A universal equation for computing the beam broadening of incident electrons in thin films

Three-Dimensional Reconstruction of Interface Roughness and Alloy Disorder in Ge/GeSi Asymmetric Coupled Quantum Wells Using Electron Tomography

Interfaces play an essential role in the performance of ever-shrinking semiconductor devices, making comprehensive determination of their three-dimensional (3D) structural properties increasingly important. This becomes even more relevant in compositional interfaces, as is the case for Ge/GeSi heterostructures, where chemical intermixing is pronounced in addition to their morphology. We use the electron tomography method to reconstruct buried interfaces and layers of asymmetric coupled Ge/Ge0.8Si0.2 multiquantum wells, which are considered a potential building block in THz quantum cascade lasers. The three-dimensional reconstruction is based on a series of high-angle annular dark-field scanning transmission electron microscopy images. It allows chemically sensitive investigation of a relatively large interfacial area of about (80 × 80) nm2 with subnanometer resolution as well as the analysis of several interfaces within the multiquantum well stack. Representing the interfaces as iso-concentration surfaces in the tomogram and converting them to topographic height maps allows the determination of their morphological roughness as well as layer thicknesses, reflecting low variations in either case. Simulation of the reconstructed tomogram intensities using a sigmoidal function provides in-plane-resolved maps of the chemical interface widths showing a relatively large spatial variation. The more detailed analysis of the intermixed region using thin slices from the reconstruction and additional iso-concentration surfaces provides an accurate picture of the chemical disorder of the alloy at the interface. Our comprehensive three-dimensional image of Ge/Ge0.8Si0.2 interfaces reveals that in the case of morphologically very smooth interfaces─depending on the scale considered─the interface alloy disorder itself determines the overall characteristics, a result that is fundamental for highly miscible material systems.

Prediction of primary knock-on damage during electron microscopy characterization of lithium-containing materials

To fulfill power and energy demands, lithium-ion battery (LIB) is being considered as a promising energy storage device. For the development of LIBs, high-resolution electron microscopy characterization of battery materials is crucial. During this characterization, the interaction of beam-electrons with Li-containing materials causes damage through several processes, especially knock-on damage. In this study, we investigated this damage by determining the probability of knock-on damage and performing Monte Carlo simulation. For this objective, the threshold displacement energies (TDEs) were computed using sudden approximation technique for three sets of materials, including pure elements, LiX (X = F, Cl, Br), and Li2MSiO4 (M = Fe, Co, Mn). By including the Climbing-Image Nudge Elastic Band (CI-NEB) method into the sudden approximation approach, it was found that the accuracy of the predicted TDEs could be improved. Results also indicated that at moderate electron energies, the knock-on damage for Li in both its elemental and compound forms maximized. In addition, it was shown that the TDE should be the principal parameter for assessing the Li sensitivity to knock-on damage across similar structures. Nonetheless, other parameters, including cross-section, density, weight fraction, atomic weight, and atomic number, were found to impact the knock-on damage.

Transmission electron microscopy of thick polymer and biological specimens

We explore the properties of elastic and inelastic scattering in a thick organic specimen, together with the mechanisms that provide contrast in a transmission electron microscope (TEM) and scanning-transmission electron microscope (STEM). Experimental data recorded from amorphous carbon are used to predict the bright-field image intensity, mass-thickness contrast and dose-limited resolution as a function of thickness, objective-aperture size, and primary-electron energy E₀. Combining this information with estimates of chromatic aberration, objective-aperture diffraction and beam broadening in the specimen, we calculate the achievable TEM and STEM resolution to be around 4 nm at E₀ = 300 keV (or below 3 nm at MeV energies) for a 10 µm-diameter objective aperture and 1 - 2 µm thickness of hydrated biological tissue. The 3 MeV resolution for a 10-μm tissue sample is probably closer to 10 nm. We also comment on the error involved in quadrature addition of resolution factors, when one or more of the point-spread functions are non-Gaussian.

