Dynamical Reflection High-energy Electron Diffraction Research Articles

Cooperative and competitive concurrency in scientific computing. A full open-source upgrade of the program for dynamical calculations of RHEED intensity oscillations

Cooperative and competitive concurrency in scientific computing. A full open-source upgrade of the program for dynamical calculations of RHEED intensity oscillations

Temperature dependence of Ga-assisted oxide desorption on GaAs(001)

Removal of native oxide by conventional thermal desorption causes large scale degradation of the initial surface layer. Ga assisted oxide removal at 440−500°C has been shown to reduce damage and so-called μpit formation. We examine surfaces prepared by this technique over the 400−580°C range with dynamic reflection high-energy electron diffraction (RHEED) and in situ scanning tunnelling microscopy (STM) analysis. Surfaces with oxide clusters, pure GaAs and Ga droplets are found to exist sequentially for sub-monolayer increases in Ga deposition. The STM imaging shows that two distinct, temperature dependent cleaned surfaces exist within the prescribed range. Ga mobility is believed to underpin the mechanisms that produce each surface whilst step-edge density defines the resulting pit density.

RHEED Rocking Curve Analysis of Si(111).RAD.3*.RAD.3-Ag Surface Phase Transition at Low Temperature

Si(111)√3×√3-Ag surface structural phase transition from honeycomb chained triangles (HCT) structure to inequivalent triangles (IET) structure is investigated using reflection high-energy electron diffraction (RHEED) rocking curves. Rocking curves are measured during spontaneous heating process of a cooled (∼120K) sample up to room temperature. The rocking curves were analyzed using many-beam dynamical RHEED calculations with three kinds of structural models, HCT (Ag triangle stays at mirror symmetry position), IET (Ag triangle rotates by 6 degrees) and rotating-HCT (r-HCT; Ag atoms are randomly rotating between ±6° which maintains the mirror symmetry) structures. At room and low temperatures, r-HCT and IET structures give the best results respectively. Rocking curves between room and low temperatures are also reproduced by mixing of r-HCT and IET structures and the mixing ratio changes almost linearly with substrate temperature. It is obtained that r-HCT coverage is almost 100 % at room temperature and IET coverage is about 60 % at 120 K. It is also found that mixing ratio of IET/r-HCT structure meets 0.5 at about 150 K which is known as a transition temperature in previous reports. [DOI: 10.1380/ejssnt.2006.414]

Dynamical calculations for RHEED intensity oscillations

A practical computing algorithm working in real time has been developed for calculating the reflection high-energy electron diffraction from the molecular beam epitaxy growing surface. The calculations are based on the use of a dynamical diffraction theory in which the electrons are taken to be diffracted by a potential, which is periodic in the dimension perpendicular to the surface. The results of the calculations are presented in the form of rocking curves to illustrate how the diffracted beam intensities depend on the glancing angle of the incident beam. Program summary Title of program: RHEED Catalogue identifier:ADUY Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADUY Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Pentium-based PC Operating systems or monitors under which the program has been tested: Windows 9x, XP, NT, Linux Programming language used: Borland C++ Memory required to execute with typical data: more than 1 MB Number of bits in a word: 64 bits Number of processors used: 1 Distribution format:tar.gz Number of lines in distributed program, including test data, etc.:982 Number of bytes in distributed program, including test data, etc.: 126 051 Nature of physical problem: Reflection high-energy electron diffraction (RHEED) is a very useful technique for studying growth and surface analysis of thin epitaxial structures prepared by the molecular beam epitaxy (MBE). Nowadays, RHEED is used in many laboratories all over the world where researchers deal with the growth of materials by MBE. The RHEED technique can reveal, almost instantaneously, changes either in the coverage of the sample surface by adsorbates or in the surface structure of a thin film. In most cases the interpretation of experimental results is based on the use of dynamical diffraction approaches. Such approaches are said to be quite useful in qualitative and quantitative analysis of RHEED experimental data. Method of solution: RHEED intensities are calculated within the framework of the general matrix formulation of Peng and Whelan [Surf. Sci. Lett. 238 (1990) L446] under the one-beam condition. The dynamical diffraction calculations presented in this paper utilize the systematic reflection case in RHEED, in which the atomic potential in the planes parallel to the surface are projected on the surface normal, so that the results are insensitive to the atomic arrangement in the layers parallel to the surface. This model shows a systematic approximation in calculating dynamical RHEED intensities, and only a layer coverage factor for the nth layer was taken into account in calculating the interaction potential between the fast electron and that layer. Typical running time: The typical running time is machine and user-parameters dependent. Unusual features of the program: The program is presented in the form of a basic unit RHEED.cpp and should be compiled using C++ compilers, including C++ Builder and g++.

