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Markov-Chain Formulation of Reaction-Diffusion Model and its Implications for Statistical Distribution of Interface Defects in Nanoscale Transistors

2010/11/14 by Ahmad E. Islam, Ahmad Ehteshamul Islam, Islam, Ahmad Ehteshamul +3
Engineering · Materials Science · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Classical Physics (physics.class-ph) #Data Analysis #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Semiconductor materials and devices #Statistics and Probability (physics.data-an) #Thermal properties of materials #cond-mat.mes-hall #physics.class-ph #physics.data-an

paper · pdf · doi:10.48550/arxiv.1011.3235

This paper has been withdrawn by the author. A similar paper is already published in Journal of Computational Electronics with the following link: http://www.springerlink.com/content/y0p362uhh3gm0u12/fulltext.pdf

openalex publication_date 2010/11/14 · arxiv created 2011/09/26 · arxiv updated 2011/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Continued scaling of nanoscale transistors leads to broad device-to-device fluctuation of parameters due to random dopant effects, channel length variation, interface trap generation, etc. In this paper, we obtain the statistics of negative bias temperature instability (NBTI)-induced interface defect generation in ultra-scaled MOSFET by Markov Chain Monte-Carlo (MCMC) solution of Reaction-Diffusion (R-D) model. Our results show that the interface defect generation at a particular stress time, i.e., NIT@tSTS in small transistors should follow a skew-normal distribution and that the generation and annealing of interface defects are strongly correlated. Next, we use a random percolative network to demonstrate (which is also consistent with previously published results in literature based on separate techniques) that the distribution of threshold voltage shift for single interface defect, i.e., ΔVT@NIT is exponential, with finite number of transistors having zero ΔVT. Finally, we show that the statistics of ΔVT@tSTS - based on the convolution of NIT@tSTS and ΔVT@NIT - is broadly consistent with the available experimental data in literature.

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