A study of the (00) LEED beam intensity at normal incidence from CdS(0001), Cu(001), Cu(111), and Ni(111)

A Faraday cage apparatus is used for the measurement of the (00) LEED beam intensity, I₍₀₀₎, and the total secondary emission coefficient, δ(E_k), for angles of incidence from 0° ± 2° to 8° ± 2°, with an energy resolution of ± 0.037 of the incident beam energy, in the energy range 1 to 200 eV. The data are normalized and expressed as a fraction of the incident beam intensity. The basic principle of operation is the separation of the incident and specularly diffracted beams in a uniform magnetic field. Monolayer, or in-plane, resonances associated with the emergence of nonspecular beams, as well as beam threshold minima, are observed in I₍₀₀₎ at normal incidence from clean CdS(0001), Cu(111), and Ni(111). Some major differences are observed in the I₍₀₀₎ profiles for the clean (111) surfaces of nickel and copper. All secondary Bragg peaks, except the 2$\text{2}\text{3}$ order, have greater intensities for Ni(111) in the energy range 50–150 eV, thus indicating that the atomic scattering cross-section for electrons in this energy range is larger for nickel than for copper. For the (111) surface of nickel, the (11) resonance is missing, but the (10) resonance and all $\text{1}\text{3}$ order secondary Bragg peaks between the second and fifth orders are observed. For Cu(111) both the (10) and (11) resonances are observed, but the $\text{1}\text{3}$, $\text{2}\text{3}$, 1$\text{2}\text{3}$, and 3$\text{1}\text{3}$ order secondary Bragg peaks are missing in this energy range. These data indicate that multiple scattering with evanescent intermediate waves, or “shadowing”, is predominate on the (111) surfaces on nickel and copper for energies above 30 eV, and that below 30 eV multiple scattering with propagating intermediate waves is predominate on Cu(111). Correlation of the (00) beam intensity profiles from clean Ni(111) at 0°, 2°, and 6° with the intensity profiles of the (10). (1̄0), and (11) non-specular beams is nearly one-to-one from 30 eV to 100 eV, thus supporting the dynamical theories of LEED in which peaks in the (00) beam are expected to occur at nearly the same energies as peaks in the non-specular beams.     

Calculation of surface peak intensity in MeV ion scattering. II

Monte Carlo calculations have been performed to evaluate the surface peak from 1 MeV He ions incident on Si(001) and Si(111) crystal surfaces. Detailed angular dependences of the surface peaks were obtained for tilt angles of ?2° and azimuthal angles of ?45° in the vicinity of axial channeling directions. The validity of the triangular background subtraction is discussed for cases of tilted incidence from axial channeling directions. The multiple scattering effect in thin adlayers on the crystal, which is important in application of MeV ion scattering to interfaces studies, is simulated and correlated with evaluation of the interface peak value of the substrate atoms.     

An analysis of the structure of the iridium (111) surface by low-energy electron diffraction

Elastic low-energy electron diffraction (LEED) intensity versus voltage (I-V) measurements for the clean Ir(111) surface have been obtained. Seven specular I-V spectra were measured from 15 to 975 eV at incident angles from 7° to 62.5° relative to the surface normal. The outermost atomic layer spacing of the unreconstructed Ir(111) surface was determined both by the convolution-transform method we have presented previously (including certain convenient modifications) and by dynamical calculations. Results from the analysis of the I-V spectra by the convolution-transform method indicate that the outermost Ir(111) layer spacing is either unrelaxed or contracts by 4% of its bulk value depending upon whether the θ=7° data or the θ = 25° data are used. In agreement with this, the dynamical calculations show that the outermost Ir(111) layer spacing contracts by 2.5± 5% and, in addition, that the registry of the first layer of the crystal surface is not shifted, maintaining the fcc structure.     

