1.2.2 Continuum Approach

A material, whether it be solid, liquid, or gas, is composed of molecules separated by empty space. On a macroscopic scale, these materials have cracks, deformation and discontinuities, while some properties can be viewed as uniformly affecting the entire material as a continuum. Therein lies the basic concept of continuum mechanics. These properties are modeled with the assumption that the matter which composes the material fills the entire region of space which it occupies, with no cracks, deformation, different molecular structures, atoms, electrons, or distributed densities, but rather one single entity with a single set of parameters.

In semiconductor processing, various methods are implemented in order to modify wafer surfaces. There is value in analyzing the different materials and their changing interfaces on a molecular level using atomistic simulations. These simulations use cellular automata or MC techniques to describe interface changes. However, atomistic analysis are very computationally intensive and are limited to structures on the level of several molecules and simulations of several nanoseconds. In order to generate a simulation for a complete semiconductor process, a continuum model is the only viable method with current computer capabilities. Continuum modeling methods for physical phenomena are traditionally formed in terms of differential equations. These can describe an array of physical properties such as density, conductivity, diffusivity, etc. in addition to inter-material properties such as stress, strain, and cracking caused by material deposition, growth, or interaction of highly charged ions with a material. The FDM and FEM are numerical techniques which are widely used to study models based on partial differential equations for continuum mechanical modeling.

If the typical structure size is much larger than the typical lattice constant, the solid body under simulation should be represented as a continuum. When a simulation is only performed in order to predict the final shape of a given structure after one or several processing steps, then a continuum model involving a topography simulation is the sole requirement. These types of simulations do not offer physical material properties, but can be performed very quickly for large structures and for long simulation times. The LS method is one way in which topography simulations can be performed with high efficiency and speed [50]. A particular downside of topography processing is the assumption that material interfaces are abrupt and can be defined by a single surface evolution, which is known not to be the case for some complex processes such as oxidation. Another downside is that material properties relevant to the simulated processing steps are homogeneous within the material region. Although these downsides of topography processing exist, their efficiency and speed in the determination of material interfaces after one or several processing steps make them a valuable modeling tool. The scope of this work deals with modeling several processing techniques using continuum topography models within the LS environment.