Introduction

Some of the most exciting condensed matter physics problems are found at the interfaces of dissimilar materials1. The behaviour of electrons at these interfaces would be governed by electronic reconstruction mechanisms2 leading to a variety of exotic quantum phenomena1. In conjunction with X-ray and electron spectroscopy techniques3,4,5,6,7 with their inherent advantages and constraints, an experimental technique that can directly reveal hidden quantum phenomena at buried interfaces is highly desirable. In this paper we demonstrate the potency of high-energy optical reflectivity coupled with spectroscopic ellipsometry and study an interface consisting of two dissimilar insulators: polar LaAlO3 and nonpolar SrTiO3 revealing the details of the charge (electron) transfer among and within the layers that govern the conductivity of the buried interface.

The quasi two-dimensional electron gas (2DEG) at the the buried interface of two different insulator oxides heterostructure, polar LaAlO3 on nonpolar SrTiO3 (LaAlO3/SrTiO3)8 has shown many interesting phenomena ranging from metal–insulator transition9, superconductivity10 and magnetism11,12,13,14. According to the controversial but compelling polarization catastrophe model, the polar sublayers of LaAlO3 ((LaO)+ and (AlO2)) give rise to a polarization field inside LaAlO3 that causes an electronic potential build-up as the LaAlO3 film thickness increases. To counter this, a charge transfer of 0.5e per unit cell (uc) (~3 × 1014 cm−2) from LaAlO3 into the LaAlO3/SrTiO3 interface is required15,16. Various techniques have shown a charge transfer much less than this. For example, X-ray-based techniques5,6 have estimated up to 1.1 × 1014 cm−2 while transport measurements9,10,11 yield substantially smaller number of carriers of ~1013 cm−2. It has been suggested that charge localization effects might limit the number of mobile charges that can be measured by transport7,17, and thus if a technique can measure and quantify both the localized and delocalized charges, one might be able to evaluate the actual charge transfer5,6,7.

Another unresolved important issue is the insulating case of LaAlO3/SrTiO3 (≤3 uc of LaAlO3). Transport measurements9 have shown that the conducting interface only exists above a certain critical thickness of LaAlO3, typically ≥4 uc (although cationic stoichiometry, for example the La/Al ratio of LaAlO3 film, may also affect the interface conductivity, with conducting LaAlO3/SrTiO3 observed to have slightly Al-rich LaAlO3 film18). This means that the charge transfer into the interface required for countering the polarization catastrophe does not happen when the thickness of LaAlO3 is below 4 uc. According to the prevalent polarization catastrophe model, this means the polarization field should be present for ≤3 uc of LaAlO3. One way to verify the model is to measure this polarization potential build-up in insulating LaAlO3/SrTiO3, which is predicted to be 0.24 V Å−1 (or ~0.9 V per uc of LaAlO3)19. However, attempts to measure this have not been successful using core-level X-ray photoemission spectroscopy (XPS)20,21, in which the measured core-level shift in LaAlO3 is only ~0.1 eV per uc of LaAlO3, much less than expected. If the changes in the band structure are predominantly near the valence bands and the Fermi level, then the appropriate technique should directly probe states near the valence bands and the Fermi level.

Let us approach the problem from a different angle. Another way to overcome the polarization potential is by charge redistribution within the LaAlO3 layers. In a Gedankenexperiment, we hypothesize an extreme case of charge redistribution of 1e between the AlO2 and LaO sublayers of LaAlO3, which is also adequate to compensate the polarization potential, although the actual amount of charge redistribution might be restricted by electrostatics. Hence, instead of measuring the potential build-up in the layers, one can measure the charge redistribution within the layers directly. This can be done by measuring the optical conductivity involving states below and above the valence bands, the conduction bands and the Fermi level, and then use the f-sum rule, which represents charge conservation, to quantify the charge redistribution.

Furthermore, recent band structure calculations and surface X-ray diffraction measurements suggest that distortions of the LaAlO3 lattice (buckling) may partly compensate the polarization field in insulating LaAlO3/SrTiO3 (refs 22, 23, 24, 25). Interestingly, when the interface becomes conducting at LaAlO3 thickness ≥4 uc, this distortion decreases and ultimately vanishes24,25, indicating that the buckling mechanism is unique to the insulating case of LaAlO3/SrTiO3. This raises another important question: since the buckling is a structural change, will the electronic structure change appropriately, and manifest as a charge redistribution within the LaAlO3 layer itself? Thus, it is again critical to be able to measure these intralayer charge redistributions.

