Space-charge distribution across internal interfaces in electroceramics using electron holography: I, pristine grain boundaries

The role and importance of interface charge and the associated space-charge in governing the electrical activity of interfaces are well appreciated, and have been the focus of a large number of investigations. Despite a considerable progress in this area, the direct determination of the sign, magnitude of the interface charge, and the space-charge potential associated with the interface double-Schottky barrier has remained elusive. We propose electron holography as a bulk sensitive tool with subnanometer resolution to obtain direct real-space evidence of space-charge, as well as determine the electrical activity of individual grain boundaires (GBs) in electroceramics. Part I of this investigation is focused on the theory and practice of electron holography of interfaces, in the context of pristine (undoped) GBs in SrTiO₃. We show that pristine GBs exhibit very little electron phase change, and that the phase change is associated with a reduction in the mean inner potential and with any residual charge, both present by the virtue of the GB. This investigation forms the basis for the electron holography investigation of doped (charged) GBs in Part II. It is shown that quantitative information about the magnitude, sign, and spatial extent of electrical potential and charge, as well as defect densities across individual GBs in electroceramics, can be obtained using transmission electron holography.