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

Depth sectioning using environmental and atomic-resolution STEM

(Scanning) transmission electron microscopy (TEM) images of samples in gas and liquid media are acquired with an environmental cell (EC) via silicon nitride membranes. The ratio of sample signal against the background is a significant factor for resolution. Depth-sectioning scanning TEM (STEM) is a promising technique that enhances the signal for a sample embedded in a matrix. It can increase the resolution to the atomic level, thereby enabling EC-STEM applications in important areas. This review introduces depth-sectioning STEM and its applications to high-resolution EC-STEM imaging of samples in gases and in liquids.

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.

Automated calculations for computing the sample-limited spatial resolution in (scanning) transmission electron microscopy

MATLAB scripts were designed to compute the sample-limited spatial resolution in transmission electron microscopy (TEM) and scanning TEM (STEM) as a function of different microscopy parameters including the electron dose eD, sample geometry, and materials parameters. The scripts can be used to select the optimum microscopy modality and optimize the experimental conditions to achieve the best possible resolution considering the limitations set by both the electron optics and the examined sample. The resolution can be computed as function of the objective opening semi-angle α for TEM and detector opening semi-angle β for STEM. Optional code for computing a range over the sample thickness t or eD are provided as well, whereby the opening angle is optimized for each data point. The spatial resolution depends on the type of material of the nanoscale object (for example, gold or carbon nanoparticles), the type of matrix holding the objects (for example, water or ice), the depth of the nanoscale object inside the matrix, and eD. The optimization is consistent with the typical situation that carbon nanoparticles are best examined with TEM embedded in a thin matrix (t = 0.1 µm), while STEM is better suited for high atomic number objects such as gold nanoparticles in water, irrespective of t. The script also calculates the reduction of beam broadening in thick samples (t > 1 µm) using bright field STEM.

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.

The influence of chromatic aberration on the dose-limited spatial resolution of transmission electron microscopy

The effect of chromatic aberration (CC) on the spatial resolution in transmission electron microscopy (TEM) was studied in thick specimens in which the sample becomes the limiting factor in the resolution. The sample influences the energy spread of the electron beam, allows only a limited electron dose, and modulates electron scattering events. The experimental set-up consisted of a thin silicon nitride membrane and a silicon wedge containing gold nanoparticles. The resolution was measured as a function of electron dose and sample thickness for different sample configurations and for different microscopy modalities including regular TEM, energy filtered TEM (EFTEM) and CC-corrected TEM. Comparison with an analytical model aided the understanding of the experimental data applied over varied conditions. The general trend for all microscopy modalities was a transition from a noise-limited resolution at low electron dose to a CC-limited resolution at high-dose in the absence of beam blurring. EFTEM required an accurate energy slit offset and an optimal energy spread to energy-slit width ratio to surpass regular TEM. The key advantage of CC correction appeared to be the best possible resolution for larger sample thickness at low electron dose outperforming EFTEM by about fifty percent. Several hypothetical sample configurations relevant to liquid phase electron microscopy were evaluated as well to demonstrate the capabilities of the analytical model and to determine the most optimal microscopy modality for this type of experiment. The analytical model included an automated optimization of the EFTEM settings and may aid in optimizing the sample-limited resolution for experimental analysis and planning.

Nanoscale Chemical and Structural Analysis during In Situ Scanning/Transmission Electron Microscopy in Liquids

Liquid-cell scanning/transmission electron microscopy (S/TEM) has impacted our understanding of multiple areas of science, most notably nanostructure nucleation and growth and electrochemistry and corrosion. In the case of electrochemistry, the incorporation of electrodes requires the use of silicon nitride membranes to confine the liquid. The combined thickness of the liquid layer and the confining membranes prevents routine atomic-resolution characterization. Here, we show that by performing electrochemical water splitting in situ to generate a gas bubble, we can reduce the thickness of the liquid to a film approximately 30 nm thick that remains covering the sample. The reduced thickness of the liquid allows the acquisition of atomic-scale S/TEM images with chemical and valence analysis through electron energy loss spectroscopy (EELS) and structural analysis through selected area electron diffraction (SAED). This contrasts with a specimen cell entirely filled with liquid, where the broad plasmon peak from the liquid obscures the EELS signal from the sample and induces beam incoherence that impedes SAED analysis. The gas bubble generation is fully reversible, which allows alternating between a full cell and thin-film condition to obtain optimal experimental and analytical conditions, respectively. The methodology developed here can be applied to other scientific techniques, such as X-ray scattering, Raman spectroscopy, and X-ray photoelectron spectroscopy, allowing for a multi-modal, nanoscale understanding of solid-state samples in liquid media.

Zn Electrodeposition by an In Situ Electrochemical Liquid Phase Transmission Electron Microscope

Alternative battery technologies are required to meet growing energy demands and to solve the limitations of the present energy technologies. As such, it is necessary to look beyond lithium-ion batteries. Zinc batteries enable high power density while being sourced from abundant and cost-effective materials. In this paper, the effect of the applied current and electrolyte flow rate on the early stage of Zn dendrite formation was characterized by in situ electrochemical liquid phase transmission electron microscopy (EC-LPTEM). For the first time, the square root relation is revealed between time and Zn dendrite growth on the lateral direction, indicating a diffusion-limited growth. It is intriguing that a higher applied current leads to longer incubation time. In situ EC-LPTEM can provide a useful strategy for understanding characteristics of unstable dendritic growth. The finding can help rationalize the electrode engineering design and parameters selection to avoid dendrite formation.

Particle diameter, signal-to-noise ratio and beam requirements for extended Rayleigh resolution measurements in the scanning electron microscope

The extended Rayleigh resolution measure was introduced to give a generalized resolution measure that can be readily applied to imaging and resolving particles that have finite size. Here, we make a detailed analysis of the influence of the particle size on this resolution measure. We apply this to scanning electron microscopy, under simple assumption of a Gaussian electron beam intensity distribution and a directly proportional emitted signal yield without detailed consideration of scattering internal to the sample, other than being proportional to the sample thickness. From this, we produce beam-width normalized characteristics relating the particle diameter and resolution measure, while also taking consideration of the reduced signal yield that occurs from smaller particles. From our analysis of these characteristics, which we fit to experimental image data, we see that particle diameters <0.7 times the beam 1/e full width, d, give agreement better than 10% with the true extended Rayleigh resolution. Furthermore, we consider the signal current that must be collected to reliably distinguish between the mid-gap and peak intensity regions in the particle images. This leads to a practical guide that the signal-to-noise ratio (SNR) occurring between large area, continuous regions made of the same materials as the particle and background should typically be 10-30 times greater than the SNR that is desired to be achieved between the peak and mid-gap regions of just resolved adjacent identical particles having diameters in the size range 0.4-0.7d.

A Study of Membrane Impact on Spatial Resolution of Liquid In Situ Transmission Electron Microscope

Microchip technology with electron transparent membranes is a key component for in situ liquid transmission electron microscope (TEM) characterization. The membranes can significantly influence the TEM imaging spatial resolution, not only due to introducing additional material layers but also due to the associated bulging. The membrane bulging is largely defined by the membrane materials, thickness, and short dimension. The impact of the membrane on the spatial resolution, especially the extent of its bulging, was systematically investigated through the impact on the signal-to-noise ratio, chromatic aberration, and beam broadening. The optimization of the membrane parameters is the key component when designing the in situ TEM liquid cell. The optimal membrane thickness of 50 nm was found which balances the impact of membrane bulging and membrane thickness. Beyond this, the short membrane window dimension and the chip nominal spacing should be minimized. However, these two parameters have practical limitations in regards to chip handling.

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.