Impact of long-range disorder on the two-dimensional electron gas formation at a ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface

A two-dimensional electron gas (2DEG) can be formed at an interface between two insulators such as ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ without any additional doping. Nevertheless, structural imperfections or defects at the interface, which may arise during the growth process or be of another origin, can definitely affect 2DEG properties either increasing or reducing the 2DEG density. In this work, we study 2DEG formation at both perfect and imperfect interfaces of ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures in the framework of the density functional theory. Using a first-principles Green function method within a coherent potential approximation, we investigate consistently the development of the 2DEG density starting from a defectless interface and introducing sequentially various kinds of long-range disorder such as cation intermixing and oxygen vacancies. Finally, we evaluate the 2DEG carrier density from the Fermi surface cross sections and effective masses of the carriers, which may be directly related to the multiple transport phenomena in the system.

Figure 1

The conduction/valence band profiles, calculated along the [001] direction of LAO/STO (001) superlattice and shown as a function of the LAO thickness varied between 2 and 12 u.c.

Figure 2

Atomic structure (a), the excessive interface charges (b), discrete layer-resolved charges (c), free charges calculated at $E_F$ (d), and the conduction/valence band profile (e) along the [001] direction of LAO/STO (001). The superlattice was constructed as the 12 u.c./12 u.c. supercell. In (a), red balls depict La atoms, blue Al, golden Sr, gray Ti, and small rose-colored balls show oxygens.

Figure 3

Density of states (DOS) projected on selected Ti in LAO/STO (001). The total DOS of (i) the distant Ti site from the $\mathrm{LaO}/{\mathrm{TiO}}_2$ interface and (ii) interfacial Ti are plotted in the two top panels (a) and (b), respectively. Below, in (c)–(g), the partial $\left(l=3,m\right)$ contributions to the $3d$ states of interfacial Ti are shown.

Figure 4

The oxygen DOS in LAO/STO (001) calculated for the bulklike LAO site and interfacial O site of ${\mathrm{AlO}}_2$ layer are plotted in the two upper panels (a) and (b), respectively. The three $p$-orbital DOS of interfacial O are plotted in (c)–(e).

Figure 5

Atomic structure (a), layer-resolved polarity (b), and band bending (c) in LAO/STO (110) heterostructure.

Figure 6

Atomic structure (a), layer-resolved polarity (b), and band bending (c) in LAO/STO (111) heterostructure.

Figure 7

Total energy of the LAO/STO (001) superlattice, which is plotted in the top panel (a) as a function of substitutional disorder $x$ in the interfacial ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x\mathrm{O}$ and ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\mathrm{O}$ layers. The panels (b), (c), and (d) show, respectively, the structure, polar discontinuity, and band profile calculated at $x=0.5$.

Figure 8

DOS of interfacial Ti at the ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x\mathrm{O}/{\mathrm{TiO}}_2$-terminated interface of LAO/STO (001), which is mapped for $x=0$ (top panel) and vs the Sr content $x$.

Figure 9

2DEG density at the Fermi level of the $n$-type LAO/STO (001) interface and shown by red (black) line against the Sr (Al) content $x$ in interfacial layer ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x\mathrm{O}\left({\mathrm{Ti}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2\right)$, respectively.

Figure 10

Atomic structure (a), (b) and Ti/Al concentrations (c), (d) at the $n$-type interface for different models: (a), (c) coherent intermixing, (b), (d) single-interface cation diffusion.

Figure 11

2DEG density at the Fermi energy $g_e\left(E_F\right)$, which is formed at the LT interface of LAO/STO. In (a), $g_e$ is shown by red (black) line as a function of the $A\left(B\right)$ cation substitutes $x$. In (b) and (c), $g_e$ is plotted against the oxygen $\left(x>0\right)$ or cation $\left(x<0\right)$ vacancies in the LaO and ${\mathrm{TiO}}_2$ layers, respectively.

Figure 12

2DHG density at the Fermi level of the ${\mathrm{AlO}}_2/\mathrm{SrO}$-terminated interface of LAO/STO (001). In (a), $g_h$ is shown by red (black) line as a function of the $A\left(B\right)$ cation substitutes $x$. In (b) and (c), $g_h$ is plotted against the oxygen $\left(x>0\right)$ or cation $\left(x<0\right)$ vacancies in the SrO and ${\mathrm{AlO}}_2$ layers, respectively.

Figure 13

Bloch spectral function, projected on the interfacial ${\mathrm{TiO}}_2\left({\mathrm{AlO}}_2\right)$ layer of the $n\left(p\right)$ interface of LAO/STO (001) and plotted in the upper (lower) panels along the high-symmetry directions of the 2D Brillouin zone.

Figure 14

The (001) cross sections of the Bloch spectral function, which was projected on the $A\mathrm{O}$ and $B{\mathrm{O}}_2$ layers of LAO/STO (001) near its $n$ (upper panels) and $p$ (lower panels) interfaces.

Figure 15

Variation of the energy band edge. Here, we take $\alpha {\xi }_0/{\rho }_0=2.02$, and the dielectric constants of STO and LAO are ${\varepsilon }_1=43$ and ${\varepsilon }_2=28$, respectively [62].