As mentioned earlier, a direct way to probe the electronic band structure and charge (localized and delocalized) redistribution mechanisms is to measure the complex dielectric response of the material from which the optical conductivity can be extracted in a broad energy range26,27,28. Here we use a combination of spectroscopic ellipsometry and ultraviolet–vacuum ultraviolet (UV-VUV) reflectivity to probe the intrinsic properties of the LaAlO3/SrTiO3 interface using photon with energies between 0.5 and 35 eV. Owing to a stabilized Kramers–Kronig transformation29,30, the strength of this experimental approach allows one to measure the charge transfer of both delocalized and localized charges accurately using the optical f-sum rule. Since localized electrons are inaccessible to electrical transport measurements, but are accessible by photons, we overcome a severe constraint. In particular, the optical transitions involving AlO2 sublayer of LaAlO3 is very distinct and well separated from the ones involving LaO sublayer, so that the internal charge redistribution within the LaAlO3 sublayers can be clearly identified. The same is also true for the TiO2 and SrO sublayers of SrTiO3.

Here we show that in conducting LaAlO3/SrTiO3 (4 and 6 uc of LaAlO3 film on SrTiO3), there is indeed a charge transfer from LaAlO3 into the interface, and that the amount of charge transfer is ~0.5e. In the insulating case (2 and 3 uc of LaAlO3 film on SrTiO3), we surprisingly observe ~0.5e charge redistribution from AlO2 to LaO sublayers, within the LaAlO3 layers. This suggests that for the insulating case the polarization catastrophe could be partly overcome by the above-mentioned charge redistribution, which may be a consequence of the buckling of the LaAlO3 lattice.

Results

Structural and transport measurements

LaAlO3/SrTiO3 samples were prepared by growing LaAlO3 film on top of TiO2-terminated (001) SrTiO3 using pulsed laser deposition12. The atomic force microscopy (AFM) topography image of the TiO2-terminated SrTiO3 substrate in Fig. 1a clearly shows the atomically flat surface with uc steps. Four high-quality samples with varying thickness of 2, 3, 4 and 6 uc of LaAlO3 film were prepared as a model interface system for the high-energy optical studies. The growth of the films was monitored using reflective high-energy electron diffraction (Fig. 1b). After LaAlO3 deposition, AFM topography measurements show that the atomically flat surface with uc step and terrace structure of SrTiO3 is preserved, with surface roughness of ~1 Å (see Fig. 1c,d). This ensures that surface roughness effects do not adversely affect the optical measurements. Transport measurements (Fig. 1e), which were taken before and after the optics measurements, show consistently that 2 and 3 uc samples are insulating with carrier density and conductivity below the measurement limit, while 4 and 6 uc ones are conducting with carrier density of 4–6 × 1013 cm−2 and conductivity of 4–8 × 10−5 Ω−1, consistent with previous transport results9,10,11.

Figure 1: Characterization results and crystal structure of LaAlO3/SrTiO3.
figure 1

(a) AFM topography image of TiO2-terminated SrTiO3 substrate. Scale bar, 1 μm. (b) Reflective high-energy electron diffraction (RHEED) oscillations obtained for growth of 3 unit cells (uc) of LaAlO3 film on SrTiO3 substrate; inset shows obtained RHEED pattern after the LaAlO3 growth. (c) AFM topography image of 4 uc LaAlO3/SrTiO3, showing the preserved atomically smooth surface. Scale bar, 1 μm. (d) The surface roughness of 4 uc LaAlO3/SrTiO3 as extracted from the AFM data, measured to be ~1 Å. For other LaAlO3/SrTiO3 samples (2, 3 and 6 uc LaAlO3/SrTiO3), the roughness variation and the surface AFM images are found to not alter very much as the LaAlO3 thickness is below 15 uc and the layer-by-layer growth mode is preserved. (e) Electrical transport data of the LaAlO3/SrTiO3 samples as a function of LaAlO3 film thickness. (f) Crystal structure of LaAlO3/SrTiO3.

The perovskite LaAlO3 uc (Fig. 1f) can be divided into two sublayers: LaO and AlO2, in which theoretical calculations have shown that the band structures of these discriminated sublayers are indeed different19,22, leading to distinct optical transitions. To accommodate the assignments of these optical transitions, we define OLa as the O in the LaO plane and OAl as the O in the AlO2 plane. Similarly, SrTiO3 also has similar layered perovskite structure and thus can also be divided into two sublayers: SrO and TiO2. Then OSr is defined as O that belongs to SrO sublayer, while OTi is defined as the one in TiO2. Similarly, the O in the different planes of SrTiO3 can also lead to distinct optical transitions. This discrimination is important, as discussed later, because it can reveal the intra- and interlayer charge transfer mechanism in LaAlO3/SrTiO3 for both the insulating and conducting samples.

