Focal series reconstruction of bismuth telluride using a conventional transmission electron microscopy
Authors: de Oliveira Thais Milagres , Balzuweit Karla , Nascimento Von Braun , Ladeira Luís Orlando , Soares Edmar Avellar , de Carvalho Vagner Eustáquio 
Published: December 2016

High Resolution Transmission Electron Microscopy allows the determination of the crystalline structure of materials through various methods of electron diffraction or direct imaging. However, the interpretation and quantification of the high‐resolution images are complex, because of the strong interaction between the electron beam and the material [1]. Besides, the material's exit wave function is modified by the components of the microscope [2]. As the high‐resolution microscopy images are a convolution between the exit wave function of the sample and the function of the microscope, the interference fringes can be modified changing the condition of defocus [3]. The aim of the research is to understand the focal series reconstruction routines and use them in the study of bismuth telluride and its alloys, in order to identify their crystalline structure.
Through focal series reconstruction is a technique consisting in obtaining high‐resolution image series with different values of defocus, generating different conditions of constructive and destructive interference fringes. At the same time, high‐resolution images are simulated from a theoretical model of the crystal convoluted with the transfer function of the microscope, considering several types of aberration of the microscope, where the spherical aberration of the objective lens and the chromatic aberration are dominant. The simulated images are compared with the experimental images and through the correlation between them the theoretical model is optimized. There are several software packages which can be used to simulate the structure and/or generate a focal series: JEMS, True Image, FTSR, IWFR and REW. The present work shows the first results on focal series reconstruction routine using REW [4].

Bismuth telluride, Bi
2
Te
3
, is a thermoelectric material with high coefficients at room temperature [5] and has recently been identified as a topological insulator [6], with rhombohedral crystal structure and space group R(‐3)m with five atoms per unit cell. When aligned in the [2,‐1,‐1,0] direction is possible to visualize the quintuple layer structure of Te‐Bi‐Te‐Bi‐Te. Studies related to the doping of Bi
2
Te
3
, in which some elements are intercalated among their quintuple layers [7], have been conducted in order to determine the variations of their basic properties. The focal series reconstruction will be used to verify the quality of the intercalation experiment.

A through focal series of 20 high resolution images was taken of a Bi
2
Te
3
sample prepared via ultramicrotomy, approximately 20‐30 nm thick, using a Tecnai G‐20 LaB6 S‐Twin (Cs = 1.2 mm) at 200 keV. A magnification of 490kx was used over a range of focus of ‐180.09 nm to 9.09 nm, with a focus variation of approximately of 10 nm. The HRTEM image at the Scherzer focus is shown in Figure 1, and the image of amplitude and phase resulting from the exit wave reconstruction of the sample using the software REW are shown in Figure 2 and Figure 3.

It is possible to identify the atomic position of bismuth and tellurium in the quintuple layers of the phase image obtained from the focal series reconstruction, as shown in Figure 4, using a conventional transmission electron microscope.