Bloch waves and multislice in transmission and reflection diffraction

1990 ◽  
Vol 46 (1) ◽  
pp. 11-32 ◽  
Author(s):  
Y. Ma ◽  
L. D. Marks
Keyword(s):  
Surface Potential ◽  
Incidence Angle ◽  
High Energy ◽  
Potential Scattering ◽  
Stationary Solutions ◽  
Bloch Wave ◽  
Picard Iteration ◽  
High Energy Electron ◽  
Reflected Wave ◽  
Transmission And Reflection

The consistency between Bloch-wave and multislice approaches to calculating high-energy electron diffraction is investigated in both transmission and reflection cases, the emphasis being upon the latter. It is first shown, in more detail than previously published, that in transmission the two yield identical results. Next, the Bloch-wave approach for reflection is shown to yield a stationary solution in multislice, except for a small effect from the surface truncation. It is pointed out that the multislice approach can be exploited to solve exactly for the reflected wave for an arbitrary surface potential by using it as a Picard iteration solution of the Schrödinger equation. The surface potential scattering is not incidence-angle related and is not significant as might be expected. The introduction of absorption improves the consistency between the two methods. Finally, the stationary solutions are compared with solutions obtained using a top-hat incident wave. The latter approach leads to partially stationary solutions, although it is very hard to identify these.

A Stationary Solution of High-Energy Electron Reflection (HEER) for An Arbitrary Surface

1990 ◽  
Vol 48 (2) ◽  
pp. 374-375
Author(s):  
YIQUN MA
Keyword(s):  
Stationary Solution ◽  
High Energy ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
High Energy Electron ◽  
Bulk Materials ◽  
Periodic Surface ◽  
Electron Transmission ◽  
Electron Reflection ◽  
Long Time

For a long time, the development of dynamical theory for HEER has been stagnated for several reasons. Although the Bloch wave method is powerful for the understanding of physical insights of electron diffraction, particularly electron transmission diffraction, it is not readily available for the simulation of various surface imperfection in electron reflection diffraction since it is basically a method for bulk materials and perfect surface. When the multislice method due to Cowley & Moodie is used for electron reflection, the “edge effects” stand firmly in the way of reaching a stationary solution for HEER. The multislice method due to Maksym & Beeby is valid only for an 2-D periodic surface.Now, a method for solving stationary solution of HEER for an arbitrary surface is available, which is called the Edge Patching method in Multislice-Only mode (the EPMO method). The analytical basis for this method can be attributed to two important characters of HEER: 1) 2-D dependence of the wave fields and 2) the Picard iteractionlike character of multislice calculation due to Cowley and Moodie in the Bragg case.

Computer studies on reflection high-energy electron diffraction from the growing surface of Ge(001)

2013 ◽  
Vol 46 (4) ◽  
pp. 1024-1030 ◽  
Author(s):  
Zbigniew Mitura
Keyword(s):  
Experimental Data ◽  
Electron Diffraction ◽  
High Energy ◽  
Bloch Wave ◽  
Energy Electron ◽  
High Energy Electron ◽  
Homoepitaxial Growth ◽  
Scattering Potential ◽  
Computer Studies ◽  
Quantitative Explanation

The results of calculations of reflection high-energy electron diffraction intensities, measured at different stages of the homoepitaxial growth of Ge(001), are described. A two-dimensional Bloch wave approach was used in calculations of the Schrödinger equation with a one-dimensional potential. The proportional model was used for partially filled layers,i.e.the scattering potential was taken to be proportional to the coverage and the potential of the fully filled layer. Using such an approach, it was shown that it is possible to obtain valuable information for the analysis of experimental data. The results of these calculations were compared with data for off-symmetry azimuths from the literature, and satisfactory agreement between the theoretical and experimental data was found. Also assessed was whether developing more advanced models (i.e.going beyond the proportional model), to make a more detailed account of the diffuse scattering, might be important in achieving a fully quantitative explanation of the experimental data.

