Fall 2006

Notes for students who are preparing for the final.

1. Time: 9:15 am, Thursday, 18 January 2006. Place: Sever Hall 206. No notes or books. Calculators are allowed.
2. There will be 3 hours and 5 problems.
   
3. Exam problems will mostly draw upon homework and parts of the lecture notes covered in class. The exam intends to test your understanding of the material covered in the course, not your creativity.
   
4. For the last two topics covered in class, finite deformation and strings and elastica, there was no homework, but some exercises are scattered in the notes. They may appear in the final.
5. For equations, you will need to memorize the most basic ones, such as equilibrium equations, Hooke's law, and strain-displacement relations. But for anything that you cannot remember, you should be able to derive.

Grade distribution

Notes are attached.  Return to the outline of the course.

Find attached my powerpoint presentation and my report.

Stress-induced voiding (SIV) is investigated in Cu-based, deep-submicron, dual damascene technology. Two failure modes are revealed by TEM failure analysis. For one mode, voids are formed under the via when the via connects a wide metal lead below it. For the via which is instead under a wide metal line, voids are formed right above the via bottom. The void source results from the supersaturated vacancies which develop when Cu is not properly annealed after electroplating and before being constrained by dielectrics. The driving force comes from the stress built up due to grain growth and the thermal expansion mismatch (CTE) between Cu interconnect and dielectrics. A diffusion model is introduced to investigate the voiding mechanism primarily for the vias connected to wide metal leads.

The notes are part of the course on advanced elasticity. 

I plan to explore the Saint-Venant torsion problem applied to prismatic bars with elastic-plastic behavior. Wagner and Gruttmann have developed a finite element method to obtain the elastic/plastic stresses of a bar using a single load step. In particular, I will present the constitutive model that they have developed, and then use ABAQUS to apply Wagner and Gruttmann’s model to various cross-sections. I will try to reproduce their results for some simple cross-sections, as well as exploring some more complicated cross sections.

Dislocations are common in epitaxial systems. For a thin film epitaxially grown on a substrate with coherent interface, it may have spontaneously-formed dislocations when its thickness is larger than certain value, i.e. critical thickness. The presence of dislocations can have an adverse effect on electrical performance of semiconductor materials, providing easy diffusion paths for dopants to lead to short circuits, or recombination centers to reduce carrier density. And, formation of dislocations is one of the most observed mechanisms of relaxation of mismatch strain. However, in optoelectric applications, strain alters the electronic bandgap and band edge alignment, and should be maintained. So, controlling formation of dislocations is very important in the manufacture of microelectronic and optoelectronic devices.

This term paper will review some basic concepts and try to produce some understanding about the control dislocation formation.

Today low-k dielectric materials are integrated into computer chips to improve the operation speed and reduce the cross-talk noise. Due to weak mechanical properties of low-k dielectric materials, cohesive failure is subjected to occur. Channel cracking is one common mode of cohesive failure. In this term paper, several potential issues relevant to channel cracking of low-k dielectric thin films are reviewed.

The mechanical performance of a homogeneous material can be varied by the addition of second-phase particles. In this project, we will model a planar composite under plastic deformation. As shown on the following figure, the composite consists of matrix material and randomly-distributed inclusion particles. The matrix is assumed to be an elastic-plastic material with isotropic or kinematic hardenings, and the inclusion particle pure elastic with a higher Young’s modulus. The stress/strain field throughout the composite will be calculated numerically with finite element method.

For films or coatings deposited on substrate at high temperature, residual compressive stresses are often induced in the surface layers because of the mismatch in the thermal expansion coefficients. Under such compressive residual stresses, the surface thin film is susceptible to buckling-driven delamination. Various shapes of buckled region are observed, including long straight-sided blisters, circular and the ‘telephone cord’ blister.