Elastic and inelastic mean free paths of 200keV electrons in metallic glasses.

The elastic and inelastic mean free paths of three metallic glass alloys, Ni60Nb40, Pd82Si18 and Ni80P20, have been measured from focused ion beam prepared thin samples with measured thickness gradients. The elastic/inelastic mean free paths of the three alloys are 35±0.5/97±3, 26±0.5/148±3 and 40±0.5/129±2.5nm, respectively. Elastic mean free paths predicted from atomic scattering cross sections consistently underestimate the experimental data. A model based on the Wentzel atomic model was developed and the fit to available data is in much better agreement with experiments, with a maximum deviation of ~4nm. The parametrized model is thus capable of predicting the elastic mean free path for other amorphous materials. Existing models for the inelastic mean free path are not in good agreement with the experimental data.

Thermal Resistance of Transferred-Silicon-Nanomembrane Interfaces.

We report measurements of the interfacial thermal resistance between mechanically joined single crystals of silicon, the results of which are up to a factor of 5 times lower than any previously reported thermal resistances of mechanically created interfaces. Detailed characterization of the interfaces is presented, as well as a theoretical model incorporating the critical properties determining the interfacial thermal resistance in the experiments. The results demonstrate that van der Waals interfaces can have very low thermal resistance, with important implications for membrane-based micro- and nanoelectronics.

Inelastic and elastic mean free paths from FIB samples of metallic glasses.

We have used focused ion beam (FIB) milling and scanning electron microscopy (SEM) to prepare samples of known thickness for measurement of the electron scattering elastic and inelastic mean free paths (EMFP and IMFP respectively) of three metallic glasses, Cu(64.5)Zr(35.5), Zr(50)Cu(45)Al(5), and Al(87)Y(7)Fe(5)Cu. After measuring the EMFP and IMFP in a scanning transmission electron microscope, we used the FIB to coat the lamellae with carbon on the top and bottom surfaces, which eliminated secondary electron emission from those surfaces and made SEM measurements of their thickness more reliable. At 200 kV, we find IMFP/ EMFP values of 146±2/43±1, 163±1/41±1, and 149±1/85±1 nm, respectively for the three glass compositions. Our results differ from available models for the IMFP by as much as 50%.

Nanoscale structure and structural relaxation in Zr50Cu45Al5 bulk metallic glass.

Hybrid reverse Monte Carlo simulations of the structure of Zr50Cu45Al5 bulk metallic glass incorporating medium-range structure from fluctuation electron microscopy data and short-range structure from an embedded atom potential produce structures with significant fractions of icosahedral- and crystal-like atomic clusters. Similar clusters group together into nanometer-scale regions, and relaxation transforms crystal-like clusters into icosahedral clusters. A model refined against only the potential does not agree with the fluctuation microscopy data and contains few crystal-like clusters.

Analytical and computational modeling of fluctuation electron microscopy from a nanocrystal/amorphous composite.

A nanocrystal/amorphous composite is an idealized model of the medium-range order structure in a variety of amorphous materials. We have investigated the fluctuation electron microscopy (FEM) signal from such a model analytically and with computer simulations. In the analytical modeling, we improved the previous model by Stratton and Voyles (Ultramicroscopy 108, 727 (2008)) by introducing the partial occupancy of nanocrystals in a column, the effect of the deviation parameter on the diffracted intensity, and a distribution of nanocrystal sizes. The improved model no longer has a maximum in the FEM signal as a function of the volume fraction of nanocrystals. In the computer modeling, we compared the variance calculated using kinematic scattering and dynamical scattering and investigated the effects of disorder and strain inside the nanocrystals on the variance. The variance based on dynamical scattering is about 15% smaller than that based on kinematic scattering. Disorder introduced in the nanocrystal reduces the variance peaks at all scattering vectors, with a much larger reduction at longer scattering vector.

Effect of sample thickness, energy filtering, and probe coherence on fluctuation electron microscopy experiments.

We have explored experimentally the effects of the TEM sample thickness, zero-loss energy filtering, and probe coherence on fluctuation electron microscopy (FEM) experiments implemented using nanodiffraction. FEM measures the variance V of spatial fluctuations in nanodiffraction. We find that V is inversely proportional to the sample thickness, as predicted by earlier models. Energy filtering increases V at all thicknesses we measured. V increases as the coherence of the probe increases. All of these factors must be carefully controlled to obtain quantitatively reliable FEM data.

Variable resolution fluctuation electron microscopy on Cu-Zr metallic glass using a wide range of coherent STEM probe size.

We report variable resolution fluctuation electron microscopy (VRFEM) measurements on Cu64.5Zr35.5 metallic glass acquired using scanning transmission electron microscopy nanodiffraction using coherent probes 0.8 to 11 nm in diameter. The VRFEM results show that medium range atomic order structure of Cu64.5Zr35.5 bulk metallic glass at the ∼ 1 nm scale has large fluctuations, but the structure becomes almost completely homogeneous at the 11 nm scale. We show that our experimental VRFEM data are consistent with two different models, the pair persistent model and the amorphous/nanocrystal composite model. We also report a new way to filter VRFEM data to eliminate the effect of specimen thickness gradient using high-angle annular dark field images as references.

A phenomenological model of fluctuation electron microscopy for a nanocrystal/amorphous composite.

