Polar/non-polar interfaces

As we mentioned above, an example of a polar interface was described: the LAO (001) surface. There is a charge discontinuity between the LaO//AlO2 stacking and the 'vacuum'.

The LAO consists in this orientation of alternating layer of (La O^{3 2 }) and (Al O^3 ₂^{2 }) while the vacuum has an effective charge of zero. Such discontinuities are often resolved by a surface reconstruction in bulk materials [17, 18]. However, such polar discontinuities can also occur inside heterointerfaces; a fact that is very famous from semiconductor physics, where it results in an ionic reconstruction at the interface between different semiconductors or in between layers of the materials have different band structures [19]. In correlated-electron materials, similar the redistribution of electrons to be found in the LTO/STO system.

Moreover, the electronic reconstruction at domain walls in BiFeO3 is also found [20, 21, 22], where the polarization discontinuity induced or enhanced to a conducting interface and the destruction of half–metal in Fe3O4/BaTiO3 due to the electron transfer across the interface [23].

2.1.3.1 Charge transfer at LaAlO₃/SrTiO₃ interfaces

The big discovery in 2004, by Ohtomo and Hwang showed that the interface between LAO and STO in the (001) direction can be conducting, depending on the termination at the heterointerface. Such an interface exhibits a polar discontinuity, as LAO has alternating planes 1, while theSr O^{2 2}and (Ti O^4 ₂²_^) planes of STO are neutral [24]. In a purely ionic picture, this discontinuity transfers either only half an electron per unit cell area from LAO into STO for a n-type interface or half a hole per unit cell area for an p-type interface.

Figure 2.4 shows how the electrons and holes are distributed in this model. The former interface is found to be conducting as shown in Figure 2.4a) with TiO2 termination took a place the top of STO (100) substrate, and we know it as n-type LAO/STO interface, while the latter, though nominally hole-doped, is insulating with SrO termination as Figure 2.4b) and is called as a p-type interface. Therefore, we can conclude that the hole-doping of closed shell ions is very difficult and complicated, moreover the compensation of holes by oxygen-vacancy would be a key point to be induced electrons results in no net free carriers [25, 26].

a) n-type interface b) p –type interface

Figure 2.4 The model of charge transfer at LAO/STO interfaces. Diagrams taken from Ref.[25].

To understand the mechanism behind that, the purely ionic picture is never complete for a correlated-electron material. In other hand, more physical way to explain clearly these results is by looking at the internal dipole that develops across the charged in the LAO layers.

In the electronically unreconstructed case, the transition of neutral to immediately charged layers results in a potential build-up due to the electric fields between the oppositely charged layers in LAO (see Figure 2.5). This 'polar catastrophe' grows with the LAO thickness and has to be compensated when the energy can no longer be accommodated by internal deformations [27–29]. In a band diagram, this happens when the potential build-up becomes larger in energy than the band gap of STO [29–32]. The valence band of LAO goes higher than the Fermi level, allowing for the charges transfer from the top surface to the interface.

This reduces the potential build-up, as seen on the right panel in Figure 2.5. Recently, an argument has been made for the existence of in-gap states to which electrons can tunnel [33].

However, their theoretical calculations prove a constant electron density does not depend on the LAO layer thickness, contrary to experimental results [34, 35].

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Figure 2.5 Illustration of the polar catastrophe in an unreconstructed case (left) and a re-constructed case (right), where only half an electron is transferred into the TiO2 layer.

Diagrams are taken from Ref.[25].