Elastic leed intensity-energy studies of clean (001), (110) and (111) nickel surfaces

Elastic low energy electron diffraction (LEED) intensity-energy (I-E) measurements for clean (001), (110), and (111) nickel surfaces were obtained at room temperature. Surface composition was monitored by Auger spectroscopy. I-E data from 15 to 220 eV were obtained at normal incidence for the non specular beams and for the specular beams at incidence angles from 4° to 20° on the 0° and 45° azimuths of (001), on the 0° and 90° azimuths of (110), and on the 0° azimuth of (111) nickel. Normalization of the data was performed electronically during data acquisition. Intensities were calibrated with the use of a shielded, biased Faraday collector. The effects of instrumental and experimental uncertainties were examined and minimized to obtain intensities accurate to ± 15 %, energy scales accurate to ± 0.35 eV, and incident and azimuthal angles accurate to ± 0.25° and ± 1.0° respectively.All nickel surfaces have I-E spectra which are characteristic of strong multiple scattering. Angular evolution features for (001) and (110) spectra may be correlated with intraplanar resonances associated with the onset of propagating beams. Only the (001) surfaces were found to have pronounced, sharp resonance features associated with surface barrier resonances and inelastic loss processes. Kinematic analysis of the Lorenzian-shaped I-E peaks on all surfaces in consistent with surface expansion using either an energy-dependent or a constant inner potential of 10.75 ± 0.5 eV. The widths of these same peaks on all surfaces were found to vary as $\text{E}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ above 40 eV and $\text{E}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ below.     

Medium energy electron diffraction on aluminum

Measurements of the specular beam intensity in the medium range of energy (645 eV and 980 eV) are presented for the aluminum (001) and (110) surfaces. They have been performed with a LEED goniometer allowing to achieve high accuracy in the determination of the angular parameters of the diffraction experiment. The experimental results are displayed in the form of iso-intensity maps in (θ, φ) coordinates at a constant primary beam energy. θ denotes the colatitude angle of incidence and is varied in the range 30° to 80°. φ denotes the azimuth and is varied between 0° and 360°. Sections of the maps at constant angle of incidence are known as rotation diagrams. A model calculation ignoring intra-layer multiple scattering, but incorporating inter-layer multiple scattering processes shows the prominent role of the latter, in many cases, and the non-negligible contribution of the former in other cases. Sections of the maps at constant azimuth are called incidence-profiles. They are very sensitive to the azimuth and very hard to compute. Using the preceding model calculation, average incidence profiles have been computed, using as input parameters the refractive and absorptive potentials and the surface normal relaxation parameter obtained by a pseudo-kinematic analysis of experimental average incidence profiles as explained in another paper. The peak position and width have been compared to those obtained from the pseudo-kinematic calculation. From the result, it is shown that if averaging is performed according to a specific set of restrictive rules, the pseudokinematic analysis of the data has a semi-quantitative meaning.     

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.     

Low-energy 3He+ ion scattering spectroscopy studies of D2 adsorption on W(211)

Direct physical evidence for occupation of a trough site by the β₂ state of deuterium adsorbed on W(211) has been obtained by angle-resolved ³He⁺/D(ads) ion-scattering spectroscopy (ISS) in combination with LEED/Auger. The W(211) surface is composed of close-packed 〈111〉 rows of W atoms separated by a wide channel. Previous thermal desorption studies have shown two clearly resolved hydrogen states: β₁ desorbing with a temperature maximum of ca. 60°C, and β₂ at ca. 400°C. Analyses of flash desorption, work-function, adsorption kinetics, stoichiometry and mixed adsorption further indicated that the more tightly bound β₂ form occupies a deep-trough position. In the present study, ISS polar-angle profiles were taken at an incident energy of 306 eV. With only the β₂ state populated, a ³He⁺ beam parallel to the close-packed 〈111〉 rows was found to scatter from D(ads) with a cutoff angle close to grazing incidence while for the perpendicular direction D(ads) scattering is observed only for angles greater than 18° away from grazing incidence. These measurements are consistent with the corrugated W(211) geometry and with the proposed β₂-D trough-site model.     