Precursor to surface melting of Si(111) at high temperature

The surface structures of Si(111) in the temperature range between 1220 and 1540 K. in which an additional phase is discovered [Phys. Rev. Lett. 85, 5150 (2000)], have been investigated with rocking curves of reflection high-energy electron diffraction (RHEED). From the analysis using the dynamical RHEED calculation, we found that the thermal vibration of surface atoms shows an anisotropic feature, where the mean-square amplitude of the thermal vibration parallel to the surface is about twice as large as the normal component, and the amplitude is extremely enhanced around 1540 K, just below the surface melting temperature, with an enhancement of the anisotoropy. The anharmonic increase in the thermal vibration of the surface atoms plays an important role in the appearance of the additional phase around 1540 K. This result suggests that this structural phase with a large vibrational amplitude acts as a precursor to the surface melting.

Surface Dynamics of GaAs Thin Film Formation by Pulsed Laser Deposition Investigated Using RHEED

ABSTRACTPost-growth surface dynamics of epitaxial GaAs (100) thin films grown by pulsed laser deposition (PLD) have been studied using dynamic reflection high-energy electron diffraction (RHEED) in an effort to better understand the growth mechanisms present in pulsed laser deposition. Results have indicated, as expected, that processes occurring at reduced substrate temperatures manifest themselves more slowly than at elevated temperatures. This has been shown through the analysis of static RHEED images and dynamic specular beam intensity as well as profile scans.

Experimental determination of the valence band structure of the InxGa1-x-As(001) surface

InxGaj1-xAs layers were grown on GaAs(00l) substrates by molecular beam epitaxy. The structure and quality of the surface and the layer thickness were monitored in situ by dynamical reflection high-energy electron diffraction (RHEED oscillations). Angle-resolved photoemission spectroscopy studies using He-I radiation were performed on the epitaxial layers. The energy-distribution curves of the photoelectrons were determined along the high symmetric directions in the surface Brillouin zone. The experimental band structure of InxGa1-xAs was determined with the help of the experimental and theoretical band structures of GaAs and In As.

Determination of the atomic geometry of the GaAs(001)2×4 surface by dynamical RHEED intensity analysis: The β2(2×4) model

Using dynamical reflection high-energy electron diffraction (RHEED) computations, experimental RHEED rocking curves from the MBE-grown As-rich GaAs(001)2×4 surface have been analysed to provide estimates of the surface structural parameters. Ab initio total-energy computations suggest that surfaces grown in such As-rich conditions are likely to exist in the so-called β2(2×4) phase. Therefore, it is assumed that the most appropriate GaAs(001)2×4 surface model with which to analyse the experimental data is that of the β2(2×4) phase. This phase has two As dimers in the surface layer and a third As dimer in the third layer. The experimental rocking curves analysed were measured in the primary beam azimuth, permitting estimates of those β2(2×4) phase surface structural parameters in the plane perpendicular to the primary beam azimuth. The best experiment–theory fit was obtained using a standard non-linear optimisation scheme (the Marquardt algorithm). We find that by using the β2(2×4) surface model we are able to get a better fit to the experimental data than in earlier work in which the data were analysed using the β(2×4) surface model. This supports the assumption that the β2(2×4) surface model is the most appropriate to describe the surface in the As-rich MBE growth conditions used to produce the sample surface upon which the RHEED experiments were performed. Our best-fit β2(2×4) surface structure is predominantly in agreement with that obtained from a surface X-ray diffraction study and from ab initio total-energy calculations. As in these other studies, our best-fit structure shows a large in-plane relaxation of the second layer threefold coordinated Ga atoms and an outward perpendicular displacement of the first layer As dimers. The good agreement in most details between all of these independent structure determinations suggests that we now have a largely consistent picture of the structure of the GaAs(001) β2(2×4) surface.

A Two-Dimensional Bloch-Wave Method for Dynamical RHEED Calculations

A new two-dimensional Bloch-wave method is developed for dynamical reflection high-energy electron diffraction (RHEED) calculations. In this two-dimensional Bloch-wave analysis, the traverse energy and the wave field for each Bloch wave are calculated by a step-by-step R-matrix method. The accuracy of the method is critically examined in comparison with Ichimiya's method on the experimental rocking curve of an Si(001)–2 × 1 surface. It is demonstrated that two-dimensional Bloch-wave analysis can be used to elucidate the mechanism causing the peaks in rocking curves.