Spectroscopic ellipsometry and high-energy reflectivity

Our main observation is the high-energy reflectivity of LaAlO3/SrTiO3 at different thicknesses of LaAlO3 as compared with bulk LaAlO3 and SrTiO3 as shown in Fig. 2a. Note that, because of the challenge in making optical measurements over such a broad energy range, in this study we have only measured a selected set of samples as representative of insulating (2 and 3 uc) and conducting (4 and 6 uc) LaAlO3/SrTiO3. Thus, further measurements on a larger set of samples may be important in further deepening our analyses. It can be seen that the reflectivity spectra of the insulating 2 and 3 uc LaAlO3/SrTiO3 are similar, and the same is true for the conducting 4 and 6 uc LaAlO3/SrTiO3. Surprisingly, there are huge differences between reflectivity of insulating and conducting samples. These differences occur more significantly at high photon energies, particularly in the energy ranges of 9–14 eV and 14–21 eV. In the 9–14-eV range, the reflectivity of conducting samples is lower than insulating samples, while in the 14–21-eV range the opposite occurs. In contrast, between 4 and 9 eV, the differences are less, and below 4 eV they are negligible. This signifies why going beyond conventional (up to ~5 eV) spectroscopic ellipsometry is important. (Note that the spectroscopic ellipsometry data are crucial for the normalization of the derived dielectric functions from the reflectivity measurements made up to 35 eV as shown in Supplementary Methods.) The electronic band structures of the insulating and conducting LaAlO3/SrTiO3 are very different at high energy, and these differences are critical in revealing the true nature of LaAlO3/SrTiO3 interface. Furthermore, since reflectivity and spectroscopic ellipsometry are sensitive to unpercolated clusters of charges31, the similarity of the reflectivity of insulating 2 and 3 uc LaAlO3/SrTiO3 also implies that there is no evidence of precursor of percolation effects in the insulating samples, especially the 3 uc LaAlO3/SrTiO3 (ref. 32).

Figure 2: Reflectivity and optical conductivity of each layer of LaAlO3/SrTiO3.
figure 2

(a) Reflectivity of LaAlO3/SrTiO3 as compared with bulk LaAlO3 and bulk SrTiO3. (b) Extracted optical conductivity (σ1) of LaAlO3 films at different thickness of LaAlO3 film, compared with bulk LaAlO3. (c) Extracted optical conductivity of the LaAlO3/SrTiO3 interface at different thickness of LaAlO3 film, compared with bulk SrTiO3. Note that the plots for 2 and 3 unit cells (uc) LaAlO3/SrTiO3 are the same because of the nature of the iteration analysis used to extract σ1 from reflectivity, and the same is true for the 4 and 6 uc LaAlO3/SrTiO3. The σ1 plots are divided into several energy regions, A1–A3 for LaAlO3 and B1–B5 for SrTiO3 and the interface. The regions are defined based on the distinct optical transitions associated with it, which in turn is based on theoretical calculations and previous reflectivity and valence electron energy loss spectroscopy36,37,38,39,40.

Discussion

For detailed analysis, we turn our discussion to optical conductivity, σ1, because it fulfils the optical f-sum rule, which is related to number of charges excited by the photons. For bulk materials like bulk LaAlO3 and bulk SrTiO3, σ1 can be extracted directly from reflectivity using the Kramers–Kronig analysis29,30. On the other hand, LaAlO3/SrTiO3 is layered along the <001> direction (perpendicular to the (001) surface of the sample) owing to its heterostructure nature as well as the presence of the conducting layer at LaAlO3/SrTiO3 interface. For this reason, the reflectivity of LaAlO3/SrTiO3 is analysed based on standard theory of wave propagation in a stratified media33,34. The analysis naturally leads to a three-layered structure for the conducting LaAlO3/SrTiO3: LaAlO3 film layer on top, bulk SrTiO3 substrate at the bottom and an interface layer sandwiched in between, representing the 2DEG of the conducting samples.

A self-consistent iteration procedure is used to extract the thickness and dielectric function of each layer, and as long as the iteration is convergent, the starting assumption of these parameters should have little effect, if any, on the final obtained values (see Supplementary Methods for details). From the analysis, it is found that the thickness of this interface layer is ~5 nm, consistent with previous observation using hard XPS5, cross-sectional conducting tip AFM35 and the upper limit for the superconducting layer thickness of LaAlO3/SrTiO3 (ref. 10). This result also suggests that the high-energy reflectivity can be used to measure the thickness of interface layer. For insulating LaAlO3/SrTiO3, the analysis naturally converges into an effective two-layered structure instead. This means for insulating LaAlO3/SrTiO3 the σ1 at interface is very similar to that of bulk SrTiO3 as discussed later. This can be easily understood owing to the absence of the conducting interface layer.

Now, σ1 of each individual layer can be extracted separately, so that we can analyse the concomitant evolution of each individual layer of LaAlO3/SrTiO3 as the interface changes from insulating to conducting. Spectra of σ1 for each layer are shown in Fig. 2b,c. It should be noted that the plots for 2 and 3 uc LaAlO3/SrTiO3 are the same owing to the nature of the iteration process (see Supplementary Methods), and the same is true for the 4 and 6 uc LaAlO3/SrTiO3.

For LaAlO3, one can, based on band structure calculations36,37, divide σ1 into three main optical regions, while σ1 of SrTiO3 can be divided into five main optical regions38,39,40. Every transition is unique and originates from different orbitals in each layer and sublayer, and these are summarized in Table 1. Furthermore, the polarization of the incident light is also taken into account in assigning the optical transitions. Since the incident light is linearly polarized parallel to the sample surface, the majority of the optical transitions occur in the in-plane direction within each sublayer, allowing us to study spectral weight transfers between the different sublayers. For example, in A1 region of LaAlO3, the transition is from OLa-2p to La-4d, 5f, both of which reside within the LaO sublayer of LaAlO3. The other transitions also follow this convention.

