Speckle Suppression by Decoherence in Fluctuation Electron Microscopy

Abstract

We compare experimental fluctuation electron microscopy (FEM) speckle data with electron diffraction simulations for thin amorphous carbon and silicon samples. We find that the experimental speckle intensity variance is generally more than an order of magnitude lower than kinematical scattering theory predicts for spatially coherent illumination. We hypothesize that decoherence, which randomizes the phase relationship between scattered waves, is responsible for the anomaly. Specifically, displacement decoherence can contribute strongly to speckle suppression, particularly at higher beam energies. Displacement decoherence arises when the local structure is rearranged significantly by interactions with the beam during the exposure. Such motions cause diffraction speckle to twinkle, some of it at observable time scales. We also find that the continuous random network model of amorphous silicon can explain the experimental variance data if displacement decoherence and multiple scattering is included in the modeling. This may resolve the longstanding discrepancy between X-ray and electron diffraction studies of radial distribution functions, and conclusions reached from previous FEM studies. Decoherence likely affects all quantitative electron imaging and diffraction studies. It likely contributes to the so-called Stobbs factor, where high-resolution atomic-column image intensities are anomalously lower than predicted by a similar factor to that observed here.

Comment on, “On the influence of the electron dose-rate on the HRTEM image contrast”, by Juri Barthel, Markus Lentzen, Andreas Thust, ULTRAM12246 (2016), http://dx.doi.org/10.1016/j.ultramic.2016.11.016

“…In this process, the traditional room temperature Debye-Waller factors for periodic structures are commonly overwritten even if moderate dose-rates are chosen around ∼ 100 e/ Å 2 s to acquire high resolution images. Our view is also consistent with reports on amorphous materials where the large electron beaminduced atom displacements can be detected in image time series, too, causing displacement decoherence [21] .…”

Entropic Comparison of Atomic-Resolution Electron Tomography of Crystals and Amorphous Materials

“…In practice, silicates are vulnerable to electron beam damage, and such specimen motions may ultimately be the limiting factor for tomographic reconstruction of amorphous materials. Broadly, and ignoring such displacement decoherence effects [31], for a given targeted recovery quality, crystalline reconstructions are systematically of higher quality, consistent with expectations from Fig. 1(a).…”

“…The resolution was adjusted by changing the reciprocal-space diameter of a circular aperture [25]. These parameters approximate typical experimental conditions, but ignore dynamical scattering and decoherence effects arising from motions in the structure [31].…”

“…For amorphous samples, a much larger number of input projections is required for comparable reconstruction quality. In practice, disruption of amorphous materials by the electron beam may prove to be a limitation [31], as it is for biological materials. Our results indicate that tomographic reconstruction of amorphous materials will not be as easy as that for crystals.…”

Detecting structural variances of Co3O4 catalysts by controlling beam-induced sample alterations in the vacuum of a transmission electron microscope

“…Exploiting the current technology and electrons accelerated by 80 kV, we estimate a S/N ratio of ~2 for the detection of one gold atom or one carbon atom if ~600 or 20,000 e/Å 2 are delivered, respectively, in the bright field phase contrast imaging mode. Beam-induced object alterations primarily affect atom sites possessing lowered binding energies, which are typically present at surfaces, interfaces, defects, or in radiation-sensitive amorphous materials and soft matter where they consistently cause undesirable contrast variations [15, 47]. …”