Oxidation of silicon: Cylinders and Spheres.

Two recent developments have stimulated an interest in the oxidation behavior of non-planar silicon surfaces. One is the evolution of VLSI technology toward three-dimensional fabrication. The other is the unusual oxidation behavior recently discovered at silicon edges. In this paper, the equations for the oxidation of a silicon cylinder or sphere or of a cylindrical hole or spherical cavity in silicon are solved exactly in the quasi- static limit. In all cases, oxidation is complete after a finite time. If the initial oxidized layer is sufficiently thin and the initial radius is sufficiently large, oxidation proceeds initially according to the planar model of Deal and Grove. If the initial radius is small, only the linear part of the planar model is initially followed. Graphical examples are presented. Calculations for both wet and dry oxidation of silicon with cylindrical and spherical radii from 10 nm to 1 micron over the temperature range 800C to 1100C are provided in the Appendices.