Table 1 Main optical transitions of bulk LaAlO3 and bulk SrTiO3.

Figure 2b shows that σ1 of LaAlO3 film of insulating and conducting LaAlO3/SrTiO3 is dramatically different as compared with bulk LaAlO3. Particularly, σ1 in A1 region of LaAlO3 film in the insulating samples is higher than the bulk value, while for the conducting samples it is lower. Meanwhile, the reverse is true in A2 region. It is very clear that there are spectral weight transfers occurring between these three regions when the thickness of LaAlO3 film increases and the interface goes from insulating to conducting state.

It can be seen (Fig. 2c) that σ1 of the interface layer to a significant extent resembles σ1 of the bulk SrTiO3. This indicates that the electronic interface layer is SrTiO3-like, and that the conducting layer mostly resides in SrTiO3 side rather than LaAlO3. The most significant change in σ1 happens at B3 region when the interface becomes conducting. In bulk SrTiO3, that region corresponds to a valley with no main optical transition. Interestingly, for the conducting samples a completely new peak emerges in that region. This implies that when the interface becomes conducting, a new characteristic interface state emerges representing the presence of the 2DEG. According to previous reports3,4,5,6,7,17,19,22, the 2DEG resides in the Ti-3d-t2g state of SrTiO3, so this new interface state should also have Ti-3d-t2g characteristic. Thus, based on the optical selection rules, the optical transition at B3 region may be assigned to originate from this new interface state to unoccupied states of higher O orbitals (see Table 1). One should note that the σ1 spectra of the interface layer of conducting LaAlO3/SrTiO3 does not show Drude response, consistent with previous infrared spectroscopic ellipsometry experiment41.

The σ1 analysis is very important because it can be linked to the effective number of electrons associated with a particular optical transition, N, using partial f-sum rule,

where e is the elementary charge, m is the electron mass and V is the unit volume. The E1 and E2 indicate the energy boundaries of that particular transition in the σ1 plot. We then define neff as the N of each layer relative to either bulk LaAlO3 (for LaAlO3 film) or bulk SrTiO3 (for interface layer) values. The advantage of this definition is that any changes in N in LaAlO3 film or the interface layer can be distinguished from the bulk properties.

In LaAlO3/SrTiO3 (and thin films in general), the thickness of the LaAlO3 film and interface layer is finite, so neff distributes over this finite thickness. If we assume that the distribution is uniform over each uc, the neff per uc, nuc, can be defined such that

where d is the thickness in uc. In this case, the unit volume V becomes the volume occupied by each sublayer (LaO and AlO2 for LaAlO3 and SrO and TiO2 for SrTiO3), so that the unit of nuc is the number of charge per sublayer. Thus, neff, which is the total amount of charge redistribution and transfer corresponding to a particular optical transition, can be obtained by integrating nuc over the layer thickness, as shown in Fig. 3. (The procedure to obtain neff is further explained in Methods).

Figure 3: The amount of charge redistribution and transfer in insulating and conducting LaAlO3/SrTiO3.
figure 3

(a) The amount of charge redistribution and transfer corresponding to different energy regions in the σ1 plots of the LaAlO3 film layer, relative to bulk LaAlO3 values and plotted against LaAlO3 film thickness. (b) The amount of charge redistribution and transfer corresponding to different energy regions in the σ1 plots of the LaAlO3/SrTiO3 interface layer, relative to bulk SrTiO3 values and plotted against LaAlO3 film thickness. Each of these energy regions can be attributed to distinct optical transitions36,37,38,39,40. The error bars are obtained from the resolution limitation of the optics measurements and the errors introduced during the reflectivity normalization procedure.

We start our discussion with insulating samples. As shown in Fig. 3a, neff of A1 region of LaAlO3 film increases by ~0.5e, while for A2 region it decreases, also by ~0.5e. The net amount of the charge transfer in LaAlO3 film is thus (+0.5e)+(−0.5e)=0. This indicates a redistribution of ~0.5e from OAl-2p (AlO2 sublayer) to OLa-2p (LaO sublayer), as shown in Table 1. On the basis of f-sum rule, this directly implies that there is no net charge transfer into the LaAlO3/SrTiO3 interface. As a result, the LaAlO3/SrTiO3 interface remains insulating. Since the LaAlO3 film (and the system as a whole) remains insulating, the ~0.5e charge redistribution does not result in the creation of electrons and holes in the LaO and AlO2 sublayers but rather an increase of covalence between the LaO and AlO2 sublayers, leading to the measured charge redistribution.

