First-principles modeling of Pt/LaAlO${}_3$/SrTiO${}_3$ capacitors under an external bias potential

We study the electrical properties of Pt/LaAlO${}_3$/SrTiO${}_3$ capacitors under the action of an external bias potential, using first-principles simulations performed at constrained electric displacement field. A complete set of band diagrams, together with the relevant electrical characteristics (capacitance and built-in fields), are determined as a function of LaAlO${}_3$ thickness and the applied potential. We find that the internal field in LaAlO${}_3$ monotonically decreases with increasing thickness; hence, the occurrence of spontaneous Zener tunneling is ruled out in this system. We discuss the implications of our results in the light of recent experimental observations on biased LaAlO${}_3$/SrTiO${}_3$ junctions involving metallic top electrodes.

Figure 1

(a) Schematic illustration of the Pt/LAO/STO capacitor: large blue spheres represent Sr atoms; small blue spheres, Ti; red spheres, O; large purple spheres, La; pink spheres, Al; and small purple spheres, Pt. (b) Pt/LAO/STO band diagram: ${\phi }_n^{(1,2)}$ are the $n$-type SBH at the LAO/STO and Pt/LAO junctions, ${\mathcal{E}}_{\mathrm{LAO}}$ is the electric field in LAO, $d_{\mathrm{LAO}}$ is the thickness of the film, $E_{\mathrm{V}}/E_{\mathrm{C}}$ are the valence/conduction band edges, $E_{\mathrm{F}}$ are the Fermi levels, and $V_{\mathrm{ext}}$ is the external bias potential.

Figure 2

Projected density of states (PDOS) of the inequivalent LaO layers in the Pt/LaAlO${}_3$/SrTiO${}_3$ capacitor (shifted along the $y$ axis in order to facilitate the visualization and expressed in arbitrary units). [(a),(c)] PDOS are obtained in the Pt/LaAlO${}_3$ slab system at zero and finite LAO internal field, respectively. [(b),(d)] Plots are analogous to (a) and (c) but obtained in the LaAlO${}_3$/SrTiO${}_3$ system. PDOS calculated in the layers closest to vacuum are shown with dashed lines. Layer ordering is explicitly shown along the $y$ axis and all Fermi energy levels have been shifted to zero. The atomic color code is the same as that explained in Fig. 1.

Figure 3

(a) Layer-resolved La $5s$ semicore energies $E_{5s}^{(1,2)}$ obtained at $D=-0.5e/S$ (left) and $-0.3e/S$ (right). Triangles represent the extrapolated values at the interfaces ${\phi }_{\mathrm{ref}}^{(1,2)}$. (b) Sketch of the Pt/LAO/STO band diagram and details of the extrapolation scheme (see text).

Figure 4

(a) Calculated $n$-SBH as a function of $D$. The curves represent the linear fits ${\phi }_n^{\left(1\right)}\left(D\right)=0.35+1.62(D+e/2S)$ and ${\phi }_n^{\left(2\right)}\left(D\right)=1.18+0.05(D+e/2S)$ (in units of $V$). (b) Calculated potential drop per unit cell of bulk LAO; $V_{\mathrm{LAO}}\left(D\right)=1.27(D+e/2S)+2.24{(D+e/2S)}^3$ (solid line) and $V_{\mathrm{LAO}}\left(D\right)=1.36(D+e/2S)$ (dashed line). (c) ${\mathcal{E}}_{\mathrm{LAO}}$ as a function of the number of LAO layers and bias potential $-0.5\le V_{\mathrm{ext}}\le 0.5$ V. The $x$ axis is in logarithmic scale. Symbols and lines represent results obtained with Eqs. (1) and (6), respectively. Inset: Static dielectric constant of bulk LAO as a function of $DS/e$ (solid curve) and the corresponding averaged value ${\overline{\epsilon }}_{\mathrm{LAO}}$ (dashed line).

Figure 5

(a) Mesoscopic band diagram of the LAO/STO junction. The electrostatic potential in STO, $V_{\mathrm{H}}$ (thick solid curve), the conduction and valence band edges (shaded dashed curves), and the Fermi level (thick dashed line) are shown. (b) Ti $t_{2g}$ density of states of our TB model ($V_{\mathrm{H}}$ is constant and set to zero). (c) $V_{\mathrm{H}}$ as calculated with the TB model (Fermi levels are shifted to zero). (d) Electrostatic potential at the interfacial Ti site as a function of $D$. Empty circles (filled squares) are calculated for a 12- (24-) layer STO slab and the solid line represents a linear fit to the data.