LEED Spectra Research Articles

Multi-slice finite difference method for full potential calculation of low energy electrondiffraction spectra

We propose a multi-slice finite difference method for full potential calculation of low energyelectron diffraction spectra. This method keeps the accuracy of the original finite difference(FD) method but reduces the required storage memory and computation time by morethan two orders of magnitude. The gain in speed and reduction in memory requirementallow, for the first time, full potential LEED spectra calculations to be carried out for manyrealistic systems. In this method, the unit cell of a crystal is divided into thinslices in the depth direction. The reflection and transmission coefficients of eachslice are calculated by the FD method. The final reflectivity of the crystal isobtained by combining contributions from all slices using a simple recurrent formula.

A COMPARISON OF LEED CALCULATIONAL METHODS FOR STEPPED SURFACES

Several methods for calculating LEED spectra from stepped surfaces, including layer doubling and transfer matrix (CHANGE), are compared for calculations of LEED spectra from vicinal (stepped) surfaces with their narrow spacings between planes. A particular type of failure which occurs only for certain spacings from top bulk layer to bottom surface layer is analyzed.

Advances in direct and diffraction methods for surface structural determination

I describe recent advances in low-energy electron diffraction holography and photoelectron diffraction holography. These are direct methods for determining the surface structure. I show that for LEED and PD spectra taken in an energy and angular mesh, the relative phase between the reference wave and the scattered wave has a known geometric form if the spectra are always taken from within a small angular cone in the near backscattering direction. By using data in the backscattering small cone at each direction of interest, a simple algorithm is developed to invert the spectra and extract object atomic positions with no input of calculated dynamic factors. I also describe the use of a convergent iterative method of PD and LEED. The computation time of this method scales as N 2, where N is the dimension of the propagator matrix, rather than N 3 as in conventional Gaussian substitutional methods. Both the Rehr–Albers separable-propagator cluster approach and the slab-type non-separable approach can be cast in the new iterative form. With substantial savings in computational time and no loss in numerical accuracy, this method is very useful in applications of multiple scattering theory, particularly for systems involving either very large unit cells (>300 atoms) or where no long-range order is present.

Segregation-induced surface structures of carbon-doped Mo 0.75Re 0.25(100)

The carbon segregation at the Mo 0.75Re 0.25(100) surface was investigated by means of AES and quantitative LEED structure determination. The equilibrium surface carbon concentration is found to be a function of the bulk concentration and the annealing temperature. With increasing surface carbon concentration four different phases have been observed: c(2 × 2), (3 × 3)diag, p(1 × 1), (1 × 1) s. The two (1 × 1) phases differ substantially both by Auger amplitudes and LEED spectra which makes evident that they indeed correspond to different structural phases. Quantitative LEED structure determination of the c(2 × 2) and (1 × 1) phases reveals the occupation of top layer hollow sites by carbon. In the case of the (1 × 1) s phase carbon atoms reside additionally in subsurface octahedral interstitial sites. There is good theory-experiment agreement as mirrored by a best fit Pendry R-factor of ≤ 0.23 for the three structures.

On the calculation of LEED spectra from stepped surfaces

Atomic steps are known to influence strongly many physical and chemical properties of surfaces and hence are attractive candidates for structural determinations by low energy electron diffraction. However, stepped surfaces present a difficult challenge to traditional computation methods because a huge plane wave basis is required to cope with both the large primitive mesh and the small interlayer spacing perpendicular to the surface. We present a new solution to the multiple scattering equations which overcomes the convergence problems of conventional techniques through the use of a three-centre layer doubling algorithm, and has permitted the calculation of converged diffraction spectra from Rh(321) and Rh(331) surfaces.

P-type overdoping at clean Si(111) surfaces upon vacuum annealing

Clean cleaved Si(111) samples have been heated under uhv at temperatures up to 1150°C. LEED, AES and photoemission yield spectra (PYS) have been measured. The (7 × 7) reconstructured surface shows an increasing p-type doping which satures at a concentration of 2(±1) × 10 19 cm −3 over a depth which does not exceed a few tens of Å with no evidence of any specific impurity.

