Atom scattering as a probe of the surface electron-phonon interaction at conducting surfaces

An atomic projectile colliding with a surface at kinetic energies in the thermal or hyperthermal range interacts with and is reflected by the electronic density well in front of the first layer of target atoms, and it is generally accepted that the repulsive interaction potential is proportional to the density of electrons extending outside the surface. This review develops a complete treatment of the elastic and inelastic scattering of atoms from a conducting surface in which the interaction with the electron density and its vibrations is treated using electron-phonon coupling theory. Starting from the basic principles of formal scattering theory, the elastic and inelastic scattering intensities are developed in a manner that identifies the small overlap region in the surface electron density where the projectile atom is repelled. The effective vibrational displacements of the electron gas, which lead to energy transfer through excitation of phonons, are directly related to the vibrational displacements of the atomic cores in the target crystal via electron-phonon coupling. The effective Debye-Waller factor for atom-surface scattering is developed and related to the mean square displacements of the atomic cores. The complex dependence of the Debye-Waller factor on momentum and energy of the projectile, including the effects of the attractive adsorption well in the interaction potential, are clearly defined. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known electron-phonon coupling constant λ. This treatment reproduces the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the mode specific mass correction components λ_Q,ν defined by the relationship λ = 〈λ_Q,ν〉. The intensities of elastic diffraction peaks are shown to be a weighted sum over the λ_Q,ν, and the Debye-Waller factor can also be expressed in terms of a similar weighted summation. In the simplest case the Debye-Waller exponent is shown to be proportional to λ and for simple metals, metal overlayers, and other kinds of conducting surfaces values of λ are extracted from available experimental data. This dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the electron-phonon coupling constant λ shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density.     

Model calculations of atom-surface scattering

The elastic scattering of light mass, thermal-energy atoms from simple surfaces is investigated. The surface is represented by the model of a single planar square array of hard spheres. The effect of the surface potential well is treated semiclassically by simply shifting the energy of the incident atom ; furthermore a constant imaginary term is added to the energy to account for inelastic scattering and adsorption. As in the multiple scattering formalism of LEED the total scattering matrix of the lattice is expanded in terms of the individual gas atom-surface atom t-matrices. Propagation of the incident atom on the surface is described in terms of a one particle Green's function propagator with complex energy. The terms in the multiple scattering series are summed to all orders, by using standard matrix inversion techniques. The size of the matrix to be inverted limits to ten the total number of phase shifts that are included in the calculation. Thermal effects are included through angle dependent Debye-Waller factors.Model calculations have been performed to study the intensity of the specular and the diffracted beams as a function of the angles of incidence. The importance of surface temperature (introduced by the Debye-Waller factors), the incident energy and the depth of the potential well of the gas-surface interaction are discussed. The main feature of the results is the decrease of the intensity of the specular beam in going from glancing incidence to normal incidence and the presence of structure due to the appearance and disappearance of diffracted beams across the surface. The azimuthal behavior of the specular beam is in agreement with experimental observations.     

Determination of characteristic surface vibration temperatures by molecular beam scattering: Application to specular scattering in the HLiF (001) system

A theory of the determination of characteristic surface vibration temperatures (so-called “surface Debye temperatures”) by molecular beam scattering is outlined. The basis of the theory is the reduction in the intensities of the elastically-scattered beams which is due to the thermal motions of the surface atoms (the “Debye-Waller effect”). A combination of the theory of this effect with the diffraction theory of Cabrera, Celli, Goodman and Manson [Surface Sci. 19 (1970) 67] and of Goodman and Tan [J. Chem. Phys. 59 (1973) 1805] allows calculation of the elastic intensities as functions of the experimental parameters [in particular, as functions of the ratio of (a) the surface temperature and (b) the characteristic surface vibration temperature]. The theory is applied to some experimental data of Hoinkes, Nahr and Wilsch [Surface Sci. 33 (1972) 516] on specular scattering in the HLiF (001) system. It is concluded that a great deal of information about the experimental system, apart from the characteristic surface vibration temperature, is contained in such experimental data.     

Scattering of low-energy atoms by metallic surfaces

The problem of a neutral low-energy atom impinging on a well-defined metallic surface is approached from first principles. The solid and its potential energy of interaction with the incident atom is treated in the most general way, but under the following assumptions: (a) the conduction electrons interact adiabatically with the lattice ions and the gas atom; (b) no chemical reactions occur; (c) the one-phonon approximation is valid. The scattering amplitudes for surface and bulk mode excitations are obtained in terms of the dynamical properties of the metallic surface. Direct collisions of the incident atoms with the lattice ions are shown to give a negligible contribution to the scattering. The most important contribution comes from the interaction of the gas atom with the surface conduction electrons; the excitation of lattice vibrational modes occurs through the electron-phonon term of the Hamiltonian. The general expressions for the scattering amplitudes obtained show that the scattering is incoherent. With further assumptions one obtains a separation of the scattering amplitude into a coherent and incoherent part.     

