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Introduction

Model

Methods

- Finite Element Analysis

- Programming

- Sample Code

Results

- Single-Boundary

- Multi-Boundary

- Multi-Layer

Conclusions

Related Studies

MODEL

MATLAB simulation codes were developed in order to simulate the particle-scale evolution of the various thin film structures. The effects of both the interface migration and the diffusion were considered in the problem. The analytical solutions to migration and diffusion problems were incorporated into finite element analyses.

Evolution of multiple grain boundaries in a single-layered thin film structure
  1. MATLAB code for simulating the structure evolution of a simple, single-layered film structure was developed. The code uses the analytical solutions (derived in Methods ) to relate the particle (node) positions to the particle (node) velocity. Then the finite element analysis using the Hamiltonian matrices calculates the force acting on each particle. After each time step of the simulation, the MATLAB code calculates the velocity using the H-Matrix and force vector. With this velocity, it calculates the updated positions of the nodes.
  2. Additional vertical grain boundaries were added to the single-layer, single grain boundary code. The interface diffusion and migration as well as the final geometries of the multi grain boundary films were analyzed.
  3. The relationship between the distance between grain boundaries and the interface migration speed was identified.
Evolution of multi-layered thin film structures
  1. The second layer of the film was added on top of the structure created in the original MATLAB code.
  2. Effects of the evolution of the bottom grain boundaries on the upper layer grain boundaries were analyzed.