Retrieving Potential Maps from Reversed Multislice Calculations

Abstract

Quantitative applications of high resolution TEM are often bottlenecked by the complexity of the formed lattice images. In general terms, lattice images do not reveal the real atomic structure of the sample directly, can be distorted, and information about the sample thickness and chemical composition are heavily encoded. These drawbacks relate to the presence of lens aberrations and dynamic diffraction. The development of Cs corrected TEM [1, 2] and software that reconstructs the complex electron exit wave function [3-6] aim at removing lens aberrations and dynamic diffraction that cause variations of the electron wave's amplitude and phase with the sample thickness and limit a direct interpretation. One approach to relate the reconstructed electron exit wave to the crystal structure and chemical composition of the sample is through utilization of the channeling theory [7] that gives an intuitive analytical description between the structure and the exit wave. This approach basically models the crystal columns as focal lenses and the wave inside the crystal can be described by a 1s state. Analyzes is then carried out column by column to retrieve the crystal structure from the exit wave [8].In this paper, we present a new concept to retrieve the potential map from the exit wave based on reversed multi-slice calculations. This algorithm uses a non-linear optimization scheme to find an optimum phase grating that satisfies two boundary conditions: knowledge of the entrance surface wave and the measured exit surface wave. After the phase grating is retrieved, the position and composition in the atomic column can be quantified. Fig. 1 shows the phase of an electron exit wave of Al:Cu bi-crystal that was reconstructed from a focal series of 20 images. Figure 2 shows retrieved potential map of the Al and Cu atoms, respectively, that reveals Cu segregation to the boundary. Result and limitations of the procedure will be discussed in detail.

Energy-filtered transmission electron microscopy based on inner-shell ionization

“…Models and techniques have been proposed to attempt to invert from the exit surface wave function to the specimen potential [5][6][7], but their application is not yet routine. If much is already known about the specimen, then there are more options for interpreting the images [8,9]. But for specimens which are unknown in detail, obtaining element specific information from HRTEM alone is challenging.…”