Interface band engineering in ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures

Novel two-dimensional electron systems at the interfaces of oxide heterostructures, such as ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$, have attracted much attention as they open a new route to harness the rich quantum phases of transition-metal oxides (TMOs) for potentially useful functionalities not available in conventional semiconductor electronics. For such applications, the controllability of these interface properties is key. For ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$, previous theoretical and experimental investigations of the band offset and the potential profile near the interface have yielded not only quantitatively different but sometimes even contradictory results, e.g., the absence vs presence of a potential gradient in the ${\mathrm{LaAlO}}_3$ film. By analyzing angle-dependent hard x-ray photoelectron spectroscopy (HAXPES) data with a Poisson-Schrödinger model, we determine the charge carrier distribution and the valence band edge profile across the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface self-consistently. By systematically controlling the oxygen vacancy concentration, i.e., the doping level, during the photoemission experiments, we derive a comprehensive picture of the band scheme and show that the two-dimensional electron system is always narrowly confined to the interface. We observe a crossover of the band alignment from type II to type I with increasing doping level, which reconciles the striking inconsistencies among the earlier studies. We further find that the strongly nonlinear dielectric response of the ${\mathrm{SrTiO}}_3$ substrates to the electric field is essential for the understanding of the band arrangement at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterointerface.

Figure 1

(a) Setup of the photoemission experiment. By a combination of O dosing and the intense x-ray irradiation we can precisely control the oxygen stoichiometry in the heterostructure during the photoemission experiment. The probing depth of the photoelectrons varies with their emission angle. (b) Making use of a wide angle acceptance lens photoelectrons emitted at an angle of $5^{\circ }$–${65}^{\circ }$ with respect to the sample surface normal can be recorded by the analyzer simultaneously. In consequence, the depth distribution of the photoelectrons can be probed without changing the measurement geometry.

Figure 2

Valence band spectra of the fully oxidized (blue lines) and the oxygen depleted state (red lines) of a ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure recorded with soft x-rays at the QP (a) and the IG resonance (b).

Figure 3

Electron emission angle dependence of substrate core level spectra for a 4 uc ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure. Ti $2p$ (top) and Sr $3d$ (bottom) spectra of the sample in the fully oxidized (a) and oxygen depleted (b) state.

Figure 4

Poisson-Schrödinger approach for different kinds of doping. 3D concentration of mobile charge carriers (dashed lines) and of ionized donors (solid lines). Blue: Doping by electronic reconstruction for fully oxidized epitaxial ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ samples. Gray: Doping by oxygen vacancies for, e.g., disordered ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ samples. Red: Combination of doping by oxygen vacancies and electronic reconstruction for oxygen depleted epitaxial ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ samples.

Figure 5

(a) Temperature dependence of the dielectric constant of a (001)-oriented ${\mathrm{SrTiO}}_3$ single crystal [65]. (b)  Electric field dependence of the dielectric constant of single-crystal ${\mathrm{SrTiO}}_3$ at $T=60\text{K}$. Experimental data from Ref. [66]. Data fitted according to (5).

Figure 6

Layer-resolved composition of an exemplary Ti $2p$ spectrum. (a) Conduction band profile near the interface. (b) Concentration of mobile electrons. (c) Concentration of trapped electrons (corresponding to the concentration of oxygen vacancies). (d) Ti $2p$ spectra of the first eight ${\mathrm{TiO}}_2$ layers. The binding energy of the single spectra is determined by the interfacial band bending at position $z$ [see arrows in (a)]. The ${\mathrm{Ti}}^{3+}$ weight of the single spectra is proportional to the sum of the mobile and trapped charge carrier concentration, which is integrated over the corresponding unit cell [see colored intervals in (b) and (c)].

Figure 7

Fits of Ti $2p$ and Sr $3d$ core level spectra with the Poisson-Schrödinger method. A comparison between the Ti $2p$ spectra at the extremal electron emission angles and the corresponding fits is shown in (a) and (b) for the fully oxidized and the O depleted state, respectively. Corresponding figures for the Sr $3d$ core level are shown in (c) and (d). The fitted curves agree well with the measured data. ${\mathrm{SrTiO}}_3$ reference spectra are shown for comparison.

Figure 8

The electrostatics at the (001)-oriented ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure in the fully oxidized and the oxygen depleted state. (a) Distribution of the mobile charge carriers. (b) Distribution of the mobile charge carriers normalized by the total mobile charge carrier concentration $Q_{\mathrm{total}}$. (c) Conduction band profile with subband structure. The Fermi energy is pinned at the conduction band minimum in the bulk of ${\mathrm{SrTiO}}_3$. (d) Profile of the electric field. (e) Profile of the dielectric constant. For details see text.

Figure 9

Angle-integrated spectra comprising the Sr $3d$, Al $2s$, and La $4d$ core levels of a ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure in the fully oxidized and the O depleted state. As a function of the oxygen stoichiometry we observe a pronounced shift in the film core level binding energies.

Figure 10

(a) Valence band spectra of the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure for the fully oxidized and the oxygen depleted state. The spectral shape as well as the onset of the valence band spectrum changes as a function of the oxygen stoichiometry. Inset: Valence band spectra of bare ${\mathrm{SrTiO}}_3$ for the fully oxidized and the oxygen depleted state. [(b),(c)] Measured data, fit and decomposition of the valence band spectra into the ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ contributions in the oxygen depleted and in the fully oxidized state, respectively. The ${\mathrm{LaAlO}}_3$ valence band contribution (dotted line) clearly shifts in binding energy as a function of the ${\mathrm{V}}_{\mathrm{O}}$ concentration.

Figure 11

Band diagram of the (001)-oriented ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure in the fully oxidized and O depleted state. The offset between the valence band edges of ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ right at the interface is fixed independent of the oxidation state. The change in the valence band offset is calculated from averaged values in Table 3, the change in the potential well depth is read out from Fig. 8. The Fermi energy is pinned at the conduction band minimum in the bulk of ${\mathrm{SrTiO}}_3$ (see Sec. 3g).

Figure 12

Analyzing the core level spectra of the ${\mathrm{LaAlO}}_3$ film. (a) Angle-integrated Al $1s$ and La $4d$ spectra. As a function of the oxidation state there is not only a shift in binding energy but also a change of the spectral shape. (b) Binding energy of the Al $1s$ and La $4d_{5/2}$ core level maxima dependent on the electron emission angle. For each core level, binding energies are referenced to the average binding energies in the fully oxidized state.

Figure 13

Modeling the potential profile in the ${\mathrm{LaAlO}}_3$ film in the oxygen depleted state. (a) Fits of the angle-integrated Al $1s$ (left) and La $4d$ (right) spectra. The fitted curves agree well with the measured data. (b) Resulting potential profile. The binding energy shifts show the difference in binding energy between the oxygen depleted state and the fully oxidized state.

Figure 14

Refined band diagram of the (001)-oriented ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructure in the fully oxidized and oxygen depleted state. The arrows indicate the changes in the band offsets at both sides of the interface upon O depletion. The Fermi energy is pinned at the conduction band minimum in the bulk of ${\mathrm{SrTiO}}_3$ (see Sec. 3g).