Editorial Feature

Non-Linear Imaging in High Resolution Transmission Electron Microscopy

The superior information limit (IL) offered by the non-linear imaging, as compared to linear imaging in high-resolution transmission electron microscopy (HRTEM), posed an important question as to whether non-linear imaging could be used to determine structure. To answer this question, researchers from the Beijing National Laboratory for Condensed Matter Physics of the University of Chinese Academy of Sciences, in collaboration with Beijing Normal University, investigated the non-linear component of this microscopy technique based on the multislice simulation of wurtzite-structure of aluminum nitride (AlN). This study found that some high-frequency non-linear information can provide excellent information on the phases of structure factors which can therefore be used to determine the structure.

High Resolution Transmission Electron Microscopy (HRTEM)

Transmission electron microscopy (TEM) is one of the most widely used microscopy techniques for several research purposes within the biological and material science fields. High-resolution transmission electron microscopy (HRTEM) is a type of TEM that enables users to examine the atomic structure of a given sample with incredible resolutions of up to 0.5 Angstroms (A°). This technique is used to obtain structural details of semiconductors, metals, nanoparticles and sp2-bonded carbon, such as graphene and carbon nanotubes.

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Information Limit of the Linear and Non-linear Components in HRTEM

The Information limit (IL), which is the inverse of the highest spatial frequency that can be transferred by the imaging system from the exit plane to the image plane, defines the performance of the HRTEM. This relation between IL and resolution obtained by the HRTEM is only applicable in the linear imaging with negligible non-linear interference. Therefore, HRTEM often requires specimens that are weak phase objects, in other words, extremely thin. It was found that the information limits are different for linear and non-linear interferences. In fact, studies have shown that non-linear imaging may offer resolutions that are larger than √2 times larger than the information limit offered by the linear imaging.

Non-Linear Component of HRTEM to Determine the Structure of AlN

The linear interference between the transmitted beam and one of the diffracted electron beams (I1(K)) was found to be negligible at sufficiently high frequencies due to the strong damping. Therefore, Binghui Ge’s team investigated the non-linear interference between the two diffracted beams (I2(K)). To determine this, this group of researchers used Reflection 012, that lies just within the linear IL and Reflection 013, which lies just beyond the IL of the linear IL in the present investigation. The [100] direction offered an advantage that the Aluminum (Al) and Nitrogen (N) atoms in the AlN structure are present at the atomic distance of 1.09 A° and do not overlap in this direction. Therefore, simulations of HRTEM images of AlN in the [100] direction were performed under different imaging parameters with different effective defocus values around the Scherezer focus. Values were chosen in the present investigation to determine the effectiveness of the non-linear component of the HRTEM to deduce the structure of AlN.

Applications of the Non-Linear Component of HRTEM

By deducing the structure of AlN utilizing multislica simulation, the use of non-linear component of the HRTEM has been demonstrated by Binghui Ge’s team in the present study. For non-aberration-corrected imaging, the phase of the non-linear information of reflection 013 was found to be close to the phases of the structure factor when the sample thickness is high. Furthermore, this group of researchers found that the Al and N atoms in the projection of [110] can be separated, indicating that higher-resolution, sufficient enough to resolve atomic structure can be obtained by conventional TEM. By demonstrating the non-linear component of HRTEM, this research puts forward a new way to employ non-aberration-corrected TEM. Future studies are required to determine the applicability of such mechanisms to other kinds of electron microscopy or crystallography techniques.

1. “Applicability of non-linear imaging in high-resolution transmission electron microscopy” Y. Chang, S. Li, et al. Microscopy. (2017). DOI: 10.1093/jmicro/dfx031.

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Benedette Cuffari

Written by

Benedette Cuffari

After completing her Bachelor of Science in Toxicology with two minors in Spanish and Chemistry in 2016, Benedette continued her studies to complete her Master of Science in Toxicology in May of 2018. During graduate school, Benedette investigated the dermatotoxicity of mechlorethamine and bendamustine; two nitrogen mustard alkylating agents that are used in anticancer therapy.


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