Elsevier

Ultramicroscopy

Volume 145, October 2014, Pages 3-12
Ultramicroscopy

Electron dose dependence of signal-to-noise ratio, atom contrast and resolution in transmission electron microscope images

https://doi.org/10.1016/j.ultramic.2014.01.010Get rights and content

Highlights

  • The definition of dose-dependent atom contrast is introduced.

  • The dependence of the signal-to-noise ratio, atom contrast and specimen resolution on electron dose and sampling is explored.

  • The optimum sampling can be determined according to different dose conditions.

Abstract

In order to achieve the highest resolution in aberration-corrected (AC) high-resolution transmission electron microscopy (HRTEM) images, high electron doses are required which only a few samples can withstand. In this paper we perform dose-dependent AC-HRTEM image calculations, and study the dependence of the signal-to-noise ratio, atom contrast and resolution on electron dose and sampling. We introduce dose-dependent contrast, which can be used to evaluate the visibility of objects under different dose conditions. Based on our calculations, we determine optimum samplings for high and low electron dose imaging conditions.

Introduction

The instrumental resolution of transmission electron microscopes (TEMs) has dramatically improved during the last decade, mainly due to the introduction and practical realisation of hardware aberration correction [1], [2], [3]. As a result, materials can now be imaged and identified down to single atomic columns [4], [5] or, in the case of the new class of two-dimensional materials, even single atoms [6], [7]. With the aim of reducing radiation damage induced by the imaging electrons, low-voltage aberration-corrected TEMs, down to voltages of 20 kV [8], [9], 30 kV [10], and 40 kV [11], are currently under development. A voltage-tunable fully-corrected (that is, corrected for higher-order geometrical aberrations as well as chromatic aberrations of the imaging lenses [12]) TEM seems close to becoming reality [13].

Achieving the improved resolution of an aberration-corrected TEM requires, however, an infinite electron dose on the studied specimen, and only few materials can withstand very high, let alone infinite doses. Materials can be damaged via the knock-on damage mechanism, where atoms are displaced by direct impacts of the imaging electrons, and in such cases lowering of the electron energy below a material specific threshold is desirable [8], [14], [15], [16], [17]. On the other hand, the electron–electron (inelastic) scattering cross section increases at lower electron energies and, depending on the material, ionization can become the dominating damage mechanism [17]. Effective ways of reducing ionization damage may be cooling of the specimen [18] or conductive coating [19]. As extreme examples of the latter, samples have been enclosed within carbon nanotubes [9], or between graphene layers [20], greatly reducing radiation damage during imaging. Such approaches are not always feasible, however, and images thus need to be acquired with limited electron doses.

The stability of the microscope is another factor limiting the electron dose in a single image. The microscope tends to drift away from the corrected state, and as a result images can be acquired only within a small time window before resolution is deteriorated [21], [22], [23]. Also all kinds of instabilities including electrostatic and magnetic field noise [24] and instabilities caused by the sample stage can lead to blurring of the images, if long exposure times are used.

With all this in mind, microscopists have to develop strategies for limited electron dose imaging. Thus, having a robust framework for estimating the effects of this limitation is necessary. Here, we address this issue, by exploring the influence of the electron dose and sampling on the signal-to-noise ratio (SNR), the atom or lattice contrast, as well as the resolution, with the help of dose-dependent image simulations. We introduce a modified definition for the image contrast, which takes the electron dose into account. The dose related noise is treated as stochastic fluctuations around the ideal electron count at each image pixel, instead of the previously used additive noise [25], [26], [27], [28], [29], [30]. Using these tools, we determine the optimal sampling for achieving atomic resolution images of graphene, as a function of the information limit and magnification of the microscope, as well as determine the required electron dose based on the calculated atom contrast. Graphene is used as the example material due to the simplicity of its structure, which allows straight forward interpretation of the results.

Section snippets

Image simulation with finite electron dose

The structural information of the sample is carried primarily by elastically scattered electrons, which is distorted by an electromagnetic lens during the propagation process in the microscope. The distorted information is transferred to the detector and the average number of electrons collected by each detector pixel is determined by the electron dose, the sampling and the probability of the electron to be found on each pixel, which is the squared modulus of the image wave. The actual number

Results

In order to study the dependence of SNR, atom contrast and specimen resolution on electron dose and sampling, we have simulated images of graphene obtained with the Cc/Cs-corrected SALVE II microscope operated at an accelerating voltage of 80 kV (Fig. 1). Subsequently, we have determined the optimum sampling based on the previous study for 20 kV, 40 kV, 60 kV and 80 kV.

The MTF data (Fig. A1) for the SALVE microscope at 20 kV, 40 kV, 60 kV and 80 kV were previously measured using averaged single electron

Summary

In this paper we have studied the influence of electron dose and sampling on the SNR, dose-dependent contrast and resolution using dose-dependent HRTEM image calculations. All three quantities improve with increasing electron dose, converging towards their values obtained at infinite dose. As sampling gets coarse, the SNR increases and the resolution deteriorates; the atom contrast improves as long as the damping of MTF is negligible. We have determined optimum sampling under high-dose and

Acknowledgments

This work was supported by the DFG (German Research Foundation) and the Ministry of Science, Research and the Arts (MWK) of Baden-Württemberg in the frame of the (Sub-Angstrom Low-Voltage Electron microscopy) (SALVE) project. We thank Dr. Peter Hartel and Dr. Heiko Müller from CEOS GmbH for the fruitful discussions and generous help with experiments.

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