Fluctuation electron microscopy (FEM) is a quantitative electron microscopy technique in which we use the variance V of spatial fluctuations in nanodiffraction as a function of the diffraction vector magnitude k and real-space resolution R to detect medium-range order in amorphous materials. We have developed a model for V(k, R) from a nanocrystal/amorphous composite, which is an idealized form of the medium-range order in various amorphous materials found by previous FEM measurements. The resulting expression for V(k, R) as a function of the nanocrystal size, nanocrystal volume fraction, and the sample thickness connects the FEM signal to well-defined aspects of the material's structure, emphasizes the need for samples of controlled thickness, and explains in some cases the relative height of peaks in V(k). We give an example of interpreting FEM data in terms of this model using recent experiments on amorphous Al88Y7Fe5.

Prospects for 3D, nanometer-resolution imaging by confocal STEM.

Confocal STEM is a new electron microscopy imaging mode. In a microscope with spherical aberration-corrected electron optics, it can produce three-dimensional (3D) images by optical sectioning. We have adapted the linear imaging theory of light confocal microscopy to confocal STEM and use it to suggest optimum imaging conditions for a confocal STEM limited by fifth-order spherical aberration. We predict that current or near-future microscopes will be able to produce 3D images with 1 nm vertical resolution and sub-Angstrom lateral resolution. Multislice simulations show that we will need to be cautious in interpreting these images, however, as they can be complicated by dynamical electron scattering.

Depth-dependent imaging of individual dopant atoms in silicon.

We have achieved atomic-resolution imaging of single dopant atoms buried inside a crystal, a key goal for microelectronic device characterization, in Sb-doped Si using annular dark-field scanning transmission electron microscopy. In an amorphous material, the dopant signal is largely independent of depth, but in a crystal, channeling of the electron probe causes the image intensity of the atomic columns to vary with the depths of the dopants in each column. We can determine the average dopant concentration in small volumes, and, at low concentrations, the depth in a column of a single dopant. Dopant atoms can also serve as tags for experimental measurements of probe spreading and channeling. Both effects remain crucial even with spherical aberration correction of the probe. Parameters are given for a corrected Bloch-wave model that qualitatively describes the channeling at thicknesses 20 nm, but does not account for probe spreading at larger thicknesses. In thick samples, column-to-column coupling of the probe can make a dopant atom appear in the image in a different atom column than its physical position.

Evidence for a new class of defects in highly n-doped Si: donor-pair-vacancy-interstitial complexes.

Electron channeling experiments performed on individually scanned, single columns of atoms show that in highly n-type Si grown at low temperatures the primary electrically deactivating defect cannot belong to either the widely accepted class of donor-vacancy clusters or a recently proposed class of donor pairs. First-principles calculations suggest a new class of defects consisting of two dopant donor atoms near a displaced Si atom, which forms a vacancy-interstitial pair. These complexes are consistent with the present experimental results, the measured open volume of the defects, the observed electrical activity as a function of dopant concentration, and the enhanced diffusion of impurities in the presence of deactivated dopants.

Imaging individual atoms inside crystals with ADF-STEM.

The quantitative imaging of individual impurity atoms in annular dark-field scanning transmission electron microscopy (ADF-STEM) requires a clear theoretical understanding of ADF-STEM lattice imaging, nearly ideal thin samples, and careful attention to image processing. We explore the theory using plane-wave multislice simulations that show the image intensity of substitutional impurities is depth-dependent due to probe channeling, but the intensity of interstitial impurities need not be. The images are only directly interpretable in thin samples. For this reason, we describe a wedge mechanical polishing technique to produce samples less than <50 A thick, with low surface roughness and no amorphous surface oxide. This allows us to image individual dopants as they exist within a bulk-like silicon environment. We also discuss the image analysis techniques used to extract maximum quantitative information from the images. Based on this information, we conclude that the primary nanocluster defect responsible for the electrical inactivity of Sb in Si at high concentration consists of only two atoms.

Fluctuation microscopy in the STEM.

Fluctuation electron microscopy is a technique for studying medium-range order in disordered materials. We present an implementation of fluctuation microscopy using nanodiffraction in a scanning transmission electron microscope (STEM) at a spatial resolution varying from 0.8 to 5.0 nm. Compared to conventional TEM (CTEM), the STEM-based technique offers a denser scattering vector sampling at a reduced sample dose and easier access to variable resolution information. We have reproduced results on amorphous silicon previously obtained by CTEM-based fluctuation microscopy, and report initial variable-resolution measurements on amorphous germanium.

Atomic-scale imaging of individual dopant atoms and clusters in highly n-type bulk Si.

As silicon-based transistors in integrated circuits grow smaller, the concentration of charge carriers generated by the introduction of impurity dopant atoms must steadily increase. Current technology, however, is rapidly approaching the limit at which introducing additional dopant atoms ceases to generate additional charge carriers because the dopants form electrically inactive clusters. Using annular dark-field scanning transmission electron microscopy, we report the direct, atomic-resolution observation of individual antimony (Sb) dopant atoms in crystalline Si, and identify the Sb clusters responsible for the saturation of charge carriers. The size, structure, and distribution of these clusters are determined with a Sb-atom detection efficiency of almost 100%. Although single heavy atoms on surfaces or supporting films have been visualized previously, our technique permits the imaging of individual dopants and clusters as they exist within actual devices.

Absence of an abrupt phase change from polycrystalline to amorphous in silicon with deposition temperature.

Using fluctuation electron microscopy, we have observed an increase in the mesoscopic spatial fluctuations in the diffracted intensity from vapor-deposited silicon thin films as a function of substrate temperature from the amorphous to polycrystalline regimes. We interpret this increase as an increase in paracrystalline medium-range order in the sample. A paracrystal consists of topologically crystalline grains in a disordered matrix; in this model the increase in ordering is caused by an increase in the grain size or density. Our observations are counter to the previous belief that the amorphous to polycrystalline transition is a discontinuous disorder-order phase transition.