smoothed out with increasing temperature

Dynamical processes at oxide surfaces studied with the virtual atomic force microscope

We present the results of calculations performed to simulate the process of atomic scale imaging with the noncontact atomic force microscope that explicitly take into account thermally induced dynamical processes occurring at the surface in real time, using a different multiscale method. Two model defect systems are studied atomistically: a Pd atom adsorbed on MgO (001) which can diffuse across the surface, and a water molecule adsorbed on the Ce O2 (111) surface which can rotate about an oxygen atom. Each of these processes is evolved in real time using a kinetic Monte Carlo method, while simultaneously being imaged using a virtual atomic force microscope which performs a simulation of the entire instrumentation. The results of these simulations show how dynamical processes can significantly change the contrast seen in noncontact atomic force microscope images and that mobile defects present on the surface may not be visible in the image. © 2007 The American Physical Society

Controlled manipulation of atoms in insulating surfaces with the virtual atomic force microscope.

We predict how single oxygen ions can be manipulated on the MgO (100) surface and demonstrate the possibility of detecting a single-atom event using a noncontact atomic force microscope. The manipulation process is simulated explicitly in real time with a virtual dynamic atomic force microscope including the full response of the instrumentation and demonstrates a strong dependence on temperature. The proposed new atomistic mechanism and protocols for the controlled manipulation of single atoms and vacancies on insulating surfaces may be relevant for anchoring molecules and metal clusters at these surfaces and controlling their electronic properties

Ionic solids at elevated temperatures and high pressures: MgF₂

A combination of periodic Hartree-Fock theory, quasiharmonic lattice dynamics, and molecular dynamics is used to study the behavior of MgF2 at elevated temperatures and/or high pressures, Particular attention is paid to the pressure-induced transition from the rutile to the fluorite structure in view of earlier theoretical estimates of the transition pressure, which differ widely. It is shown that previously reported potentials obtained by fitting to empirical data fail to reproduce thermodynamic properties. To rectify this, a new set of consistent two-body potentials has been derived from nb initio periodic Hartree-Fock calculations. Lattice dynamics calculations in the quasiharmonic approximation based on these potentials has been used to study the two phases of MgF2 at high T and P. The resulting transition pressure and that obtained directly from Hartree-Fock calculations in the static limit are both less than or equal to 30 GPa, which is close to the experimental value but appreciably lower than a previous molecular dynamics value of over 130 GPa. The variation of quantities such as (partial derivative P/dT)(V) which play a central role in the formulation of approximate equations of state is also considered. (C) 1997 American Institute of Physics.</p

Modelling atomic scale manipulation with the non-contact atomic force microscope

We present the results of calculations performed to model the process of lateral manipulation of an oxygen vacancy in the MgO(001) surface using the non-contact atomic force microscope (NC-AFM). The potential energy surfaces for the manipulation as a function of tip position are determined from atomistic modelling of the MgO(001) surface interacting with a Mg terminated MgO tip. These energies are then used to model the dynamical evolution of the system as the tip oscillates and at a finite temperature using a kinetic Monte Carlo method. The manipulation process is strongly dependent on the lateral position of the tip and the system temperature. It is also found that the expectation value of the point at which the vacancy jumps depends on the trajectory of the oscillating cantilever as the surface is approached. The effect of the manipulation on the operation of the NC-AFM is modelled with a virtual dynamic AFM, which explicitly simulates the entire experimental instrumentation and control loops. We show how measurable experimental signals can result from a single controlled atomic scale event and suggest the most favourable conditions for achieving successful atomic scale manipulation experimentally. © 2006 IOP Publishing Ltd