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Obtaining model-independent growth rates from experimental data of dry thermal oxidation of silicon



Empirical time-oxide layer thickness data of dry thermal oxidation of silicon were converted numerically into instantaneous growth rates by Tikhonov regularization. These growth rates are independent of any assumed kinetics of oxidation or functional form of the original data and can, therefore, be used in model testing of this important industrial process. A number of numerical issues in the Tikhonov regularization computation, for example, the expected monotonic decrease in growth rate with time and the large time span of some of the datasets, are addressed. Numerical results indicate that kinetic data presented in the form of growth rate-oxide layer thickness plots are more sensitive than the traditional time-oxide thickness plots for use in model testing and for parameter determination. The advantages of this new approach are demonstrated by three case studies covering the complete oxide thickness spectrum of interest to the microelectronic industry. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1810–1820, 2014