Interface structure and film polarization in epitaxial SrTiO${}_3$/Si(001)

Phenomenological models suggest that thin epitaxial SrTiO${}_3$ films on silicon will exhibit ferroelectric behavior as a result of compressive strain. However, such models do not include atomic-scale interface effects, which can dramatically alter the predicted behavior. In this paper, we use density functional theory computations to systematically elucidate the effects of the interface atomic structure and composition on the properties of SrTiO${}_3$/Si heterostructures. We show that while the band alignment and metallicity of the heterostructure are highly sensitive to the chemical composition and geometry of the interface, the system also exhibits several important features that are universal to all compositions. These universal features, which include an electronic dipole across the interface and a large cation-oxygen displacement in the interfacial oxide layer, conspire to induce a net positive polarization in ultrathin SrTiO${}_3$ films. We demonstrate that, due to its origin in the chemical bonds at the interface, this polarization is pinned in a single direction. Our results provide a fundamental understanding of the important role played by interfacial chemical bonds within the general class of atomically abrupt, oxide-semiconductor heterostructures and, furthermore, suggest guidelines for the future design of coupled functional oxide-semiconductor devices.

Figure 1

Example of a simulation supercell with a top electrode, showing the relaxed atomic structure of the experimentally realized interface composition. The silicon surface is passivated with H in the calculation to facilitate simulation of a thick silicon substrate. The Au electrode provides an electron reservoir; computations are performed both with and without such a reservoir.

Figure 2

Relaxed atomic structures and schematics of the computed band alignment for various interface compositions with a Sr-based interface layer and a first oxide layer composed of SrO. Oxygen concentration increases from top to bottom; Sr concentration increases from left to right. The band diagrams also indicate the energetic range and spatial position of interface states (shaded red areas), and are discussed in Sec. 5a. The naming convention (in parentheses) connects the structures to the properties reported in Tables .

Figure 3

Relaxed atomic structures and schematics of the computed band alignment for various interface compositions with a Sr-based interface layer and a first oxide layer composed of TiO${}_2$. Oxygen concentration increases from top to bottom; Sr concentration increases from left to right. The band diagrams also indicate the energetic range and spatial position of interface states (shaded red areas), discussed in Sec. 5a.

Figure 4

Relaxed atomic structures and schematics of the computed band alignment for compositions with a Ti-based interface layer. The band diagrams also indicate the energetic range and spatial position of interface states (shaded red areas), discussed in Sec. 5a.

Figure 5

Relaxed atomic structures and schematics of the computed band alignment for Si-rich interface compositions: (a) C0-T, (b) C0-S, and (c) F0-S. Si, Sr, Ti, and O atoms are gray, cyan, blue, and red spheres, respectively. The band diagrams also indicate the energetic range and spatial position of interface states (shaded red areas), discussed in Sec. 5a.

Figure 6

Electron rearrangement in the $xz$ plane (averaged over $y$) due to interface formation for compositions with a SrO plane adjacent to the interface layer. The interfacial oxygen concentration increases from left to right and the interfacial Sr concentration increases from top to bottom. Red and blue contours indicate electron loss and gain, respectively. Atom positions are indicated by the superimposed spheres.

Figure 7

Electron rearrangement in the $xz$ plane (averaged over $y$) due to interface formation for compositions with a TiO${}_2$ plane adjacent to the interface layer. The interfacial oxygen concentration increases from left to right and the interfacial Sr concentration increases from top to bottom. Red and blue contours indicate electron loss and gain, respectively. Atom positions are indicated by the superimposed spheres.

Figure 8

Electron rearrangement due to interface formation in the plane parallel to the interface, illustrating the ionic bonding between an interfacial Sr cation and the two oxygen anions per $1\times 1$ unit cell in the adjacent TiO${}_2$ layer [i.e., composition A0-T, Fig. 7d].

Figure 9

Atom-projected DOS in TiO${}_2$ (summed over the relevant Ti and O DOS) and Si layers in structure A0-T as a function of the Hubbard $U$ applied to the (a) Ti $d$ orbitals or the (b) Si $p$ orbitals, showing that the Fermi level is pinned to the conduction-band edge by the interface states.

