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 

http://www.castdiv.org/WebCAST.htm)



Abstract:

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.