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. 2017 Oct 26;7:14163. doi: 10.1038/s41598-017-14215-0

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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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Grain-boundary band profiles. Grain-boundary A (B) refers to a large (small) ${Δ X}_{B I}$ . Grain-boundary A has a larger potential barrier to holes at the valence-band minimum. All grain boundaries are presumed to be doped n-type from alkali incorporation, where both have a positive potential. Grain-boundary A also exhibits larger potential fluctuations due to increased compensation. Dashed lines in the “Charge Neutral” and “Negatively Charged” diagrams represent the Fermi energy, and the position of the defect states, V_Cu and In_Cu, in the “Compensated” diagram. E_A and E_D are activation energy of acceptors (V_Cu) and donors (In_Cu) respectively.