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. 2023 Dec 12;13:22002. doi: 10.1038/s41598-023-49097-y

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© The Author(s) 2023

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Comparison about the net-charge arrangement characters over the NOAs with different apex-appearance but the same lower frustum, whose top and bottom radius are 10 nm and 140 nm, respectively. The cross-sectional net-charge distribution density of the NOAs with (a) cone-apex and (b) sphere-apex in the y–z plane are also given, and a typical structure of the latter is displayed in the inset. The contour of the Au-NOA and the silicon NOA are also plotted along a long and a short dashed-line, respectively. (c) The net-charge distribution density over the surface of the NOAs with a cone-apex (blue line) and a sphere-apex (red line).