Origin of the 2DEG at the LAO/STO Interface

Origin of the 2DEG at the LAO/STO Interface Umberto Scotti di Uccio S. Amoruso, C. Aruta, R. Bruzzese, E. Di Gennaro, A. Sambri, X. Wang and F. Miletto Granozio University FEDERICO II & CNRSPIN, Napoli (Italy) D. Maccariello, P. Perna IMDEA, Madrid (Spain) C. Cantoni, J. Gazquez, M. P. Oxley, M. Varela, A.R. Lupini, S.J. Pennycook Oak Ridge National Laboratory 1 This presentation regardsthe still open issue of the origin of the two dimensional electron gas at the LAO/STO interface. I will show some experimental data and make comments on this subject, but I d like to state that my contribution is not completely general because it is limited to epitaxial samples. I will not speak of amorphous LAO samples, that have very different fabrication procedure and structure.

1. Introduction 2D Electron Gas in semiconductors donors Main ingredients: Quantum well Donor states 2 2deg s are observed in several different systems, such as for instance semiconducting structures based on gallium compounds. But in any cases they share two main ingredients, that are the existence of a quantum well and of donor states that populate the well with charge carriers. In the case of STO/LAO interfaceseverybody agrees that the quantum well is formed within STO, close to the interface. So when I say origin of the 2deg I specifically refer to the nature and location of the donor states.

Two alternative mechanisms for crystalline STO/LAO 1. Introduction Electronic reconstruction Oxygen vacancies charge AlO 2 (1) LaO (+1) AlO 2 (1) LaO (+1) TiO 2 (0) SrO (0) TiO 2 (0) O O (Sr +2 ) (Ti +4 ) (O 2 ) 3 reduction 1 O 2 LaAlO 3 e 2 ( g) + 2 e' + VO O (g) CB e V V V VB VB STO LAO SrTiO 3 3 Grossly speaking, there are two alternative models. The first one is the electronic reconstruction model. Instead, one may consider defects as donors, such as oxygen vacancies, or some kind of cation intermixing at the interface.

Two alternative mechanisms for crystalline STO/LAO 1. Introduction Electronic reconstruction Oxygen vacancies/ intermixing + + + + + + + LaAlO 3 LaAlO 3 LaAlO 3 + + + + + + + SrTiO 3 SrTiO 3 + + + + + + + SrTiO 3 Donors are on the top of LAO Donors are at the interface Donors are within STO Different local electric field expected 4 One interesting difference between the models is the location ofdonors. In the electronic reconstruction case they are on the top of LAO, in the other cases they are at the interface or within STO. And as a consequence of the different location, different local electric fields are expected.

An HRTEM+EELS experiment to probe local fields 1. Introduction Can we directly determine E? Not so easy. But we can measure: the injected charge σ the polarization of both layers + + + + + + + Polar state Polar state Injected charge SrTiO 3 5 Unfortunately, the direct determination of the local electric field is not that easy. As I will show, we can instead measure the injected charge and the polarization of both layers.

An HRTEM+EELS experiment to probe local fields 1. Introduction Preliminary considerations: Simple electrostatics (see, e.g., M. Stengel, PRL 2011) The electric displacement D depends on the injected charge (i.e., the free charge) STO P r o + + AlO 2 LaO AlO 2 LaO TiO 2 SrO TiO 2 Highk dielectric r r r P = ε k' 1 P rst D ST O o ( ) E LAO Highk dielectric plus topological polar state r r r r P = ε k 1 E + P P LAO o ( ) o LAO O r r Po D + k 6 However, this is enough, because based on the theoretical work by Stengel we can define the microscopic electrical displacement in STO/LAO, and the displacement is directly connected to the injected charge. Then we can write electrostatics equations that directly connect displacement and polarization. The case ofsto is simple. STO is a highk dielectric and we immediately get that the displacement is approximately equal to the polarization. The epitaxial layer of LAO is different, because it possesses a builtin, topological polar state, with polarization Po. Besides, it can also react to the field, and this gives a dielectric polarization. But again it is easy to find out a relation between polarization and displacement. Now we have a theoretical framework and we can look at experiment.

RHEEDassisted PLD KrF Excimer laser λ = 248 nm, 1 Hz, 2 J cm 2 2. Experimental T s = 800 C Buffer Gas: P(O 2 ) = 10 3 mbar Thickness 510 u.c. LAO 7 Conducting samples were fabricated by PLD at 103 mbar oxygen pressure at Napoli. I skip the details

STEM + EELS 2. Experimental Electron EnergyLoss Spectroscopy with atomicscale resolution in the aberration corrected microscope 5 u.c. LAO 10 3 P(O 2 ) Conducting sample C. Cantoni, et al. ADV. MAT. 2012 8 and analyzed by Scanning Tunneling Electron Microscopy and Electron Energy Loss Spectroscopy in an aberration corrected microscope. This slide shows the microstructure of the interface and an EELS scan across the interface to show the sample quality and the capability of EELS to determine the localchemical composition with atomic resolution.

