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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.