One way to interpret these data is by considering that the charge redistribution is uniform for all LaAlO3 layers. In this case, the covalence of AlO2 becomes modified from −1 to −(1−nuc) and the covalence of LaO from +1 to +(1−nuc) (Fig. 4a). The nuc is ~0.25e−0.3e for the 2 uc LaAlO3/SrTiO3, and ~0.17e−0.2e for the 3 uc LaAlO3/SrTiO3 (see Methods). This charge redistribution within the LaAlO3 sublayers (electronic reconstruction2) can thus help to decrease the potential build-up in the LaAlO3 film and partially compensate the polarization catastrophe. Combined with ionic reconstruction mechanisms such as the buckling and ionic relaxations effects predicted22,23 and observed earlier using surface X-ray diffraction24,25 and second harmonic generation32, what we are measuring in terms of charge redistribution may arise from such a mechanism.

Figure 4: Simplified pictorial layer-resolved electronic configuration model of LaAlO3/SrTiO3.
figure 4

(a) Layer-resolved electronic configuration model of insulating LaAlO3/SrTiO3, showing the charge redistribution from AlO2 sublayer into LaO sublayer if the redistribution is assumed to be uniform across the LaAlO3 film. The nuc is ~0.25e−0.3e for the 2 uc LaAlO3/SrTiO3 and ~0.17e−0.2e for the 3 uc LaAlO3/SrTiO3. The charge redistribution can partially counteract the potential build-up due to polarization catastrophe15,16 and keep the system insulating. (b) Layer-resolved electronic configuration model of conducting LaAlO3/SrTiO3, showing the overall charge transfer of 0.5e from LaAlO3 film into the LaAlO3/SrTiO3 interface, consistent with the polarization catastrophe model. In this simple picture, the extra 0.5e is depicted to reside only within the first uc of interface, while in our results it is distributed over the ~5 nm thickness on the interface. To ensure charge conservation, one of the upper layers of LaAlO3 (that is, in the dot-signed region above the depicted third layer of LaAlO3) should have AlO2 sublayer with valence state of (AlO2)0.5− instead of (AlO2).

Another possible scenario that can be considered to interpret the data is that, instead of involving the whole LaAlO3 layers, the charge redistribution only happens at the topmost (that is, surface) LaAlO3 layer. In this case, the covalence of surface AlO2 becomes modified from −1 to −0.5 and the covalence of surface LaO from +1 to +0.5, but the deeper LaAlO3 layer remains unchanged, since the charge redistribution is confined only in the surface (that is, surface reconstruction). In this scenario, the surface charge redistribution is still able to partially compensate the polarization catastrophe, but it is in less of an agreement with the buckling effects, since the buckling was observed experimentally, and supported by theoretical calculations22,23,24,25, to affect the whole LaAlO3 film, and not only the surface.

On the other hand, for conducting samples we observe a different phenomenon. The neff of both A1 and A2 regions of LaAlO3 film decreases (Fig. 3a). For A1 region it decreases by ~0.3e−0.4e, while for A2 region it decreases by ~0.2e, leading to an overall ~0.5e decrease of neff in the LaAlO3 film. At the same time, for the interface layer the most significant change that happens when LaAlO3/SrTiO3 becomes conducting is the increase of neff of B3 region by ~0.5e (Fig. 3b). The total charge transfer within the whole LaAlO3/SrTiO3 sample is thus again 0, with the decrease of ~0.5e in LaAlO3 film compensated by the increase of ~0.5e at the interface. On the basis of f-sum rule, this clearly indicates that there is a charge transfer of ~0.5e from the LaAlO3 film into the interface to form the 2DEG (Fig. 4b), consistent with the polarization catastrophe model15,16. On the basis of the definition of neff, this ~0.5e extra charge at the interface is distributed over the ~5 nm thickness of the interface (which mostly resides in the SrTiO3 side).

Moreover, it can be seen from Fig. 2c that the B3 peak, which involves the transition from the new interface state that contains this ~0.5e extra charge, is very broad (~4 eV wide), which means that the ~0.5e is distributed over a rather wide energy range. This may be one of the reasons why transport experiments can only measure a fraction of this ~0.5e, since only a small portion of the charge is delocalized and thus able to contribute to electrical conductivity.

Furthermore, Fig. 3b also shows that the neff of B1 and B5 regions, both of which involve transitions into the unoccupied Ti-3d-t2g states, decrease by ~0.05e (that is, ~10% of 0.5e). This implies that the new interface state of conducting LaAlO3/SrTiO3 has Ti-3d-t2g characteristic3,4,5,6,7,17,19,22, so the extra ~0.5e also partially fills the previously unoccupied Ti-3d-t2g state of SrTiO3. This decrease is consistent with previous observations using X-ray absorption spectroscopy experiments3,6. In X-ray absorption spectroscopy at Ti-L3,2 edges of conducting LaAlO3/SrTiO3, the excitation to the unoccupied Ti-3d-t2g states also decreases compared with bulk SrTiO3. Intriguingly, these decreases are much smaller if one assumes that all of the ~0.5e extra charge partially fills the Ti-3d-t2g-unoccupied density of state (DOS). This is because, based on this assumption, one would expect to observe the decrease of Ti-3d-t2g-unoccupied DOS (and thus the neff of B1 and B5 regions) in conducting LaAlO3/SrTiO3 also by an equivalent of ~0.5e. However, this is not the case, which implies that the ~0.5e extra charge contained within the new interface state does not only reduce the number of unoccupied Ti-3d DOS, but surprisingly also other states at even higher energies, implying the importance of strong correlations and hybridizations effects in explaining the interlayer charge transfer in conducting LaAlO3/SrTiO3 (refs 26, 42, 43).

