Effects of structural relaxation, interdiffusion, and surface termination on two-dimensional electron gas formation at theLaAlO3/SrTiO3(001) interface

Abstract

First-principles (generalized gradient approximation) calculations are presented for symmetric ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}/{\mathrm{LaAlO}}_{3}$ (001) orientation slab models with varying thickness (3, 4, 5 unit cells) of the ${\mathrm{LaAlO}}_{3}$ (LAO) layers. The buckling of the layers and their effect on the slope of the layer-averaged electrostatic potential and layer-projected densities of states are studied. We find the buckling of the LAO layers to increase from the interface toward the surface, while the buckling of the ${\mathrm{AlO}}_{2}$ layers decreases toward the surface. The critical layer thickness for obtaining electrons in the Ti-$d$ band of the ${\mathrm{SrTiO}}_{3}$ (STO) is determined to be 4 layers within this model. Beyond this point, the sloped potential is confined to the 4 layers of LAO nearest to the interface. The electrons in the Ti-$d$ states extend throughout the 5.5-layer-thick STO region of our calculation. The sheet charge density of electrons in the STO conduction band is determined and found to be of order $(1--3)\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.28em}{0ex}}e/{\mathrm{cm}}^{2}$, in fair agreement with experimental values and an order of magnitude smaller than required by the polar discontinuity model. We also find still a significant change in the sheet density between the 4-LAO layer and 5-LAO layer model. It results in only ${d}_{xy}$-like states being occupied for the 4-LAO layer case but other ${t}_{2g}$ bands becoming occupied for the 5-LAO layer case. The effects of H adsorption on surface O and OH adsorption on the surface Al are investigated for a model with $1/8$ coverage of H and $1/4$ coverage of OH. The former leads to electron doping of the STO layer while the latter leads to a p-type surface. When both together are present, they cancel each other. For high H coverage, we find that only a certain fraction of the electrons donated by H can be accommodated at the interface while the remaining go to the surface and lead to a reversal of the slope of the potential in the LAO region. The addition of 25% Ti on Al sites into the first layer of LAO already leads to a cancellation of the field in the LAO layer. It does not lead to ${\mathrm{Ti}}^{3+}$ embedded in the LAO site but rather the Ti donates its additional electron to the interface two-dimensional electron gas (2DEG) confined to the STO ${\mathrm{TiO}}_{2}$ layers. A swap of Al with Ti in the layers closest to the interface does not produce a 2DEG because the Al in the ${\mathrm{TiO}}_{2}$ interface layer provides holes compensating the electron doping from the Ti. Interdiffusion of Sr and La between the layers nearest to the interface does not lead to a 2DEG. These species are just electron donors in their own respective materials. In a swap compensating dipoles result from the different nuclear charges but the electronic states near the gap are not affected. Thus no 2DEG formation occurs. On the other hand a ${\mathrm{Sr}}_{\mathrm{La}}$ placed in the middle of the LAO layer is found to facilitate electron transfer from the surface to the interface and could lead to a 2DEG. However, the latter had only a small sheet density.