RHEED intensities from two-dimensional heteroepitaxial nanoscale systems

Abstract

A practical computing algorithm has been developed for calculating the reflection high-energy electron diffraction (RHEED) from the molecular beam epitaxy growing surface. The calculations are based on the use of the 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 computer program presented in this paper enables calculations for three basic types of diffuse potential for crystalline heteroepitaxial structures, including the possible existence of various diffuse scattering models through the layer parallel to the surface. Program SummaryProgram title: RHEED_DIFFCatalogue identifier: AETW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 68483No. of bytes in distributed program, including test data, etc.: 480831Distribution format: tar.gzProgramming language: C++.Computer: Intel i7-based PC.Operating system: Windows, Linux.RAM: The presented algorithm belongs to the linear memory class of the computational complexity O(n).Word size: 64 bitsClassification: 4.6, 6.2, 7.2.Nature of problem:RHEED rocking curves (the specular beam intensities versus the glancing angle) recorded from heteroepitaxial layers are used for the non-destructive evaluation of epilayer thickness and composition with a high degree of accuracy. Rocking curves from such heterostructures are often very complex because the thickness fringes from every layer beat together. Simulations based on the dynamical diffraction theory are generally used to interpret the rocking curves of such structures from which very small changes in thickness and composition can be obtained. Rocking curves are also used to determine the level of strain and its relaxation mechanism in a lattice-mismatched system.Solution method:RHEED intensities are calculated within the framework of the general matrix formulation described in Ref. [1] under the one-beam condition [2,3]. 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 onto the surface normal, so that the results are insensitive to the atomic arrangement in the layers parallel to the surface. In this paper, an approach in which oscillating changes in the intensity appear as a combined effect of changes in the refraction conditions and changes in diffuse scattering for different models of the scattering potential is implemented.Running time:Numerically, the problem of calculating the changes in RHEED oscillation intensity from growing layers is an NP problem. The time computational complexity of the presented algorithm depends on the number of layers for both the substrate and the growing layers included in the calculations. The time-computational complexity of the presented solution is O(n2), where n is the total number of layers used in the calculations.