Relativistic effects on LEED intensities from Au(111)

Comparison of relativistically and nonrelativistically calculated intensity versus energy profiles in low energy electron diffraction (LEED) from the (111) surface of Au (Z = 79) reveals that relativistic corrections are quite significant. They can however, be obtained in very good approximation by quasirelativistic calculations, in which spin-averaged relativistic phase shifts are used as input for the nonrelativistic multiple scattering formalism. Further, relativistic effects on intensities are found to be comparable to differences arising from different approximations to the exchange part of the ion core potential.     

General aspects of beam threshold effects in LEED

We present in this paper some general aspects of beam threshold effects in LEED concerning their observation, their extension and their detection. The observation is possible on LEED intensities but also on crystal to ground current and total reflected current. We discuss the various types of profiles due to threshold effects for LEED intensities. From universal relations coming from emergence conditions of a new beam we draw universal charts for the “speed of emergence” versus E, θ or φ. These charts are used for a discussion of the range in I(E) or I(φ) profiles, where threshold effects may affect the LEED intensities. The same relations are used for a discussion of the detection of threshold effects. Assuming a Gaussian distribution (in energy and angles) for the incident beam, we derive a “total equivalent experimental resolution” and we discuss the consequence on intensity profiles and on the optimal conditions of detection.     

On the contraction of the W(001)-(1 × 1) surface using LEED intensity analysis

Three recent independent attempts at deducing the W(001)-(1 × 1) surface structure by LEED beam intensity analysis have yielded contractions of the topmost layer spacing of 6 ± 6%, 11 ± 2%, 4.4 ± 3% normal to the surface plane. We investigate possible reasons for the discrepancies by comparing published experimental and theoretical profiles of these workers as well as our own. Our main conclusions are that the direct comparison of experimental data of different investigators shows deviations which are comparable to the changes in the calculated profiles for various surface contractions. Also the deviations between calculated intensity profiles using different (but still realistic) assumed scatteting potentials are comparable to the changes in the calculated profiles for various surface contractions. The main uncertainty in the scattering potential is the choice between the Slater free electron exchange-correlation term (coefficient α = 1) or the Kohn-Sham version ($\text{α =}\text{2}\text{3}$) or a value in between. For tungsten the corrections due to relativistic atomic scattering must also be considered. These uncertainties in the calculated and experimental profiles lead to the conclusion that the surface layer contraction of W(001)-(1 × 1) is not known at the present time. To assess the potential of LEED in deducing surface structures of this type further comprehensive analyses are required where the uncertainties in the theoretical scattering potential are also examined.     

Electron-spin-dependent 4He+ ion scattering on Bi surfaces

We studied low-energy (～ 1.55 keV) electron-spin-polarized ⁴He⁺ ion scattering on a Bi(111) ultrathin film epitaxially grown on a Si(111) substrate. We observed that the scattered ion intensity differed between the incident He⁺ ions with up and down spins even though Bi is a non-magnetic element. To analyze the origin of this spin-dependent ion scattering (the spin asymmetry), we investigated the detailed relationship between the spin asymmetry and the incident angle, the azimuthal angle, the scattering angle, and the incident energy. All the data indicate that the spin asymmetry originates from the scattering cross section owing to the non-central force in the He⁺–Bi atom binary collision. The non-central force is most likely attributed to the spin–orbit coupling that acts transiently on the He⁺ 1s electron spin in the binary collision.     

Reply to comment on the use of “Kramers-kronig analysis for the determination of the optical constants of thin surface films”

A LEED data reduction method is described and applied to Al (001) surface. The method consists of averaging rotation diagrams (azimuthal intensity profiles) obtained at constant electron energy between 500 and 1000 eV in the whole range of the colatitude angle of incidence. The method avoids certain difficulties, stemming e.g. from the energy dependence of the mean optical potential, that are present in other methods in which data obtained at different energies are averaged. The averaged data are analyzed using the two-beam Darwin theory. Values for the surface normal relaxation and mean optical potential are obtained from the study of the position, width and profiles of the averaged peaks. The (100) surface of aluminum is found not relaxed while the (110) surface is contracted. The values found for the mean optical potential are similar to those obtained from other sources. The precision of the averaging method for surface structure is not better than that of direct calculation. Experimental factors limiting the precision of the method (surface roughness, background interference due to Kikuchi lines) are specified.     

