A Boundary Integral Equation Approach to Oxidation Modeling

Thermal oxidation of silicon involves the diffusion of oxidant molecules from the gas-oxide interface to the oxide-silicon interface, and the transport of newly formed oxide away from the latter. Under suitable formulations these two processes can be shown to be boundary-value problems of harmonic and biharmonic nature. Based on these properties, a boundary integral equation method (BIEM) has been developed for modeling oxidation. This method achieves simplicity and efficiency by solving a two-dimensional problem using line integrals on the boundaries. The use of source distributions as intermediary solutions facilitates direct calculations of a wide variety of boundary parameters.