Structure of ${\mathrm{SrTiO}}_3$ Films on Si

The epitaxial deposition of oxides on silicon opens the possibility of incorporating their diverse properties into silicon-device technology. Deposition of ${\mathrm{SrTiO}}_3$ on silicon was first reported over a decade ago, but growing the coherent, lattice-matched films that are critical for many applications has been difficult for thicknesses beyond 5 unit cells. Using a combination of density functional calculations and x-ray diffraction measurements, we determine the atomic structure of coherent ${\mathrm{SrTiO}}_3$ films on silicon, finding that the Sr concentration at the interface varies with the film thickness. The structures with the lowest computed energies best match the x-ray diffraction. During growth, Sr diffuses from the interface to the surface of the film; the increasing difficulty of Sr diffusion with film thickness may cause the disorder seen in thicker films. The identification of this unique thickness-dependent interfacial structure opens the possibility of modifying the interface to improve the thickness and quality of metal oxide films on silicon.

Figure 1

The lowest energy structures of ${\mathrm{SrTiO}}_3$ films on Si(001) at thicknesses of 1 (A), 2 (B), and 5 (C) unit cells. Sr atoms are blue, Ti are yellow, O are red, and Si are grey. The film thicknesses are defined by the number of ${\mathrm{TiO}}_2$ layers. The SrO interface in (A) is energetically preferred; it is positively charged, and the surface assumes a compensating negative charge by forming Sr vacancies, resulting in a ${\mathrm{Sr}}_{1/2}\mathrm{O}$ surface. As the films grow, the charge of the interface is reduced by the formation of Sr vacancies, and the Sr content at the surface increases. At a thickness of 2 unit cells, the optimal interface and surface combination is ${\mathrm{Sr}}_{15/16}\mathrm{O}$ (interface) and ${\mathrm{Sr}}_{9/16}\mathrm{O}$ (surface), while at 5 unit cells it is ${\mathrm{Sr}}_{11/16}\mathrm{O}$ (interface) and ${\mathrm{Sr}}_{13/16}\mathrm{O}$ (surface). Note the polarization of the film as indicated by the upward displacement of the Ti atoms. The polarization decreases with increasing film thickness while the rotation of the O octahedra increases.

Figure 2

Energy as a function of surface and interface Sr concentration for 1, 2, and 5 unit cell films computed with DFT. The stoichiometry of the interface is ${\mathrm{Sr}}_x\mathrm{O}$, the surface is ${\mathrm{Sr}}_y\mathrm{O}$, and $x+y=3/2$ is satisfied for these low-energy structures as described in the text. The energies have been shifted so the minimum for each thickness is zero. The structures plotted in Fig. 1 are those with minimal energy for each thickness. The purple square indicates the 5 unit cell structure with a ${\mathrm{Sr}}_{3/4}\mathrm{O}$ interface that best agrees with the experimentally measured x-ray diffraction.

Figure 3

The experimental x-ray diffraction curve of a 5 unit cell film of ${\mathrm{SrTiO}}_3$ on Si(001) compared with calculated curves from three structures with low energies in DFT. The calculated curves use the structures from the ${\mathrm{Sr}}_{3/2}{\mathrm{O}}_2$ interface of Först et al., Ref. 19, the ${\mathrm{Sr}}_{1/2}\mathrm{O}$ interface of Zhang et al., Ref. 18, and the $x=3/4$ structure from the present work. Note the correspondence between the features of the experimental diffraction curves and the $x=3/4$ structure that is absent in the other structures.

Figure 4

The $c/a$ ratio as a function of in-plane strain. Measured values for 5 and 10 unit cell ${\mathrm{SrTiO}}_3$ films on Si(001), determined from the ${\mathrm{SrTiO}}_3(002)$ and (202) diffraction peaks, are plotted in blue with error bars [12, 36]. The 5 unit cell film is under approximately $-1.7\%$ strain and is coherent with the Si substrate. The 10 unit cell film has substantially relaxed. The red squares show $c/a$ ratios computed from three theoretical 5 unit cell structures with low free energies: the $x=3/4$ structure, the ${\mathrm{Sr}}_{3/2}{\mathrm{O}}_2$ interface of Först et al., Ref. 19, and the ${\mathrm{Sr}}_{1/2}\mathrm{O}$ interface of Zhang et al., Ref. 18.