Another interesting observation to note is that in the conducting samples, the neff of A3 region of LaAlO3 film also decreases by ~0.2e. The transition in this region corresponds to O-2s state, which is strongly localized and directly corresponds to the availability of oxygen in the LaAlO3 film. Thus, the decrease of O-2s DOS can indicate the presence of oxygen vacancies in the LaAlO3 film of the conducting samples. For 4 uc LaAlO3/SrTiO3, there are 24e in O-2s state of LaAlO3; thus, the ~0.2e decrease is equivalent to ~1% oxygen vacancy. This is interesting because it has been suggested that the presence of oxygen vacancies in LaAlO3 film may enhance the charge transfer from LaAlO3 film into LaAlO3/SrTiO3 interface7,44,45. Because of the charge transfer into the interface, the LaAlO3 film lacks ~0.5e (that is, has additional ~0.5 holes), so the extra e created by the oxygen vacancy may partially compensate these holes and stabilize the charge transfer. Interestingly, in insulating LaAlO3/SrTiO3, this oxygen vacancies signature is not observed.

It is noteworthy to reconcile our results with photoconductivity effects observed in LaAlO3/SrTiO3. Previous transport results46,47 have shown that when LaAlO3/SrTiO3 was illuminated by photons with energies higher than the SrTiO3 bandgap, its conductivity could increase because of the presence of photo-generated carriers. On the basis of hard XPS data5, the amount of these photo-generated carriers is estimated to be 2.1 × 1013 cm−2 (~0.03e), which is much smaller than the number of e contributed to the charge transfer and charge redistributions observed in our results (~0.5e). Thus, the photoconductivity effects might only influence the estimated neff by ~6%, and do not affect our analysis adversely.

Recent observations have also indicated that the cationic stoichiometry, for example, the La/Al ratio in LaAlO3 film, may affect the electrical properties of LaAlO3/SrTiO3 (refs 18, 48, 49). How this cationic stoichiometric effects would influence the high-energy optical conductivity of insulating and conducting LaAlO3/SrTiO3 is an important open question. Thus, its interplay with the charge transfer and redistribution phenomena as observed in high-energy optical conductivity still remains to be answered.

In summary, we have shown that high-energy reflectivity and spectroscopic ellipsometry studies of LaAlO3/SrTiO3 have revealed significant differences between the charge redistribution of insulating (2 and 3 uc of LaAlO3) and charge transfer mechanisms of conducting (4 and 6 uc of LaAlO3) LaAlO3/SrTiO3. In insulating LaAlO3/SrTiO3, ~0.5e charge redistribution is observed between the AlO2 and LaO sublayers and partially compensates the polarization catastrophe. In the conducting samples, ~0.5e is measured to be transferred from LaAlO3 film into the interface, which is consistent with the polarization catastrophe model. We believe that this study reveals the nature of the intra- and interlayer charge redistributions and charge transfers in LaAlO3/SrTiO3, and hence opens a path to understand the various electronic reconstructions involving the interfaces of complex oxides heterostructures. Furthermore, the use of high-energy reflectivity coupled with spectroscopic ellipsometry could be extended to other similar polar and nonpolar oxide interface systems.

Methods

Sample preparation

LaAlO3/SrTiO3 samples were prepared by growing LaAlO3 film on top of (001) SrTiO3 substrates obtained from Crystec using pulsed laser deposition12. Before the growth, the SrTiO3 substrates were treated using HF and are annealed at 950 °C for 2 h in O2 flow to achieve the desired TiO2 surface termination50. The AFM topography image of the TiO2-terminated SrTiO3 substrate in Fig. 1a clearly shows the atomically flat surface with uc steps. The growth target was LaAlO3 single crystal, also obtained from Crystec. The deposition pressure was 10−3 Torr, with background pressure of 10−9 Torr. The deposition temperature was 750 °C, with cooling rate of 10 °C min−1 at the deposition pressure. The laser pulse frequency was 1 Hz. Four samples with varying thickness of 2, 3, 4 and 6 uc of LaAlO3 film were made, as monitored using reflective high-energy electron diffraction (Fig. 1b). After LaAlO3 deposition, AFM topography measurements show that the atomically flat surface with uc step and terrace structure of SrTiO3 is preserved, with surface roughness of ~1 Å (see Fig. 1c,d).

