טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentDerkach Vadim
SubjectSurface and Grain Boundary Evolution in Thin Single-and
Poly-Crystalline Films
DepartmentDepartment of Applied Mathematics
Supervisor Professor Amy Novick-Cohen


Abstract

We focus on boundary migration and exterior surface evolution in idealized 3D isotropic systems containing a small number of grains embedded within a thin film, employing numerical simulations based on a parallel parametric algorithm to study the evolution of systems of three grains possessing columnar structure in triangular geometries, and single and bi-crystalline films on a substrate with a hole of various sizes and shapes. Our study is relevant to the stability of the thin polycrystalline and monocrystalline films used in numerous technological applications.

In considering the coupled motion of the grain boundaries and the exterior surfaces along thermal grooves, we assume the grain boundaries and the exterior surfaces to be governed by motion by mean curvature and by motion by surface diffusion, respectively. Along the thermal grooves and contact curves, balance of mechanical forces, continuity of the surface chemical potential, and balance of mass flux are assumed. At the quadruple junction and along the exterior boundary, boundary conditions are formulated in accordance with the physical principles indicated above in addition to certain symmetry assumptions. This enables us to study phenomena such as hole formation at quadruple junctions and annihilation of small grains, as well as thermal groove formation and its effect on the grain boundary migration and exterior surface evolution. For single and bi-crystalline systems with a hole we consider only the evolution of the exterior surface, which is attached to a substrate along a contact curve, and which is also attached to a grain boundary along a thermal groove in the bi-crystalline systems. This allows us to investigate wetting/dewetting phenomena, as well as the stability of holes depending on their initial sizes and shapes, and the effects of the grain boundaries on their evolution.

Our numerical algorithm employs an equi-spaced parametric description for each of the evolving surfaces which yields a system of partial differential equations (PDEs) which we solve using a finite difference scheme based on staggered grids with ghost points. Our approach generalises the approach developed by Pan & Wetton 2008 for 2D systems. Our algorithm is second order accurate in space and first order accurate in time; it conserves mass and dissipates free energy. The algorithm is implemented using "C" and MATLAB, and the simulations were run on the Tamnun − a high-performance RBNI computer cluster at the Technion.

Using our numerical algorithm, we followed the evolution of a variety of systems of grains in various geometries. In 3D systems of three grains in triangular geometries, we found that either grain annihilation which is usually accompanied by sinking and shrinking of the annihilating grain or hole formation at quadruple junctions can occur, depending on the parameters. In some cases, however, thermal grooving need not lead to film break up, instead convergence to steady state may occur. In 3D single and bi-crystalline films on a substrate with a hole of various sizes and shapes, we saw that while wetting may lead to void formation, dewetting may result in accelerated hole growth along grain boundaries.