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.

We describe ratcheting plastic deformation in a thin-film structure

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

We introduce surface stress, and show how it might drive 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. This mode of growth, from layer-by-layer to three-dimensional islands, is known as the Stranski-Krastanov growth. Many other heteroepitaxial semiconductor films also grow this way.

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.

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.

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.

The cause for grain growth is readily understood. Atoms at a grain boundary are poorly packed, and have higher energy than atoms in the lattice. As the grains grow in size and their numbers decrease, the net of amount of grain boundary reduces, and thereby the free energy of the system reduces. But how does each atom know about this global agenda of reducing the energy of the system? If you cannot wait for an answer, jump to the last paragraph of this lecture.

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.

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.

Similar instability in solids. Phenomena similar to the Rayleigh instability occur in solid state; see Rodel and Glaeser (1990) for an experimental demonstration and for a literature survey. For example, at a high temperature, a penny-shaped pore in a solid first blunts its edge, from which finger-like tunnels emerge, and the tunnels then break into small cavities (Lange and Clarke 1982).

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. The process conserves the total mass. The process of grooving was modeled by Mullins (1957).

Some phenomena due to surface diffusion:

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

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

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.

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.

Below the melting point, a pure metal is a crystal. Each atom vibrates around its lattice site. If you look at one atom, its motion is chaotic; the atom jiggles rapidly, once in this direction and then in another. Its vibration amplitude also changes from time to time. But if you look at many atoms, they appear to be a periodic lattice. That is, if you find one atom at a point, you'll almost certainly find another atom any multiple of the lattice spacing away. Well, almost. The crystal is imperfect. It has defects: vacancies, dislocations and grain boundaries. They are the imperfections in the nearly perfect crystal.

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?