Aberration-Corrected TEM
Figure 2: Theoretical electron-wave basis for HR-TEM imaging, showing (a) change in electron wavelength due to material density, (b) electron phase-front delay or “bending” due to passage through an atom, and (c) effect on electron EW phase-front in a sample with several atoms (after [5]).
resolution and high signal-to-noise ratio, we can actually count individual atoms and ultimately infer their vertical position in the 3-D structure.
Complications Due to the Non-Ideal TEM In an ideal TEM, this desired sample EW phase would be
perfectly magnified by the microscope without any aberration, by a large scaling factor M (such as 500,000×) and then somehow recorded aſter this magnification process. In a real microscope (see Figure 3), at least two complications prevent this from happening directly: (a) the magnified image, even in an HR-TEM microscope with hardware Cs-correction, still has residual aberrations, and (b) typical image recording methods such as CCD camera are not capable of detecting electron phase, but only electron intensity (essentially the amplitude squared). As noted above, for a very thin sample, the amplitude does not change during the electron-sample interaction. A true
aberration-free microscope would have zero image contrast in HR-TEM because it measures only the amplitude, which does not change! Luckily, in this case, the microscope aberrations actually help us in our task to image the sample. Te effect of the microscope optical aberrations is to “couple” or mix the exit-wave amplitude and phase [7]. Tis scrambling ensures that there is some contrast change in the electron amplitude at the image plane of the CCD camera.
Deconvolving the Microscope Transfer Function Imaging in the HR-TEM is an electron wave-coherent
process, so if we know the microscope’s exact optical parameters, theoretically we should be able to mathematically deconvolve the scrambling of phase and amplitude to get back to the desired pure EW phase function. Focal series reconstruction (FSR) is a technique [2, 8] used to perform this deconvolution of amplitude and phase. It requires a series of HR-TEM CCD images; typically up to twenty individual images, each taken at a different numerical value of defocus (around the real focus value). Although the signal-to-noise ratio can be improved by averaging [9], this operation is more than just averaging twenty images to improve signal-to-noise ratio: by changing the experimental focus and feeding the known microscope optical parameters into a numerical FSR calculation, the FSR program can deconvolve or “subtract” the microscope’s optical transfer function. Te result is that the soſtware [8] can output two processed experimental images, the pure EW phase and the exit-wave amplitude, with the scrambling effect fully unraveled. In the limit of a very thin sample and perfect deconvolution, the EW amplitude goes virtually to zero, leaving only the desired EW phase information.
Imaging of Graphene: Experimental Setup and Details For this HR-TEM study, graphene sheets were carefully
Figure 3: HR-TEM schematic. An ideal TEM would magnify the sample exit-wave information by a large magnification factor M, but the electron optics of a real microscope will also introduce aberrations in the image recorded at the image plane. This optical transfer function, including residual aberrations, can be deconvolved by using FSR as described in the text (after H. Lichte, TU Dresden).
2011 May •
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prepared [4], and the experiments were performed using an FEI Titan G2 60-300 microscope operated at 80 kV, equipped with a high-brightness, low-energy-spread X-FEG/monochromated field-emission electron source, as well as a CEOS aberration corrector to correct the spherical aberration of the objective lens. Te CEOS aberration corrector was tuned to a spherical aberration Cs value of about –15 µm (to optimize the details in the image intensity) [10].
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