Vinod K. Tewary

Surface acoustic wave methods to determine the anisotropic elastic properties of thin films

We have developed experimental and analytical methods to measure the anisotropic elastic properties of thin supported films. In this approach, surface acoustic waves (SAWs) were generated using a line-focused laser. Waves with frequency components up to 400 MHz were detected by a Michelson interferometer. Dispersion relations for the SAW phase velocity were calculated from displacement waveforms acquired with source-detector separations of 5-15 mm. To determine film properties from the dispersion relations, we developed a new inversion algorithm based on the delta-function representation of the fully anisotropic, elastodynamic Green function for wave propagation. Our methods were first applied to an elastically isotropic aluminium film on an isotropic fused silica substrate. The results show the validity of our methods and were in good agreement with literature values. The results also illustrate various aspects of measurement uncertainty. The same SAW methods were used to examine a series of titanium nitride films on single-crystalline silicon wafers. The inversion results assuming orthotropic elastic symmetry indicated that c11 increased and c13 decreased with increasing film thickness. Values for the film thickness determined by our analysis were in good agreement with destructive measurements of the actual thicknesses.

Thin-Film Elastic-Property Measurements With Laser-Ultrasonic SAW Spectrometry

Abstract We have developed laser-ultrasonic methods to evaluate the elastic properties of thin films. Our method, called SAW spectrometry, used broadband surface acoustic waves (SAWs) generated by a line-focused, pulsed laser. SAWs with frequency components up to ∼400 MHz were detected by a Michelson interferometer. Dispersion relations for the phase velocity vs. frequency were calculated from displacement waveforms acquired over a range of source–detector separations. Quantitative elastic-property information was obtained from the dispersion relations with a newly developed inversion algorithm. The algorithm was based on the delta-function representation of the elastodynamic Greens function for anisotropic layered systems. The methods were tested by applying them to a molybdenum film on a single-crystal silicon wafer. Values obtained for the films Poisson ratio and Youngs modulus were consistent with literature values. We also used SAW spectrometry to investigate several samples containing titanium nitride films on silicon substrates. Assuming literature values for the film density and Poisson ratio, we applied the inversion algorithm to determine the thickness and Youngs modulus of each film. Youngs modulus in the films was found to increase monotonically with increasing film thickness from 368 to 453 GPa. Inversion results for the film thickness were in very good agreement with destructive measurements of the actual thicknesses.

Greens functions for boundary element analysis of anisotropic bimaterials

We present several Greens functions for anisotropic bimaterials for two-dimensional elasticity and steady-state heat transfer problems. The details of the various Greens functions for perfect, slipping, and cracked interfaces are given for mechanical loading conditions. Previously reported formulations for cubic materials are extended to materials with general anisotropy in which plane strain deformations can exist. We also give the steady-state Greens function for thermal loading of a bimaterial with a perfectly bonded interface. The Greens functions are incorporated in boundary integral formulations and method of fundamental solutions formulations for analysis of finite solids under general boundary conditions.

Simulation of lattice strain due to a CNT–metal interface

We report an atomistic molecular statics study of strains in single wall carbon nanotubes (SWCNTs) interfaced with a planar nickel surface. We calculate axial and radial strain distributions along the SWCNT axis. We demonstrate axial strains of up to 2% extending over a distance of ∼ 10 nm away from the interface along the CNT axis. In addition to the effect of strains on the thermal and mechanical properties of a CNT-metal contact, our results suggest a significant contribution to the contact electrical resistance via local strain-induced modification in the SWCNT electron energy band structure.

Theory of elastic wave propagation in anisotropic film on anisotropic substrate: TiN film on single-crystal Si.

The delta-function representation of the elastodynamic Greens function is used to derive an expression for the elastic wave forms on the surface of an anisotropic thin film on an anisotropic substrate due to a point or a line source located at the surface of the film. The dispersion relation for surface acoustic waves (SAWs) is obtained from the poles of the Greens function. A computationally efficient algorithm is formulated to obtain the elastic constants and the density of the film from the SAW dispersion data. The theory is used to analyze measured SAW dispersion relations in a titanium nitride film on silicon. The analysis yields values of the elastic constants and the density of the film. Excellent agreement is obtained between the theoretical and experimental dispersion results. Calculated wave forms for the surface wave due to a pulsed line source on the surface of the film are reported.

