SPECIAL PHYSICAL MATHEMATICS SEMINAR

TOPIC:	CONTINUUM APPROACH TO PROFILE SCALING IN
	NANOSTRUCTURE DECAY BELOW THE ROUGHENING 	TEMPERATURE


SPEAKER:    DIONISIOS MARGETIS
	    Massachusetts Institute of Technology

ABSTRACT:

Advances in the fabrication of small devices have stimulated interest in
low-temperature kinetic processes on crystal surfaces.  In most
experimental situations, nanoscale solid structures decay in time with a
lifetime that is a large power of the feature size and typically increases
with decreasing temperature.  Strategies for skirting the lifetime
limitations involve processing at ever-lower temperatures for ever-smaller
feature sizes.  At temperatures below the roughening transition crystal
surfaces evolve via the motion of interacting steps at the nanoscale, and
may develop macroscopically flat parts known as facets.  The prediction of
macroscopic surface evolution at such temperatures is an open problem.

The subject of this talk is a continuum, analytical description of the
morphological relaxation of crystal surfaces with a single facet below the
roughening temperature by use of PDEs.  For diffusion-limited (DL) and
attachment-detachment limited (ADL) kinetics, the slope profile $F$
outside the facet is described via a nonlinear, fourth-order PDE that
accounts for step line-tension energy $g1$ and step-step repulsive
interaction energy $g$3.  The PDE is derived from the step-flow difference
equations, which describe the motion of individual steps, and,
alternatively, via a continuum surface free energy.  The facet evolution
is treated as a free-boundary problem recognizing that there is a region
of rapid variations of $F$, a boundary layer, near the facet.  For long
times, axisymmetric shapes and $g3/g1< O(1)$, singular perturbation theory
is applied for self-similar shapes close to the facet. For DL kinetics,
scaling laws with $g3/g1$ are derived for the boundary-layer width,
maximum $F$ and facet radius; and a universal ODE for $F$ is derived and
solved uniquely via applying effective boundary conditions at the facet
edge.

For the more intricate case of ADL kinetics a different scaling with
$g3/g1$ is found for the boundary-layer width.  The scaling results
compare favorably with kinetic simulations. Geometries other than the
axisymmetric one are discussed.

DATE:		FRIDAY, FEBRUARY 13, 2004

TIME:		2:30 PM

LOCATION:	Building 2, Room 338


Massachusetts Institute of Technology, Department of Mathematics
Cambridge, MA  02139