Electron Trapping Mechanism in ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Heterostructures

In ${\mathrm{LaAlO}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ heterostructures, a still poorly understood phenomenon is that of electron trapping in back-gating experiments. Here, by combining magnetotransport measurements and self-consistent Schrödinger-Poisson calculations, we obtain an empirical relation between the amount of trapped electrons and the gate voltage. The amount of trapped electrons decays exponentially away from the interface. However, contrary to earlier observations, we find that the Fermi level remains well within the quantum well. The enhanced trapping of electrons induced by the gate voltage can therefore not be explained by a thermal escape mechanism. Further gate sweeping experiments strengthen that conclusion. We propose a new mechanism which involves the electromigration and clustering of oxygen vacancies in ${\mathrm{SrTiO}}_3$ and argue that such electron trapping is a universal phenomenon in ${\mathrm{SrTiO}}_3$-based two-dimensional electron systems.

Figure 1

(a) $V_G$ dependence of sheet resistance ($R_s$) at 4.2 K. The solid circles are $R_s(B=0)$ in magnetoresistance curves. The blue, green, and red arrows indicate the irreversible forward sweep (${\mathrm{FS}}_{\mathrm{irrev}}$), backward sweep (BS), and reversible forward sweep (${\mathrm{FS}}_{\mathrm{rev}}$), respectively. The sweep order is indicated by the circled numbers. Two BSs were performed at 50 V ($V_G^{\max 1}$) and 200 V ($V_G^{\max 2}$). The gray dashed line indicates the metal-insulator transition (MIT). The inset shows a schematic of the Hall bar device. Source and drain are labeled as S and D. The longitudinal resistance ($R_{xx}$) is measured between $V_{+}$ and $V_{-}$ and the transverse resistance ($R_{xy}$) between $V_H$ and $V_{-}$. $V_G$ is applied between the back of the substrate and the drain. (b) $V_G$ dependence of the carrier density in different regimes. The red and blue circles represent the carrier density of the $d_{xy}$ band ($n_{xy}$) and $d_{xz,yz}$ band ($n_{xz,yz}$). The black circles are the total carrier density ($n_{\mathrm{tot}}$) which is the sum of $n_{xy}$ and $n_{xz,yz}$.

Figure 2

(a), (b) $V_G$ dependence of the calculated gate-induced total charge density ($n_G^{\mathrm{tot}}$, purple), trapped charge density ($n_G^{\mathrm{tr}}$, yellow), mobile charge density ($n_G^m$, green) and measured gate-induced mobile charge density ($n_G^m$ Exp., open black circle) in (a) ${\mathrm{FS}}_{\mathrm{irrev}}$ and (b) BS regimes. The inset of (a) shows an illustration of the interface for Schrödinger-Poisson calculations. (c), (d) $V_G$ dependence of S-P calculations that are calculated (solid circles) and measured (open circles) $n_{xy}$ (red), $n_{xz,yz}$ (blue), and $n_{\mathrm{tot}}$ (black) in (a) ${\mathrm{FS}}_{\mathrm{irrev}}$ and (b) BS regimes.

Figure 3

(a)–(c) S-P calculations confining potential profile (solid line), Fermi energy (dotted line), and spatial distribution of mobile electrons occupying $d_{xy}$ (red) and $d_{xz,yz}$ (blue) bands at (a) 0, (b) 50, and (c) 200 V. (d) Confining potential and Fermi energy in a larger range. (e), (f) S-P calculated subband dispersions in parabolic approximation at (e) 0, (f) 50, and (g) 200 V.

Figure 4

$V_G$ dependence of $R_s$ at 4.2 K. The sweep order is similar to that in Fig. 1. Backward sweeps were performed from 10 to 50 V. Note that BS and ${\mathrm{FS}}_{\mathrm{rev}}$ overlap perfectly.

Figure 5

(a), (b) Dynamic change of $R_s$ during $V_G$ sweeps in (a) ${\mathrm{FS}}_{\mathrm{irrev}}$ and (b) BS regimes. $V_G$ was swept at a rate of $0.1\mathrm{V}/\mathrm{s}$. $R_s$ measurements kept on going for several minutes after the stabilization of $V_G$. (c), (d) Dynamic change of $R_s$ after $V_G$ sweeps in (c) ${\mathrm{FS}}_{\mathrm{irrev}}$ and (d) BS regimes.