Static responses of a multilayered anisotropic piezoelectric structure to point force and point charge

This paper studies three-dimensional (3D) static responses of a multilayered anisotropic piezoelectric structure due to a point force and point charge. The materials in each layer are homogeneous, generally anisotropic, and linearly piezoelectric, and in general different from one another. The interfaces between adjacent layers are perfectly bonded. The generalized Stroh formalism and two-dimensional (2D) Fourier transforms are employed to find the responses in terms of a 2D integral. For a layered structure made of ten alternating layers of piezoelectric AlN and InN on an InN substrate, we show that the responses due to the point force and point charge are greatly influenced by the material layering, showing complicated patterns through the layer thickness. Furthermore, the responses exhibit the asymptotic behavior in the case of homogeneous infinite space/half-space in a very short distance to the point source, about one tenth of the layer thickness. The complicated responses due to the layered heterogeneity dictate the need for a general 3D analysis in the design of such smart structures.

Lattice-Statics Model for Edge Dislocations in Crystals

Abstract A semianalytical lattice-statics model is described for calculating the lattice distortion due to an edge dislocation in a crystal lattice to a desired degree of approximation. The edge dislocation is created by introducing a half-plane of vacancies. The defect space is decomposed into a part that has translation symmetry and a localized end space. The displacement field in the translationally symmetric part is calculated in terms of a constant Kanzaki force that is related to the Burgers vector. The Dyson equation for the defect Greens function is then solved by using a matrix partitioning technique in the localized end space. The technique is illustrated by applying it to a sc lattice model.

Application of Time Dependent Green’s Function Method to Scattering of Elastic Waves in Anisotropic Solids

The propagation and scattering of elastic waves provides a valuable tool for the QNDE of composite materials. Since, in general, the composite materials are highly anisotropic, it is important to develop theoretical methods for calculation of wave propagation characteristics in anisotropic media. A lot of work has been done on transient wave propagation in isotropic media but not much in anisotropic media (see, for example [1,2] and other references given there).

2 – Modeling electromigration using the peridynamics approach

: This chapter presents a summary of the information and reasoning needed to justify learning about peridynamics for the purpose of analyzing electromigration and provides guidance for the development of a complete peridynamics analysis. The additions needed to convert the original peridynamics model as developed for mechanics problems to a multiphysics model capable of treating electromigration are reviewed. Experimental data on void drift by electromigration are introduced to provide a specific target for a demonstration of the peridynamical approach. Model results for the basic phenomena of this experiment are presented. The peridynamics approach appears capable of simultaneously accommodating both constitutive laws and explicit treatment of multibody interactions, for handling different aspects of the behavior of the material system to be modeled.

NSF NSDL Materials Digital Library & MSE Education

The National Science Foundation created the National Science Digital Library (NSDL) in order to establish a technical, communal, and organizational framework for access to high quality resources and tools that support innovations in teaching and learning at all levels of science, technology, engineering, and mathematics education. As part of the NSDL, the Materials Digital Library (MatDL) Pathway focuses specifically on serving the materials science (MS) community with a target audience that includes MS undergraduate and graduate students, educators, and researchers. MatDL is a collaborative effort involving the Materials Science and Engineering Laboratory at the National Institute of Standards and Technology, Kent State University, Massachusetts Institute of Technology, University of Michigan, Iowa State University, and Purdue University. Our network of collaborations also includes a Nanoscience Interdisciplinary Research Team, Materials Research Science and Engineering Center, and International Materials Institute. A primary goal of MatDL is to bring materials science research and education closer together. MatDL provides innovative uses of digital libraries and the web as educational media in the MS community with particular emphasis on providing: 1) tools to describe, manage, exchange, archive, and disseminate scientific data 2) workspace for open access development of modeling and simulation tools 3) services and content for virtual labs in large undergraduate introductory science courses, and 4) workspace for collaborative development of core undergraduate MS teaching resources for emerging areas. This paper will provide an overview of the NSDL MatDL Pathway, details about specific aspects of the project, as well as interactions between research and education.