I. Bartoš

Electronic structure of crystals via VLEED

Abstract Dispersion relations E (k) of electrons in crystals preserve their meaning in many-electron systems. Interacting electrons become quasiparticles, which apart from energies, are also characterised by lifetimes. As for real systems these characteristics are difficult to evaluate, some experimental evidence is desirable. Attention will be focused on two methods applicable at energies above the vacuum level. Interaction of external beam of slow electrons with crystals in target current spectroscopy (TCS), and in very low energy electron diffraction (VLEED), will be discussed in context with the unoccupied part of the electronic band structure. Knowledge of electron dispersion relations above the vacuum level is important for interpretations of angular resolved photoelectron spectroscopy. Comparison of experimental TCS and VLEED data with theoretical band structure calculations determines positions of energy gaps and more detailed theoretical interpretations of the intensity profiles provides information about electron lifetimes in metals and semiconductors.

Cu(111) SURFACE RELAXATION BY VLEED

Very-low-energy electron diffraction (VLEED) intensities from a clean Cu(111) surface have been measured in detail in the energy range 15–100 eV by low-energy electron microscope (LEEM). This enabled the elimination of possible disturbances due to stray magnetic fields. Corresponding theoretical I–V curves have been obtained in good agreement with experimental data when an image-type surface barrier and anisotropy of the electron attenuation were taken into account. The reliability factor analysis indicates a slight expansion of the topmost interatomic spacing of Cu(111) relative to its bulk value.

Polarity of semipolar wurtzite crystals: X-ray photoelectron diffraction from GaN{101¯1} and GaN{202¯1} surfaces

Polarity of semipolar GaN(101¯1) (101¯1¯) and GaN(202¯1) (202¯1¯) surfaces was determined with X-ray photoelectron diffraction (XPD) using a standard MgKα source. The photoelectron emission from N 1s core level measured in the a-plane of the crystals shows significant differences for the two crystal orientations within the polar angle range of 80–100° from the 〈0001〉 normal. It was demonstrated that XPD polar plots recorded in the a-plane are similar for each polarity of the GaN{101¯1} and GaN{202¯1} crystals if referred to 〈0001〉 crystal axes. For polarity determinations of all important GaN{h0h¯l} semipolar surfaces, the above given polar angle range is suitable.

Angle - resolved photoemission study of two phases of the GaAs(100)-c(4×4) surface

We prepared two surface phases of the Ga(001)-c(4×4) reconstruction (α, β) by molecular beam epitaxy (MBE) using As4 and As2 molecular beams and examined the surfaces by angle-resolved ultraviolet photoelectron spectroscopy (UPS) and core level photoelectron spectroscopy with the synchrotron radiation as the excitation source. It is demonstrated that the photoelectron spectroscopy can distinguish between the phases. Appearance of intensive surface state 0.5 eV below the top of the valence band at lower energies is linked to the presence of the β-phases on the surface while in the α-phase spectra the peak is missing. Both As 3d and Ga 3d photoelectron lines show substantial differences between the phases in line shapes as well as in their deconvoluted components. The 3d data are in agreement with different surface composition and atomic structure of both phases.

Relation Between Surface Crystallography and Surface Electron Structure of the Superlattice

Profound gradual changes of surface state energies were predicted for varying surface terminations of the periodic crystal potential in one-dimensional models.1 This situation can be realized in superlattices with different thicknesses of topmost layers. For the ideally terminated (100) surface of a very thin superlattice (GaAs)2(AlAs)2, the shift of the energy of the surface state over the whole minigap in the lower part of the valence band has been found for different terminations of the topmost layer. In the center of the surface Brillouin zone the surface state shift follows model trends. The changes of the energy distribution of photoemitted electrons as determined from the one-step photoemission calculation2 indicate that experimental observation by the surface-sensitive technique of angle-resolved photoemission should be feasible, and preliminary data indicate this. The results show a straigthforward tuning of surface electron structure by geometrical means.

