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Stress-Induced Voiding in Interconnects

Early aluminum lines had the width much larger than the thickness. They behaved like blanket films. When narrow aluminum lines were introduced, in early 1980s, with the width comparable to the thickness, voids were observed in such narrow interconnects on wafers held in ovens, or even on wafers left on shelves at room temperature. The voids may sever the interconnects.

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Grain growth

A polycrystal, held at temperature for some time t, the average grain diameter grows. A grain grows at the expense of its neighbors: small grains disappear and big ones get bigger. Total number of atoms is conserved.

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Grain Boundary Cavitation

Hull and Rimmer (1959) studied grain boundary cavitation. Small voids were observed at grain boundaries, particularly those transverse to the applied tensile stress. Fracture results from the growth and coalescence of these voids.

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Rayleigh Instability

Rayleigh (1878) examined a common experience: a thin jet of liquid is unstable and breaks into droplets. When a jet is thin enough, the effect of gravity is negligible compared to surface energy. The jet changes its shape to reduce the total surface energy. Liquid flow sets the time.

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Grain boundary grooving

A polished polycrystal has a flat surface. At room temperature, the surface remains flat for a long time. At an elevated temperature atoms move. The surface grows grooves along triple junctions, where the surface meet grain boundaries. The grooves reveal the grain boundaries in the microscope. Atoms may move in many ways. They may diffuse in the lattice, diffuse on the surface, or evaporate into the vapor phase. Here we will only consider surface diffusion. Atoms diffuse on the surface away from the triple junction, making a dent along the junction, and piling two bumps nearby.

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Surface diffusion

Some phenomena due to surface diffusion:

  • Flattening a surface.
  • Spherodizing.
  • Rayleigh instability.
  • Grain boundary grooving.
  • Sintering
    Self-assembled quantum dots
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Creep and Self-diffusion

Diffusion and creep involve the same atomic process: atoms must change neighbors, aided by thermal energy. We explore their relation in this lecture.

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The algorithm of thermodynamics

I have taught this course four times before, but have never devoted lectures on basic thermodynamics. It is a subject I’m not good at, but I have used it often in research, in a loose way. One can ride a bicycle without knowing Newton’s laws, even though bicycle-riding is governed by Newton’s law. If thermodynamics gives me so much trouble, perhaps it also gives my students a lot of trouble. I have taken lectures from many teachers on the subject. None have really made me feel comfortable with it. Now I’m trying to teach you. I hope that I can help you become comfortable with the subject. Maybe you already are. Maybe you never will. I have no evidence that I can be more effective than these other teachers, but I have the enthusiasm of an amateur.

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Vacancy diffusion

Cavity Growth Is Caused by a Series of Tiny Effects

  • A tiny fraction of lattice sites are vacant.
  • The tensile stress increases the vacancy concentration at the external surface by a tiny fraction.
  • The tiny nonunifomity in the vacancy concentration drives diffusion.
  • A tiny fraction of vacancies change site, by an atomic distance.
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Cavity growth

A solid contains a spherical cavity, subject to a hydrostatic stress. For now, we assume that the solid is stiff so we ignore its deformation. The cavity can still change its size by a special mechanism: atoms diffuse through the solid between the cavity surface and the external surface. We will concentrate in this lecture on the question, Will the cavity shrink or enlarge? We will consider the diffusion process in some detail in the next lecture, and answer the question, How fast will the cavity change its size?

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How does temperature become a number

An essential step to “understand” thermodynamics is to get to know temperature: how temperature comes down as an abstraction from empirical observations, and how it rises up as a consequence of the fundamental postulate.  I have just updated my notes on temperature.  The beginning paragraphs of the notes abstract temperature from empirical observations.  These paragraphs are posted here.

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Memories of IT. Part 2

Looking back at episodes of our lives, we reflect on how people meet and how such meetings change lives.  Information technology, broadly interpreted as means of communication among people, is always part of these narratives.  But central to such narratives are nearly always people themselves and the content of their communication, rather than the means of their communication. 

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iMechanica has reached 10,000 registered users

The number of registered users of iMechanica exceeded 10,000 the other day.  The total number of posts is 4379, and the total number of comments 9222.  iMechanica was launched in September 2006, with the following mission:

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Mechanics thrives whenever it participates in advancing a new technology

This morning I was looking at the book Mechatronic Reliability by Wei Yang.  The forword I wrote for the book brought back memories of days he and I spent in Santa Barbara and Princeton.  The text of the forword follows.

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iMechanica will be down briefly at 10 am this Friday

Just got a message from Lesley Lam, iMechanica user number 1, as follows.  Harvard School of Engineering and Applied Sciences IT is in the process of moving our servers to a faster, newer host.  As part of this process, I would like to take down iMechanica for about 10 minutes on Friday October 3rd at 10am.  I am hoping this will improve performance and reliability on the machine as well.

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The 2012 IUTAM Congress will be held in Beijing

Hello from Adelaide, Australia.  I'm at the IUTAM Congress.  The big news today:  the 2012 IUTAM Congress will be held in Beijing.  The Chinese delegates made a brilliant bidding.  Among promised items are good food, low registration fee (which will pay for all lunches), National Conference Center in the Olympic Village, and a tour to the Great Wall (which is also included in the registration fee).  So start planning for the trip.

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Number of registered users passed 8000 on the first day of 08 08

The number of registered users of iMechanica passed 8000 this afternoon.  The total number of posts is 3622, and the total number of comments 8429.  The total number of hits was 3.4 millions in March, 5.6 millions in April, 2.4 millions in May, and 2.7 millions in June.

iMechanica was launched on 11 September 2006, with the mission

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iMechanica is ranked among top engineering blogs

From time to time people ask if I know other websites like iMechanica but focusing on different branches of engineering.  This morning I saw a recently compiled list of Top Engineering Blogs, and was delighted that iMechanica was ranked close to the top.  I'm aware of the widespread cynicisms among iMechanicians about rankings of all kinds.  But, heck, ranking is good if you are ranked high.  As Freeman Dyson would say, being consistent is a weakness of mind. 

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Memories of IT. Part 1

I finally got around to read Does IT Matter, the 2004 book by Nicholas Carr.  He used the phrase IT (Information Technology) in "its commonly understood sense today, as denoting all the technology, both hardware and software, used to store, process, and transport information in digital form."  He explained, "The meaning of "IT" does not encompass the information that flows through the technology or the talent of the people using the technology."

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Mechanics of Soft Active Materials

At the invitation of David Clarke on behalf of the UCSB/Los Alamos Institute of Multiscale Materials and Structures, I gave the following three lectures:

  1. Large deformation and instability in dielectric elastomers
  2. Large deformation and instability in swelling polymeric gels
  3. Mechanics and electrochemistry of polyelectrolyte gels

The abstracts follow, and the slides are attached at the end of this post.

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Use RSS feeds to read iMechanica rapidly

People sometimes complain that reading iMechanica takes time.  This is because iMechanica has a large number of pages, and new pages are added frequently.  If you go directly to iMechanica, you have to load individual pages one by one.  

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