COMPUTATION OF THE HYDRODYNAMICS OF 2D OXIDATION PROCESSES USING BOUNDARY FITTED COORDINATE SYSTEMS

Simulation of semiconductor device is very difficult In 2 or 3 dimensional cases because of their Irregular boundaries involved. Usually finite element method is prelered in these cases. But, despite of the flexibility to adapt to any geometry, this method doesn't have a whole approval of the scientific community because Its programmation Is long and tedious, except It a well documented subroutine library Is available. Another method i. e. finite difference method is conceptually easier but requires a mapping from physical plane to rectangular coordinate plane. There are many procedures to generate this coordinate system. Among them, use of the Laplace equations, because of the simplicity of formulation and possibility of coordinate-line-spacing control, Is very attractive. Oxide here is considered as very viscous fluid floating upon a rigid silicon layer. System will contain besides Navier-Stokes equations and oxygen diffusion equation, two elliptic equations (actually their Inverses arc used). The first two groups of equations (which we refer as phisical) determine boundary of oxide domain which will be Infected to the inverse elliptic equations (which wc refer as transformation) to fix boundary conditions of the latters. Since physical equations require the transformation equations to be formulated, we have a system of completely coupled 6 equations. Increase of the number of equations is counterbalanced by the fact that we have now a partial differential equation system specified In fixed rectangular plane, so It is very easy to formulate in terms of the finite difference. Moreover there is no need for additional interpolation due to movement of the physical domain, because this is geniously incorporated in the above system. 1