Acta Physica Academiae Scientiarum Hungaricae 51. (1981)
1981 / 3. szám - Condensed Matter - A. Stachulec: Temperature Dependence of Low Energy Electron Diffraction in Pseudoharmonic Approximation
A. STACHULEC Since LEED represents a surface phenomenon it is very important to take into consideration the influence of the boundary conditions for the electron distribution as well as the thermal vibrations. The pseudoharmonic procedure was extended to the case of thin films [5], so that its application to the surface layers does not bring any additional troubles. Moreover, experience in that case shows that the properties of surface atoms are rather essentially different from those situated inside a sample and the character of this difference can be easily explained in terms of the pseudoharmonic model. II. Low energy electron diffraction In order to underline the relations between parameters describing the thermal properties of the surface we assume the simple model of the scattering system from the point of view of its crystallographic structure and roughness of the surface. Thus we assume that a sample is a thin film sufficiently large supported on the substrate, and it is an ideal crystal with s.c. structure, cut off along the orientation (100) with respect to the surfaces. The electron beam falls perpendicularly to the surface and it is scattered around the axis normal to the surface. The geometry of the scattering system and the notation for atomic position vectors are shown in Fig. 1. The monoatomic layers are labelled by V £ (1, n). The atomic positions inside a layer v are given by the vectors j„. The distance between two atomic sites is denoted by R„y with respect to the origin of the coordinate system. The electronic properties of the system are described additionally by the atomic orbitals J|> = <pm(r — Rvj)%rr, where m stands for the electron quantum numbers in an isolated atom and a is the spin orientation. Then A denotes the index referring to the set of parameters A = (v,ji, m, a) (e.g. [6]). The cross-section for the scattering of low energy electron beam in the effective field VT(r) is given by means of the scattering amplitude /(K) as [1 ] I(K) = |/(K)|2, (1) Fig. 1. The scheme of the scattering system Acta Physica Academiae Scientiarum Hungaricae 51, 1981