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August 2007


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"Richard D. Braatz" <[log in to unmask]>
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Richard D. Braatz
Sat, 25 Aug 2007 18:56:21 -0500
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WebCAST seminar on "Materials Surface Engineering by Simultaneous Action of 
Multiple External Forces"

by Dimitrios Maroudas
Professor of Chemical Engineering at the University of Massachusetts at Amherst

DATE: September 20, 2007, 2-4 pm EST

Dial-in from the comfort of your office to hear the presentation

Deadline to Register: September 17, 2007 (details at

Understanding the response of materials surfaces to the simultaneous action
of multiple external forces is required for the systematic generation and
stabilization of certain surface features and patterns that play important
roles in the tailoring of materials properties and function. In this
presentation, we focus on the surface morphological stability and dynamics
of stressed crystalline solids, which underlies various materials
processing and reliability problems in numerous technological applications
ranging from aerospace to microelectronics and nanotechnology. An example
of such an important problem in microelectronics is the
electromigration-driven dynamics of void surfaces in mechanically confined
metallic films that are used as device interconnections in modern
integrated circuits. Surfaces of stressed elastic solids have been shown
to undergo morphological instabilities. For example, the competition
between elastic strain energy and surface energy can cause the growth of
perturbations from a planar surface morphology under certain conditions and
trigger the so-called Asaro-Tiller or Grinfeld instability. It has been
demonstrated experimentally and computationally that a planar surface of a
stressed elastic solid can evolve rapidly into a cusped surface, with
smooth tops and deep crack-like grooves by surface diffusion. However, the
effects of the simultaneous action of an electric field on the
morphological response of a conducting stressed solid surface have not been
explored systematically.

In this presentation, we explore surface morphological response to the
simultaneous action of electric fields and mechanical stresses of
crystalline solid conductors, such as Cu or Al, and of voids in thin films
of such conductors. The analysis is based on a surface transport model
that accounts for curvature-driven surface diffusion, surface
electromigration, and stress-driven surface diffusion along with surface
diffusional anisotropy. The computational predictions for the surface
morphological evolution are based on self-consistent dynamical numerical
simulations according to the fully nonlinear surface mass transport model,
which is solved self-consistently with the electric field and stress field
distributions on the solid (or the void) surface computed through a
Galerkin boundary integral method.
First, we report results of linear stability analysis for the morphological
response of a planar solid surface to the combined action of an applied
electric field and mechanical stress, assuming that the solid responds
elastically to stress. We derive a dispersion relation, which describes
the growth or decay rate of a perturbation from the planar surface
morphology of the stressed solid under the simultaneous action of the
electric field. We find that application of a sufficiently strong electric
field can stabilize the surface of the stressed electrically conducting
solid material that would be otherwise vulnerable to surface cracking under
certain thermomechanical conditions; therefore, the electric current
protects the material against cracking and inhibits its damage.
Furthermore, we report the effects on the surface morphological stability
of key material properties, such as the strength of surface diffusional
anisotropy and the material's texture that is set by the surface
crystallographic orientation. We find that the morphological response of
face-centered cubic metal surfaces with <111> crystallographic orientation
is easier to stabilize than that of surfaces with <100> or <110>
crystallographic orientation. In addition to the linear stability
analysis, we report computational results for the morphological evolution
of a solid surface perturbed from an initially planar morphology under the
simultaneous action of an electric field and mechanical stress. The
numerical results confirm the main conclusions of the linear stability
analysis. Our findings can be used toward development of systematic
surface engineering strategies for improved materials reliability over a
broad range of electromechanical conditions.

Next, we examine the surface morphological response of voids in metallic
thin films under the combined action of electric fields and mechanical
stresses. Our analysis predicts that, in the absence of stress, increasing
the electric field strength, or the void size, or the strength of the
diffusional anisotropy past certain critical values leads to transitions
from steady states to time-periodic states; the latter states are
characterized by wave propagation on the surface of the void, which
migrates along the film at a constant speed. The transition onset
corresponds to a Hopf bifurcation that may be either supercritical or
subcritical, depending on the symmetry of the surface diffusional
anisotropy that is determined by the crystallographic orientation of the
film plane. We focus on low-symmetry anisotropy and analyze the current
driven void surface morphological response under the simultaneous
application of tensile biaxial stress starting from conditions close to the
Hopf point in the stress-free case. Propagation of stable surface waves on
the void is observed again as the applied stress level increases beyond a
critical value. Further increase of the applied stress level leads to a
period-doubling bifurcation associated with more complex surface wave
propagation. Such period-doubling bifurcations continue with increasing
stress level, setting the system on a route to chaos. With further
increase in the stress level, the system exits from the chaotic regime to a
periodic window characterized by a complex time-periodic state with three
periods. Further increase in stress drives the system to another chaotic
regime, through a period-doubling bifurcation sequence, and ultimately to
film failure beyond a certain maximum stress level. Detailed
characterization of the complex shape evolution is performed over the range
of stress levels examined and the nature of the resulting chaotic state
(strange attractor) is discussed. These results are used to motivate
surface engineering studies toward formation of desirable surface patterns
in solid material systems of interest in electronics, optoelectronics,
energy technologies, and various areas of nanotechnology.

Biographical Sketch:
Dr. Maroudas is currently Professor of Chemical Engineering at the
University of Massachusetts at Amherst. He received his Diploma from the
National Technical University of Athens in 1987 and PhD at the
Massachusetts Institute of Technology in 1992, both in chemical
engineering. After a postdoctoral research fellowship at IBM T.J. Watson
Research Center in 1992-1994, he was a faculty member at the University of
California at Santa Barbara before moving to his current position. His
research has been in computational materials science and electronic
materials. His honors and awards include the CAREER Award from the National
Science Foundation and the Camille Dreyfus Teacher-Scholar Award.