Work function changes produced by chemisorption due to site heterogeneity

A quantum theory of elastic scattering of atoms from crystal surfaces is presented, based on a hard corrugated surface model. It is shown in detail how the rainbow effect arises and determines the diffraction probabilities, such a rainbow effect being the quantum analogon of McClure's classical rainbow. Further topics considered are the influence of a potential well and the reasons why diffraction hardly occurs from metal surfaces. The basis for a possible extension to inelastic scattering is sketched.     

Classical theory of atom–surface scattering: The rainbow effect

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom–surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom–surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle–surface interactions.     

Diffuse x-ray scattering near Bragg peaks from point defects in a general lattice

Using the continuum theory of linear elasticity, diffuse x-ray scattering has been calculated in the immediate neighbourhood of Bragg peaks from point defects in a lattice containing more than one atom in the unit cell. General expressions are obtained for the Debye-Waller factor, Huang diffuse scattering and the asymmetric scattering due to the defect. For lattices with one atom per unit cell, these expressions reduce to the well-known formulae of diffuse scattering.     

Selection rules for Bloch wave scattering for HREM imaging of imperfect crystals along symmetry axes

A Bloch wave analysis is used to investigate high-resolution electron microscope (HREM) imaging of crystals containing atomic displacements due to strain. In the absence of interband scattering, the shifts of peaks and troughs in the image will correspond to the displacements of the atoms in the exit surface. Interband scattering will shift the image peaks away from the actual atom positions and modify the apparent magnitude of the displacement identified by the observed image peak positions. By considering the case of seven-beam imaging of a cubic crystal aligned along a ?111? axis, it is shown that the symmetry of the Bloch waves leads to selection rules for the interband scattering, similar to those seen for dipole electron excitations in atoms. It is also shown that, to first order, no intraband scattering can occur.     

The anomalous Debye-Waller factor of hydrogen in niobium as determined by quasielastic neutron scattering

The integrated intensity of quasielastic neutron scattering by protons in polycrystalline NbH_0.16 and in a single crystal of NbH_0.045 was investigated as a function of the scattering vector Q. Strong deviations from a harmonic Debye-Waller factor behavior were observed at elevated temperatures. The results show a temperature dependent delocalization of the proton extending as far as the neighboring sites of the interstitial lattice. Experiments on the single crystal indicate a directional dependent mean-square amplitude of the proton even at room temperature.     

Analysis of surface composition with low-energy backscattered ions

The use of low-energy (< 3 keV) ion beam scattering to characterize the surface properties of solids is reviewed. The elemental composition of the first monolayer of surface atoms can be derived from the energy spectrum of backscattered noble gas ions. Positive identification of surface impurity atoms is based on a simple, yet valid collision model involving only the primary ion and a single, isolated surface atom. Backscattered active gas ion spectra, in contrast, yield little information due to pronounced background similar to that observed in the high-energy Rutherford scattering experiments. These differences are ascribed to complicated neutralization phenomena and can be minimized in single crystal targets by utilizing channeling effects. This simple technique is shown to offer several advantages over existing techniques for characterizing thin films.     

Matter-wave decoherence due to a gas environment in an atom interferometer

Decoherence due to scattering from background gas particles is observed for the first time in a Mach-Zehnder atom interferometer, and compared with decoherence due to scattering photons. A single theory is shown to describe decoherence due to scattering either atoms or photons. Predictions from this theory are tested by experiments with different species of background gas, and also by experiments with different collimation restrictions on an atom beam interferometer.     

On the neutron diffraction in crystals in the field of a sound wave

Diffraction of neutrons in crystals under influence of a sound wave is considered. The probability of scattering of neutrons at the elastic interaction with the crystal is calculated. On the contrary, scattering of neutrons by an acoustical phonon has inelastic character. The possibility to control the Debye-Waller factor is shown.     

The influences of the local impact site and incident energy on the transport behaviors of single copper atom onto Cu (0 0 1) surface

Molecular dynamics (MD) simulation is carried out to study the transport behaviors of a single deposited atom in Cu film homoepitaxy. We consider the normal Cu incident atoms impinging on the Cu (0 0 1) surface at four possible local impact sites (top, bridge, hollow and general). The observed transport behaviors of the deposited atom onto the surface include: direct adsorption (DA), penetration by atomic exchange, and transient penetration (TP), which a deposited atom penetrates the interstitial site and then rapidly migrates to a stable site on the surface. The results show that transport behaviors of the deposited atom are closely related to both the local impact site and the incident energy. The maximum increment of kinetic energy at every impact site approaches to a certain value except for the incident energy below 2.0 eV. Furthermore, as the incident energy is higher than the penetration threshold, TP behavior could be observed again in some energy ranges. This interesting phenomenon, which cannot be explained by the existing theories, is possibly attributed to the dynamical competition between the deposited atom and substrate atoms.     

