1. Dewetting of Solid Films

Abstract

The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is
extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak to strong,
such that sharp corners and slightly curved facets occur on the corresponding Wulff shape). Through detailed parametric
studies it is shown that a combination of a wetting interaction and strong anisotropy, and even a wetting interaction alone
results in complicated linear stability characteristics of strained and unstrained films.

Stability of a strongly anisotropic thin epitaxial film in a wetting interaction with elastic substrate, with Wondimu Tekalign
and Margo Levine, Eur. Phys. Lett. 93,  26001 (2011).


Abstract

An evolution partial differential equation for the surface of a non-wetting single-crystal film
in an attractive substrate potential is derived and used to study the dynamics of a pinhole for the
varying initial depth of a pinhole and the strengths of the potential and the surface energy anisotropy.
The results of the simulations demonstrate how the corresponding parameters may lead to complete
or partial dewetting of the film. Anisotropy of the surface energy, through faceting of the pinhole walls,
is found to most drastically affect the time to film rupture. In particular, the similations support the
conjecture that the strong anisotropy is capable of the complete suppression of dewetting even when the
attractive substrate potential is strong.

Dewetting of an ultrathin solid film on a lattice-matched or amorphous substrate, Phys. Rev. B 77, 165414 (2008)

Abstract

The surface evolution model based on geometric partial differential equation
is used to numerically study the kinetics of dewetting and dynamic morphologies for the
localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic
surface energy. Depending on parameters such as the initial depth and width of the pinole,
the strength of the attractive substrate potential and the strength of the surface energy anisotropy,
the pinhole may either extend to the substrate and thus rupture the film, or evolve to the
quasiequilibrium shape while the rest of the film surface undergoes phase separation into a
hill-and-valley structure followed by coarsening. Overhanging (non-graph) morphologies are
possible for deep, narrow (slit-like) pinholes.

Morphologies and kinetics of a dewetting ultrathin solid film, Phys. Rev. B 77, 245445 (2008)

Abstract

We compare dewetting characteristics of a thin nonwetting solid film in the absence of stress, for two models
of a wetting potential: the exponential and the algebraic. The exponential model is a one-parameter (r) model,
and the algebraic model is a two-parameter (r,m) model, where r is the ratio of the characteristic wetting length
to the height of the unperturbed film, and m is the exponent of h (film height) in a smooth function that interpolates
the system's surface energy above and below the film-substrate interface at z=0. The exponential model gives
monotonically decreasing (with h) wetting chemical potential, while this dependence is monotonic only for the m=1
case of the algebraic model. Linear stability analysis of the planar equilibrium surface is performed. Simulations of
the surface dynamics in the strongly nonlinear regime (large deviations from the planar equilibrium) and for large
surface energy anisotropies demonstrate that for any m the film is less prone to dewetting when it is governed by the
algebraic model. Quasiequilibrium states similar to the one found in the exponential model
(M. Khenner, Phys. Rev. B 77, 245445 (2008)) exist in the algebraic model as well, and the film morphologies are similar.

Comparative study of a solid film dewetting in an attractive substrate potentials with the exponential and the algebraic decay,
Math. Model. Nat. Phenom. 3(5), 16-29 (2008).  Journal web site


Sample surface morphologies:




2. Stability of Nanowires


I've been intermittently involved in the computational research on stability of deposited thin-film wires (rods)  
(PI: Professor Harris Wong, LSU).  I also directed one PhD Thesis (Phu Vu, 2009)  where novel numerical methods for the
computation of geometrically constrained 3D evolution of surfaces by surface diffusion are explored.

Abstract

We introduce a marker-particle method for the computation of three-dimensional solid surface
morphologies evolving by surface diffusion. The method does not use gridding of surfaces or
numerical differentiation, and applies to surfaces with finite slopes and overhangs. We
demonstrate the method by computing the evolution of perturbed cylindrical wires on a substrate.
We show that computed growth rates at early times agree with those predicted by the linear
stability analysis. Furthermore, when the marker particles are redistributed periodically to
maintain even spacing, the method can follow breakup of the wire. 

  P. Du, M. Khenner, and Harris Wong,
``A tangent-plane, marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate",
Journal of Computational Physics 229(3), p. 813-827 (2010; due to copyright restrictions, fulltext is available on request only).


3. Tailoring of Thin Film Morphology by Surface Diffusion in 

Nonuniform Temperature Fields



result1_pattern.jpg
 
 Equilibrium nanostructured 1D surface of a growing crystal subject to  interference pulsed  heating. Distance between interference fringes decreases  from (a) to (f).

 Figure to the right shows coarsening kinetics for the isothermal situation (lower  data set) and two non-isothermal cases characterized by different separation    distances between fringes.		result2_pattern.jpg


M. Khenner, V.K. Henner,
     Temperature of Spatially Modulated Surface of Solid Film Heated by Repetitive Laser Pulses   
      Journal of Physics D: Appl. Phys. 38 (2005) 4196-4201; due to copyright restrictions, fulltext is available on request only         

M. Khenner,
     Influence of Pulsed Laser Heating on Morphological Relaxation of Surface Ripple   
     Physical Review E  72 (2005) 011604                ( MRS Fall'05 Meeting paper (refereed) )

M. Khenner,
     Tailoring of Crystal Surface Morphology by Induced Spatio-Temporal Oscillations of Temperature   
     Physical Review E  75 (2007) 021605                ( MRS Fall'06 Meeting paper (refereed) )


4. Selective Area Epitaxial Crystal Growth

M. Khenner, R.J. Braun,
       Numerical Simulation of Liquid Phase Electro-Epitaxial Selective Area Growth     
      Journal of  Crystal Growth 279 (2005) 213-228; due to copyright restrictions, fulltext is available on request only       
 
M. Khenner,
       Motion of Contact Line of a Crystal Over the Edge of Solid Mask in Epitaxial lateral Overgrowth      
       Computational Materials Science 32 (2005) 203-216; due to copyright restrictions, fulltext is available on request only     

M. Khenner,
      Computation of the Material Indicator Function Near the Contact Line (in Tryggvason's method)     
      Journal of Computational Physics 200(1) (2004) 1-7; due to copyright restrictions, fulltext is available on request only     

M. Khenner,
     Enhancement of Epitaxial Lateral Overgrowth by Vapor-Phase Diffusion   
     International Journal of Engineering Science 42 (2004) 1439-1457; due to copyright restrictions, fulltext is available on request only  

M. Khenner, R.J. Braun, M.G. Mauk,
     A Model for Anisotropic Epitaxial Lateral Overgrowth     
     Journal of  Crystal Growth 241 (2002) 330-346; due to copyright restrictions, fulltext is available on request only     

M. Khenner, R.J. Braun, M.G. Mauk,
      A Model for Isotropic Crystal Growth from Vapor on a Patterned Substrate     
     Journal of  Crystal Growth 235 (2002) 425-438; due to copyright restrictions, fulltext is available on request only