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Kinetics of oxide film growth on metal crystals: Space-charge-modified thermal electron emission and ionic diffusion. Part 1. Pertinent equations

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Abstract

A complete prototype coupled-currents calculation for metal oxidation has been carried out for a model based on ionic diffusion and thermal electron emission in the presence of space charge of the diffusing ionic species. This theoretical and numerical work is presented in two parts. In Part 1, the analytical equations for species transport are developed, and the approach for coupling these equations to deduce the kinetics of metal oxidation is outlined. The space-charge-modified ionic defect profiles can be expressed exactly in terms of Airy functions. These profiles lead in turn to analytical expressions for the total energy barrier for thermal electron emission. This is important both for metal oxidation and in devices utilizing electron emission from metals which are covered with oxides and similar dielectric layers. In Part 2, the results of extensive numerical computations for the model are presented. These calculations have led to a full understanding of the predictions of the model, the most important of which are the following: (a) In the early growth stage, the negative surface-charge field is an order of magnitude or so larger than its homogeneous field counterpart; this significantly aids the injection of rate-limiting electronic carriers into the conduction band of the oxide, and the oxide growth rate is thereby enhanced, (b) In the later stages of growth where the ionic species becomes rate-limiting, the space charge of the diffusing ions causes a marked retardation of the ionic current and the accompanying oxide film growth, (c) The transition from electron rate-limited growth occurs shortly after the classical electron energy barrier maximum switches from inside the film (Schottky-type emission) to a space-charge-produced barrier maximum at the outer interface of the film.

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Author notes

  1. R. B. Mosley

    Present address: Physics Department, Virginia Commonwealth University, Richmond, Virginia

Authors and Affiliations

  1. Department of Physics, Auburn University, Auburn, Alabama

    R. B. Mosley & A. T. Fromhold Jr.

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  1. R. B. Mosley
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  2. A. T. Fromhold Jr.
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Additional information

This research was performed at Auburn University in partial fulfillment of the requirements for the Ph.D. degree.

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Mosley, R.B., Fromhold, A.T. Kinetics of oxide film growth on metal crystals: Space-charge-modified thermal electron emission and ionic diffusion. Part 1. Pertinent equations. Oxid Met 8, 19–46 (1974). https://doi.org/10.1007/BF00612173

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  • DOI: https://doi.org/10.1007/BF00612173

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