Mean free paths for inelastic electron scattering in silicon and poly(styrene) nanospheres

Interpretation of mean free path values derived from off-axis electron holography amplitude measurements

In this work, we have explored the factors which govern mean free path values obtained from off-axis electron holography measurements. Firstly, we explore the topic from a theoretical perspective, and show that the mean amplitude reconstructed from off-axis holograms is due to the coherent portion of the direct, central object-transmitted beam only - it is not affected by the presence or absence of other scattered beams. Secondly, we present a detailed experimental study which compares mean free path values obtained from hologram sideband, centreband, EELS, and TEM measurements as a function of optical collection angle and energy-loss-filtering. These results confirm that the coherent portion of the direct beam defines the mean amplitude, and additionally show that the coherent portion corresponds to the conventional energy-filtered signal (with threshold 5 eV in this work). Finally, we present summary measurements from a selection of different materials, and compare the results against a simple electron scattering model. This study reinforces the claim that the mean amplitude is defined by the energy-filtered direct beam, and confirms that the contributions of elastic and inelastic scattering to the total mean free path are broadly in line with theoretical expectations for these different materials. These results in aggregate indicate that neither experimental collection angles nor enhanced sensitivity to low-loss phonon scattering affect the mean amplitude signal arising from off-axis holography reconstructions, nor the associated mean free path values which are derived from this mean amplitude.

Nanoscale x-ray imaging of circuit features without wafer etching

Modern integrated circuits (ICs) employ a myriad of materials organized at nanoscale dimensions, and certain critical tolerances must be met for them to function. To understand departures from intended functionality, it is essential to examine ICs as manufactured so as to adjust design rules, ideally in a non-destructive way so that imaged structures can be correlated with electrical performance. Electron microscopes can do this on thin regions, or on exposed surfaces, but the required processing alters or even destroys functionality. Microscopy with multi-keV x-rays provides an alternative approach with greater penetration, but the spatial resolution of x-ray imaging lenses has not allowed one to see the required detail in the latest generation of ICs. X-ray ptychography provides a way to obtain images of ICs without lens-imposed resolution limits, with past work delivering 20-40 nm resolution on thinned ICs. We describe a simple model for estimating the required exposure, and use it to estimate the future potential for this technique. Here we show for the first time that this approach can be used to image circuit detail through an unprocessed 300 μm thick silicon wafer, with sub-20 nm detail clearly resolved after mechanical polishing to 240 μm thickness was used to eliminate image contrast caused by Si wafer surface scratches. By using continuous x-ray scanning, massively parallel computation, and a new generation of synchrotron light sources, this should enable entire non-etched ICs to be imaged to 10 nm resolution or better while maintaining their ability to function in electrical tests.

Quantitative measurement of mean inner potential and specimen thickness from high-resolution off-axis electron holograms of ultra-thin layered WSe2

The phase and amplitude of the electron wavefunction that has passed through ultra-thin flakes of WSe₂ is measured from high-resolution off-axis electron holograms. Both the experimental measurements and corresponding computer simulations are used to show that, as a result of dynamical diffraction, the spatially averaged phase does not increase linearly with specimen thickness close to an [001] zone axis orientation even when the specimen has a thickness of only a few layers. It is then not possible to infer the local specimen thickness of the WSe₂ from either the phase or the amplitude alone. Instead, we show that the combined analysis of phase and amplitude from experimental measurements and simulations allows an accurate determination of the local specimen thickness. The relationship between phase and projected potential is shown to be approximately linear for extremely thin specimens that are tilted by several degrees in certain directions from the [001] zone axis. A knowledge of the specimen thickness then allows the electrostatic potential to be determined from the measured phase. By using this combined approach, we determine a value for the mean inner potential of WSe₂ of 18.9±0.8V, which is 12% lower than the value calculated from neutral atom scattering factors.

Electronic and thermal transport study of sinusoidally corrugated nanowires aiming to improve thermoelectric efficiency

Improvement of thermoelectric efficiency has been very challenging in the solid-state industry due to the interplay among transport coefficients which measure the efficiency. In this work, we modulate the geometry of nanowires to interrupt thermal transport with causing only a minimal impact on electronic transport properties, thereby maximizing the thermoelectric power generation. As it is essential to scrutinize comprehensively both electronic and thermal transport behaviors for nano-scale thermoelectric devices, we investigate the Seebeck coefficient, the electrical conductance, and the thermal conductivity of sinusoidally corrugated silicon nanowires and eventually look into an enhancement of the thermoelectric figure-of-merit [Formula: see text] from the modulated nanowires over typical straight nanowires. A loss in the electronic transport coefficient is calculated with the recursive Green function along with the Landauer formalism, and the thermal transport is simulated with the molecular dynamics. In contrast to a small influence on the thermopower and the electrical conductance of the geometry-modulated nanowires, a large reduction of the thermal conductivity yields an enhancement of the efficiency by 10% to 35% from the typical nanowires. We find that this approach can be easily extended to various structures and materials as we consider the geometrical modulation as a sole source of perturbation to the system.

