Interface Fermi States of ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ and Related Heterostructures

The interfaces of ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ and $({\mathrm{LaAlO}}_3{)}_x({\mathrm{SrTiO}}_3{)}_{1-x}/{\mathrm{SrTiO}}_3$ heterostructures have been investigated by soft x-ray photoelectron spectroscopy for different layer thicknesses across the insulator-to-metal interface transition. The valence band and Fermi edge were probed using resonant photoemission across the Ti $L_{2,3}$ absorption edge. The presence of a Fermi-edge signal originating from the partially filled Ti $3d$ orbitals is only found in the conducting samples. No Fermi-edge signal could be detected for insulating samples below the critical thickness. Furthermore, the angular dependence of the Fermi intensity allows the determination of the spatial extent of the conducting electron density perpendicular to the interface.

Figure 1

(a) Ti $L_{2,3}$ absorption-edge spectra taken in total-electron-yield mode for insulating and conducting LAO/STO; in red, adapted from Ref. 26, is the Ti $L_{2,3}$ absorption edge spectrum of ${\mathrm{LaTiO}}_3$, which only contains ${\mathrm{Ti}}^{3+}$ ions. (b) Intensity map of binding energy varying the photon energy ($h\nu$) for conducting LAO/STO. Intensity maps close to the Fermi level of (c) conducting LAO/STO and of (d) insulating LAO/STO. (c) and (d) have the same intensity scale. (e) constant initial state intensity spectra at the Fermi edge for insulating and conducting LAO/STO. The photon energies of 458 and 460.5 eV, indicated with filled and open circles, respectively, correspond to the $L_3$, $t_{2g}$, and $e_g$ peaks. The maximum intensity lies at 459.6 eV, indicated with an asterisk.

Figure 2

Photoemission spectra for conducting (a) 4.5 u.c. LAO/STO and (b) 6 u.c. LASTO/STO and for insulating (c) 2.5 u.c. LAO/STO and (d) 4 u.c. LASTO/STO. The color map corresponds to different emission angles $\theta$, indicated on the right of each panel, from 0° (normal emission, black lines) to 80° (grazing emission, pink lines) in 5° steps. The enlarged near-Fermi-edge spectra in (a), (b), (c), and (d) are normalized to the valence band integrated intensity. The $x$ axis in (c) have been corrected for charging shifts in this sample.

Figure 3

(a) Function describing spatially [$R(z)$] the conducting layer of thickness $d$ at the interface. $z$ is the distance from the film surface. $t$ is the thickness of the film. In this example, $t=16.9\AA$ is the thickness of the 4.5 u.c LAO layer. (b) Normalized Fermi edge integrated intensity as a function of $\theta$ for the conducting LAO/STO sample, and (c) the conducting LASTO/STO sample. The best fits, drawn as solid lines in (b) and (c), yield in both cases $d=1\mathrm{u}.\mathrm{c}.$. The dashed lines in (b) and (c) represent the calculated curves for $d=5\mathrm{u}.\mathrm{c}.$