Inner potential measurements in electron diffraction

Abstract

The concept of the inner potential is introduced in the Bethe approximation of the dynamical theory of electron diffraction to explain the shift of apparent Bragg maxima to lower electron energies than those predicted kinematically. Because of the presence of strong dynamical interactions, the measured shape and width of the Bragg reflections become distorted from the kinematical predictions. Minima appear on a dynamically broadened reflection which are due to the reduction of the reflection coefficient upon the excitation of strong forward scattered (Laue) beams, giving rise to what can be mistaken for the superposition of reflections of presumably different origin. This introduces difficulty in both the indexing of the Bragg reflection and the determination of the diffraction conditions for its excitation. The inner potential can be associated with the refraction correction which allows a determination to be made of the voltage at which a reflection should occur for an arbitrary incident direction. This voltage shift as a function of angle is proportional to 1 sin 2θ leading to large corrections at glancing angles. By taking advantage of this magnification of the inner potential, careful measurements far from normal incidence for orientation which do not excite strong multiple diffraction yield a constant value of the inner potential of 20 ± 1 eV for tungsten (110).