Boundary Element Techniques for Modeling Thermal Oxidation of Silicon
Abstract
This thesis advances boundary element techniques to model thermal oxidation of silicon in two dimensions. At temperatures encountered in thermal oxidation, silicon dioxide flows viscoelastically. A reduced-dimension, generalized boundary element method for modeling such a problem has been developed. With a Laplace transform technique, a viscoelastic kernel function in derived from Kelvin's solution, which is the fundamental solution to linear elasticity. Constant-velocity loading is chosen to operate with a wide range of stress relaxation times. This scheme is capable of replacing boundary methods developed for slow viscous flow and elastic deformation. The oxidant diffusion problem is solved using a standard potential method for Laplace problems. Generated by oxide growth, stress affects both oxidant diffusion and oxide flow. In particular, it changes the diffusivity of oxidants and viscosity of oxide, rendering the diffusion and flow problems nonhomogeneous. Domain solutions are needed for both processes. A unified initial stress/built-in filed formulation has been developed to account for the nonlinear effects, using interior cells that are placed where stress is significant.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1988
- Accession Number
- ADA204209
Entities
People
- Thye-lai Tung
Organizations
- Massachusetts Institute of Technology