The effect of edge compliance on the contact between a spherical indenter and a high-aspect-ratio rectangular fin.

In the last two decades, significant progress has been made on developing new nanoscale mechanical property measurement techniques including instrumented indentation and atomic force microscopy based techniques. The changes in the tip-sample contact mechanics during measurements uniquely modify the displacement and force sensed by a measurement sensor and much effort is dedicated to correctly retrieve the sample mechanical properties from the measured signal. It turns out that in many cases, for the sake of simplicity, a simple contact mechanics model is adopted by overlooking the complexity of the actual contact geometry. In this work, a newly developed matrix formulation is used to solve the stress and strain equations for samples with edge geometries. Such sample geometries are often encountered in today's nanoscale integrated electronics in the form of high-aspect-ratio fins with widths in the range of tens of nanometers. In the matrix formulation, the fin geometries can be easily modeled as adjacent overlapped half-spaces and the contact problem can be solved by a numerical implementation of the conjugate gradient method. This method is very versatile in terms of contact geometry and contact interaction, either non-adhesive or adhesive. The discussion will incorporate a few model examples that are relevant for the nanoscale mechanics investigated by intermittent contact resonance AFM (ICR-AFM) on low-k dielectric fins of high-aspect-ratio. In such ICR-AFM measurements, distinct dependence of the contact stiffness was observed as a function of the applied force and distance from the edges of the fins. These dependences were correctly predicted by the model and used to retrieve the mechanical changes undergone by fins during fabrication and processing.

Relationships between chemical structure, mechanical properties and materials processing in nanopatterned organosilicate fins.

The exploitation of nanoscale size effects to create new nanostructured materials necessitates the development of an understanding of relationships between molecular structure, physical properties and material processing at the nanoscale. Numerous metrologies capable of thermal, mechanical, and electrical characterization at the nanoscale have been demonstrated over the past two decades. However, the ability to perform nanoscale molecular/chemical structure characterization has only been recently demonstrated with the advent of atomic-force-microscopy-based infrared spectroscopy (AFM-IR) and related techniques. Therefore, we have combined measurements of chemical structures with AFM-IR and of mechanical properties with contact resonance AFM (CR-AFM) to investigate the fabrication of 20-500 nm wide fin structures in a nanoporous organosilicate material. We show that by combining these two techniques, one can clearly observe variations of chemical structure and mechanical properties that correlate with the fabrication process and the feature size of the organosilicate fins. Specifically, we have observed an inverse correlation between the concentration of terminal organic groups and the stiffness of nanopatterned organosilicate fins. The selective removal of the organic component during etching results in a stiffness increase and reinsertion via chemical silylation results in a stiffness decrease. Examination of this effect as a function of fin width indicates that the loss of terminal organic groups and stiffness increase occur primarily at the exposed surfaces of the fins over a length scale of 10-20 nm. While the observed structure-property relationships are specific to organosilicates, we believe the combined demonstration of AFM-IR with CR-AFM should pave the way for a similar nanoscale characterization of other materials where the understanding of such relationships is essential.

Nanoscale tomographic reconstruction of the subsurface mechanical properties of low-k high-aspect ratio patterns.

In this work, intermittent contact resonance atomic force microscopy (ICR-AFM) was performed on high-aspect ratio a-SiOC:H patterned fins (100 nm in height and width from 20 to 90 nm) to map the depth and width dependencies of the material stiffness. The spatial resolution and depth sensitivity of the measurements were assessed from tomographic cross-sections over various regions of interest within the 3D space of the measurements. Furthermore, the depth-dependence of the measured contact stiffness over the scanned area was used to determine the sub-surface variation of the elastic modulus at each point in the scan. This was achieved by iteratively adjusting the local elastic profile until the depth dependence of the resulted contact stiffness matched the depth dependence of the contact stiffness measured by ICR-AFM at that location. The results of this analysis were assembled into nanoscale sub-surface tomographic images of the elastic modulus of the investigated SiOC:H patterns. A new 3D structure-property representation emerged from these tomographic images with direct evidence for the alterations sustained by the structures during processing.