To examine the n-type LAO/STO interface where the terminations at interface controlled by TiO2-LaO, the crossing of the potential build-up and the band gap implies that up to a critical thickness of the LAO layer, this dipole can be accommodated by the strain within the LAO and no electronic reconstruction (i.e. electron-doping into the TiO2 layer) occurs. That critical thickness has been found to be 4uc, below that it was still insulating, however, when the LAO thickness reaches 4uc, an abrupt change into conductivity interface [36]. Thicker LAO layers show a decreasing mobility, though the mechanism behind that behavior is one of the many unsolved mysteries in this system [35]. Theoretical calculations actually show a larger critical thickness, but this can have several explanations. One is that the supercell used in the calculations is too small, so we did not include all possible reconstructions of electrons [28, 37]. Another explanation is that in real samples there are surface defects that form in-gap states, so the LAO band needs to shift less before electrons are doped [29, 38]. Finally, (Density functional theory) DFT always has a problem calculating the band structure of materials, which may make these calculations only qualitative, not quantitative. This thickness effect can be used to pattern structures into the conducting layer by selectively depositing thick LAO [39]. Only in those areas where the LAO layer is thicker than 4uc the built in potential is large enough to trigger the electronic reconstruction at the interface and create a conducting interface. Or, by having the dipole develop to just below the threshold value for electronic reconstruction, the conducting state can then be induced by introduction to the LAO layer an electric field and thus altering the dipole across this layer. This can be

done either by a back-gate field-effect transistor configuration [36, 40] or by writing with a conducting AFM tip [41, 42]. Interestingly, this minimum thickness of LAO required for a conducting interface does not seem to apply when the LAO layer itself is again capped with STO. The created two different interfaces of LAO/STO (one is n-type, another is p-type) where n-type LAO/STO is conducting down to a single monolayer (unit cell) of LAO embedded in STO [34, 43, 44]. There is, however, a clear interaction between the two interfaces. Below a LAO thickness of about 6 uc the sheet resistance increases. Hall measurements show that this is due to a decrease of the electron density in the 2DEG, while the electron mobility is constant (as opposed to single interfaces, where the mobility decreasing with increasing thickness [35]). More interestingly, about half a year earlier a jump in the optical absorption spectrum of LAO/STO superlattices samples as observed which does not appear in alloyed films of the same chemical composition [45]. The LaNiO3/SrMnO3

system also undergoes an insulator-to-metal transition upon increasing the thickness of LaNiO3 layer [46]. Ionically, the system does have a polarization discontinuity ( spectroscopy [50]. Though in general the electron-electron interactions are weaker than electron-phonon interactions at room temperature, in STO they are typically weak (as seen from the poor heat conduction) and would give rise to different temperature dependence [34].

The electron density depends on so much of fabrication parameters such as substrate termination [47], oxygen pressure during deposition [24, 49, 51, 52] and, laser frequency in PLD chamber [53]. There is some argument for intermixing [25, 54, 55], but transmission electron microscopy images do not give conclusive evidence. Also, if intermixing would occur, the complimentary p-type interface should also become conducting [47]. A thermally-activated behavior of the electron density, similar to that in semiconductors, with an activated energy of about 6 meV was observed [34]. This point is weakly-bound donors as the source of the electrons [42]. In general, electron densities on the order of 10 cm^{14 2} at room temperature are achieved.

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Remarkably, at low temperatures almost all data converge to a value around

13 2

2 10 cm ^ [34, 36, 52, 56–58]. These values for the electron density would translate to, respectively, about 0.15 and 0.03 electron per unit cell area at room temperature and 5 K. This value is far below the nominal half electron per unit cell area transferred in the purely ionic model above. One explanation might be that the electrons are distributed over different sub-bands, of which only some contribute to the (Hall) free electron density [59]. However, XPS detects both free and bound electrons and the densities observed with this technique are close to those obtained from Hall measurements [60]. Table 2.2 compares the transport properties of semiconductor (Si and GaAs) and correlated-electron (LTO/STO and LAO/STO) systems. The electron mobilities in semiconductors are always higher than those in correlated-electron materials. This is not surprising, because the mobility is limited by the scattering of electrons, either from ions or with other electrons. Thus correlated-electron materials, with their higher electron densities, will almost always display lower mobilities than semiconductors.

Table 2.2 Comparison of the transport properties at room temperature for semiconductor and correlated-electron systems, [12–14, 34, 61].

To study the possibility of quantum effects in these electron gases, the requirements for Shubnikov-de Haas oscillations can be studied. The occurrence of these oscillations is a clear sign of the quantum nature of the electron gas (see Table 2.2 and discussion).