In their first seminal paper [44], Ohtomo and Hwang already reported that then-type interface is conducting while thep-type interface is insulating. This robust result has been confirmed by different research groups since then [54,55,120–122], including our group in Geneva. The interface termination dependence cannot be explained by any extrinsic doping scenarios but can only be understood by the "polar catastrophe" model.
Some other key experimental observations have also been successfully explained by the "polar catastrophe" model. Let us give a few other examples here.
2.3.1 LaAlO3critical thickness
A remarkable piece of evidence for the "polar catastrophe" model is the observation of a threshold thickness for the LaAlO3layer to obtain interfacial conductivity [55].
The value observed experimentally is in perfect agreement with the predictions from first principles calculations [69,71,123] on SrTiO3/LaAlO3/vacuum stacks, as we mentioned in Section2.2.2. The details for the calculation of this threshold will be discussed later in this chapter (Section2.4). Figure2.4shows data of interface sheet conductance versus the LaAlO3thickness, both from Geneva and [55]. Samples with LaAlO3thickness less than 4 u.c. show insulating behaviour while a sharp insulator-to-metal transition occurs when the thickness reaches 4 u.c.. It was also shown that the metallic/insulating states (on/off) can be switched by an electric field-effect in samples at the verge of the transition [55,59,60,124].
2.3.2 The electric field in the LaAlO3layer
One prediction of the "polar catastrophe" model is that there is a built-in electric potential in the LaAlO3layer below the critical thickness. Above this thickness, the charge transfer due to the tilting of the LaAlO3valence band would be progressive (see next section for details). This implies that even above the LaAlO3critical thickness, a remnant electric field in the LaAlO3 layer should be also present. Efforts were made to observe such a phenomenon. Pauliet al.[125] showed in a surface X-ray diffraction experiment that a buckling of the atomic planes in the ultra thin LaAlO3layer (typically 2 u.c.) and an expansion of the out-of-plane lattice parameter of LaAlO3 thin-films can be linked to the presence of an internal electric field in LaAlO3. These atomic displacements have also been observed in an ultra high resolution scanning transmission electron microscopy study [126].
However, in some experiments the presence of this internal electric field in LaAlO3
layers has been questioned. For instance, in core-level photoemission spectroscopic measurements, Segalet al.[127] do not observe an energy shift for the atomic levels of
Figure 2.4 – Sheet conductanceσsas a function of the LaAlO3film thicknesst(in unit-cells):Data was taken at room-temperature. The red dash line indicates the LaAlO3
threshold thickness for the onset of the conductivity. Data from Thiel et al. are extracted from [55].
lanthanum and aluminium as a function of film thickness (2-9 u.c.) for both SrTiO3
surface terminations. This seems to suggest the absence of an electric field. Takizawa and coworkers [128] found an electric field roughly 10 times smaller than the one predicted by the "polar catastrophe" model.
In Geneva, we measured thec-axis lattice parameter in ultra-thin LaAlO3layers using a synchrotron X-ray source. Due to the presence of an electric field an elec-trostriction effect will elongate thec-axis of LaAlO3. Figure2.5shows a largec-axis expansion at very low LaAlO3 thicknesses, which is in agreement with an electrostric-tive effect. Indeed, for films of thickness less than 6 u.c., thec-axis of the LaAlO3 layer is significantly larger than the valuec0 expected from a purely strain induced deformation by the SrTiO3substrate [129]. This observation is a strong indication of the presence of abuilt-inelectric field in LaAlO3for thicknesses under or around 4 u.c..
DFT calculations (within LDA) considering electrostriction could reproduce thisc-axis expansion. For films of thickness between 6 and 20 u.c., an observed constantc-axis value agrees perfectly withc0, indicative of a fully strained epitaxial LaAlO3film. For films of thickness above 20 u.c., the epitaxial strain is released with botha-axis and c-axis relaxing to their bulk values.
2.3.3 New theoretical considerations
We have seen that the "polar catastrophe" model predicts correctly the presence of a critical LaAlO3 thickness for the appearance of conductivity and the behaviour for the different interface terminations. Nevertheless, an interpretation of the observed conductivity purely based on this model faces three main challenges: it predicts the presence of holes in the valence band (VB) of the top LaAlO3surface, which should
Figure 2.5 – LaAlO3 a- andc-axis parameters as a function of the film thickness (number of u.c.,n): The solid lines are a guide to the eye. The dashed horizontal line indicates the pseudocubic LaAlO3bulk lattice constant. The inset shows the expansion of thec-axis for low LaAlO3thicknesses. From [65].
open hole pockets in the Brillouin zone, present as2pO surface states - this has never been observed by ARPES measurements [70]; the experimentally observed carrier density is typically one order of magnitude lower than the value predicted by the model [65] and independent of the LaAlO3thickness; the presence of an electric field in the LaAlO3layer below and above the critical LaAlO3thickness is still under debate.
Other theoretical considerations based on the "polar catastrophe" have been pro-posed to try explaining the experimental observations more precisely. These models suggest alternative sources of charges to compensate the polar discontinuity. These elec-tron reservoirs can be oxygen vacancies formed at the top LaAlO3surface through redox processes involving surface adsorbates, or anti-site defects. Bristoweet al.[56,64]
developed a model usingfirst principlescalculations that describes the redox formation in presence of the polar discontinuity for different LaAlO3thicknesses. They argue that thebuilt-inpotential can favour surface redox reactions of surface adsorbates, which then create oxygen vacancies: the electrons released at the surface are transferred to the interface due to the effect of the electric field. In another proposal, Yu and Zunger [63]
performed calculations of defect configurations and their electronic properties. They show that the polar discontinuity across the interface thermodynamically triggers the spontaneous formation of cationic anti-site defects that partially cancel the polar field induced by the polar discontinuity. Above the critical thickness, the ionisation of the spontaneously formed surface oxygen vacancies leads to interface conductivity, whereas the unionised Ti-on-Al anti-site defects lead to interface magnetism (Ti would be in a Ti3+state).