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. 2017 Sep 11;7:11204. doi: 10.1038/s41598-017-11165-5

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Statistical results of Monte Carlo simulation under VSM, CSV and GVR. (a) Box plot of V _SET extracted from 3000 cycles for different initial values of n. The distribution of all the points is shown in the “total” column. Inset of (a) The scatter plot showing the relationship between R _OFF and V _SET (blue dots) and moving geometric mean (red dots), by calculating the geomean of 20 adjacent voltage values. (b) Weibull distributions of V _SET in 3000 cycles for different n. (c) Weibull slope and scale factor extracted from (b). Both parameters are linearly dependent on n. (d–f) The distribution of t _SET under CSV. (g,h) Histogram of conductance distribution (when G > G ₀) in 100 continuous cycles under VSM and GVR, showing Gaussian distribution and skew normal distribution, respectively. Inset of (h) The magnified histogram when G > 3.5G ₀. (i) The distribution of gap thickness (when G < G ₀).