Thermodynamically Stable Colloidal Solids: Interfacial Thermodynamics from the Particle Size Distribution.

True thermodynamic stability of a solid colloidal dispersion is generally unexpected, so much that thorough experimental validation of proposed stable systems remains incomplete. Such dispersions are under investigated and would be of interest due to their long-term stability and insensitivity to preparation pathway. We apply classical nucleation theory (CNT) to such colloidal systems, providing a relationship which links the size-dependent interfacial free energy density of the particles to their size distribution, and use this expression in the fitting of previously reported size distributions for putatively thermodynamically stable nanoparticles. Experimental data from a gold-thiol system exhibiting inverse coarsening or "digestive ripening" can be well-described in terms of a power-law dependence of the interfacial free energy γ on radius based on capacitive charging of the nanoparticles, going as r - 3 , as suggested by prior authors. Data from magnetite nanoparticles in highly basic solutions also can be well-fit using the CNT relation, but with γ going as r - 2 . Slightly better fits are possible if the power of the radius is non-integral, but we stress that more complex models of γ will require richer data sets to avoid the problem of overfitting. Some parameters of the fits are still robustly at odds with earlier models that implicitly assumed absolute thermodynamic stability: first, the extrapolated free energy density of the flat surface in these systems is small and positive, rather than strongly negative; second, the shape of the distributions indicates the solution phase to be supersaturated in monomer relative to the bulk, and thus that these two systems may only be metastable. For future work, we derive expressions for the important statistical thermodynamic and chemical parameters of the interface energy in terms of 1) the surfactant concentration, 2) the temperature dependence, and 3) the concentrations of particles in the tail of the distribution.

Microscale Mapping of Structure and Stress in Barium Titanate.

Cross-correlation of electron backscatter diffraction (EBSD) patterns was used to generate rotation, strain, and stress maps of single-crystal tetragonal barium titanate (BaTiO3) containing isolated, small, sub-micrometer a domains separated from a c-domain matrix by 90° domain boundaries. Spatial resolution of about 30 nm was demonstrated over 5 µm maps, with rotation and strain resolutions of approximately 10-4. The magnitudes of surface strains and, especially, rotations peaked within and adjacent to isolated domains at values of approximately 10-2, i.e., the tetragonal distortion of BaTiO3. The conjugate stresses between a domains peaked at about 1 GPa, and principal stress analysis suggested that stable microcrack formation in the c domain was possible. The results clearly demonstrate the applicability of EBSD to advanced multilayer ceramic capacitor reliability and strongly support the coupling between the electrical performance and underlying mechanical state of BaTiO3-containing devices.

Electron Reflectometry for Measuring Nanostructures on Opaque Substrates.

Here, we present a method for measuring dimensions of nanostructures using specular reflection of electrons from an electronically opaque surface. Development of this method has been motivated by measurement needs of the semiconductor industry1-4, and it can also be more broadly applicable to any periodic, pseudo-periodic or statistically stationary nanostructures or nanopattern on an opaque substrate. In prior work5,6, it was demonstrated through the presentation of proof of concept experiments and simulated examples that Reflective Small Angle Electron Scattering (RSAES) can meet certain dimensional metrology requirements of the semiconductor industry. In RSAES, an entire reflected scattering pattern is measured, with the scattered electrons being of primary interest. Later, in the process of further simulating RSAES, it was serendipitously discovered that dimensional measurement using reflected electrons might be greatly simplified by Electron Reflectometry (ER), whereby the intensity of the specularly reflected electron beam is measured and the scattered beams ignored.7 This innovation may allow faster and cheaper development and deployment or at the very least provide an alternate pathway to exploit the phenomenon of reflected electrons for dimensional measurement. Here we discuss how ER complements existing dimensional measurement techniques, show simulated applications with an emphasis an defect detection and line-width measurements.

Strain measurement of 3D structured nanodevices by EBSD.

We present a new methodology to accurately measure strain magnitudes from 3D nanodevices using Electron Backscatter Diffraction (EBSD). Because the dimensions of features on these devices are smaller than the interaction volume for backscattered electrons, EBSD patterns from 3D nanodevices will frequently be the superposition of patterns from multiple material regions simultaneously. The effect of this superposition on EBSD strain measurement is demonstrated, along with an approach to separate EBSD patterns from these devices via subtraction. The subtraction procedure is applied to 33 nm wide SiGe lines, and it provides accurate strain magnitudes where the traditional EBSD strain analysis method undervalues the strain magnitude by an order of magnitude. The approach provides a strain measurement technique for nanoscale 3D structures that is high spatial resolution, nondestructive, and accurate.

