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. 2017 May 19;7:2160. doi: 10.1038/s41598-017-02113-4

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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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Main optical modes contributing to the large static dielectric constant for STO bulk (top) and for a slab of 7 layers under −1.305% strain (bottom). The bulk TO modes are represented as black and red sticks. Meanwhile, only the large LO-TO shift for the TO₁ mode (shift ~700 cm) is illustrated with a red arrow. At the bottom of the figure, the main optical modes for a 7 layers slab under −1.305% strain are presented. The black sticks represent modes which derive their intensities from atoms further from the surfaces (bulk like modes). The blue sticks are transverse modes from atoms at the TiO₂-terminated surface. The red stick at 210 cm⁻¹ corresponds to a TO mode from Ti-O bending (bulk like mode). The very large LO-TO shift of the 210 cm⁻¹ mode (indicated by a red arrow) contributes strongly to the high value of ε(0)_//. Insets top and bottom: the elementary cell for bulk and for 7 layers slab (Sr: big green sphere, Ti: medium blue sphere, O: small red sphere).