A theoretical investigation of photoemission spectra from (GaAs)2(AlAs)2 superlattices

Abstract We calculated photoemission spectra within the one-step model for the (001) surface of the (AlAs) 2 (GaAs) 2 superlattice structure. The purpose is to discriminate between spectral features which are caused by the surface, and those which are characteristic properties of the superlattice. Direct transitions indicate the opening of band gaps at the Brillouin zone edge, which are characteristic for the modified periodicity of the superlattice. Furthermore, the layer resolved photocurrent shows that one can also identify excitations from AlAs which are hidden below the first two GaAs layers and from As atoms at the boundary between the different semiconductors. Furthermore, emissions from surface states and resonances are also recognized.

Cu(111) Electron Band Structure and Channeling by VLEED

Very-low-energy electron diffraction (VLEED) intensities from clean Cu(111) surface have been measured in detail in the energy range 15 to 35 eV by low-energy electron microscope. Corresponding theoretical I-V curves are obtained in good agreement with experimental data when the anisotropy of the electron attenuation is taken into account. The coincidence of the peaks in the I-V curves at normal incidence with two kinds of energy gaps of the electron band structure of the copper crystal (Ek d =0) is interpreted. The small width of the resonance peak in the I-V curve at normal incidence is explained in terms of electron surface channeling. VLEED thus provides information about the unoccupied part of the electron band structure of copper which complements that obtained from angular resolved photoemission.

Photoemission from Al(100): experiment and one-step theory

Experimental and theoretical study of angle resolved photoemission from the Al(100) surface is presented. Photoelectron spectra are calculated with an ab initio one-step theory of photoemission within the augmented plane wave formalism and are found to be in excellent agreement with the experiment. The lifetime of the (100) surface state and the photon energy dependence of the intensity of photoemission from the surface state are determined. The treatment of inelastic scattering by the optical potential within the one-step theory perfectly describes the surface sensitivity of the photoemission from Al(100) for energies up to 100 eV.

Edges of two-dimensional electron systems under strong magnetic fields

Abstract Two-dimensional electron systems, which exist e.g. at interlaces between two different semiconductors, exhibit interesting physical properties under strong magnetic fields. In interpreting the quantum Hall effect the role of one-dimensional system edges begins to be taken into account. The electron structure, connected with Landau quantization of 2D electron states under magnetic field, has been studied in the vicinity of system edges. Model systems with abrupt confinement barriers exhibit electron dispersions with edge plateaus above the barrier tops, accompanied by regions of substantially reduced gaps between neighbouring Landau branches. Selfconsistent results for smoothly confined systems provide alternating channels of compressible and incompressible Fermi liquids along the system edges. Recent investigation illustrates the transition between the two limiting confinement barrier cases. In order to evaluate the Hall conductivity, the Kubo formula has been adopted in a straightforward manner to two-dimensional stripes confined by arbitrary barriers. Total deviation of the Hall conductivity from the integer values is given by the product of two factors: the geometrical factor is inversely proportional to the sample width and the edge factor is proportional to the derivative of the electron dispersion at the Fermi level and is thus governed by the shape of the confinement barrier. The deviations have been evaluated for model systems of various widths and a qualitative agreement with recent experimental data for quantum wires has been found. The formulas provide also current densities and this enables to investigate spatial distributions of the electron current across the Hall stripes. Application to the abruptly confined model shows that the quantized part of the total current takes place within the interior of the stripe whereas the edge currents distribution is affected by the confinement barrier.

Simple edge-state models of two-dimensional electron gas in magnetic field

Abstract Electron states localized to the edges of the twodimensional electron gas in perpendicular magnetic field are investigated on simple models. Two kinds of states are discussed: states which only exist due to the magnetic field and states which are localized to edges even in the absence of the magnetic field. Methods, enabling to treat cases with comparable strengths of the magnetic and crystalline potential fields, are used. Interesting behaviour of electron structure dispersions, consisting in flat plateau regions closely approaching the neighbouring branches has been found.