Band Alignment and Charge Transfer in Complex Oxide Interfaces

The synthesis of transition metal heterostructures is currently one of the most vivid fields in the design of novel functional materials. In this paper, we propose a simple scheme to predict band alignment and charge transfer in complex oxide interfaces. For semiconductor heterostructures, band-alignment rules like the well-known Anderson or Schottky-Mott rule are based on comparison of the work function or electron affinity of the bulk components. This scheme breaks down for oxides because of the invalidity of a single work-function approximation as recently shown in [Phys. Rev. B 93, 235116 (2016); Adv. Funct. Mater. 26, 5471 (2016)]. Here, we propose a new scheme that is built on a continuity condition of valence states originating in the compounds’ shared network of oxygen. It allows for the prediction of sign and relative amplitude of the intrinsic charge transfer, taking as input only information about the bulk properties of the components. We support our claims by numerical density functional theory simulations as well as (where available) experimental evidence. Specific applications include (i) controlled doping of ${\mathrm{SrTiO}}_3$ layers with the use of $4d$ and $5d$ transition metal oxides and (ii) the control of magnetic ordering in manganites through tuned charge transfer.

Popular Summary

Semiconductors have revolutionized technology. By sandwiching together compounds with different amounts of impurities (a construction known as a heterostructure), semiconductor devices can be designed with a wide range of electrical properties. One of the reasons for the success of semiconductors is the availability of simple rules that help predict the behavior of these heterostructures without complex calculations or expensive experimental testing. Intrinsic limitations of semiconductors, however, present hurdles to continued advancement. Transition metal oxides—compounds made up of oxygen atoms bound to transition metals such as titanium—exhibit several properties that make them leading candidates to replace conventional semiconductors, though the old rules for predicting behavior do not work. We propose a simple but powerful scheme to estimate electronic properties of oxide interfaces starting from very basic information about bulk properties of the components.

Our framework depends on the observation that, across interfaces within a heterostructure, there must be an overlap in the energies of the outer electrons in the oxygen atoms. We formulate rules that allow for the prediction of how the magnetic properties or the number of mobile charge carriers can be controlled by stacking different oxide materials. With numerical simulations and comparison to experiments (where available), we present a proof of concept that our rules can be used to design materials and heterostructures for future generations of electronic devices.

Figure 1

(a) Schematic figure of Anderson’s rule in semiconductor heterojunctions: The vacuum energy levels of the two semiconductors on either side are aligned. (b) Schematic figure of a perovskite (001) interface ${\mathrm{ABO}}_3/{\mathrm{AB}}^{\prime }{\mathrm{O}}_3$ emphasizing the common network of oxygen sites across the interface. (c) Alignment of oxygen states at the interface would generally yield a mismatch in the heterostructure’s Fermi energy [see Eq. (1)]. This mismatch drives a charge transfer, which itself alters interface and local potentials. The final equilibrium state is shown in panel (d), with indications (black arrows) of the three different contributions in the energy balance equation [Eq. (2)]. Note that ${ϵ}_p$ and ${ϵ}_d$ are the local energy levels of oxygen $p$ and TM $d$ states.

Figure 2

(a) Sketch of the energy-level scheme, and (b)–(d) layer-resolved DFT density of states for the $({\mathrm{SrTiO}}_3{)}_5/({\mathrm{SrZrO}}_3{)}_5$ superlattice. Oxygen $p$ states (dark gray) and TM $d$ states (red) are shown with the Fermi level marked by the dotted black line. Additionally, we show as a solid black line the layer-dependent center of mass of the oxygen states, which corresponds to the layer-dependent ${ϵ}_p^i$. We plot the DOS for the two ${\mathrm{BO}}_2$ layers directly at the interface as well as for the ${\mathrm{TiO}}_2$ two-unit cell further away. The alignment of oxygen states in this band-insulator heterostructure is practically perfect.

Figure 3

Upper panel: Sketch of the energy-level scheme before (a) and after (b) electron transfer. Lower panels: Same plots as in Fig. 2 but now for the heterostructure $({\mathrm{SrTiO}}_3{)}_5/({\mathrm{SrNbO}}_3{)}_5$. Opposed to the $({\mathrm{SrTiO}}_3{)}_5/({\mathrm{SrZrO}}_3{)}_5$, we see a clear transfer of electrons across the interface and the expected structure in the alignment of the layer-dependent ${ϵ}_p^i$ in the layers shown. The electrons transferred into interfacial and bulk ${\mathrm{TiO}}_2$ layers are $0.23e$ and $0.17e$, respectively.

Figure 4

Summary of bulk ${ϵ}_p$ (filled symbols) and ${ϵ}_d$ (empty symbols) with respect to the Fermi level ($E_F=0$) for different ${\mathrm{SrBO}}_3$ (solid line) materials. For the B site, we consider $3d$ (black), $4d$ (red), and $5d$ (blue) elements. With this reference bulk data, the charge transfer in heterostructures consisting of these materials can be anticipated. The simple criterion for the direction of the charge transfer at the ${\mathrm{ABO}}_3/{\mathrm{AB}}^{\prime }{\mathrm{O}}_3$ interface is that the component with lower ${ϵ}_p$ will donate electrons to the other one. Additionally, we plot data for ${\mathrm{LaBO}}_3$ (dashed line) for $\mathrm{B}=3d$, which is used for estimates for ${\mathrm{ABO}}_3/{\mathrm{A}}^{\prime }{\mathrm{BO}}_3$ interfaces. (For numerical data of the plot and additional compounds, please refer to Table 3 in Appendix pp2.)

Figure 5

Same plot as in Figs. 2 and 3 for a $({\mathrm{SrTiO}}_3{)}_5/({\mathrm{SrVO}}_3{)}_5$ heterostructure. In this case, alignment of oxygen bands will not drive electron transfer, and (as expected from Fig. 4) ${\mathrm{SrVO}}_3$ is a bad candidate for doping ${\mathrm{SrTiO}}_3$

Figure 6

Same plot as in Fig. 3 but now including an additional buffer layer between ${\mathrm{SrTiO}}_3$ and ${\mathrm{SrNbO}}_3$. The unit cell of this three-component symmetric heterostructure has the form $({\mathrm{SrTiO}}_3{)}_5/({\mathrm{SrZrO}}_3{)}_2/({\mathrm{SrNbO}}_3{)}_1/({\mathrm{SrZrO}}_3{)}_2$. As can be seen, the electron transfer from Nb to Ti remains intact even after inclusion of the buffer layer, excluding a pivotal role of microscopic details in the orbital degrees of freedom at the ${\mathrm{SrTiO}}_3/\mathrm{SrNb}{\mathrm{O}}_3$ interface.

Figure 7

Plot of the density of states with the usual color or marker convention (now also including $3d\text{−}{e}_g$ states plotted in blue). We show results for magnetically ordered calculations, starting with bulk results in the upper two panels. ${\mathrm{SrMnO}}_3$ is G-type antiferromagnetic ordered and ${\mathrm{SrTaO}}_3$ paramagnetic. In the lower two panels, we plot the data for the two layers in a $({\mathrm{SrMnO}}_3{)}_1/({\mathrm{SrTaO}}_3{)}_1$ heterostructure, including a ${\mathrm{GdFeO}}_3$ distortion. We see the dramatic influence of the electron transfer from Ta to Mn and the induction of ferromagnetic-ordered metallic ${\mathrm{MnO}}_2$ layers.

Figure 8

Projected density of TM $t_{2g}$ states of the ${\mathrm{BO}}_2$ layer with two layers away from interface. Red indicates a clean interface, while blue indicates a rough interface with 25% cation intermixing.