Elements of
Chemical Reaction Engineering
6th Edition



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Essentials of
Chemical Reaction Engineering
Second Edition

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Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Additional Homework Problems

CDP14-FC

The oxidation of silicon to form SiO2 is an important step in the fabrication of microelectronic devices. The oxidation process can be modeled by three events: (1) the diffusion of oxidant from the bulk gas to the surface of the oxide layer, (2) the diffusion of oxidant through the growing oxide layer to the Si-SiO2 interface, and (3) the reaction of oxidant with Si at the Si-SiO2 interface [J. Appl. Phys. 36, 3770 (1965)]. Refer to the sketch below for additional details.

image 11eq7.gif



The reaction at the Si surface is assumed to be first-order in oxidant and zero-order in Si. Derive an expression for the oxide layer thickness as a function of time, and show that it can be written in the following form:

image 11eq8.gif
image 11eq8a.gif

(P. E. Savage, The University of Michigan)

State explicitly any further assumptions you make. Assume that the oxide layer has some initial thickness T0 at time t = 0.

[2nd Ed. P10-17]