![]() , but our screen is rotated by 180° to closely reproduce pulsed laser deposition conditions. In fact, we follow concepts presented by Larsen et al. In our case, we use the vector terminal point. , it is assumed that the initial point of the incident beam wave vector is attached to the zeroth rod. For example, in the paper of Mahan et al. Furthermore, for RHEED, the Ewald construction can be employed in different, equivalent ways. However, in general, the Ewald construction can be carried out for reciprocal space points or for rods. In other words, in such cases we assume a regular arrangement of atoms in planes near the crystal–vacuum interface. In the manuscript, the term “flat surface” is used to mean that the sample surface is without structural defects such as vacancies, adatoms or small islands at the crystal top. If the surface is relatively flat, then the pattern can be predicted with the help of the Ewald construction for rods as shown in Figure 1. Information on the arrangement of atoms at the sample surface can be extracted by analyzing the diffraction patterns. RHEED observations can be conducted both for low-index surfaces and vicinal surfaces (e.g., ). Nowadays, diffraction patterns can be typically recorded with the help of CCD cameras. In RHEED experiments, electrons are scattered by atoms forming a crystal. However, we also show an example of interpretation of experimental data for complex oxides, which are the subject of increasing interest. In this article, for simplicity, we discuss theoretical results for Ag and its fcc structure, and for Si and its diamond-type structure. need a crystallographic characterization. In the current paper, we follow a similar route for the case of RHEED.Īll materials used for modern materials engineering, electronics, etc. He wrote a respective computer code to be applied for X-ray diffraction. However, recently Barbour showed that its details can be demonstrated more efficiently by employing modern tools of three-dimensional (3D) computer graphics. In any case, a good introductory depiction of the Ewald sphere and its derivation on the basis of a single scattering (kinematical) description is given in the book of Kittel. It seems important to add that the concept of the Ewald sphere can be also employed in the area of photonics. The characterization of solids with X-ray or electron diffraction methods using the concept of the Ewald construction is well known. For example, for crystals with unit cells containing atoms of different types, partial cancelling of individual scattering contributions may happen and such effects cannot be examined within the approaches employing only geometrical analysis. Still, it is worth pointing out that there are some offshoots of such simplification. Consequently, the drawing of respective Ewald spheres can be applied. Furthermore, if the focus is only on determining the basic geometrical relations for the observed patterns and not on the amplitudes of the features observed on the screen, a simple theoretical analysis can be carried out to find the conditions of the maxima for interfering waves. Such treatment may be quite effective in use because, in principle, it enables the description even of quite irregular arrangements of atoms (for such cases, the use of multiple scattering theories is very difficult). This is a basic concept of the kinematical approach. If only single scattering events are considered, then diffraction patterns can be found by direct summing of contributions coming from all atoms that form a particular structure. In analyses of many features observed in diffraction patterns, the use of single scattering theories has been continually unavoidable. However, theoretical treatment of this kind for real samples is still incomplete. Namely, the movement of electron waves in a crystal can be successfully described within the two-dimensional (2D) Bloch wave approach. The patterns for ideally flat surfaces can be analyzed using dynamical diffraction theory, in which elastic multiple scattering is taken into account. This is because the scattering of electrons by surface atoms is complex and, in principle, multiple elastic and inelastic scattering events should be taken into account. The development of a theoretical description of RHEED for an arbitrary surface still constitutes the subject matter of many recent investigations (e.g., ). RHEED patterns may be quite complicated, in particular for disordered surfaces of solids. One of them is reflection high-energy electron diffraction (RHEED), employed to monitor changes at surfaces of films grown both by molecular beam epitaxy and pulsed laser deposition. The ordering of atoms at the surface of samples can be verified by a number of different characterization techniques. High-quality thin films and related structures can be obtained using molecular beam epitaxy (e.g., ) or pulsed laser deposition (e.g., ). ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |