Abstract
Strontium titanate is a promising dielectric material for device applications including capacitors and gate dielectrics. However, oxygen vacancies, which are inevitable donor defects mobile under bias at room temperature, lead to undesirable leakage current in SrTiO3 thin films. Epitaxially grown SrTiO3 on lattice mismatched substrates leads to strained SrTiO3, inducing structural phase transitions from a cubosymmetric non-ferroelectric geometry to tetragonal and orthorhombic structures, depending upon the sign of the strain. In this study, density functional calculations have been performed to determine the impact of isotropic biaxial tensile strain in a (001) plane upon the phase of SrTiO3 and the activation energy for the migration of oxygen vacancies in such strained SrTiO3. The phase transition of the host material yields anisotropy in oxygen vacancy diffusion for diffusion within and between planes parallel to the strain. We found a general reduction in the barrier for diffusion within and normal to the plane of tensile strain. The inter-plane diffusion barrier reduces up to 25% at high values of strain. The variation in the barrier corresponding to in-plane diffusion is smaller in comparison to inter-plane diffusion. Finally, we reflect upon how the interplay between lattice strain with native defects plays a crucial role in the conduction mechanism of thin film, strained SrTiO3.
I. INTRODUCTION
II. COMPUTATIONAL METHOD AND MODELS
III. RESULTS AND DISCUSSION
A. In-plane V _{O} migration
1. Path
2. Paths and
3. Path
B. Inter-plane V _{O} migration
IV. DISCUSSION AND CONCLUSIONS
Key Topics
- Diffusion
- 43.0
- Diffusion barriers
- 21.0
- Vacancies
- 11.0
- Chemical interdiffusion
- 6.0
- Crystal structure
- 6.0
Figures
Schematics of (a) the (001) projection of centrosymmetric unstrained SrTiO3, (b) tetragonal SrTiO3 with bi-axial tensile strain within (001)-plane, showing the displacements and in the oxygen sub-lattice, and (c) bi-axially strained SrTiO3 indicating the sequence of TiO2 and SrO (001)-planes parallel to the plane of tension. The oxygen sites 1–4 are within same TiO2 (001)–plane, and sites 5 and 6 are within the adjacent SrO (001)-plane.
Schematics of (a) the (001) projection of centrosymmetric unstrained SrTiO3, (b) tetragonal SrTiO3 with bi-axial tensile strain within (001)-plane, showing the displacements and in the oxygen sub-lattice, and (c) bi-axially strained SrTiO3 indicating the sequence of TiO2 and SrO (001)-planes parallel to the plane of tension. The oxygen sites 1–4 are within same TiO2 (001)–plane, and sites 5 and 6 are within the adjacent SrO (001)-plane.
Projection the TiO2-(001) plane showing the V O in-plane diffusion steps, , and . and are equivalent. Ti ions are labeled, with the remaining sites being oxygen.
Projection the TiO2-(001) plane showing the V O in-plane diffusion steps, , and . and are equivalent. Ti ions are labeled, with the remaining sites being oxygen.
In-plane V O migration barrier as a function of isotropic, (001) bi-axial tensile strain, for path (Fig. 2 ), each panel showing the results for a different charge state.
In-plane V O migration barrier as a function of isotropic, (001) bi-axial tensile strain, for path (Fig. 2 ), each panel showing the results for a different charge state.
In-plane V O migration barrier as a function of isotropic, (001) bi-axial tensile strain, for path (Fig. 2 ), each panel showing the results for a different charge state.
In-plane V O migration barrier as a function of isotropic, (001) bi-axial tensile strain, for path (Fig. 2 ), each panel showing the results for a different charge state.
In-plane V O migration barrier as a function of isotropic, (001) bi-axial tensile strain, for path (Fig. 2 ), each panel showing the results for a different charge state.
In-plane V O migration barrier as a function of isotropic, (001) bi-axial tensile strain, for path (Fig. 2 ), each panel showing the results for a different charge state.
Schematic view showing the four inter-plane migration steps labeled , and . and represent V O diffusion from the TiO2 (001)-plane to the adjacent SrO (001)-plane, and diffusion from the SrO (001)–plane to the next TiO2 (001)-plane are represented by and .