Electron scattering factors of ions and dynamical RHEED from surfaces of ionic crystals

Electron scattering factors of ions are represented in a parametrized form which separates the diverging Coulomb term due to ionic charge from the contribution of the screened atomic field. Using this representation it is shown how dynamical reflection high-energy electron diffraction (RHEED) calculations can be performed for ionic surfaces using conventional numerical techniques. Following the classification of ionic surfaces proposed by Tasker [Surf. Sci. 78, 315 (1979)], we analyze the effect of ionicity on RHEED intensities for three classes of ionic surfaces. In the first case both positive and negative ions are located in the same plane and this leads to the cancellation of long-range Coulomb contribution to the crystal potential. The second class of ionic surfaces consists of layers of ions having net nonzero charge. Ionic layers may be grouped into repeat units of planes of the form (anion)-(cation)-(anion) characteristic of the (111) surface of the fluorite structure so that each repeat unit satisfies the charge neutrality condition and also has zero net dipole moment perpendicular to the surface. For this class of surfaces the Coulomb term leads to unusual features in the distribution of the potential in the crystal. The third type of the termination of an ionic crystal lattice gives rise to a sequence of repeat units characterized by a nonzero net dipole moment resulting in a divergent behavior of the potential. Our calculations show that charge transfer between lattice sites occurring in an ionic crystal affects very substantially the form of RHEED rocking curves. The effect can be interpreted in terms of the change in the effective inner potential. This in turn can be used for quantitative determination of the degree of charge transfer occurring in the surface layer of an ionic crystal.

Ionicity of nickel oxide: Direct determination by reflection diffraction of high-energy electrons from the (100) surface

The degree of ionicity and the inner potential of crystalline nickel oxide have been determined by using reflection high-energy electron diffraction (RHEED) and reflection electron microscopy. By matching experimental RHEED patterns obtained from an atomically flat NiO(100) surface with dynamical RHEED calculations, we found that the degree of ionicity of this oxide is close to 0.3, and that the inner potential equals 21.21 V.

Atomic structures on a GaAs(001) surface grown by molecular beam epitaxy

A unique apparatus for in-situ atomic-resolution study of solid state structures grown by molecular beam epitaxy (MBE) is developed, in which a scanning tunneling microscope (STM) is combined with an MBE chamber within the same vacuum system. The utility of the apparatus is demonstrated by examining atomic structures on a molecular-beam-epitaxial GaAs(001) surface over a wide range of [As]/[Ga] ratios. By varying the As surface coverage, the 2×4 – α, β, γ and c(4×4) phases are examined in detail. High-resolution STM images indicate that 2×4 – α, β, and γ phases in the outermost surface layer have essentially the same unit cell consisting of two As dimers and two As dimer vacancies. Using the STM images, reflection high-energy electron diffraction (RHEED) patterns and dynamical RHEED calculations, the existing structural models for the 2×4 phases are analysed and a new model of the As-rich GaAs(001) surface is proposed, found to be consistent with most of the previous observations.

The NO-induced (1 × 2)→(1 × 1) structural transition of Pt(110): a quantitative RHEED investigation

The adsorption of NO on Pt(110) and its induced (1 × 2)→(1 × 1) structural transition was studied with quantitative reflection high-energy electron diffraction (RHEED). Time/exposure series of rocking curve sets were recorded during on-going adsorption processes. A direct evaluation focusing on the development of reflection intensities and rocking curve shapes in dependence on the NO exposure allowed dosages to be found for the most rapid structural change and for saturation. 10 sets of rocking curves from room temperature adsorption were quantitatively evaluated using an automated fitting procedure in conjunction with dynamic RHEED theory to determine the values of a comprehensive set of structural parameters for the substrate and the adsorbate. We found considerable changes of the Pt relaxations just prior to the transition from the (1 × 2) missing-row reconstruction into the (disordered) (1 × 1) structure. As long as the substrate is (1 × 2) reconstructed, NO adsorbs on bridge sites on the first Pt layer and on hollow sites on the (111) microfacets while in the case of the (1 × 1) structure first-layer top sites are occupied too. As soon as the transition begins, the rearrangement of the first Pt layer provides for additional vacant bridge and top sites in the second layer. These are then occupied while the hollow sites loose their population.

Approximate Methods in Dynamical RHEED Calculations

Approximate methods have been examined in the context of dynamical reflection high-energy electron diffraction (RHEED) calculations using two-dimensional Bloch waves. These approximate methods include Bethe potentials, the utilization of the block structure of the scattering matrix and the perturbation treatment of anomalous absorption effects. It is shown that the use of Bethe potentials provides a very efficient and accurate means for dealing with evanescent waves and numerical examples show that the use of Bethe potentials speeds up the calculations typically more than 15 times. The other two methods examined are less powerful and the improvement in computation efficiency varies from 30 to 60%. It is found that in general the perturbation method for dealing with anomalous absorption effects does not work with high precision.

