Dynamical diffraction effects on the geometric phase of inhomogeneous strain fields

Abstract

In specimens with an inhomogeneous displacement field in electron beam direction dynamical diffraction effects lead to complex non-linear properties of the diffracted electron wave. Consequently, the diffracted beam’s phase contains information about the inhomogeneous displacement field. These phases are experimentally and theoretically investigated under different excitation errors and specimen thicknesses as well as for different depths of the displacement field. An inclined InGaAs layer with a larger lattice constant than the surrounding GaAs matrix serves as controlled displacement field, which is inhomogeneous in electron beam direction with a continuously changing depth. The phase and amplitude of the diffracted beam are measured by dark-field electron holography. The measurements agree with calculations performed by numerical propagation of the electron wave using the Darwin-Howie-Whelan equations. A strong dependency on the excitation conditions is found showing that the interplay between dynamical effects and the strain field must be considered in the interpretation of the geometric phase.