High-Energy Electron Scattering in Thick Samples Evaluated by Bright-Field Transmission Electron Microscopy, Energy-Filtering Transmission Electron Microscopy, and Electron Tomography

Energy-filtering transmission electron microscopy (TEM) and bright-field TEM can be used to extract local sample thickness $t$ and to generate two-dimensional sample thickness maps. Electron tomography can be used to accurately verify the local $t$. The relations of log-ratio of zero-loss filtered energy-filtering TEM beam intensity ($I_{{\rm ZLP}}$) and unfiltered beam intensity ($I_{\rm u}$) versus sample thickness $t$ were measured for five values of collection angle in a microscope equipped with an energy filter. Furthermore, log-ratio of the incident (primary) beam intensity ($I_{\rm p}$) and the transmitted beam $I_{{\rm tr}}$ versus $t$ in bright-field TEM was measured utilizing a camera before the energy filter. The measurements were performed on a multilayer sample containing eight materials and thickness $t$ up to 800 nm. Local thickness $t$ was verified by electron tomography. The following results are reported:• The maximum thickness $t_{{\rm max}}$ yielding a linear relation of log-ratio, $\ln ( {I_{\rm u}}/{I_{{\rm ZLP}}})$ and $\ln ( {I_{\rm p}}/{I_{{\rm tr}}} )$, versus $t$.• Inelastic mean free path ($\lambda _{{\rm in}}$) for five values of collection angle.• Total mean free path ($\lambda _{{\rm total}}$) of electrons excluded by an angle-limiting aperture.• $\lambda _{{\rm in}}$ and $\lambda _{{\rm total}}$ are evaluated for the eight materials with atomic number from $\approx$10 to 79.The results can be utilized as a guide for upper limit of $t$ evaluation in energy-filtering TEM and bright-field TEM and for optimizing electron tomography experiments.

UV Emission from GaN Wires with m-Plane Core-Shell GaN/AlGaN Multiple Quantum Wells

The present work reports high-quality nonpolar GaN/Al_0.6Ga_0.4N multiple quantum wells (MQWs) grown in core-shell geometry by metal-organic vapor-phase epitaxy on the m-plane sidewalls of c̅-oriented hexagonal GaN wires. Optical and structural studies reveal ultraviolet (UV) emission originating from the core-shell GaN/AlGaN MQWs. Tuning the m-plane GaN QW thickness from 4.3 to 0.7 nm leads to a shift of the emission from 347 to 292 nm, consistent with Schrödinger-Poisson calculations. The evolution of the luminescence with temperature displays signs of strong localization, especially for samples with thinner GaN QWs and no evidence of quantum-confined Stark effect, as expected for nonpolar m-plane surfaces. The internal quantum efficiency derived from the photoluminescence (PL) intensity ratio at low and room temperatures is maximum (∼7.3% measured at low power excitation) for 2.6 nm thick quantum wells, emitting at 325 nm, and shows a large drop for thicker QWs. An extensive study of the PL quenching with temperature is presented. Two nonradiative recombination paths are activated at different temperatures. The low-temperature path is found to be intrinsic to the heterostructure, whereas the process that dominates at high temperature depends on the QW thickness and is strongly enhanced for QWs larger than 2.6 nm, causing a rapid decrease in the internal quantum efficiency.

Unmixing noisy co-registered spectrum images of multicomponent nanostructures

Analytical electron microscopy plays a key role in the development of novel nanomaterials. Electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDX) datasets are typically processed to isolate the background-subtracted elemental signal. Multivariate tools have emerged as powerful methods to blindly map the components, which addresses some of the shortcomings of the traditional methods. Here, we demonstrate the superior performance of a new multivariate optimization method using a challenging EELS and EDX dataset. The dataset was recorded from a spectrum image P-type metal-oxide-semiconductor stack with 7 components exhibiting heavy spectral overlap and a low signal-to-noise ratio. Compared to peak integration, independent component analysis, Baysian Linear Unmixing and Non-negative matrix factorization, the method proposed was the only one to identify the EELS spectra of all 7 components with the corresponding abundance profiles. Using the abundance of each component, it was possible to retrieve the EDX spectra of all the components, which were otherwise impossible to isolate, regardless of the method used. We expect that this robust method will bring a significant improvement for the chemical analysis of nanomaterials, especially for weak signals, dose-sensitive specimen or signals suffering heavy spectral overlap.

Wave-packet numerical investigation of thermal diffuse scattering: A time-dependent quantum approach to electron diffraction simulations

The effects of thermal diffuse scattering on diffraction of highly-accelerated electrons by crystal lattices are investigated with a method that combines the frozen phonon approximation with an exact numerical solution of the time-dependent Schrödinger equation. The phonon configuration for each single-electron diffraction process is determined by means of Einstein's model. It is shown that this procedure provides the possibility of describing and explaining, in a natural way, after averaging over a number of electron realizations, how the typical diffraction features that characterize a fully coherent pattern are gradually suppressed by thermally-induced incoherence. This is achieved by a controlled increase of the lattice atomic vibrations and is in contrast to the use of attenuating Debye-Waller factors and complex potential absorbers. A lattice with reduced dimensionality is first considered as a working model, where the method renders results compatible with those reported in the literature. Subsequently, a full three-dimensional system is simulated and results are compared to experimental imaging displaying the method's reliability.

