Quick Prototyping for Nonequilibrium
Diffusion Models
As the semiconductor industry continues pushing technology to
produce smaller devices, wafer processing is moving toward shorter
times and/or lower temperatures to produce less impurity movement.
Unfortunately, under these conditions, the effects of implant damage
or oxidation begin to dominate. Current process simulators use
models that were developed during the 70s and 80s for equilibrium
diffusion and are only valid after the damage is annealed out or
when the excess point defects are in semiequilibrium. Furthermore,
the equations to model the nonequilibrium effects are not well
characterized at this time, but typically consist of systems of
coupled reaction-diffusion equations. Existing simulators, being
highly tuned to quickly solve a few fixed sets of equations for the
equilibrium diffusion models, are ill equipped to handle the
formulation needs to quickly prototype simulators for these
nonequilibrium systems. My research involves developing an
environment to support quick prototyping for nonequilibrium
diffusion models.
The requirements of this environment are demanding; it must be able
to support complex real-world models. The complexity not only
involves coupling of an arbitrary number of fields (e.g. diffusing
species) via a system of PDEs, but also coupling of these fields
through boundary conditions (e.g. injection of interstitials into
the bulk during oxidation). To manage this complexity, a very
general information model was developed for an object-oriented
FEM-based PDE solver. This multi-dimensional PDE solver supports an
arbitrary number of fields and multiple regions. Equation
formulation is provided via a dial-an-operator mechanism, which
directly maps the system of equations into a set of data structures
that know how to generate the element matrices.
Dan Yergeau (yergeau@gloworm.Stanford.EDU)
CISX 300
Stanford University
Stanford, CA 94305-4075