Molecular Simulations of a Thin Film under Biaxial Stress

Sim1:  Perfect crystal hin film under biaxial stress. Simulation performed at T = 0.12 
and Strain Rate = 0.005. Use mouse to rotate.

Sim2:  Thin film under biaxial stress. Simulation performed at 
T = 0.12 and Strain Rate = 0.005. 
Crystal containing initial void. The atoms surrounding the void are shown in red.
 

Fig1:  Stress - Strain as a function of temperature and strain rate.
Simulations for perfect FCC crystal structure.

Fig2:  Stress - Strain as a function of temperature at 0.005 strain rate. 
Simulations for perfect crystal(empty symbols) and film containing 
initial void (solid symbols).
 
 
 

Abstract

Simulations were performed on a free-standing thin film (two opposing free surfaces) under a biaxial state of stress. Simulations were run at two different temperatures and strain rates, for a perfect crystal and for a film containing an internal void. The dependence of the stress-strain behavior on temperature and strain rate was analyzed.

Introduction

Thin films have applications in optoelectronic devices as well as coatings for structural materials. Thin films are usually deposited on a substrate or they are part of more complex multi-layer systems. Therefore, they are often under a state of stress caused by lattice mismatch or different physical or mechanical properties from the substrate. The mechanical response of the film under stress limits in many cases the performance and reliability of the entire system.

Simulation

The system consists of 1200 particles of the same species in a Lennard-Jones potential.  The initial positions of the particles describe a FCC monocrystal structure, with the (001) plane parallel to the film surface and the [100] direction along the x-axys. Both the upper and the lower surfaces of the film are free.
Constant Energy and Constant Volume-Temperature simulations are run first to stabilize the structure. Then the pressure is brought to zero to facilitate comparison among different simulations.
Constant strain rate is applied in the [100] and [101] directions. Simulations are run at constant temperatures (0.12 and 0.42) using a Nose-Hoover thermostat.
Same simulations are carried out for a film containing an initial internal void (8 atoms) to study the influence of the defect on the stress-strain behavior.

Data Analysis

The results of the simulation are shown to the left (Sim1 and 2).  Effective stress and strain were calculated from the simulated data and plotted as a function of temperature and strain rate.
At low temperature the film shears and yields. For the perfect crystal increasing the strain rate from 0.001 to 0.005 did not affect much the stress-strain behavior (Fig1). At high temperature the deformation is assisted by the increased thermal vibration and the stress levels are lower. The internal void causes earlier yielding at low temperature (Fig2). The evolution in void size and shape during the straining can be observed in Sim2.
 

Initial shape of the internal void for Sim2.