Non-Ohmic Variable-Range Hopping and Resistive Switching in ${\mathrm{SrTiO}}_3$ Domain Walls

We report observation of electric field driven conductivity with negative differential conductance and resistive switching in insulating ${\mathrm{SrTiO}}_3$ samples over a wide range of applied voltages at low temperatures. The observed current follows $I=I_0\exp [-{(E^{*}/E)}^{1/2}]$ at large applied electric field, corresponding to variable range hopping conduction with a Coulomb gap in domain walls. Our data are sufficient to discriminate unambiguously between Shklovskii and Mott hopping via their different electric field exponent. Under some conditions space-charge-limited currents are observed, and the charge mobility limit is determined to be in the range of 17 and $210{\mathrm{cm}}^2/\mathrm{Vs}$.

Figure 1

Experimental setup and ferroelastic or ferroelectric domain walls in STO. Schematic illustration of the transport experimental setup and device scheme by using gold electrodes (a) and conducting $n$-type STO 2DEG layer induced by LAO (b) on insulating STO. (c),(d) Schematic band diagram for metal-STO-domain wall structure and STO–$n$-type STO 2DEG-domain wall structure. $E_{\mathrm{im}}$ indicates impurity bands and $E_{\mathrm{dm}}$ indicates domain wall bands. In ferroic domain walls, either impurity bands (semiconducting) or domain wall bands (metallic) could exist, or both of them coexist. (e),(f) Electrical images taken for $n$-type STO samples with differently orientated conducting domain walls at 5 K.

Figure 2

Different types of current-voltage ($IV$) curves in insulating bulk STO. (a) Symmetric $IV$ hysteresis loops of insulating bulk STO with gold electrodes as shown in Fig. 1. (b) Nonlinear $IV$ curve insulating bulk STO with 2DEG conducting STO electrodes as shown in Fig. 1. Enhanced current appears for low temperatures at 10 K in ferroelastic domain walls (always first scan with big loops) and in ferroelectric domain walls (when one decreases gate voltages in the first scan or afterwards with small loops.) comparing to thermal tunneling current at 120 K. (c) $IV$ curves with nonlinearity and hysteresis loops at 10 K in different scans. (d) Largely enhanced current limited by space charge above threshold voltage. (e) Space charge limited current after large voltage scans.

Figure 3

$IV$ characteristic behavior in STO single crystal with hysteresis and resistive switching. (a) $IV$ curves at 10 K after cooling down from room temperature and 120 K. (b) $IV$ curves showing space charge limited current after several scans at 10 K, and then followed scans at 50, 100, and 120 K. (c) Detailed $IV$ scans at 10 K with directions indicated by arrows. (d) Log-log plot of $IV$ curves shown in (c).

Figure 4

Negative differential conductance. (a) $IV$ curves. (b) Conductance $G=I/V$ as a function of voltage with slope $dG/dV<0$ indicating negative differential conductance.

Figure 5

Shklovskii hopping conduction. (a) Semilog plot of $I$ as a function of $V^{-1/2}$. (b) Conductance as a function of voltage in a log-log plot.

Figure 6

Space charge limited currents at domain walls. (a) $IV$ curves showing space charge limited currents at different temperatures of 10, 50, 100 and 120 K. (b) Extracted coefficient of $IV$ curves ($I=A_{\text{coeff}}{V}^2$) at different temperatures.