2DEG DOS: free charge injection Information from EELS Ti L2,3 lines 2. Experimental Ti 3d e g Ti 3d t 2g E E ψ > CB c d E ψ> Core level a b Ti 2p 3/2 Ti 2p 1/2 Energy loss Ti 2p3d excitation Peak intensity decreases when the final state is occupied 9 EELS also allows one to determine the occupancy of the conduction band. To this aim we can investigate the Ti L2,3 lines

2DEG DOS: free charge injection Information from EELS Ti L2,3 lines 2. Experimental Ti 3d e g Ti 3d t 2g c d a b Energy (ev) Ti 2p 3/2 Ti 2p 1/2 LAO STO c/d decreases if the CB is occupied 10 doing that at different distance from the interface

2DEG DOS: free charge injection Information from EELS O K lines 2. Experimental c d O 2p + Ti 3d e g a O 2p + Ti 3d t 2g b multiple scattering a b O 1s LAO a decreases if the CB is occupied STO E decreases if the CB is occupied 11 We can also investigate the O K line

2DEG confinement within STO (u.c.) depth 2. Experimental ρ (e / u. c.) LAO STO Fabrication P(O2) = 10 3 mbar T s = 800 C depth of confinement: 1 nm integral: 0.3 e / square unit cell 12 and this is the summary. From the map we extract the plot of theinjected charge density vs. distance from the interface. The main results are the depth of confinement, that is about 1 nm, and the total injected charge, amounting to 0.3 electrons per unit square cell.

Polarization measurement 2. Experimental P i z = unit. cell j q j z j Assuming the formal charge of ions Neglecting the deformation of valence orbitals AlO 2 LaO Al AlO 2 LaO TiO 2 SrO TiO 2 Ti La Sr interface C. Cantoni, et al. ADV. MAT. 2012 13 Let s come now to the measurement of polarization. We determine fromstem the average position of each cation and define the polarization in aclassical way, assuming the formal charge of ions and neglecting the deformation of valence orbitals.

STO Polarization 2. Experimental Ti Sr O STO LAO measurement 14 Here are the results for STO. We observe the rumpling of each crystal plane and a polarization close to the interface and quickly approaching to zero when moving toward the bulk.

LAO Polarization 2. Experimental La Al O STO LAO measurement 15 In LAO, instead, the polarization is uniform.

Discussion 1. The STO side depth of confinement: 1 nm integrated charge σ o 0.3 e / square u.c. P STO D electrostatics Ti 3+ fraction P STO 0.4 0.3 0.2 0.1 0.0 0.1 0.4 0.3 0.2 0.1 0.0 0.1 3. Discussion 0 2 4 6 8 distance (u.c.) Impossible, the polarization has the wrong sign 16 So we can now discuss the results. Let s first consider the STO side. Here we roughly see the same lengthscale for both charge and polarization. And we also see that the displacement calculated by the integrated injected charge corresponds to the measured polarization at the surface. This confirms the correctness of the approach based on classical electrostatics. There is a second consequence. We can exclude that the donors are deep within STO, because in that case we would have found a different orientation of polarization.

Discussion 1. The STO side After charge injection, the lattice is deformed 3. Discussion Second harmonic generation Requirement Breaking of the centrosymmetry E r Conducting LAO/STO has efficient SHG A. Rubano, et al. PRB 2011 17 Since we have a strong polarization, we have a strong deformation of unit cells. But if the cubic environment is distorted, also the 3d orbitals of Ti atoms are deformed. This breaking of symmetry explains why STO/LAO interfaces emit so strongly in second harmonic, as we observed for our samples.

Discussion 2. The LAO side r P LAO r D + 3. Discussion r P o k No electric displacement the dielectric response almost conceals the topological polarization P o r P LA O r P r o << Po k Add electric displacement the dielectric response decreases r r r Po PLAO D + k 18 Now let s come to the LAO side. Let s start from the characteristic equation in the green square. If we have no electric displacement, the equation foresees a strong suppression of the topological polarization, due to the dielectric polarization. But if we have electric displacement, the dielectric polarization decreases and the net polarization increases.

Discussion 2. The LAO side 3. Discussion but we do observe a large polarization! So, there is a finite displacement Add electric displacement the dielectric response decreases r r r Po PLAO D + k 19 In fact, we do observe a large net polarization. Then we conclude that there is a displacement in LAO

Discussion 2. The LAO side 3. Discussion but we do observe a large polarization! So, there is a finite displacement Consistent explanation of LAO state D 0.3 e /u.c. k 20 P o 0.5 e/u.c. P 0.32 e/u.c. P LAO 0.35 e/u.c. 20 and based on a few simple assumptions we deduce that it is about0.3 electronic charges per square unit cell.

Discussion 3. Where are the donors? 3. Discussion Experiment + simple electrostatics The electric displacement is continuous at the interface Most donors are on the top of LAO Consistent explanation of LAO state D 0.3 e /u.c. k 20 P o 0.5 e/u.c. P 0.32 e/u.c. P LAO 0.35 e/u.c. 21 So, the estimated displacement in LAO is the same as in STO. In other terms, D is continuous. This brings us back to the question: Where the donors are? Well, they can t accumulate at the interface, or we would not observe the displacement continuity. They must be on the top of LAO. This is consistent with the electronic reconstruction. Can we exclude at all that some donors are at the interface? Well we can t, the experimental errors are large enough to allow for a fraction of donors to be there. But most of them must be far away in LAO.

Conclusions 1. LAO/STO Interfaces with a lot of V(O) do conduct 2. LAO/STO Interfaces with negligible V(O) content do conduct 3. Different types of donors bring to essentially the same 2DEG a) In amorphous samples, V(O) are the donor states b) In samples with negligible V(O), the polarization state of LAO is compatible with the electronic reconstruction 22