RHEED intensities from two-dimensional heteroepitaxial nanoscale systems of GaN on a Si surface

Abstract

This paper presents a computer program, which facilitates the calculation of changes to the intensity of RHEED oscillations from the heteroepitaxial structures of (0001)GaN films nucleated on a Si surface. The calculations are based on the use of a dynamical diffraction theory and different models of scattering crystal potential. New version program summaryTitle of program: RHEED_DIFF_WProgram Files doi:10.17632/hn3pt6ytky.1Licensing provisions: GNU General Public License 3Programming language used: C++Journal reference of previous version: Computer Physics Communications 185 (2014) 3001–3009Does the new version supersede the previous version?: No. It does supersede version AETW_v1_0.Reasons for the new version: Responding to the users’ feedback we presented a practical procedure of construction of simulation program, which facilitates the calculation of changes to the intensity of RHEED oscillations in the function of the glancing angle of incidence of the electron beam, employing various models of scattering crystal potential for heteroepitaxial structures of hexagonal (0001)GaN films nucleated on a Si surface. GaN has a wurtzite crystal structure with alternating planes of Ga and N atoms and lattice constants a=3.189Å and c=5.185Å [1]. Choosing the top surface to be z=0, the N atoms are located at z=nd where d=5.185/2Å and n is an integer, and Ga atoms are at z=nd−u, where u=3c/8 (as shown in Fig. 1).The nature of physical problem: Since the discovery of molecular beam epitaxy, which allows formation of layers (crystals) with a controlled composition of subsequent monolayers, the research attempts of many laboratories have been focused on studying the dynamics of formation of both monolayers and specific heterojunction structures, that is the structures with monocrystalline interfaces created by materials of various chemical compositions (different physical and chemical properties). The fundamental scientific problem in such research is to specify both interface type and growth mechanism for subsequent layers. Researchers and technologists manufacturing two-dimensional nanoscale systems frequently use RHEED rocking curves (the specular beam intensities versus the glancing angle) to control growth of films at the atomistic level of accuracy. The structural properties of the GaN/Si interface have been meticulously studied by many [3–5], and crucial problem of the direct growth of GaN on Si is the formation of amorphous silicon nitride (SiN) at the GaN/Si interface.Typical running time: The typical running time is machine and user-parameters dependent, i.e. the number of layers for both the substrate and the growing layers included in the calculations.The method of solution: RHEED intensities are calculated within the general framework described in Ref. [2] with the model of the scattering potential for heterostructures: (1)UCombined(z)=∑nUsubstrate(z)+∑n(Ulayer(z)+Uaddlayer(z)), where the Uaddlayer represents the diffuse scattering on the topmost layer.Summary of revisions: The presented version of computer program implements original algorithms of self-consistent calculations for scattering potentials GaN(0001)/Si(111) and solving a time-independent Schrödinger equation for high-energy electrons (Fig. 2). [Display omitted] [Display omitted] [Display omitted] [Display omitted] During the numerical calculations of the changes in the intensity of the specular beam in the function of the glancing angle, it was assumed that the electron energy equals 10 keV, the glancing angle was increased from 0.5° to 7°, and the value of α parameter =0.1 and β=0.5 for the MODEL3 of the scattering potential [2]. Figs. 3–4 present the situation where on the crystalline Si(111) substrate a single GaN layer was placed, where the GaN growth on Si is having a thin amorphous layer. It can be observed that for a very thin layer of GaN, a clear minimal amplitude of RHEED oscillation occurs with the coverage of the GaN layer equal to about 0.5.