Intrinsic origin of interface states and band-offset profiling of nanostructured $\mathrm{LaAlO}{}_3/\mathrm{SrTiO}{}_3$ heterojunctions probed by element-specific resonant spectroscopies

The origin of electronic states at the basis of the 2DEG found in conducting $\mathrm{LaAlO}{}_3/\mathrm{SrTiO}{}_3$ interfaces (5 u.c. $\mathrm{LaAlO}{}_3$) is investigated by resonant photoemission experiments at the Ti $L$${}_{2,3}$ and La $M_{4,5}$ edges. As shown by the resonant enhancement at the Ti $L_{2,3}$ edge, electronic states at $E_F$ receive a dominant contribution from Ti $3d$ states. Both Ti and La resonance effects in the valence-band region are used to estimate the valence-band maxima at the two sides of the junction. Through a comparison with the valence-band states of the $\mathrm{LaAlO}{}_3$ and $\mathrm{SrTiO}{}_3$ parent compounds, we reconstruct the band diagram of the heterojunction, which is revealed to be type I (straddling gap), with a large notch of the band profile at the interface as compared with the reference insulating (3 u.c. $\mathrm{LaAlO}{}_3$) interface.

Figure 1

Sketch of the two excitation channels (1, $2a+2b)$ that can quantum mechanically interfere in a ResPES process (left panel). Resonant photoemission data at the Ti $L_{2,3}$ edge of the 5-u.c. (mid panel) and 3-u.c. (right panel) LAO-STO samples, normalized to the incident photon intensity.

Figure 2

(A) Resonant photoemission spectra of insulating 3-u.c. (upper curves, red lines) and conductive 5-u.c. (lower curves, black lines) LAO-STO films, measured off-resonance (dashed line, $h\nu =450\mathrm{eV})$, at $\mathrm{Ti}{}^{4+}$ resonance maximum (thin line, $h\nu =458.2\mathrm{eV}$), and at the $\mathrm{Ti}{}^{3+}$ resonance maximum (thick line, $h\nu =459.6\mathrm{eV}$). The vertical arrows mark the position of valence-band maxima (VBM-3 and VBM-5). Normalized RSW (off-resonance: $h\nu =450\mathrm{eV}$; $\mathrm{Ti}{}^{3+}$ resonance: $h\nu =459.6\mathrm{eV}$) of the 5 u.c. sample (shaded gray area) and of the 3-u.c. sample (dotted line). (B) Detailed view of the interface states F. Labels as in panel (A). For the two samples, the intensities have been normalized to the maxima of the peaks measured at $h\nu =459.6\mathrm{eV}$. (C) CIS spectra on $\mathrm{Ti}{}^{3+}$ (filled circles, BE $=$ $1.0\pm 1.0$ eV) and $\mathrm{Ti}{}^{4+}$ features (filled squares, BE $=7.5\pm 1.0$ eV); XAS spectra of the 5-u.c. sample (squares) and of a reference $\mathrm{LaTiO}{}_3$ sample (circles). The vertical dashed lines mark the photon energies (458.2 and 459.6 eV) of the resonant spectra shown in panels (A) and (B).

Figure 3

(Left) RSW spectra $\left(h\nu =459.6–450\mathrm{eV}\right)$ for the 3-u.c. and 5-u.c. LAO-STO samples, compared to DFT + $U$ $(U$ $=8\mathrm{eV})$ $d$-projected DOS calculations of a STO bulk crystal. (Inset) High-resolution interface states spectra of the 5-u.c. and 3-u.c. HJs. The intensities have been normalized to the peak maxima. (Right) High-resolution spectra of the 5-u.c. sample interface states (b), Fermi edge of the gold film deposited on the clip in contact with the HJ (a), resonant spectra of the Nb:$\mathrm{SrTiO}{}_3$ (adapted from Ref. [38]) (g), 5-u.c. LAO-STO (adapted from Ref. [19]) (e, f), $\mathrm{La}{}_x$$\mathrm{Sr}{}_{1-x}$$\mathrm{TiO}{}_3$ (adapted from Ref. [41]) (d), and $\mathrm{TiO}{}_{2-x}$ [39] (c).

Figure 4

(a) ResPES data collected at the La $M_{4,5}$ edge, in the VB and shallow-core-levels region of the 5-u.c. sample. (b) XAS spectrum and CIS curves collected at the La $M_{4,5}$ on the 5-u.c. sample. The CIS curves have been tracked for the C band at BE = 5.5 eV (in panel A) and for the in-gap states at BE = 0.5 eV. (c) Enlarged view of the photoemission spectra in the 0.0–2.0 BE range.

Figure 5

Photoemission spectra of 5-u.c. LAO-STO heterostructure at the La $M_{4,5}$ edge, collected out-of-resonance (black, $h\nu =820\mathrm{eV}$) and on-resonance (blue, $h\nu =836\mathrm{eV}$ (scaled by a factor of 0.2) conditions. Spectral difference (red line) and f-DOS DFT calculations on a LAO bulk crystal (filled orange). (Inset) Comparison of La $4f$ and Ti $3d$ resonating contribution with d-DOS DFT calculations on a STO bulk crystal (filled gray).

Figure 6

(Left) Band diagram for the LAO-STO 5-u.c. heterojunction. The horizontal red lines represent the energy shift for the 3-u.c. sample. (Right) Band diagram for the LAO-STO 3-u.c. heterojunction. All energies are defined within $\pm$0.1 eV, with the exception of ${\Delta }_{\mathrm{VBM}}^{\mathrm{int}}$ values ($\pm$0.2 eV).

Figure 7

(a) DDF-based calculation of the contribution to Ti $3d$ photoemission peak intensity of the first three STO layers and of the bulk in the 450.0–1500 eV photon energy range. The band profile depicted in the inset has been considered for the calculation. This profile has been drawn on the basis of the energy profile shown in Fig. 6. (b, c) Calculated photoemission spectra for Ti $3d$ levels at $h\nu =$ 450.0 and $h\nu$ = 1486.6 eV. (d) Calculation of the XPS Ti $3p$ (black) and ResPES Ti $3d$ (red) photoemission peak shifts for the various band profiles shown in (e). The horizontal dashed lines represent the observed ${\Delta }_{\mathrm{VB}}^{\mathrm{int}}$ and ${\Delta }_{\mathrm{VB}}^{\mathrm{bulk}}$ values, while the blue line represents the standard deviation $\left(\sigma \right)$.