Grants and Contracts Details
Morphological and compositional instabilities during the epitaxy of single- and multi-speciesself-assembling films are of central importance. In particular, the onset of one- and twodimensional morphological (step bunching, meandering, and faceting) and compositional (phase segregation) instabilities is viewed as a versatile approach to the manufacturing of nanoscale structures (quantum wires and dots) through self-organization processes. Hence the need for a better mathematical understanding of the mechanisms whose interplay triggers these instabilities. The proposed research effort is four-fold. Its first part is concerned with a novel instability in single-species epitaxy resulting from the presence of a term, the jump in the terrace grand canonical potential, in the step evolution equations which is absent from the boundary conditions of more standard models. The goal here is to characterize this instability both in one- and two-dimensions and to determine if it can be offset by anisotropic step and terrace kinetics. In the second part, the focus is on an instability triggered during the growth of binary compounds where surface chemistry is expected to playa role. This instability differs from that resulting from the presence of impurities as proposed by KANDEL & WEEKS and does not seem to be due to an effective inverse Ehrlich-Bchwoebel barrier for one of the two deposited species as suggested recently by PIMPINELLI & VIDEcOQ. Hence the need to better understand its mechanisms as well as to determine, via phase diagrams, the unstable regions in parameter-space. The third part is based on experimental evidence of step faceting. The objective is to derive, in a dissipative setting, a regularized model that captures the features of this faceting instability both during growth and sublimation. This microscopic model will then be implemented in collaboration with Drs. VOIGT and HAUSSER using algorithms that were developed at CAESAR to tackle the problem of faceting and coarsening at the mesoscale. The last part deals with intermixing and phase separation during the growth of binary substitutional alloys. In contrast with existing theories, the microstructure of a growing vicinal surface is explicitly accounted for. The proposed model captures the multifaceted physics (surface kinetics, bulk elasticity and atomic diffusion, etc.) that underlies growth/sublimation and is multiscale in that it views the film as a layered structure which allows to resolve the different scales in the lateral and epitaxial directions. Its finite-element implementation should yield insight how step flow impacts on alloying and segregation. Intellectual merits: The proposed research is a step toward understanding the mechanisms underlying step bunching and meandering in single- and multi-species crystals. Given that self-assembly is a potential path for the fabrication of nanostructures, the results obtained should be of interest to crystal growers. The PI will develop a partnership with the Crystal Growth group at the Center of Advanced European Studies and Research so that modeling and computations can be combined to better understand the issues at hand. Broader impact: On the educational side, the PI has recently introduced a course on the dynamics of defects and microstructures (for graduate students in Mathematics and Engineering). The contents of this course will be expanded to include topics of crystal growth during the course of this project and beyond. Finally, one graduate student will conduct his dissertation reseach in the framework of this project.
|Effective start/end date||6/1/06 → 5/31/11|
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