M. Zschornaka, b, 
, 
, S. Gemminga, E. Gutmannb, T. Weißbachb, c, H. Stöckerb, T. Leisegangb, T. Riedld, e, M. Tränknerd, e, T. Gemmingd and D.C. Meyerb, f
Abstract
Strontium titanate (STO) is a preferred substrate material for functional oxide growth, whose surface properties can be adjusted through the presence of Ruddlesden–Popper (RP) phases. Here, density functional theory (DFT) is used to model the (1 0 0) and (0 0 1) surfaces of SrO(SrTiO3)n RP phases. Relaxed surface structures, electronic properties and stability relations have been determined. In contrast to pure STO, the near-surface SrO–OSr stacking fault can be employed to control surface roughness by adjusting SrO and TiO2 surface rumpling, to stabilize SrO termination in an SrO-rich surrounding or to increase the band gap in the case of TiO2 termination. RP thin films have been epitaxially grown on (0 0 1) STO substrates by chemical solution deposition. In agreement with DFT results, the fraction of particular RP phases n = 1–3 changes with varying heating rate and molar ratio Sr:Ti. This is discussed in terms of bulk formation energy.
Keywords: Density functional theory; Surface energy; Surface structure; Thin films; Layered structure
Article Outline
- 1. Introduction
- 2. Materials and methods
- 2. Materials and methods
- 3. Results and discussion
- 3.1. Influence of preparation parameters on thin film phase content
- 3.2. Bulk structure modeling
- 3.3. Surface modeling
- 3.2. Bulk structure modeling
- 3.3.1. Surface relaxations
- 3.3.2. Density of states
- 3.3.3. Surface energies
- 3.3.2. Density of states
- 4. Conclusions
- Acknowledgements
- References
- Acknowledgements
Fig. 1. WAXRD patterns of thin film SrO(SrTiO3)n RP phases prepared by CSD under (a) variation of the heating rate of the final annealing step (700 °C, 1 h duration, molar ratio of Sr:Ti = 1.75:1) and (b) variation of the molar ratio Sr:Ti in the precursor solution (heating rate of 20 K min−1).
Fig. 2. HRTEM image near Scherzer defocus of an RP phase n = 1 film cross-section with an inset (white frame) corresponding to a simulation (a). From comparison of experimental and simulated data the position of the atomic columns (Ti–O in white, Sr in gray, and O in black) can be obtained as shown in the magnification (b).
Fig. 3. Calculated energies for the formation of RP phases according to Eq. (1). The integration of the SrO–OSr stacking fault into STO shows exothermic character for all phases and saturates at n = 3. Choice of LDA or GGA exchange–correlation functional and unit cell sampling (tetragonal or primitive cell) do not influence the results.
Fig. 4. Two distinct cross-sections of the density difference of valence electrons before (i.e. red maxima) and after surface relaxation (i.e. blue minima) for the RP n = 2 (1 0 0) surface (blue). Scaled displacement vectors (square root of length) visualize TiO6 octahedral distortions and twisting as well as a large atomic displacement where the SrO stacking fault perpendicularly hits the surface (upper center of right section). Isosurfaces of the electron density outline the type of atoms and their relaxed surface positions. The inset shows a unit cell of the structure of the same orientation.
Fig. 5. Grand canonical potential Ω of the RP (1 0 0) and (0 0 1) surfaces of different terminations in SrO-rich surrounding. SrO terminations (green) show in comparison to TiO2 terminations (brown) smaller surface energies. Configurations with interacting stacking fault (squares) give intermediate values. Reference calculations for SrO and STO surfaces are included.
Fig. 6. Density of states of (1 0 0) and (0 0 1) RP surface structures. Solid, dashed and plotted lines indicate TiO2, SrO and SrO DL configuration types according to surface cuts sketched in Fig. 5. For (1 0 0) plots, the DOS of the bulk RP phases was included in shaded gray. Surface states shift the valence band for TiO2 terminations which is less effective for a near-surface SrO DL. Additional energy splitting for Sr 4p states is induced by an SrO DL surface (see arrows).
Fig. 7. Calculated grand canonical potential Ω as a function of the normalized chemical potential
Table 1.
Cell parameters of the relaxed RP phases with n = 0–3, ∞ calculated with LDA and GGA in comparison to tabulated experimental data Exp. [69] as well as results from our measurements [37].
Table 2.
Formation energies Ef (eV) from bulk STO and SrO calculated according to Eq. (1) for RP phases with n = 1–5 (GGA) compared to other results.
a Most stable of several configurations.
Table 3.
Calculated atomic displacements δz of near-surface layers with respect to bulk phases (note: for n = 1, 2, 3 layers out of mirror planes have ΔzMe–O ≠ 0 in the bulk phase already) and Me–Me interlayer distance changes dij as a per cent of the bulk lattice constant a0 next to absolute surface rumpling s in Å compared to experimental data. Positive signs denote displacements towards the slab and rumpling with an outer layer of oxygen. Termination types are labeled according to surface cut sketches in Fig. 5.
Corresponding author at: Institut für Ionenstrahlphysik und Materialforschung, FZ Dresden-Rossendorf, D-01314 Dresden, Germany
