Charge origin and localization at the $n$-type ${\text{SrTiO}}_3/{\text{LaAlO}}_3$ interface

We report a first-principles study of ${\left({\text{LaAlO}}_3\right)}_m/{\left({\text{SrTiO}}_3\right)}_n$ heterostructures using density-functional theory at the $\text{LDA}+U$ level. Our results support the original explanation of Ohtomo and Hwang [Nature (London) 427, 423 (2004)] that the charge at the $n$-type interface may be due to electrostatic doping. The internal electric field in the ${\text{LaAlO}}_3$ layer is calculated to be $0.24\text{V}/\text{Å}$. Though it is not sufficient to cause the dielectric breakdown in a wide band-gap La aluminate, it causes charge transfer into the adjacent narrower gap ${\text{SrTiO}}_3$ layer. The quasi-two-dimensional nature of the charge distribution is caused by a combination of the crystal-field effect, pseudo-Jahn-Teller distortion, and interface chemistry. Our theoretical estimate suggests that the interfacial carrier density of about $2\times {10}^{13}{\text{cm}}^{-2}$ can be easily achieved.

Figure 1

The symmetric vacuum terminated ${\left(\text{LAO}\right)}_m{\left(\text{STO}\right)}_n{\left(\text{LAO}\right)}_m$ slab with two identical $n$-type interfaces.

Figure 2

(a) The $xy$-averaged electrostatic potential across the ${\left(\text{LAO}\right)}_3{\left(\text{STO}\right)}_{4.5}{\left(\text{LAO}\right)}_3$ simulation slab. The field is estimated to be $0.24\text{V}/\text{Å}$. (b) Comparison of the electrostatic potential in precritical ${\left(\text{LAO}\right)}_3{\left(\text{STO}\right)}_{4.5}{\left(\text{LAO}\right)}_3$ and postcritical ${\left(\text{LAO}\right)}_5{\left(\text{STO}\right)}_{4.5}{\left(\text{LAO}\right)}_5$ structures.

Figure 3

(a) The density of states projected onto atomic planes across the ${\left(\text{LAO}\right)}_3{\left(\text{STO}\right)}_{4.5}{\left(\text{LAO}\right)}_3$ simulation cell. (b) The density of states projected onto atomic planes across the ${\left(\text{LAO}\right)}_5{\left(\text{STO}\right)}_{4.5}{\left(\text{LAO}\right)}_5$. The 2D electron-gas regions are clearly seen at both interfaces. The extent of the 2DEG region is about 1 nm. Note that the thickness of the LAO layer in (b) is larger than that in (a).

Figure 4

The partial density of states projected onto the interfacial Ti atom. The $d_{xy}$ orbital is split and is occupied (the Fermi energy is set to zero). Integration of the charge density gives the value of ${10}^{13}{\text{cm}}^{-2}$ (see text). The charge distribution in the interface plane strongly resembles the $d_{xy}$ orbital (inset).