Optics measurements

The optical conductivity were obtained using a combination of spectroscopic ellipsometry (0.5–5.6 eV) and UV–VUV reflectivity (3.7–35 eV) measurements26,27,28. The details of the optical measurements are as follow. The spectroscopic ellipsometry measurements were performed in the spectral range between 0.5 and 5.6 eV by using an SE 850 ellipsometer at room temperature51. Three different incident angles of 60°, 70° and 80° from the sample normal were used, and the incident light was 45° linearly polarized from the plane of incident. For reflectivity measurements in the high-energy range between 3.7 and 35 eV, we used the SUPERLUMI beamline at the DORIS storage ring of HASYLAB (DESY)52. The incoming photon was incident at the angle of 17.5° from the sample normal with linear polarization parallel to the sample surface. The sample chamber was outfitted with a gold mesh to measure the incident photon flux after the slit of the monochromator. The measurements were performed in ultrahigh vacuum environment (chamber pressure of 5 × 10−10 mbar) at room temperature. before these measurements, the samples were heated up to 400 K in ultrahigh vacuum to ensure that there was no additional adsorbate layers on the surface of the samples. The obtained UV–VUV reflectivity data were calibrated by comparing it with the luminescence yield of sodium salicylate (NaC7H5O3) and the gold mesh current. These as-measured UV–VUV reflectivity data were further normalized by using the self-normalized reflectivity extracted from spectroscopic ellipsometry34,51, and the two normalized data were appended to obtain the combined reflectivity from 0.5 to 35 eV (see Supplementary Fig. 1).

Analysis of optics data

Both the spectroscopic ellipsometry and the combined reflectivity data were analysed using a combination of the Drude–Lorentz oscillator multilayer fitting33,34 and self-consistent iteration method (see Supplementary Methods). Owing to its multilayered nature, the LaAlO3/SrTiO3 samples, especially the conducting cases, are considered to have the following three layers: the LaAlO3 film on top, the SrTiO3 substrate at the bottom and the interface layer in between (see Supplementary Fig. 2), consistent with previous observation using cross-sectional conducting tip AFM35. Since the spectroscopic ellipsometry data were taken at three different incident angles of 60°, 70° and 80°, it was fitted using angle-dependent iteration method (see Supplementary Methods), and the fitting results are shown in Supplementary Figs 3, 4, 5, 6 and 7. Supplementary Figure 4 also shows that the thickness of the conducting interface layer is ~5 nm, consistent with previous observations5,10,35. Furthermore, from these variable angle spectroscopic ellipsometry results, the absence of absorbate layer and the absence of significant anisotropy can also be inferred. On the other hand, the normalized UV–VUV reflectivity data were fitted using thickness-dependent iteration method (see Supplementary Methods), and the results of the fitting are shown in Supplementary Fig. 8.

Complex dielectric function of LaAlO3/SrTiO3

From the analysis described above, the complex dielectric function, ε(ω), of each layer of LaAlO3/SrTiO3 can be extracted from the high-energy reflectivity of LaAlO3/SrTiO3 (Fig. 2a), as presented in Fig. 5. In turn, this ε(ω) can be converted into optical conductivity σ1 using σ1(ω)=ε0ε2(ω)ω, as presented in Fig. 2b,c. In Fig. 5a,b, it can be seen that the ε(ω) of the LaAlO3 film layer for both insulating and conducting LaAlO3/SrTiO3 is very different than that of bulk LaAlO3, which shows that the band structure of LaAlO3 film is very different than bulk LaAlO3. Meanwhile, the ε(ω) at the interface of the insulating samples (2 and 3 uc LaAlO3/SrTiO3, see Fig. 5c) is very similar to that of bulk SrTiO3, which can be explained by the absence of the 2DEG in the insulating samples. Interestingly, for the conducting samples (4 and 6 uc LaAlO3/SrTiO3, see Fig. 5d) there are new features around 8–12 eV for ε1 and 11–16 eV for ε2, which, on further analysis (see Discussions), are related to the presence of the conducting interface in those sample.

Figure 5: Complex dielectric function of each layer of LaAlO3/SrTiO3.
figure 5

(a) Real part of complex dielectric function (ε1) of LaAlO3 film, compared with bulk LaAlO3. (b) Imaginary part of complex dielectric function (ε2) of LaAlO3 film, compared with bulk LaAlO3. (c) The ε1 of LaAlO3/SrTiO3 interface, compared with bulk SrTiO3. (d) The ε2 of LaAlO3/SrTiO3 interface, compared with bulk SrTiO3. Note that the plots for 2 and 3 unit cells (uc) are the same because of the nature of the thickness-dependent iteration, and the same is true for the 4 and 6 uc case.