Electron beam broadening in electron-transparent samples at low electron energies

Scanning transmission electron microscopy (STEM) at low primary electron energies has received increasing attention in recent years because knock-on damage can be avoided and high contrast for weakly scattering materials is obtained. However, the broadening of the electron beam in the sample is pronounced at low electron energies, which degrades resolution and limits the maximum specimen thickness. In this work, we have studied electron beam broadening in materials with atomic numbers Z between 10 and 32 (MgO, Si, SrTiO₃ , Ge) and thicknesses up to 900 nm. Beam broadening is directly measured using a multisegmented STEM detector installed in a scanning electron microscope at electron energies between 15 and 30 keV. For experimental reasons, the electron beam diameter is defined to contain only 68% of the total intensity instead of the commonly used 90% of the total beam intensity. The measured beam diameters can be well described with calculated ones based on a recently published model by Gauvin and Rudinsky. Using the concept of anomalous diffusion the Hurst exponent H is introduced that varies between 0.5 and 1 for different scattering regimes depending on t/Λ_el with the specimen thickness t and the elastic mean free path length Λ_el . The calculations also depend on the fraction of the beam intensity that defines the electron beam diameter. A Hurst exponent H of 1 is characteristic for the ballistic scattering regime with t/Λ_el → 0 and can be excluded for the experimental conditions of our study with 6 ≦ t/Λ_el ≦ 30. We deduced H = 0.75 from measured beam diameters which is larger than H = 0.5 that is expected under diffusion conditions. The deviation towards larger H values can be rationalised by our definition of electron diameter that contains only 68% of the total beam intensity and requires therefore larger sample thicknesses before the diffusion regime is reached. Our results clearly deviate from previous analytical approaches to describe beam broadening (Goldstein et al., Reed, Williams et al., Kohl and Reimer). Measured beam diameters are compared with simulated ones, which are obtained by solving the electron transport equation. This approach is advantageous compared to the commonly used Monte Carlo simulations because it is an exact solution of the electron transport equation and requires less computer time. Simulated beam diameter agree well with the experimental data and yield H = 0.80. LAY DESCRIPTION: In scanning transmission electron microscopy (STEM), a focused electron beam is scanned over an electron-transparent sample and an image is formed by detecting the intensity of the transmitted electrons by a STEM detector. STEM resolution is ultimately limited by the electron beam diameter and can be better than 0.1 nm for the best microscopes. However, the electron-beam diameter increases with increasing specimen thickness because electrons are scattered by the interaction of the specimen material and electrons. Electron scattering leads to a change of the electron propagation direction and reduces focusing of the electron beam. The associated electron-beam broadening degrades the lateral resolution of STEM and generally limits the maximum specimen thickness that can be imaged with good resolution. STEM is up to now mainly performed at high electron energies of 80 keV and above. Lower electron energies are beneficial for the study of weakly scattering and radiation-sensitive materials but electron beam broadening becomes more pronounced with decreasing electron energies. Knowledge of beam broadening is therefore particularly important for the interpretation of STEM images that are taken with low-energy electrons. In this work we have studied electron-beam broadening in different materials with thicknesses up to 900 nm at low electron energies between 15  and 30 keV. Beam broadening is directly measured with a newly developed technique. We compare measured beam diameters with different models on beam broadening from literature and find that only a recently published model is well suited to describe the experimental results under our experimental conditions. In addition, beam broadening is simulated by modelling electron propagation in the specimen. The simulation results agree well with the measured beam diameters.

The Influence of Beam Broadening on the Spatial Resolution of Annular Dark Field Scanning Transmission Electron Microscopy

The spatial resolution of aberration-corrected annular dark field scanning transmission electron microscopy was studied as function of the vertical position z within a sample. The samples consisted of gold nanoparticles (AuNPs) positioned in different horizontal layers within aluminum matrices of 0.6 and 1.0 µm thickness. The highest resolution was achieved in the top layer, whereas the resolution was reduced by beam broadening for AuNPs deeper in the sample. To examine the influence of the beam broadening, the intensity profiles of line scans over nanoparticles at a certain vertical location were analyzed. The experimental data were compared with Monte Carlo simulations that accurately matched the data. The spatial resolution was also calculated using three different theoretical models of the beam blurring as function of the vertical position within the sample. One model considered beam blurring to occur as a single scattering event but was found to be inaccurate for larger depths of the AuNPs in the sample. Two models were adapted and evaluated that include estimates for multiple scattering, and these described the data with sufficient accuracy to be able to predict the resolution. The beam broadening depended on z 1.5 in all three models.