Thermal oxidation is a process that converts silicon at the wafer
surface into silicon dioxide. The reaction of oxygen with silicon causes
silicon dioxide to develop at the surface, whilst also penetrating the
silicon wafer. The final oxide is appropriately 56% above and 44% below
the original surface. Modeling of thermal oxidation has a tradition
dating back to the late 60's when the Deal-Grove model was developed,
which is still used in modern simulators. The model is based on two
parameters, the linear and parabolic rate constants, in which all the
physics of the oxidation process are included.
Recently, it has been suggested that the growth of silicon dioxide can
be described using the Navier-Stokes equation, which describe the motion
of fluid substances, or substances with flow. Combined with this theory,
the growth of silicon dioxide can be modeled as the movement of two
boundaries that both originate at the wafer surface. One boundary
penetrates the silicon wafer with a negative velocity, while the second
moves above the original wafer surface and is assigned a positive
velocity. The simulation of a moving boundary has been developed at this
institute by O. Ertl in his work on describing the topography changing
processes for Micro-Electro-Mechanical Systems (MEMS) manufacturing
using the level set method.
The level set method is a technique that represents the moving boundary
as the zero level set of an implicit function. The evolution of this
function with time is calculated by solving the level set equation. A
very efficient existing simulator uses the sparse-field method with
Hierarchical Run-Length-Encoding (HRLE). The advantages of the existing
topography simulator will be inherited by the thermal oxidation
simulator. The goal is to model the simulation of oxide growth, stress
sources, and various three-dimensional effects in an efficient 3D
simulator using the level-set method and the Navier-Stokes equation.
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