Modeling Growth and Viscous Flow of Oxide on Cylindrical Silicon Surfaces Including Piezoviscous Inhibition

Abstract

A baseline constant-parameters non-dimensional cylindrical oxidation model was first revisited, normalizing oxide thickness to oxidant diffusivity/reaction rate ratio instead of the original cylinder radius, allowing this radius to remain evident in model output, which in this baseline case predicted oxides increasingly thicker for convex surfaces of decreasing radius as compared to that on a flat surface, with oxide thicknesses on concave surfaces instead predicted to decrease with decreasing radius from the flat case. As this convex behavior conflicts with the reported experiment, where oxide thickness on convex surfaces rather decreases with decreasing radius from the flat case though less strongly than for concave surfaces, potential stress-dependent kinetics parameters were investigated, with stresses determined from viscous treatment of oxide flow during growth to accommodate its molecular volume exceeding that of the silicon consumed in its production. While oxidant diffusivity and solubility both considered to decrease with increasing hydrostatic pressure instead cause model predictions to further deviate from experimental observation, the rate of its volume-producing reaction with the silicon considered to decrease with increasingly compressive radial stress across their interface successfully brought model predictions of convex curvatures into agreement with reported experiments. In conjunction with such stress-dependent reaction rate, additional consideration of viscosity as increasing with hydrostatic pressure can also contribute toward bringing convex modeling closer to experimental observation, though it also introduces a potential piezoviscous inhibition where concave cases of smaller curvature radius become predicted incapable of even initiating oxidation.