Angle-resolved ups measurements in a modified LEED system

A LEED chamber has been modified to include a differentially pumped discharge lamp (He or Ne) and an additional retarding grid electron energy analyser for UPS. This small analyser is located at right angles to the LEED analyser and does not interfere with normal LEED and Auger operations. The UPS signal is amplified by a channel plate multiplier and accelerated onto a phosphor-coated screen. Directional information is obtained by scanning this screen with a collimated photomultiplier detector. A phase-lock amplifier is used to differentiate the signal from the photomultipler. Alternatively the phosphor screen can be used as a collector to measure a total spectrum. The acceptance angle of the UPS analyser is 90°. In the angular resolving mode it is possible to observe emission from a (100) fcc crystal in the 〈100〉, 〈110〉 and 〈111〉 directions with a fixed incident photon angle in the range 20–40° to the normal. The acceptance angle of the detector was usually ~7° but this can be varied by changing the collimating tube on the photomultipler. The direction dependent features of the d-band spectrum of clean nickel with a (100) surface have been examined. Characteristic features were observed for each of the 〈100〉, 〈111〉 and 〈110〉 directions. These are compared with those reported for crystals with the corresponding surface orientations. The effects resulting from the chemisorption of nitric oxide on this nickel crystal have also been investigated.     

Random distribution of islands explains the oscillatory intensity in He/Si(111)-(7 × 7)

It is shown that the oscillatory specular beam intensity observed in He/Si(111)-(7 × 7) scattering is consistent with a random distribution of islands of height ~3.05 Å. Each of these islands may be reconstructed, totally or partially, in a (7 × 7) structure according to the more favourable models proposed by LEED. This could be a possibility to explain, with the same (7 × 7) unit cell, He scattering and LEED experiments.     

电子衍射条件对Si(111)外延时反射式高能电子衍射强度振荡的影响

本文研究了不同电子衍射条件对Si(111)外延时的反射式高能电子衍射(RHEED)强度振荡的影响,在保持生长条件不变的情况下,沿[112]方位观测时,不同入射角下其强度振荡的相位和初始瞬态响应变化很大,甚至会发生180°相位变化,而在[011]方位观测时,其相位的变化不明显,结合Si(111)面的RHEED强度摇摆曲线测量结果,表明这种与电子衍射条件有关的振荡特性变化,实际上反映了由电子多重散射机理引起的RHEED强度振荡两种情形,对RHEED强度的初始瞬态响应机理也作了探讨。 关键词：     

The scattering of hydrogen,deuterium, and the rare gases from silver (111) single crystals

The scattering of hydrogen, deuterium, and the rare gases from the (111) face of silver has been studied at ultrahigh vacuum. The surfaces were prepared by argon ion bombardment and high temperature annealing. Incident angles between 20° and 65° and surface temperatures between room temperature and 573°K have been investigated. The scattering data exhibit quasi-elastic scattering (He, H₂, D₂), inelastic scattering (Ne, Ar, Kr), and trapping dominated scattering (Xe). Identification of these scattering regimes correlates with D/kT_g and is consistent with similar data from Pt(111) and W(110). The separate effects of microscopic surface roughness and thermal roughening have been identified and thermal attenuation in the elastic regime correlated with dynamical interactions rather than thermal roughening. Trapping and rotational coupling are discussed. Comparison of the data with scattering from epitaxial (111) silver indicates that the epitaxial surfaces are significantly more disordered than the single crystal surfaces.     