Reflective Small Angle Electron Scattering to Characterize Nanostructures on Opaque Substrates.

Features sizes in integrated circuits (ICs) are often at the scale of 10 nm and are ever shrinking. ICs appearing in today's computers and hand held devices are perhaps the most prominent examples. These smaller feature sizes demand equivalent advances in fast and accurate dimensional metrology for both development and manufacturing. Techniques in use and continuing to be developed include X-ray based techniques, optical scattering and of course the electron and scanning probe microscopy techniques. Each of these techniques have their advantages and limitations. Here the use of small angle electron beam scattering measurements in a reflection mode (RSAES) to characterize the dimensions and the shape of nanostructures on flat and opaque substrates is demonstrated using both experimental and theoretical evidence. In RSAES, focused electrons are scattered at angles smaller than 1° with the assistance of electron optics typically used in transmission electron microscopy. A proof-of-concept experiment is combined with rigorous electron reflection simulations to demonstrate the efficiency and accuracy of RSAES as a method of non-destructive measurement of shapes of features less than 10 nm in size on flat and opaque substrates.

Near-theoretical fracture strengths in native and oxidized silicon nanowires.

In this letter, fracture strengths σ f of native and oxidized silicon nanowires (SiNWs) were determined via atomic force microscopy bending experiments and nonlinear finite element analysis. In the native SiNWs, σ f in the Si was comparable to the theoretical strength of Si〈111〉, ≈22 GPa. In the oxidized SiNWs, σ f in the SiO2 was comparable to the theoretical strength of SiO2, ≈6 to 12 GPa. The results indicate a change in the failure mechanism between native SiNWs, in which fracture originated via inter-atomic bond breaking or atomic-scale defects in the Si, and oxidized SiNWs, in which fracture initiated from surface roughness or nano-scale defects in the SiO2.

Stochastic behavior of nanoscale dielectric wall buckling.

The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties-all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts.

Assessing strain mapping by electron backscatter diffraction and confocal Raman microscopy using wedge-indented Si.

The accuracy of electron backscatter diffraction (EBSD) and confocal Raman microscopy (CRM) for small-scale strain mapping are assessed using the multi-axial strain field surrounding a wedge indentation in Si as a test vehicle. The strain field is modeled using finite element analysis (FEA) that is adapted to the near-indentation surface profile measured by atomic force microscopy (AFM). The assessment consists of (1) direct experimental comparisons of strain and deformation and (2) comparisons in which the modeled strain field is used as an intermediate step. Direct experimental methods (1) consist of comparisons of surface elevation and gradient measured by AFM and EBSD and of Raman shifts measured and predicted by CRM and EBSD, respectively. Comparisons that utilize the combined FEA-AFM model (2) consist of predictions of distortion, strain, and rotation for comparison with EBSD measurements and predictions of Raman shift for comparison with CRM measurements. For both EBSD and CRM, convolution of measurements in depth-varying strain fields is considered. The interconnected comparisons suggest that EBSD was able to provide an accurate assessment of the wedge indentation deformation field to within the precision of the measurements, approximately 2×10(-4) in strain. CRM was similarly precise, but was limited in accuracy to several times this value.

Combining nanocalorimetry and dynamic transmission electron microscopy for in situ characterization of materials processes under rapid heating and cooling.

Nanocalorimetry is a chip-based thermal analysis technique capable of analyzing endothermic and exothermic reactions at very high heating and cooling rates. Here, we couple a nanocalorimeter with an extremely fast in situ microstructural characterization tool to identify the physical origin of rapid enthalpic signals. More specifically, we describe the development of a system to enable in situ nanocalorimetry experiments in the dynamic transmission electron microscope (DTEM), a time-resolved TEM capable of generating images and electron diffraction patterns with exposure times of 30 ns-500 ns. The full experimental system consists of a modified nanocalorimeter sensor, a custom-built in situ nanocalorimetry holder, a data acquisition system, and the DTEM itself, and is capable of thermodynamic and microstructural characterization of reactions over a range of heating rates (10(2) K/s-10(5) K/s) accessible by conventional (DC) nanocalorimetry. To establish its ability to capture synchronized calorimetric and microstructural data during rapid transformations, this work describes measurements on the melting of an aluminum thin film. We were able to identify the phase transformation in both the nanocalorimetry traces and in electron diffraction patterns taken by the DTEM. Potential applications for the newly developed system are described and future system improvements are discussed.

Prototype cantilevers for quantitative lateral force microscopy.

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements.