Electron scattering factors of ions and dynamical RHEED from surfaces of ionic crystals

Electron scattering factors of ions are represented in a parametrized form which separates the diverging Coulomb term due to ionic charge from the contribution of the screened atomic field. Using this representation it is shown how dynamical reflection high-energy electron diffraction (RHEED) calculations can be performed for ionic surfaces using conventional numerical techniques. Following the classification of ionic surfaces proposed by Tasker [Surf. Sci. 78, 315 (1979)], we analyze the effect of ionicity on RHEED intensities for three classes of ionic surfaces. In the first case both positive and negative ions are located in the same plane and this leads to the cancellation of long-range Coulomb contribution to the crystal potential. The second class of ionic surfaces consists of layers of ions having net nonzero charge. Ionic layers may be grouped into repeat units of planes of the form (anion)-(cation)-(anion) characteristic of the (111) surface of the fluorite structure so that each repeat unit satisfies the charge neutrality condition and also has zero net dipole moment perpendicular to the surface. For this class of surfaces the Coulomb term leads to unusual features in the distribution of the potential in the crystal. The third type of the termination of an ionic crystal lattice gives rise to a sequence of repeat units characterized by a nonzero net dipole moment resulting in a divergent behavior of the potential. Our calculations show that charge transfer between lattice sites occurring in an ionic crystal affects very substantially the form of RHEED rocking curves. The effect can be interpreted in terms of the change in the effective inner potential. This in turn can be used for quantitative determination of the degree of charge transfer occurring in the surface layer of an ionic crystal.