caa a22 4500 445820446 CHVBK 20180317145242.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10825-011-0369-4 doi (NATIONALLICENCE)springer-10.1007/s10825-011-0369-4 Analyzing the distribution of threshold voltage degradation in nanoscale transistors by using reaction-diffusion and percolation theory [Elektronische Daten] [Ahmad Islam, Muhammad Alam] Continued scaling of transistors into the nanoscale regime has led to large device-to-device variation in transistor characteristics. These variations reflect differences in substrate doping, channel length, interface and/or oxide defects, etc. among various transistors. In this paper, we develop a theory for the statistical distribution of threshold voltage degradation (ΔV T ) due to the Negative Bias Temperature Instability (NBTI). First, we model the time dynamics of interface defects within the Reaction-Diffusion (R-D) framework and calculate the statistics of interface defect using Markov Chain Monte-Carlo method. We show that the generation and annealing of interface defects are strongly correlated and that the statistics of interface defect at a given stress time (N IT @t STS ) follows a skew-normal distribution. Second, we explore the differential effect of the spatial distribution of interface defects in nanoscale transistors pre-populated with a discrete number of randomly placed substrate dopants. We model the effect of spatial distribution of defects using a percolative network and demonstrate that the distribution of threshold voltage degradation for a single additional interface defect, i.e., ΔV T @ΔN IT =1, is exponential, with a fraction of transistors having ΔV T ∼0. Finally, we obtain the statistics of ΔV T @t STS by convolving the statistics of N IT @t STS with that of ΔV T @ΔN IT =1. The resultant statistics of ΔV T @t STS compares favorably with a broad range of experiments reported in the NBTI literature. Springer Science+Business Media LLC, 2011 Reaction-diffusion model nationallicence Markov Chain Monte-Carlo nationallicence Interface defect statistics nationallicence Skew-normal distribution nationallicence Exponential distribution nationallicence Threshold voltage degradation nationallicence Islam Ahmad Department of Materials Science and Engineering, University of Illinois, 61801, Urbana, IL, USA aut Alam Muhammad School of Electrical and Computer Engineering, Purdue University, 47907-2035, West Lafayette, IN, USA aut Journal of Computational Electronics Springer US; http://www.springer-ny.com 10/4(2011-12-01), 341-351 1569-8025 10:4<341 2011 10 10825 https://doi.org/10.1007/s10825-011-0369-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10825-011-0369-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Islam Ahmad Department of Materials Science and Engineering, University of Illinois, 61801, Urbana, IL, USA aut NATIONALLICENCE 700 1- Alam Muhammad School of Electrical and Computer Engineering, Purdue University, 47907-2035, West Lafayette, IN, USA aut NATIONALLICENCE 773 0- Journal of Computational Electronics Springer US; http://www.springer-ny.com 10/4(2011-12-01), 341-351 1569-8025 10:4<341 2011 10 10825 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer