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ES 242r

Zhigang Suo's picture

Evolving small structures

I taught this course at the University of California, Santa Barbara, in Winter 1994, Winter 1995, Spring 1996; at Princeton, Spring 2003; at Harvard, Spring 2004.  The notes posted here are those distributed to the class in Spring 2004.


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We describe ratcheting plastic deformation in a thin-film structure

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electric field-induced self-assembly

We describe an example of self-assembly driven by electric field

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Surface stress driven self-assembly

We introduce surface stress, and show how it might drive self-assembly.

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Strain-induced self-assembly

Semiconductor particles in the size rage 1-100 nm have special optoelectronic properties dictated by the quantum mechanics of the potential well. These particles are known as quantum dots. Fabricating structures in this size range has been a great challenge of our time. Self-assembly has become an attractive method to fabricate quantum dots. By 1990, it was known that when Ge was deposited on Si substrate, cube on cube, the Ge film is flat up to a few monolayers, and then forms three-dimensional islands.

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In service, an interconnect line carries an intense electric current. The conduction electrons impact metal atoms, and motivate the atoms to diffuse in the direction of electron flow. The process, known as electromigration, has been the most menacing and persistent threat to interconnect reliability.

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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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Homework problems 26-31

This is the last homework set for ES 242r / ENGM 940

Lecture 18--Aspects of dynamic fracture

A very breif introduction to aspects of dynamic fracture mechanics.

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Lecture 15 Ratcheting induced slow crack (RISC)

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Homework problems 20-25, Fracture Mechanics

This set is related to buckle-driven delamination, crack bridging, and interfacial cracks.

Lectures 14 & 16; Matrix cracking, cracks intersecting an interface, and crack kinking

Matrix cracking in composites and the competition between penetration and deflection when a crack approaches an interface, and the competition between advance in the interface and kinking out of the interface for an interface crack.

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Lecture 13 Crack bridging

G. Bao and Z. Suo, " Remarks on crack-bridging concepts," Applied Mechanics Review. 45, 355-366 (1992).


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