On the interpretation of rainbow scattering in gas atom/surface collisions

A model is proposed to explain the scattering of thermal energy atoms from surfaces. The model allows the behaviour of the scattering trajectories to be assessed. It is shown that when a collimated beam of Neon atoms is scattered from the LiF(100) surface, the peaks observed in the inplane distribution of scattered atoms versus angle of reflection arise from trajectories with one and two repulsive collisions with the same surface atom.     

Island mediated sticking of the rare gases on Cu(110)

The sticking of Ar, Kr, and Xe on the Cu(110) surface is investigated by He-atom scattering. For all three rare gas species the sticking coefficient is strongly coverage dependent. It first increases with coverage and decreases again towards monolayer completion. This behavior is explained by the formation and coalescence of 2D rare gas islands during adsorption. Surprisingly, the trapping efficiency of these islands is larger than expected from their actual geometric size. This is interpreted in terms of a highly mobile transient state of the rare gas atoms impinging on the bare Cu(110) surface.     

Scattering of O? from a graphite surface

Recently an extensive series of measurements has been presented for the angular distributions of oxygen molecules scattered from a graphite surface. Incident translational energies ranged from 291 to 614 meV with surface temperatures from 150 to 500 K. The measurements were taken with a fixed angle of 90° between the source beam and the detector and the angular distributions consisted of a single broad peak with the most probable intensity located at an angle slightly larger than the 45° specular position. Analysis with the hard cubes model for atom-surface scattering indicated that the scattering is primarily a single collision event with a surface having a collective effective mass much larger than a single carbon atom. Limited analysis with a classical diatomic molecular scattering theory was also presented. In this paper a more complete analysis using the classical diatomic molecular scattering theory is presented. The energy and temperature dependence of the observed angular distributions are well described as single collision events with a surface having an effective mass of 1.8 carbon graphite rings. In agreement with the earlier analysis and with other experiments, this suggests a large cooperative response of the carbon atoms in the outermost graphene layer.     

Xe原子吸附对GaAs(110)表面重构的影响

基于第一性原理的自洽场密度泛函理论(DFT)和广义梯度近似(GGA),利用缀加平面波加局域轨道(APW+lo)近似方法，建立了五层层晶超原胞模型，模拟了GaAs(110)表面结构和单个Xe原子在其表面的吸附.利用牛顿动力学方法，对GaAs(110)表面原子构形的弛豫和Xe原子在GaAs(110)表面的吸附进行了计算.从三种不同的初始构形出发，即Xe原子分别在Ga原子的顶位，As原子的顶位以及桥位，都发现Xe原子位于桥位时体系能量最低.由此，认为Xe原子在GaAs(110)表面的吸附位置在桥位，并且发现吸附Xe原子后GaAs(110)表面有趋向于理想表面的趋势，表面重构现象趋于消失，表面原子间键长有一定的恢复,这与理论预言相符合. 关键词： 密度泛函理论 表面结构 APW 表面原子吸附     

Al(100)表面原子结构的高能离子散射研究

本文介绍了用高能(MeV)离子散射研究表面、界面原子结构的方法、实验装置;报道了获得Al单晶清洁表面的方法,用高能离子散射、沟道效应研究Al(100)表面原子结构的实验结果:Al(100)表面层原子的热振动振幅较体内原子大20—30％,Al(100)表面层原子的弛豫量小于-0.05?。 关键词：     

Nonradiative transition to the ground state and superelastic scattering of exited atoms upon impact on the surface of wide-bandgap dielectrics

The impact of excited cesium atoms on sapphire and glass surfaces have been experimentally studied. It is established that the probability of electron excitation quenching upon impact of an atom on the dielectric surface is close to unity. The velocity distribution of unexcited atoms upon scattering from the surface has been determined using the time-of-flight technique. The kinetic energies of most of these atoms are several tens of times greater than the energy of thermal motion of the excited atoms impinging on the surface. Conversion of the internal energy of atoms into their kinetic energy is explained in terms of nonradiative electron transitions with simultaneous excitation of lattice vibrations in the dielectric crystal. This mechanism of atomic excitation quenching near the dielectric surface explains the significant difference between the energies of atoms upon superelastic scattering and upon photodesorption from an adsorbed state.     

Diffusion of hydrogen in the β-phase of pd-H studied by small energy transfer neutron scattering

The diffusion of hydrogen in β-PdH_x has been studied by quasielastic neutron scattering. It is shown that the diffusion occurs through jumps between adjacent octahedral interstitial sites. The observed integrated quasielastic intensities cannot be described by a simple Debye-Waller factor. The phase transition from the β-phase to the α-phase has also been studied. No dramatic changes in the scattering patterns were observed. It is concluded that the diffusion mechanism is remarkably similar for the low concentration α-phase and the high concentration β-phase.