One-dimensional multiple scattering model for normal photoelectron diffraction

A one-dimensional multiple scattering model is used to construct a model for normal photoelectron diffraction (NPD). The model which is an extension of earlier work on NPD and which we recently applied to LEED with some success, proves successful in interpreting experimental NPD data of Se(3d), S(2p) and O(1s) on Ni(001). The model can be used to rapidly estimate NPD structural parameters such as d from experimental data. In addition, we exhibit NPD spectra for the fictitious adsorbate Ni(001)Ni and Cu(001)Cu systems. When these spectra masquerade as LEED spectra, they exhibit the observed secondary peaks absent in the simple one-dimensional calculated LEED spectra but present experimentally. This calculation complements our previous work showing how the normal geometry LEED data on Ni(001) and Cu(001) can be described in a one-dimensional model.

Leed study of Fe epitaxially grown at 190°C on Cu(100)

We report a LEED study of iron deposited on Cu(100) at 190°C. Very sharp LEED patterns were obtained for high iron coverages. We observed evidence of an ill defined Fe/Cu interface for one monolayer of iron deposited at 190°C. The stability of the iron overlayers was tested as a function of time for various coverages. For one monolayer the intensity versus energy curve for the (00) beam shows time dependence at 190°C. For four layers, no significant changes were observed in the LEED spectra over a period of one hour. We measured for five layers of iron a top layer expansion of 2.8% relative to the bulk. The interplanar spacing for bulk fcc Fe at 190°C remains equal to the room value. In these experiments the samples were deposited at 190°C and kept at this temperature during the LEED measurements.

LEED intensities of TiSe 2 including off-normal electron incidence

LEED spectra from the (001) surface of ITTiSe 2 are measured and calculated for various diffracted beams including off-normal electron incidence. Normal incidence data confirm former work concerning the potential model and the surface relaxation. Slight deviation from normal incidence causes pronounced variations in the calculated spectra yielding a better understanding of the experimental results. The effect of distinct off-normal incidence was examined for the (00) beam.

Electronic structure of chemisorbed formate layers on copper surfaces

Much can be learned about the bonding of adsorbates on transition- and noble-metal surfaces from calculations of the electronic structure of chemisorbed overlayers on thin slabs. We demonstrate the technique here applied to formate on copper {110} and {100} surfaces. After consideration of the molecular orbitals of the free formic acid and formate radicals, we show the changes in electronic structure accompanying chemisorption in the various potential surface sites suggested by LEED, X-ray absorption, and vibrational spectra. For both atop and bridge sites occupied adsorbate bands fall into three main groups, 12 (4a1), 9 (5a1, 3b1, 1b2) and 5 (1a2, 6a1 and 4b1) eV below EF, close to the peaks seen in photoemission studies; the closest agreement is probably for the formate in bridge sites, oriented along [110] with its oxygen atoms almost directly above surface copper atoms.

Computation of TiSe 2 LEED spectra

The LEED spectra of 1T-TiSe 2 are calculated numerically and compared with experimental data. Ionic properties of the compound are simulated in the calculations by overlapping muffin-tin potentials and confirmed by the final results. The variation of the spectra with surface parameters and the deduced available range of these quantities are reported.

Interpretation of a threshold effect on Al(001) in terms of the discontinuity of non-specular beam intensities at grazing emergence

A widely known threshold effect in very low energy electron diffraction (VLEED) is the appearance of rapid oscillations of diffracted intensities just before the emergence of one or several diffracted beams. Their maxima and minima are arranged in a Rydberg-like series due to the coulombic long range behaviour of the surface potential barrier. Another curious consequence of this behaviour is the discontinuity of non-specular beam intensities at their emergence threshold. Contrarily to the prediction of the classical LEED theory, non-specular beams appear in vacuum with a non-zero current. Although this discontinuity has already been theoretically predicted, it has never been noticed in measured LEED spectra. However, measurements of current transmitted from crystal to ground performed by Henrich on Al(001) near the normal incidence show the existence of such a discontinuity. At about 18.5 eV, four new diffracted beams emerge from the crystal and thus the backscattered electron discontinuity induces a discontinuity in the transmitted current. In this paper, VLEED spectra on Al(001) near normal incidence are reinvestigated in details. In order to take into account the energy spread of the incident beam, calculated VLEED spectra are convoluted with a gaussian distribution. In this way, they can be compared with experimental spectra. The rapid Rydberg-like oscillations are completely smoothed and the discontinuity effects subsist alone in convoluted spectra. These effects are actually large at normal incidence for which four beams simultaneously emerge. In accordance with Henrich's observations, they disappear as soon as the incident beam deviates from normal incidence.

