Empirical determination of transmission attenuation curves in mass–thickness contrast TEM imaging
Introduction
Transmission electron microscopes (TEMs) are indispensable instruments for observing localized nanostructures in materials such as dislocations, precipitates, and grain boundaries. Since the properties of a material are strongly influenced by their density and distribution, the ability to perform observations over large dimensions within a bulk material, in particular, to perform observations of a thick specimen is important for conducting efficient and reliable analyses. Investigations on the maximum observable thickness have become important also for recent research trends such as electron tomography of micron-sized materials [1], [2] and in-situ observations in gas [3], [4] or liquid environments [5]. To efficiently design those experimental studies, a pre-estimation of the maximum observable thickness for TEM is desirable.
Numerous studies have been performed to estimate the observable thickness for many years, especially using high-voltage electron microscopy (HVEM). In recent developments, the maximum thickness for observing dislocations has been examined by not only conventional TEM imaging but also energy-filtered TEM imaging [6] and scanning TEM (STEM) imaging [7], [8]. Over the last fifty years, many studies have focused on conventional TEM imaging to examine the maximum thickness as a function of voltage for a variety of localized structures, such as dislocations [9], grain boundaries [10], and stacking faults [11]. Nevertheless, systematic and quantitative descriptions of the maximum thickness have not been reported yet. This lack of research can be partially attributed to poorly controlled conditions between each experiment (such as objective aperture (OA) radius, matrix material, and configuration of the localized structure) and each qualitative definition of visibility by each researcher. The complexity of multiple scattering involving inelastic scattering may also be a cause of difficulty in obtaining a clear understanding of this phenomenon. Both multiple scattering and inelastic scattering increase with increasing thickness, inducing image blurring [6], [12], [13], [14], [15] and image intensity attenuation in TEM imaging [1], [12], [13], [15], [16], [17], [18], [19], [20], [21]. An object localized in bulk cannot be identified by TEM when the blurring range exceeds the object size or when the image contrast of the object is masked by noise in a dark image due to the intensity attenuation. Therefore, estimations of the observable thickness must be determined based on quantitative descriptions of both image blurring and intensity attenuation [12].
Thus, establishing a mathematical description of the transmission attenuation is an important step towards obtaining an estimation of the observable thickness. As described in the next section, several functions representing attenuation curves have been previously proposed. However, in most cases, these functions have been compared with measurements in a semi-quantitative manner and only for limited experimental conditions. Therefore, it remains unclear which function is the most accurate, how closely the function can reproduce experimental results, and the conditions to which a function can be applied. In the present study, we aim to empirically determine a mathematical formula representing the transmission attenuation based on precise experiments. The validity of this function and that of other existing functions are examined by comparison with attenuation curves measured over a wide range of experimental conditions.
Section snippets
Previously proposed transmission attenuation models
Most high-energy incident electrons pass through a TEM specimen that is thinner than several microns, except for back-scattered electrons near the entrance surface. Note that, in this article, we use the term “transmission” in association with virtual absorption by an OA instead of substantial physical absorption by a material. Most image contrast in amorphous materials consists of mass–thickness contrasts since the diffraction contrast is negligibly low. Assuming that an incident electron
Materials and methods
As discussed later, one of the requirements for precise and efficient acquisition of transmission data is the use of amorphous specimens with uniform compositions and well-defined three-dimensional (3D) shapes instead of film specimens, which have been frequently used in previous research [12], [13], [15], [17], [18], [20], [21], [32]. We used polystyrene spheres (latex spheres, Magsphere Inc. and Nisshin EM Co., Ltd.) and a carbon micro-coil (CMC, Microphase Co., Ltd.), with typical densities
Results
Fig. 2(a) presents attenuation curves measured for polystyrene spheres with diameters of approximately 10 μm at 500–3000 kV by UHVEM. All of the measurements presented in the figure were obtained using the second largest OA (approximately 100 μm in diameter) mounted in the UHVEM. The spatial frequency accepted by the OA increases with increasing voltage (see the figure caption for each value). As explained previously, the data for the thinnest ranges are neglected. In Fig. 2(b), the measured
Intuitive explanation of the characteristic attenuation curves
Fig. 6(a) schematically summarizes the clarified characteristics of the attenuation curves; (1) In the early stage of attenuation denoted by I, the curves show a slightly upward convex trend. (2) In the intermediate stage II, the curves deviate from the linear attenuation in the direction of larger intensities. (3) In the later stage III, the transmission asymptotically approaches a stationary value. Characteristic 2 has been known as a general feature of the nonlinear transmission attenuation
Conclusions
The electron transmission in mass–thickness contrast TEM imaging was precisely measured as a function of thickness using two types of carbon-related amorphous materials with well-defined 3D shapes. Based on the measurements, a function containing three parameters was proposed for the transmission attenuation curve with increasing thickness. The validity of the attenuation function was proven with a high degree of precision over a wide range of experimental conditions. Thus, more than a century
Declaration of interest
None.
Acknowledgments
The authors are grateful to Prof. H. Mori of Osaka University and Prof. K. Arakawa of Shimane University for invaluable discussions. We also thank Mr. E. Taguchi, Dr. T. Sakata, and Mr. T. Yasuda of Osaka University and Mr. A. Ohsaki, Dr. S. Ohta, and Mr. S. Takakuwa of JEOL Co., Ltd., and Prof. S. Arai of Nagoya University for their assistance with the experiments. This work was partly supported by MEXT KAKENHI (grant number 26105009).
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