Surface structure of GaAs(001)-(2 × 4) α, β and γ phases

The As-rich GaAs(001)-(2 × 4) α, β and γ phases grown by molecular-beam epitaxy (MBE) and migration enhanced epitaxy (MEE) have been investigated by field ion-scanning tunneling microscopy and in-situ reflection high-energy electron diffraction (RHEED). The high-resolution STM images show that the α, β and γ phases all have the same unit structure in the outermost surface layer which consists of two As dimers and two As dimer vacancies. The structure models are examined based on the STM observations and dynamical RHEED calculation. We propose a new structure model: The α phase is the two-As-dimer model proposed by Farrell and Palmstrom with relaxation incorporated by Northrup and Froyen. The β phase is the two-As-dimer model proposed by Chadi. The γ phase consists of the local structure same as the β phase and the open areas with a disordered As double-layer structure similar to that of the c(4 × 4) phase.

Surface structure of GaAs(001)-(2×4) α, β and γ phases

The As-rich GaAs(001)-(2 × 4) α, β and γ phases grown by molecular-beam epitaxy (MBE) and migration enhanced epitaxy (MEE) have been investigated by field ion-scanning tunneling microscopy and in-situ reflection high-energy electron diffraction (RHEED). The high-resolution STM images show that the α, β and γ phases all have the same unit structure in the outermost surface layer which consists of two As dimers and two As dimer vacancies. The structure models are examined based on the STM observations and dynamical RHEED calculation. We propose a new structure model: The α phase is the two-As-dimer model proposed by Farrell and Palmstrom with relaxation incorporated by Northrup and Froyen. The β phase is the two-As-dimer model proposed by Chadi. The γ phase consists of the local structure same as the β phase and the open areas with a disordered As double-layer structure similar to that of the c(4 × 4) phase.

Systematic study of PbTe (111) molecular-beam epitaxy using reflection high-energy electron-diffraction intensity oscillations

Molecular beam epitaxy of PbTe on BaF2 (111) is studied using reflection high-energy electron diffraction (RHEED). The influence of growth parameters (substrate temperature and growth rate) on surface kinetics and the steady-state growth surface morphology is investigated employing dynamical RHEED measurements (RHEED oscillations). For a well adjusted stoichiometric PbTe beam flux composition, two-dimensional layer-by-layer growth can be achieved from substrate temperatures as high as 410 °C down to temperatures below 95 °C, with a maximum number of 230 RHEED oscillations observed at substrate temperatures in the 160 °C range. At temperatures above 400 °C, the growth kinetics start to be modified by PbTe reevaporation from the layer surface. The dependence of the RHEED oscillations on substrate temperature and growth rate indicates the importance of adatom surface diffusion for the surface morphology developed under steady-state growth conditions, and for all growth conditions, a close correlation between steady-state growth surface step density and damping of RHEED oscillations is observed. Furthermore, it is shown that even very small changes in the beam flux composition have a dramatic influence on the RHEED intensity oscillations as well as the surface processes involved in the growth. With only a small additional Te2 flux used for the growth, an abrupt growth mode transition from layer-by-layer to step flow growth is induced. This is the first evidence that PbTe molecules impinging on the layer surface do not dissociate upon adsorption, but remain in a molecular state until incorporated in the crystal lattice.

Origin of phase shift phenomena in RHEED intensity oscillation curves

A phase shift of reflection high-energy electron diffraction (RHEED) intensity oscillations, which is interpretable neither by kinematic diffraction theory nor by a previously adopted “step density” approach, is shown to be derivable by dynamical RHEED calculations. Using a steplike potential for each uncompleted grown layer, we give a simple model for the derivation of the phase shift in RHEED oscillations, which is then checked against the results from a more realistic model. We show that the potential of a grown surface layer plays an important role in the phase shift and frequency doubling, and that the phase shift observed is a property of surfaces with high nucleation densities.

The effect of the surface on thermal diffuse intensities in reflection high energy electron diffraction

The contributions of bulk and surface vibrational excitations to thermal diffuse scattering (TDS) in reflection high energy electron diffraction (RHEED) patterns are investigated. It is shown that the surface phonon contribution to the differential cross-section for TDS is comparable to that from bulk phonons. Many-beam dynamical TDS RHEED calculations are presented, and both the positions and heights of diffuse peaks are shown to differ appreciably from predictions of kinematical TDS RHEED theory

A treatment of RHEED from a rough surface of a crystal by an optical potential method

The general formalism of the optical potential method has been applied to the problem of reflection high energy electron diffraction (RHEED) from the rough surface of a crystal. For the case where short-range disorder dominates an explicit analytical expression for the effective absorption potential has been obtained, and procedures for evaluating this potential have been developed which utilize the conventional approaches and computer routines developed earlier for transmission high energy electron diffraction (THEED). This potential has been combined with dynamical RHEED calculations for a molecular beam epitaxy (MBE) growing surface. It is found that under certain circumstances the optical potential due to the roughness of the MBE growing surface has an appreciable effect on the shape of the corresponding RHEED rocking curve.