Impurity effects in the adsorption and dissociation of CO 2 on Rh

The adsorption and dissociation of CO2 on Rh(111) and Rh foil surfaces have been studied in UHV using Auger electron, electron energy loss (in the electronic range) and thermal desorption spectroscopy. CO2 adsorbs weakly with a low sticking probability on clean Rh samples at 110 K. The adsorption is accompanied by the appearance of a loss feature at 14 eV. The adsorption of CO2 took place in two stages, with Tp = 244–233 K (α) and 170 K (β). Adsorption of 180 L CO2 at 3 × 10−7 Torr on clean Rh(111) at 300 K produced no observable changes in the LEEd, Auger electron, EEL or TD spectra and there was no indication of the dissociation of CO2 either. Similar results were obtained for a clean Rh foil. However, boron impurity segregated on the surface of Rh exerted a dramatic influence on the adsorptive properties of this surface and caused the dissociation of CO2 at 270–300 K. This was exhibited by the appearance of an intense loss in the EEL spectrum due to chemisorbed CO, by the buildup of surface oxygen and by the thermal desorption of CO at higher temperatures.

Structure determination of the clean Co(112̄0) surface by LEED

The atomic structure of the (112̄0) surface of cobalt has been determined by LEED using six intensity spectra at normal incidence. The surface exhibits the truncated bulk structure with a contraction of the first interlayer spacing by about 8.5% with respect to the bulk value. Quantitative evaluation of the LEED spectra was done using Zanazzi and Jona's and Pendry's r-factors. The minimum averaged r-factors are r ZJ = 0.09 and r P = 0.22 . No change of the interatomic distances within the plane could be detected and no rearrangement of the surface structure takes place up to temperatures shortly below the transition temperature.

LEED intensity analysis of epitaxial Ag/Au systems. I. the influence of the single ion-core scattering on the LEED spectra

In order to apply the LEED intensity analysis to Ag/Au epitaxial systems the differences in the ion-core scattering of Ag and Au atoms are investigated and their influence on the calculated LEED spectra is analyzed. Although the phase of the atomic scattering factor is important for the superposition of the waves scattered by individual atoms, the LEED spectra reflect the qualitative features of the different ion-core scattering cross sections. Approximations neglecting the intralayer multiple scattering or the partial wave expansion are not applicable to preliminary assessments to trial structures containing Ag or Au atoms. Um die LEED-Intensitätsanalyse auf epitaktische Ag/Au-Systeme anzuwenden, werden die Differenzen der lonenrumpfstreuung der Ag- und Au-Atome untersucht und ihr Einfluß auf die berechneten LEED-Spektren analysiert. Obwohl die Phase des atomaren Streufaktors für die Überlagerung der an den einzelnen Atomen gestreuten Wellen wesentlich ist, spiegeln die LEED-Spektren die qualitativen Merkmale der verschiedenen Atomstreuquerschnitte wider. Approximationen, die die Intraschicht-Mehrfachstreuung oder die Partial Wellenentwicklung vernachlässigen, sind für vorläufige Abschätzungen von Modellstrukturen, die Ag- oder Au-Atome enthalten, nicht anwendbar.

The reliability of LEED I-V spectra: incidence angle errors and symmetry effects on W (100)(1*1)

A recently published assessment of the reproducibility of experimental LEED intensity data from the tungsten (100)(1*1) surface by Stevens and Russell (1981) is evaluated. I-V curves are presented which suggest that the independently obtained LEED spectra which they compared, including their own, were not at precisely normal incidence, this being the major cause of the differences among the curves. The importance of a valid criterion for establishing normal incidence is emphasised, especially when studying subtle changes in surface-structure symmetry. This is demonstrated by data which suggest the W(100) surface above 370K shows a very subtle loss of mirror-plane symmetry in the direction parallel to the steps existing on the crystal surface studied. Just as below 370K the observed 2 mm point group symmetry of the ( square root 2* square root 2)R45 degrees structure can be attributed to a preferred orientation of p2mg domains, this apparent 1 m point group symmetry of the (1*1) structure is suggested to be a direct step-induced preference for one p1m1 orientation rather than a consequence of deviations from normal incidence.