Estimation of charge transfer and redistribution

From equations (1) and (2), we can extract the nuc, which is the amount of charge redistribution and transfer per uc associated with a particular optical transition relative to the bulk values. To get the accurate number, we need to carefully consider within what volume V in the uc the electrons reside. Both LaAlO3 and SrTiO3 crystal structures can be thought of as an alternating layer structure. LaAlO3 consists of alternating polar (LaO)+ and (AlO2) sublayers, while SrTiO3 consists of alternating nonpolar SrO and TiO2 sublayers (see Figs 1d and 4). Owing to this layered structure, in a first approximation each cation (La and Al for LaAlO3, Sr and Ti for SrTiO3) only occupies a volume of half uc (instead of the full one uc). For example, the La of LaAlO3 has to share the space of one uc with Al (with each getting half), and similarly the Sr of SrTiO3 has to share with Ti. Furthermore, for LaAlO3, the valence electrons of the O atoms that belong to the two different sublayers (LaO and AlO2) contribute to two different optical transitions in the σ1 spectra (Fig. 2b and Table 1). For simplicity, OLa is defined as the O in the LaO plane and OAl as the O in the AlO2 plane. Thus, OLa also has to share the space of one uc with OAl, with each getting the space of half uc. The same is true for SrTiO3, where the OSr in the SrO plane also has to share the space of one uc with the OTi in the TiO2 plane. This implies that the valence electrons belonging to the different ions can also be approximated to reside in a volume of half uc. For this reason, to obtain the nuc the volume V is chosen to be the volume of half uc of LaAlO3 (lattice constant a0=3.81 Å) or SrTiO3 (a0=3.905 Å), whichever applicable. This consideration makes the unit of nuc to be the number of charge per sublayer. The result for this nuc estimation is shown in Fig. 6. For 2 uc LaAlO3/SrTiO3, the nuc is ~0.25e−0.3e, while for 3 uc LaAlO3/SrTiO3, the nuc is ~0.17e−0.2e. Then, the neff, which is the total amount of charge redistribution and transfer corresponding to a particular optical transition can be obtained by integrating nuc over the layer thickness, as shown in Fig. 3.

Figure 6: Effective number of charge per unit cell (uc) of LaAlO3 and interface layer of LaAlO3/SrTiO3.
figure 6

(a) The effective number of charge per uc, nuc, of LaAlO3 film, if the charge distribution is assumed to be uniform over the LaAlO3 thicknesses (2, 3, 4 and 6 uc). (b) The nuc of the LaAlO3/SrTiO3 interface, if the charge distribution is assumed to be uniform over the interface thickness (~5.3 nm). Each of these energy regions can be attributed to distinct optical transitions36,37,38,39,40. The error bars are obtained from the resolution limitation of the optics measurements and the errors introduced during the reflectivity normalization procedure.

The error bars in Figs 3 and 6 are estimated as follows. It is assumed that there are two main sources of random errors in the data: from the resolution limitation of the optics measurements (estimated to be ~2%) and from the errors introduced in the normalization process (estimated to be ~5%). These errors affect the reflectivity data (that is, ΔR), and to obtain the corresponding errors for σ1σ) and thus neff, the errors are propagated using

LaAlO3 band structure calculation

Unlike SrTiO3 that has been studied very thoroughly38,39,40, previous reports that study the band structure and high photon-energy properties of LaAlO3 in a detailed and comprehensive manner remain quite scarce36,37. Because of this, we performed our own band structure calculation of LaAlO3 to complement those previous studies. The results can be used as a tool to determine the high photon-energy optical transition assignments of LaAlO3, as listed in Table 1.

The details of the calculation are as follows. Cubic LaAlO3 has a space group of with an experimental lattice parameters of a=b=c=3.8106 Å at 821 K (ref. 53). The calculations were performed using CASTEP code54. Geometry optimization had been carried out with local density approximation functional using cutoff energy of 1,500 eV and a 15 × 15 × 15 Monkhorst–Pack grid55 that corresponds to 120 k-points in the irreducible Brillouin zone. The cutoff energy and k-point mesh had been tested and converged to energy differences of 1 × 10−5 and 4 × 10−5 eV per atom, respectively. Ultrasoft pseudopotentials were generated ‘on the fly’ with valence states 4f, 5s, 5p, 5d, 6s for La, 3s, 3p for Al and 2s, 2p for O. The electronic minimization method used for the self-consistent field calculation was density mixing56 with a self-consistent field tolerance of 2.0 × 10−6 eV per atom. The geometry optimization was carried out by the Broyden–Fletcher–Goldfarb–Shanno algorithm57 with energy, force and displacement tolerances of 5.0 × 10−6 eV per atom, 1.0 × 10−2 eV Å−1 and 5.0 × 10−4 Å, respectively. The optimized lattice parameter was found out to be 3.73 Å. Converged DOS calculation was carried out with a k-mesh of 20 × 20 × 20 and consistent with previous calculations36,37. The calculation results are displayed in Fig. 7.

Figure 7: Theoretical band structure of LaAlO3.
figure 7

(a) Total density of states (DOS) of LaAlO3. (b) Partial DOS of La. (c) Partial DOS Al. (d) Partial DOS of O. The dotted lines are the Fermi level.

Additional information

How to cite this article: Asmara, T. C. et al. Mechanisms of charge transfer and redistribution in LaAlO3/SrTiO3 revealed by high-energy optical conductivity. Nat. Commun. 5:3663 doi: 10.1038/ncomms4663 (2014).