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

TL;DR

This paper models the statistical distribution of interface defects in nanoscale transistors using a Markov Chain approach to Reaction-Diffusion processes, revealing skew-normal and exponential distributions that align with experimental observations.

Contribution

It introduces a Markov Chain Monte-Carlo method for Reaction-Diffusion models to analyze defect statistics in ultra-scaled MOSFETs, linking defect generation to threshold voltage shifts.

Findings

Interface defect generation follows a skew-normal distribution.

Threshold voltage shift distribution is exponential.

Statistics align with experimental data.

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., {\Delta}VT@NIT is exponential, with finite number of transistors having zero {\Delta}VT. Finally, we show that the statistics of {\Delta}VT@tSTS - based on the convolution of NIT@tSTS and {\Delta}VT@NIT - is broadly consistent with the available experimental data in literature.