Electron beam-induced formation of crystalline nanoparticle chains from amorphous cadmium hydroxide nanofibers

Quantum dots (QDs) and especially quantum dot arrays have been attracting tremendous attention due to their potential applications in various high-tech devices, including QD lasers, solar cells, single photon emitters, QD memories, etc. Here, a dendrimer-based approach for the controlled synthesis of ultra-thin amorphous cadmium hydroxide nanofibers was developed. The fragmentation of the obtained nanofibers in crystalline nanoparticle chains under the irradiation with electron beam was observed in both ambient and cryo-conditions. Based on the experimental results, a model for the formation of amorphous nanofibers, as well as their transformation in crystalline nanoparticle chains is proposed. We foresee that these properties of the nanofibers, combined with the possibility to convert cadmium hydroxide into CdX (X=O, S, Se, Te), could result in a new method for the preparation of 2D and 3D QDs-arrays with numerous potential applications in high performance devices.

Quantitative electron phase imaging with high sensitivity and an unlimited field of view

As it passes through a sample, an electron beam scatters, producing an exit wavefront rich in information. A range of material properties, from electric and magnetic field strengths to specimen thickness, strain maps and mean inner potentials, can be extrapolated from its phase and mapped at the nanoscale. Unfortunately, the phase signal is not straightforward to obtain. It is most commonly measured using off-axis electron holography, but this is experimentally challenging, places constraints on the sample and has a limited field of view. Here we report an alternative method that avoids these limitations and is easily implemented on an unmodified transmission electron microscope (TEM) operating in the familiar selected area diffraction mode. We use ptychography, an imaging technique popular amongst the X-ray microscopy community; recent advances in reconstruction algorithms now reveal its potential as a tool for highly sensitive, quantitative electron phase imaging.

Highly automated electron energy-loss spectroscopy elemental quantification

A model-based fitting algorithm for electron energy-loss spectroscopy spectra is introduced, along with an intuitive user-interface. As with Verbeeck & Van Aert, the measured spectrum, rather than the single scattering distribution, is fit over a wide range. An approximation is developed that allows for accurate modeling while maintaining linearity in the parameters that represent elemental composition. Also, a method is given for generating a model for the low-loss background that incorporates plural scattering. Operation of the user-interface is described to demonstrate the ease of use that allows even nonexpert users to quickly obtain elemental analysis results.

Water mapping in hydrated soft materials

We present a method based on spatially resolved electron energy-loss spectroscopy in the cryo-STEM to map the spatial distribution of water in frozen-hydrated polymers. The spatial resolution is limited by the dose constraints imposed by radiation damage, and to stay within these constraints, the use of fine electron-probe sizes comes at the cost of reduced counts in the energy-loss spectra. Thus, at the resolution limit, the detection of isolated water-rich pixels or the identification of minor variations in water content across the specimen is complicated because one must distinguish significant fluctuations from noise. Here we develop a criterion with which to guide such a distinction. We characterize the intrinsic noise associated with spectral measurements under given illumination and acquisition conditions. We then use that noise in combination with scatter diagrams to threshold spectrum images and objectively identify statistically significant compositional fluctuations. We illustrate these ideas using a simulated spectrum dataset for a hypothetical blend of hydrophilic and hydrophobic homopolymers. We show that while a direct inspection of the water map may not allow any meaningful conclusions to be drawn, after applying the thresholding approach we can clearly identify the regions of the specimen that are rich in water. We also experimentally study a model blend system comprised of hydrophilic poly(vinyl pyrrolidone) (PVP) dispersed in a hydrophobic matrix of poly(styrene) (PS). By MLS fitting using damaged and undamaged PVP reference spectra, we determine that the critical dose characteristic of dry PVP is approximately 8000 e/nm2 using 200 keV incident electrons. Irradiating frozen-hydrated PVP gives rise to noticeable hydrogen evolution at doses of approximately 1500 e/nm2. To stay within this constraint we use doses of 400 e/nm2 and a pixel spacing in the spectrum imaging of 100 nm. In order to quantitatively map the water, PVP, and PS compositions, we measure their total inelastic scattering cross-sections. Direct inspection of the composition maps reveals the presence of large water-rich domains of the order of approximately 1 microm and the scatter-diagram thresholding approach identifies small water-rich domains one pixel in size.