Energy shift procedure for the inner potential in LEED crystallography

The accuracy of the assumption that LEED spectra for differing inner potentials can be found by shifting calculated spectra along the energy axis is studied. The spread in angle of refraction in typical conditions up to angle of incidence θ = 25° is shown to be small. The variation of θ with energy that minimizes the spread is found. Statistical analysis of data from three different surface structures shows the assumption to be adequate at least up to θ = 25°.

Fast LEED intensity measurements with a video camera and a video tape recorder

The measurement of LEED intensities with a TV camera-computer system, which has been published in an earlier paper, is reported to be improved with respect to the speed of data collection by a factor of about 102. Other properties such as sensitivity, reliability and handling facility have also been improved. The new measuring mode, which applies a video tape recorder, allows the simultaneous measurement of all appearing diffraction spots down to a beam current of 10−11 A with a rate of 50 energy points/s. This pushes the total measuring time for LEED spectra to the order of seconds and makes possible to monitor non-stable surfaces. As an example intensity measurements for different adsorption stages of hydrogen on W(100) are presented.

The clean thermally induced W {001} (1 × 1) → (√2 × √2) R 45° surface structure transition and its crystallography

A (√2 × √2)R45° surface structure on W {001} produced only by cooling below ~370 K, first reported by Yonehara and Schmidt, has been investigated by LEED, AES, work function change, characteristic loss and low energy Auger fine structure measurements. No significant changes at any energy up to 520 eV occur in the standard Auger spectrum upon cooling to 220 K for as long as 30 min after a flash to >2 500 K. The work function of the (√2 × √2) R45° at 210 K is 20 ± 10 mV below that of the (1 × 1) surface, and a sensitive feature in the fine structure of the N 7VV AES transition shows approximately 60% attenuation. Unlike for H 2 adsorption, the “surface plasmon” loss peak exhibits little if any measurable attenuation and no measurable shift in energy as the crystal cools to form the (√2 × √2)R45°. The rate of intensity buildup in the 1 2 -order LEED beams is strictly temperature dependent, and significant differences exist between the 1 2 -order LEED spectra produced by cooling and those produced by H 2 adsorption. Only 2-fold symmetry was observed in the LEED beam intensities at exactly normal incidence, rather than 4-fold as expected for statistically equal numbers of rotationally equivalent domains. The LEED I- V spectra for 24 fractional order beams and 12 integral order beams, taken over large energy ranges at normal incidence, clearly establish that the beam intensities display 2 mm point group symmetry, and hence a preference of one domain orientation over the other. No beam broadening or splitting effects were apparent, implying only incoherent scattering from the various domains. The half-order beam spectra (± h/2, ± h/2) are identical in relative intensity to the (± h/2, ± h/2) spectra but different in absolute intensity by a constant factor, which can be explained only by domains with p2mg space group symmetry rather than just p2mm. Adsorption of H 2 onto the cooled (√2 × √2)R45° structure restores the 4-fold symmetry in the LEED beam intensities at normal incidence, giving a c(2 × 2) hydrogen structure, the same as when adsorbing H 2 onto the above room temperature (1 × 1) crystal. This strongly supports the observed p2mg symmetry as being a true property of the cooled (√2 × √2)R45° surface structure. These results show that the (1 × 1) → (√2 × √2) R45° transition produced by cooling is a transition involving displacement of surface W atoms, and that it apparently can be characterized as an order-order, second degree, homogeneous nucleation process, which is strongly prohibited by the presence of impurities or defects.

LEED analysis of the Co{001}c(2 × 2)O structure

A LEED intensity analysis of the c(2 × 2) structure obtained upon adsorption of oxygen gas on Co {00l} is reported. Three structural models have been tested on the basis of a total of 13 LEED spectra for three angles of incidence and one azimuth. The correct model has oxygen atoms chemisorbed in the four-fold symmetrical hollows formed by four adjacent substrate atoms. Atomic arrangement and metal-oxygen distances are analogous to those found in Ni{001}c(2 × 2)O.