Simulation of electron phase shifts by electrostatic potential across electroceramic interfaces

An expression for the electron-wave phase shifts caused by the potential of an electric dipole is extended to a general equation representing the phase shifts caused by the electrostatic potential across a parallel-plate capacitor. The capacitor is then used to construct a simple model for the phase shifts caused by the potential barriers present across internal interfaces in solids. The phase simulations yields phase shifts for electroceramic interfaces in good agreement with the phase images reconstructed from off-axis electron holograms of acceptor-doped grain boundaries in SrTiO₃.