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. 2020 Mar 18;10:4938. doi: 10.1038/s41598-020-61675-y

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© The Author(s) 2020

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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Charge transition levels (CTLs) based on DFT total energy methods. (a) Illustrative description of CTL. Formation energies of impurity (X) at different charge states, i.e. +1, 0, and −1, are shown as a function of Fermi level (i.e., electron chemical potential). The Fermi level at the crossing point of the two lines designated by X° (blue) and X⁻ (orange) is the CTL ε(0/−) from neutral state to negatively charged state. (b) Calculated CTLs based on the DFT total energy method are indicated by orange bars with the mark 0/+ or 0/−. For clear comparison, KS eigenvalues of impurity states are also shown (blue bars). Valence and conduction bands are represented by gray shaded columns. Here, valence band maximum is set to be the reference energy. The red (blue) arrows indicates how much the Fermi level should change with respect to valence band maximum (conduction band minimum) to induce the charge state transition of the impurities.