Suryaprakash Ganti

Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities

The effect of surface energies, strains, and stresses on the size-dependent elastic state of embedded inhomogeneities are investigated. At nanolength scales, due to the increasing surface-to-volume ratio, surface effects become important and induce a size dependency in the otherwise size-independent classical elasticity solutions. In this letter, closed-form expressions are derived for the elastic state of eigenstrained spherical inhomogeneities with surface effects using a variational formulation. Our results indicate that surface elasticity can significantly alter the fundamental nature of stress state at nanometer length scales. Additional applications of our work on nanostructures such as quantum dots, composites, etc. are implied.

Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies

The classical formulation of Eshelby (Proc. Royal Society, A241, p. 376, 1957) for embedded inclusions is revisited and modified by incorporating the previously excluded surface/interface Stresses, tension and energies. The latter effects come into prominence at inclusion sizes in the nanometer range. Unlike the classical result, our modified formulation renders the elastic state of an embedded inclusion size-dependent making possible the extension of Eshelbys original formalism to nano-inclusions. We present closed-form expressions of the modified Eshelbys tensor for spherical and cylindrical inclusions. Eshelby original conjecture that only inclusions of the ellipsoid family admit uniform elastic state under uniform stress-free transformation strains must be modified in the context of coupled surface/interface-bulk elasticity. We reach an interesting conclusion in that only inclusions with a constant curvature admit a uniform elastic stale, thus restrict-ing this remarkable property only to spherical and cylindrical inclusions. As an immediate consequence of the derivation of modified size-dependent Eshelby tensor for nano-inclusions, we also formulate the overall size-dependent bulk modulus of a composite containing such inclusions. Further applications are illustrated for size-dependent stress concentrations on voids and opto-electronic properties of embedded quantum dots.

Templated wide band-gap nanostructures

In this two-pronged work we report (a) a study of defect nucleation in three-dimensional confined nanoislands and (b) a surface-elasticity induced size effect in the optoelectronic properties of embedded and templated semiconducting nanostructures. Several key features in the design of nanostructure templates are analyzed and dislocation free contour maps are presented for combination of various lattice mismatches, substrates, and geometrical dimensions. Unlike the case for thin epitaxial films, it is found that for nanostructures, below a certain critical lateral dimension, dislocation free structures of any thickness can be grown. With regards to the optoelectronic properties of nanostructures, while size dependency due to quantum confinement and electrostatic interactions are well known, we show that an additional size-dependent strain is caused by the distinct elastic behavior of surfaces and interfaces at the nanoscopic scale compared to the macroscopic scale. This is in contrast to the usual way str...

Gauge-field-theory solution of the elastic state of a screw dislocation in a dispersive (non-local) crystalline solid

The relaxed state of a type of topological defect (screw dislocation) located in a dispersive (non-local) elastic solid is discussed from a viewpoint of gauge field theory. The starting point of this work is the non-local elastic Lagrangian, that is, like its classic elastic counterpart, globally gauge invariant under the Euclidean group of transformations O(3)▹(3). When compared with gauge solutions of the same problem predicated on the classical elastic Lagrangian, the present solution sheds some interesting insights into the nature of non-locality-gauge field interactions. Both the (3) gauge theory of dislocations (predicated on breaking of the translational symmetry) and the phenomenological non-local elasticity introduce their own respective characteristic length-scale parameters in the elastic equilibrium of dislocations while removing unphysical singularities. In the present work we show that, surprisingly, attempts to elucidate gauge interactions in a dispersive or non-local medium lead to functionally the same solution as in the gauge theory based on local elasticity, albeit, the gauge length-scale must be replaced by an effective length-scale measure. In particular, the non-local and the gauge length-scale combine in a nonlinear fashion to yield the aforementioned effective length-scale. Our results allow one to immediately write the solution of most screw dislocation problems in the gauge non-local theory of defects, provided the counterpart gauge solution based on classical elasticity is known.

On the scaling of thermal stresses in passivated nanointerconnects

Much work has been done in the approximation of the stress state of microelectronic interconnects on chips. The thermally induced stresses in passivated interconnects are of interest as they are used as input in interconnect reliability failure models (stress-driven void growth, electromigration-driven void growth). The classical continuum mechanics and physics typically used is, however, intrinsically size independent. This is in contradiction to the physical fact that at the size scale of a few nanometers, the elastic state is size dependent and a departure from classical mechanics is expected. In this work, we address the various physical causes (and the affiliated mathematical modeling) of the size dependency of mechanical stresses in nanointerconnects. In essence, we present scaling laws for mechanical stresses valid for nanosized interconnects.

Prediction of rate-independent constitutive behavior of Pb-free solders based on first principles

This paper presents a methodology for the theoretical estimation of rate-independent plastic constitutive properties of Pb-free solders using three approaches. The first approach is based on a nonlinear effective medium theory (NEMT) that is scale independent. The second approach is based on the micromechanics and physics of plastic slip in heterogeneous alloys (henceforth called the physical model). This approach explicitly includes microstructural features such as grain size, particle size etc. The third approach is a combination of NEMT and the physical model. Our estimates involve no adjustable calibration parameters and are based on first principles and constituent properties. Parametric studies are conducted to show that the physical model is more effective for small particles sizes (nanoscale 5%), large particle sizes (micron size) and large particle spacing (micron scale). The proposed hybrid approach, however, appears to be valid for a wider range of particle sizes and volume fractions. Limited comparison with experimental data is also made and implications of our work in the economical design of novel Pb-free solders is discussed.

Scaling of thermal stresses in passivated nano-interconnects

Much work has been done in the approximation of the stress state of microelectronics interconnects-on-chips. The thermally induced stresses in passivated interconnects are of interest as they are used as input in interconnect reliability failure models (stress-driven void growth, electromigration driven void growth). The typically used classical continuum mechanics and physics is, however, intrinsically size-independent. This is in contradiction to the physical fact that at the size-scale of a few nanometers, the elastic state is size-dependent and a departure from classical mechanics is expected. In this work, we address the various physical causes (and the affiliated mathematical modeling) of the size-dependency of mechanical stresses in nano-interconnects. In essence, we present scaling laws for mechanical stresses valid for nano-sized interconnect.