##### Department of Mathematics,

University of California San Diego

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### Special Numerical Analysis Colloquium

## Stephen Watson

#### Northwestern University

## Coarsening Dynamics of Faceted Crystal Surfaces: The Annealing-to-Growth Transition

##### Abstract:

*RECRUITMENT TALK* The current renaissance in the study of evolving faceted crystal surfaces was prompted by the discovery of nano-scale faceted pyramidal islands (quantum dots) on Si films, as well as the appearance of novel in situ imaging techniques. We consider the coarsening dynamics of faceted crystal surfaces that pertain to two distinct continuum models; so-called thermal annealing (A) and net-growth (G) regimes. We present a novel theoretical framework which unites the two problems by recognizing their common (leading-order) kinematic framework; namely, piecewise-affine surfaces evolving on a suitably slow time scale. Dynamic evolution laws, intrinsic to such surfaces, are then found for each problem through novel matched asymptotic analysis. Our theory resolves the long-standing annealing-to-growth enigma, whereby the scaling law for the increase in time, t, of the characteristic facet size, L, is observed to undergo a transition when switching from (A) to (G). In addition, the nature of the transition in surface morphology between (A) and (G) follows readily from the stability properties of the associated dynamical systems. Large scale simulations, which are rich in both topological and statistical terms, will also be presented.

Host: Michael Holst

### March 5, 2004

### 1:00 PM

### AP&M 6438

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