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AN ANALYTICAL APPROACH FOR THE BREAKDOWN DISTRIBUTION OF A THIN OXIDE

Published online by Cambridge University Press:  08 April 2020

Peter C. Kiessler Open the ORCID record for Peter C. Kiessler [Opens in a new window]  and
Kanoktip Nimitkiatklai
Peter C. Kiessler
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA E-mail: kiesslp@clemson.edu
Kanoktip Nimitkiatklai
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA E-mail: kiesslp@clemson.edu
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Abstract

Dielectric breakdown in a thin oxide is presented in terms of an interacting particle system on a two-dimensional lattice. All edges in the system are initially assumed to be closed. An edge between two adjacent vertices will open according to an exponentially distributed random variable. Breakdown occurs at the time an open path connects the top layer of the lattice to the bottom layer. Using the extreme value theory, we show that the time until breakdown is asymptotically Weibull distributed.

Keywords

Weibull distributionextreme value theoryinteracting particle systemsdielectric breakdown
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 595 - 610
Copyright
© Cambridge University Press 2020

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