Why the Bloch Wave Solution for Reflection Fails on the Au(110) Surface

1990 ◽  
Vol 48 (2) ◽  
pp. 372-373
Author(s):  
YIQUN MA
Keyword(s):  
Electron Diffraction ◽  
Wave Solution ◽  
Incident Angle ◽  
High Energy ◽  
Bloch Wave ◽  
Energy Electron ◽  
Wave Method ◽  
High Energy Electron ◽  
Real Potential ◽  
Electron Reflection

The Bloch wave method has been widely used for interpreting reflection high energy electron diffraction (RHEED) patterns and the consistency between the theory and high energy electron reflection (HEER) experiments has been claimed by different authors. The recent rigorous investigation on the consistency between the Bloch wave method and the multislice approach due to Cowley and Moodie in the reflection case for Au(001) surface has also provided a clear theoretical proof for the validity of the Bloch wave method in reflection case. However, a severe deviation of the Bloch wave solution for the Au(110) surface in the reflection case from the stabilized solution of its multislicing via the multislice iteration has recently revealed by the BMCR method (Bloch wave + Multislice Combined for Reflection).Fig.1 shows the results calculated for the Au(110) surface using the BMCR method. The incident angle is 30mRad and the absorption is included by taking the imaginary potential as 10% of the real potential in both the Bloch wave and multislice calculation.

Bloch-wave solution in the Bragg case

1989 ◽  
Vol 45 (2) ◽  
pp. 174-182 ◽  
Author(s):  
Y. Ma ◽  
L. D. Marks
Keyword(s):  
Electron Diffraction ◽  
Current Flow ◽  
High Energy ◽  
Bloch Wave ◽  
Zone Axis ◽  
Wave Method ◽  
High Energy Electron ◽  
Stepped Surfaces ◽  
Reflection Electron Microscopy ◽  
Wave Phenomena

The Bloch-wave method for reflection diffraction problems, primarily electron diffraction as in reflection high-energy electron diffraction (RHEED) and reflection electron microscopy (REM), is developed. The basic Bloch-wave approach for surfaces is reviewed, introducing the current flow concept which plays a major role both in understanding reflection diffraction and determining the allowed Bloch waves. This is followed by a brief description of the numerical methods for obtaining the results including specific results for GaAs near to the [010] zone axis. A number of other Bloch-wave phenomena are also discussed, namely resonance diffraction and its relationship to internal and external reflection and variations in the boundary conditions and Bloch-wave character, splitting of diffraction spots due to stepped surfaces, which can be completely explained, and the reflection equivalent of thickness fringes.

Parabolas from Reconstructed Surfaces Observed in Convergent-Beam RHEED Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 398-399
Author(s):  
M. Gajdardziska-Josifovska
Keyword(s):  
Electron Microscopy ◽  
High Energy ◽  
Two Dimensional ◽  
High Energy Electron ◽  
Reflection And Transmission ◽  
Experimental Diffraction Pattern ◽  
Surface Resonance ◽  
Reconstructed Surfaces ◽  
Reflection Electron Microscopy ◽  
Convergent Beam

Parabolas have been observed in the reflection high-energy electron diffraction (RHEED) patterns from surfaces of single crystals since the early thirties. In the last decade there has been a revival of attempts to elucidate the origin of these surface parabolas. The renewed interest stems from the need to understand the connection between the parabolas and the surface resonance (channeling) condition, the latter being routinely used to obtain higher intensity in reflection electron microscopy (REM) images of surfaces. Several rather diverging descriptions have been proposed to explain the parabolas in the reflection and transmission Kikuchi patterns. Recently we have developed an unifying general treatment in which the parabolas are shown to be K-lines of two-dimensional lattices. Here we want to review the main features of this description and present an experimental diffraction pattern from a 30° MgO (111) surface which displays parabolas that can be attributed to the surface reconstruction.

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