Figure 2 | Scientific Reports

Figure 2

From: Ab initio description of oxygen vacancies in epitaxially strained \(\hbox {SrTiO}_{{3}}\) at finite temperatures

Figure 2

Physical properties of stoichiometric (001) \(\hbox {SrTiO}_{{3}}\) thin films estimated with first-principles methods. (a) The electric polarization along the out-of-plane (\(P_{z}\)) and in-plane (\(P_{xy}\)) directions expressed as a function of expitaxial strain, \(\eta \). (b) Different Ti–O bond lengths expressed as a function of epitaxial strain. (c) Antiphase out-of-plane (\(\hbox {AFD}_{z}^{-}\)) and in-plane (\(\hbox {AFD}_{xy}^{-}\)) antiferrodistortive \(\hbox {O}_{{6}}\) rotations expressed as a function of epitaxial strain. (d) Energy band gap of (001) \(\hbox {SrTiO}_{{3}}\) thin films estimated with the range-separated hybrid functional HSE0645 on the geometries determined at the PBE+U level. The vertical lines indicate different phase stability regions, namely, 1. I4cm, 2. I4/mcm, 3. Ima2 and 4. Amm2. The solid lines are simply guides for the eye.

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