Origin of insulating behavior of the $p$-type ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ interface: Polarization-induced asymmetric distribution of oxygen vacancies

It is revealed from first-principles calculations that polarization-induced asymmetric distribution of oxygen vacancies plays an important role in the insulating behavior at $p$-type ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ interface. The formation energy of the oxygen vacancy $\left(V_{\text{O}}\right)$ is much smaller than that at the surface of the ${\text{LaAlO}}_3$ overlayer, causing all the carriers to be compensated by the spontaneously formed $V_{\text{O}}$’s at the interface. In contrast, at an $n$-type interface, the formation energy of $V_{\text{O}}$ is much higher than that at the surface, and the $V_{\text{O}}$’s formed at the surface enhance the carrier density at the interface. This explains the puzzling behavior of why the $p$-type interface is always insulating but the $n$-type interface can be conducting.

Figure 1

(Color online) The supercells of (a) the $p$-type and (b) the $n$-type interfaces of ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ used in the calculations.

Figure 2

(Color online) The formation energies [Eq. (1)] of oxygen vacancies in the ${\text{LaAlO}}_3$ overlayer for (a) $p$-type and (b) $n$-type interfaces at the oxygen-rich $\left({\text{O}}_2\right)$ growth condition. The designations of the layers correspond to those in Fig. 1. The dashed lines indicate the formation energy in the bulk.

Figure 3

(Color online) (a) The dependence of the formation energy of $V_{\text{O}}$ on the thickness of the ${\text{LaAlO}}_3$ overlayer for the $n$-type interface. For the $p$-type interface, a similar trend is expected. (b) Formation energies as a function of ${\mu }_{\text{O}}$ for $V_{\text{O}}$ in ${\text{p}}_1$, ${\text{p}}_3$, and ${\text{p}}_5$ layers with the $p$-type interface.

Figure 4

(Color online) (a) Schematics showing the electron processes during the formation of $V_{\text{O}}$ at (left) $n$-type and ($p$-type) surface or interface of the polarized ${\text{LaAlO}}_3$ overlayer. (b) Schematic showing the electron process when the vacancy site is away from the $p$-type surface or interface. The energy shift $\left(E_{shift}\right)$ is because of the polarization of the overlayer.