1.2.1 Atomistic Approach

Since all materials are made up of atoms, a material's atomic structure plays an essential role in determining material properties and deformations under various ambient conditions. Atomistic methods are used to describe fundamental properties of materials, material deformation during various processes, and material interfaces. Atomistic (or molecular) modeling attempts to model or mimic the behavior of molecules by implementing all available theoretical methods and computational techniques.

The goal of atomistic simulations is to understand and model the motion of each atom in the material, resulting in an analysis of the collective behavior of atoms. The collective behavior provides an understanding of material deformations, phase changes, stress and other phenomena, linking atomic scale events to material meso-scale phenomena. The information which is required on the molecular level in order for a simulation to proceed is the position of atoms, atom vibrations, atom velocities, forces acting on each atom, and the force exerted from an atom onto surrounding atoms.

One simulation method relies on placing atoms in an unstable environment, such as an oxide layer sharing a sharp interface with a crystalline silicon surface. The forces acting on the individual atoms will result in the interface rearranging into an environment where the interface is stable, meaning that the force exerted by each atom is equal to the force acted upon the atom.

Another method refers to introducing new atoms, such as oxygen, into a crystalline silicon environment. The forces exerted by the atom on the silicon structure can generate a simulation showing how the oxygen atom bonds with the surface silicon atoms.

The DFT is a method in which atomic modeling is implemented in order to investigate the electronic structure of a many-body system. The properties of the system containing multiple electrons are determined with the use of functionals (functions of the spatially dependent electron density).

Ab-initio quantum chemistry methods are another form of molecular simulations which deal with quantum-level chemistry to calculate the ground state of individual atoms and molecules, as well as their excited and transition states which occur during chemical reactions. Calculations of quantum chemistry use semi-empirical or iterative solvers in order to deal with time dependent problems.

This leads to the main limitations of such methods - the computation time and cost increases as a power of the number of atoms involved in the simulation.

The main dilemmas which arise with simulations on the molecular level are based on timescales. No matter how many processors and how powerful the computer in use, often only nanosecond-long simulations can be performed. The time domain computation cannot be parallelized. In order to simulate the timely evolution of a large number of particles, statistical mechanics and stochastic methods are implemented. Therefore, in order to convert the microscopic information gathered through atomistic modeling to macroscopic properties such as pressure, stress, strain, energy, heat capacity, etc, statistical mechanic strategies are developed. Although atomistic simulations are very powerful and complement experiment and theory, the limitations with time simulations must be understood.

In order to deal with the large-scale problems introduced with atomistic simulations, stochastic techniques utilizing MC methods are developed. They overcome some of the limitations of atomistic calculations, whereby the integration of all energies associated with the movement of atoms and electrons is replaced by a random walk of particles in order to measure desired properties. The geometry of the molecular system is probed with a random distribution, which enables the diffusion and other slower processes to be modeled. MC methods are very useful when systems with multiple degrees of freedom must be simulated. Such systems usually involve fluids, disordered materials, strongly coupled solids, and cell structures or extremely scaled down systems where atomistic and quantum properties cannot be neglected.

L. Filipovic: Topography Simulation of Novel Processing Techniques