Figure 10

Change in the occupation of the interfacial Ti $d_{xy}$ (solid lines) and hybrid Si/Sr (dashed lines) states with the Ti-Si distance for the A0-T interface. The SrTiO${}_3$ film is artificially fixed in a paraelectric state and the (fixed) TiO${}_2$-Si distance is varied.

Figure 11

Polarization profiles $\delta z$ (cation-anion separation) for 3-unit-cell-thick films with different interface compositions. Compositions with a SrO and TiO${}_2$ FOL are shown in (a) and (b), respectively. The dashed horizontal lines show the computed value for strained bulk SrTiO${}_3$ ($\delta z_{\mathrm{bulk}}$).

Figure 12

DFT-computed displacements $\delta z$ for each SrTiO${}_3$ atomic plane in Au/SrTiO${}_3$/Si heterostructures of varying thickness with the (a) A0-T, (b) A0-S, and (c) B0-S interface compositions. For reference, the computed bulk $\delta z$ is given by the black dashed line; $\delta z=0$ is marked by the horizontal blue line in (c).

Figure 13

(a) $\delta z$ of the interface and the film (averaged) as a function of metal electrode for interface A0-T. (b) Interfacial $\delta z_{\mathrm{int}}$ for heterostructures with a top gold electrode vs $\delta z_{\mathrm{int}}$ for the same heterostructures without a top electrode (vacuum) for a range of interface compositions. The solid red line is a fit to the data; the dashed black line is of unit slope and zero intercept.

Figure 14

(a) DFT-computed atomic structure for a 5-unit-cell-thick SrTiO${}_3$ film with one oxygen vacancy (dashed circles) per surface unit cell. The high oxygen vacancy coverage stabilizes a head-to-head domain in the center of the SrTiO${}_3$ film, with a positive interface polarization and a negative surface polarization, as indicated by the red arrows. Si, Sr, Ti, and O are gray, cyan, blue, and red, respectively. (b) Cation-O displacements for SrTiO${}_3$/Si films of various thickness with one oxygen vacancy per unit cell ($\theta =1$) at the surface. For comparison, the triangles show the displacements in the 9-unit-cell-thick SrTiO${}_3$/Si film with no oxygen vacancies ($\theta =0$) and no top electrode.

Figure 15

Schematic of the relevant charges in the Au/SrTiO${}_3$/Si system.

Figure 16

$P\left(l\right)$ from first-principles DFT calculations for SrTiO${}_3$ films with a SrO termination and a gold electrode. Each data point corresponds to a system with a different SrTiO${}_3$/Si interface structure and/or a different film thickness. Also included are points for Au/SrTiO${}_3$/Au films of various thickness. The data are fit to determine the expression for the boundary condition $P\left(l\right)$.

Figure 17

(a) Comparison of polarization profiles obtained via DFT and the model, illustrating the different contributions from the terms in Eq. (5) (see text). (b) Average monodomain polarization as a function of film thickness for Au/SrTiO${}_3$/Si heterostructures with the A0-T interface composition. Results for Au/SrTiO${}_3$/Au are shown for comparison. Solid lines are results from the model; symbols indicate DFT-computed values. The horizontal dashed lines indicate the bulk value.

Figure 18

$\delta z_{\mathrm{int}}$ for SrTiO${}_3$/Si heterostructures with modified A0-T interface compositions in which the Ti in the FOL is replaced by various transition-metal cations. The most common oxidation state(s) of each substitutional cation is shown in parentheses.

Figure 19

Computed electrostatic potential (red curve) for isolated Si and SrTiO${}_3$ slabs in the same DFT supercell illustrating the method for determining the reference band and internal potential alignments between bulklike Si and SrTiO${}_3$ (i.e., in the absence of interfacial effects). The symmetric SrTiO${}_3$ slab is terminated with TiO${}_2$ planes and the silicon surface is compensated with hydrogen.