Rotationally mediated selective adsorption in rigid rotor/rigid surface scattering

We present a detailed investigation of a new effect in molecule/surface scattering, rotationally mediated selective adsorption, which has been first observed by Cowin et al. (J. Chem. Phys. 75 (1981) 1033) in rotationally inelastic HD/Pt (111) scattering. It is due to resonance between an asymptotically closed rotational channel and a vibrational bound state of the molecule/surface system. Exact close-coupling and diffractionally sudden calculations are performed for HD scattered from a rigid, flat and weakly corrugated surface. Both variation of the collision energy and variation of the incident angle are considered. In the latter case we include the averaging over the collision energy of the initial beam and compare qualitatively our results with the experiment. Taking into account the resonances below they j = 0 → 1 threshold we are able to explain all of the experimentally observed resonances and to assign them with the appropriate rotational-vibrational quantum numbers. The largest deviation between experimental and theoretical resonance angles is ~ 1.6° at a collision energy of E = 109 meV. An interesting interference effect is found in the case of weak surface corrugation. Although the diffractionally sudden approximation generally gives only poor results, it also reproduces this effect and provides a simple explanation of it in terms of the Breit-Wigner representation of the S-matrix.     

The adsorption of activated nitrogen on platinum single crystal faces

The adsorption of activated nitrogen on a stepped Pt(S)-[9(111) × (111)] face was investigated by LEED, AES and flash desorption. Nitrogen was supplied to the crystal from a high frequency discharge tube. For comparison some orienting measurements were also carried out on smooth (111) and (100) platinum faces. Activated nitrogen is adsorbed at room temperature on all three faces up to about half a monolayer coverage. No additional LEED patterns indicating long range order of the adsorbed layer were found. By flash heating a small desorption peak at 120°C and a large peak between 175 and 230°C depending on the initial coverage were observed on the (111) type faces. The desorption can be described approximately by a second order rate law with an energy of activation of 25± 3 kcal/mole. No influence of surface steps on the properties of the adsorbed layer was detected. On the (100) face two coverage independent desorption maxima at 120 and 170°C of about equal intensities were found.     

A practical cross-section for scattering from rough surfaces at very low grazing angles in both the forward and backward directions

In this paper we develop an extension of the small slope approximation (SSA) for scattering from randomly rough Dirichlet surfaces, which includes some multiple scattering. This extension is designated by SSA+. We focus on scattering at very low grazing angles where multiple scattering of both the incident and scattered fields is of importance. Numerical results for the SSA+ bistatic scattering cross-section for very low forward grazing angles are presented using the Gaussian roughness spectrum and for both very low forward and very low backward grazing angles using the Pierson–Moskowitz and modified power law spectra. The results are restricted to an angle of incidence of 80°. It is shown that when the lowest-order SSA gives reasonably accurate results, the SSA+ increases the accuracy up to at least the final 0.2° of grazing in the forward direction. In the backward direction, the SSA+ gives good results for the Pierson–Moskowitz spectrum, but the results are less dramatic.     

Double diffraction spots in RHEED patterns from clean Ge(111) and Si(001) surfaces

In RHEED patterns from clean Ge(111) and Si(001) surfaces, extra diffraction spots have been observed with superlattice reflection spots due to Ge(111) 2 × 8 and Si(001) 2 × 1 surface structures. The extra spots have not been found out in many previous LEED and RHEED patterns of clean Ge(111) and Si(001) surfaces. When the Ge(111) and Si(001) samples were rotated about an axis normal to the surfaces so as to vary the incident direction of the primary electron beam, the intensity of the extra spots showed a remarkable dependence upon the incident direction and they became invisible in some incident directions, in spite of the experimental condition that an Ewald sphere intersected reciprocal lattice rods of the extra spots. In this study, the extra spots are understood as forbidden reflection spots resulting from double diffraction of superlattice reflections of the surface structures, and the remarkable dependence of their intensity upon the incident direction is explained in terms of excitation of the surface wave of the superlattice reflections. These results suggest that the intensity of diffraction spots in RHEED patterns may be greatly influenced by the surface wave excitation of fundamental and superlattice reflections.