The thermal oxidation of a silicon wafer to form a thin film of protective oxide on the surface can be modeled as follows:

a. Oxygen from the atmosphere is transported to the surface of the wafer and diffuses through the thin oxide layer to reach the silicon substrate. The partition coefficient between the film and air is \(K_{e q}=c_{\text {film }} / c_{\text {air }}=10\).

b. Oxygen reacts with the silicon at the interface. Since the silicon is in great excess the reaction can be modeled as first order in \(\mathrm{O}_{2}\) concentration.

Show that the thickness of the oxide at any time, \(t\), can be represented by:

You may assume diffusion occurs at steady state and couple that with a transient mass balance about the oxide.

Transcribed Image Text:

D k" C 08 og hox + ahox = azt -oxygen diffusivity rate constant (m/s) -O concentration a = 2Dog 4-204(+) 1 1 Pg density of SiO a = 2DogCog Mwg Pg k-mass transfer coefficient (m/s) M -molecular weight of SiO2 wg M-molecular weight of O