Analysis of Local Charges at Hetero-interfaces by Electron Holography - A Comparative Study of Different Techniques

Interface charges confined within a few nanometers of hetero-interface can be characterized by measuring the phase shift of the transmitted beam using different electron holography techniques. However, reliable measurement of the electrostatic potential arising from the interface charges is challenging as the mean inner potential difference (ΔV₀) between two adjoining materials as well as local variation of the sample thickness affect the phase shift. In the present study, we show how electron holography can be used to characterize the confined charges at an oxide hetero-interface and evaluate the applicability of different techniques for this purpose. The model system chosen for this study is a LaAlO₃/SrTiO₃ (LAO/STO) (111) hetero-interface featuring a two-dimensional electron gas (2DEG), where the ΔV₀ between LAO and STO is about 2 eV, which is unignorably large and dominates the net potential variation across the interface. For transmission electron microscopy specimens prepared by focused ion beam we applied three different variants of electron holography techniques: off-axis, inline and hybrid electron holography; and compare the results obtained by these approaches in terms of the information transfer in the spatial frequency domain, and the signal-to-noise ratio of the electric field and charge density maps. To correctly assess the information pertinent to the interface-confined charges, we calculate the electrostatic potential and electric field distribution based on a charge model with taking account of the ΔV₀ between LAO and STO and compared the calculated profiles with the experimental results after calibrating the local thickness variation across the LAO/STO interface. The results show that hybrid electron holography recovers the information across a wide range of spatial frequencies, and as a result, delivers the most reliable charge density information, albeit convoluted with the unavoidable effects arising from ΔV₀.