Schematic view showing the four inter-plane migration steps labeled , and . and represent V O diffusion from the TiO2 (001)-plane to the adjacent SrO (001)-plane, and diffusion from the SrO (001)–plane to the next TiO2 (001)-plane are represented by and .
(a) V O inter-plane migration NEB profile for the V O migrating along the path indicated in (b) for 4% strain. (b) shows schematic views for V O migration between two TiO2-planes (sites 1 and 3) via a SrO-plane (site 2). Both diagrams represent processes indicated as followed by .
(a) V O inter-plane migration NEB profile for the V O migrating along the path indicated in (b) for 4% strain. (b) shows schematic views for V O migration between two TiO2-planes (sites 1 and 3) via a SrO-plane (site 2). Both diagrams represent processes indicated as followed by .
Calculated inter-plane V O migration barriers as a function of in-plane biaxial tensile strain for diffusion along (diamonds) and (triangles), with (a), (c), and (e) representing neutral, +1, and +2 charge states, respectively. For the (open circles) and (squares) the neutral, +1, and +2 charge states are plotted in (b), (d), and (f), respectively. The paths are shown in Fig. 7 . In each plot, the filled circles represent the energy difference between V O in the TiO2 and SrO planes, equal to the difference in the forward and reverse barrier heights.
Calculated inter-plane V O migration barriers as a function of in-plane biaxial tensile strain for diffusion along (diamonds) and (triangles), with (a), (c), and (e) representing neutral, +1, and +2 charge states, respectively. For the (open circles) and (squares) the neutral, +1, and +2 charge states are plotted in (b), (d), and (f), respectively. The paths are shown in Fig. 7 . In each plot, the filled circles represent the energy difference between V O in the TiO2 and SrO planes, equal to the difference in the forward and reverse barrier heights.
Schematic views of V O diffusion process for (a) in-plane diffusion completely within TiO2 (001)–plane. (b) in-plane diffusion involving both TiO2 (001) and SrO (001) planes. (c) The inter-plane diffusion. The long Ti-O bonds along [100] and [010] directions are highlighted with yellow colors. The red arrows point to the rate limiting step for each diffusion process.
Schematic views of V O diffusion process for (a) in-plane diffusion completely within TiO2 (001)–plane. (b) in-plane diffusion involving both TiO2 (001) and SrO (001) planes. (c) The inter-plane diffusion. The long Ti-O bonds along [100] and [010] directions are highlighted with yellow colors. The red arrows point to the rate limiting step for each diffusion process.
Tables
Calculated parameters for isotropic bi-axial (001) tensile strained SrTiO3. (Å) is the displacement of the oxygen ions along [100] (and [010]) relative to Ti and Sr. is the equilibrium ratio obtained for the ferroelectric distorted structures under strain. Relative energies per formula unit (meV) are calculated relative to cubic, unstrained SrTiO3 (E 1), and relative to biaxially strained, centro-symmetric SrTiO3 (E 2). is the equilibrium ratio for the cubo-symmetric phase.
Calculated parameters for isotropic bi-axial (001) tensile strained SrTiO3. (Å) is the displacement of the oxygen ions along [100] (and [010]) relative to Ti and Sr. is the equilibrium ratio obtained for the ferroelectric distorted structures under strain. Relative energies per formula unit (meV) are calculated relative to cubic, unstrained SrTiO3 (E 1), and relative to biaxially strained, centro-symmetric SrTiO3 (E 2). is the equilibrium ratio for the cubo-symmetric phase.
Diffusion barriers for the rate limiting steps for the in-plane and inter-plane paths shown in Fig. 9 . For in-plane, the values in parentheses refer to path (b). For each value of strain, the value in bold face indicates which in-plane path ((a) or (b)) is lower in energy, and the underline indicates which of (a), (b), or (c) has the lowest barrier. The unstrained values are included for comparison.
Diffusion barriers for the rate limiting steps for the in-plane and inter-plane paths shown in Fig. 9 . For in-plane, the values in parentheses refer to path (b). For each value of strain, the value in bold face indicates which in-plane path ((a) or (b)) is lower in energy, and the underline indicates which of (a), (b), or (c) has the lowest barrier. The unstrained values are included for comparison.
Article metrics loading...
Full text loading...
Commenting has been disabled for this content