Spatial inhomogeneities at the LaAlO${}_3$/SrTiO${}_3$ interface: Evidence from second harmonic generation

Phase-sensitive, spatially resolved optical second-harmonic-generation experiments were performed on LaAlO${}_3$/SrTiO${}_3$ heterostructures. Lateral inhomogeneities on a length scale of $\approx 30$ $\mu$m are found when a one-unit-cell-thick epitaxial monolayer of LaAlO${}_3$ is grown on TiO${}_2$-terminated SrTiO${}_3$ single crystals. The inhomogeneity is absent in samples with LaAlO${}_3$ layers of more than one unit cell. The results are discussed in the framework of electronic, oxidic, and chemical inhomogeneities.

Figure 1

RHEED oscillations for the growth of $n=8$ (black) and $n=1$ (red) unit cells of LaAlO${}_3$ on the TiO${}_2$-terminated SrTiO${}_3$ substrate. The growth process is calibrated with the help of the $n=8$ sample, which reveals that 19 pulses complete a monolayer (vertical lines). In the subsequent growth of the $n=1$ sample, the deposition is stopped after 19 pulses have been applied. The RHEED signal equilibrates at maximum intensity.

Figure 2

(a,b) Spatially resolved SHG images of SrTiO${}_3$ covered with $n$ epitaxially grown monolayers of LaAlO${}_3$. The images show the area illuminated with the Gaussian laser beam and are scaled to the respective minimum (black) and maximum (white) intensity. Resolution is 25 $\mu$m. (c) Deviation from Gaussian laser beam profile shown for typical horizontal line scans across the camera chip, vertically averaging across three neighboring pixels. The sample with $n=3$ is chosen as representative for all the samples with $n\ne 1$. Lines are guides to the eye.

Figure 3

(a) Inhomogeneity parameter describing the statistical variation of SHG intensity in line scans as in Fig. 2c for different values of $n$, normalized to $n=0$. Reproducibility is confirmed by values obtained on other samples at $n=1$ (open symbols). (b) Polarization-averaged SHG susceptibilities for different values of $n$ show that the abrupt change of SHG yield at $n=3$ and the precursor behavior in the vicinity of $n=3$ have no effect on the inhomogeneity parameter. Lines are guides to the eye.

Figure 4

(a) High-resolution (1 $\mu$m) SHG image of a LaAlO${}_3$/SrTiO${}_3$ heterostructure at $n=1$. The 50$\%$ contour lines show that the “inhomogeneity length scale” of the sample is about 30 $\mu$m. The grainy substructure of the image is explained in the text. (b,c) Typical AFM images of the same sample show a perfectly flat SrTiO${}_3$ surface with substrate steps. The step height corresponds to one unit cell of the SrTiO${}_3$ substrate. The long-range fluctuation of brightness in panel (b) is caused by a known artifact of the scanning process related to nonlinearities of the piezoelectric scanner of the AFM. It is not caused by structural variations across the surface, as is furthermore evidenced by the straight parallel monolayer steps which are still clearly recognizable. (d) No micrometric inhomogeneities are revealed by linear optical light microscopy.

Figure 5

Intensity of $p$-polarized contributions to the SHG signal as a function of the polarization of the incident fundamental light for LaAlO${}_3$/SrTiO${}_3$ heterostructures with (a) $n=1$ and (b) $n\ne 1$, here represented by the sample with $n=12$. Note that the $s$-polarized lobes in panel (b) are magnified by a factor 5.