Uniting Gradual and Abrupt set Processes in Resistive Switching Oxides

Identifying limiting factors is crucial for a better understanding of the dynamics of the resistive switching phenomenon in transition-metal oxides. This improved understanding is important for the design of fast-switching, energy-efficient, and long-term stable redox-based resistive random-access memory devices. Therefore, this work presents a detailed study of the set kinetics of valence change resistive switches on a time scale from 10 ns to ${10}^4\mathrm{s}$, taking $\mathrm{Pt}/{\mathrm{SrTiO}}_3/\mathrm{TiN}$ nanocrossbars as a model material. The analysis of the transient currents reveals that the switching process can be subdivided into a linear-degradation process that is followed by a thermal runaway. The comparison with a dynamical electrothermal model of the memory cell allows the deduction of the physical origin of the degradation. The origin is an electric-field-induced increase of the oxygen-vacancy concentration near the Schottky barrier of the $\mathrm{Pt}/{\mathrm{SrTiO}}_3$ interface that is accompanied by a steadily rising local temperature due to Joule heating. The positive feedback of the temperature increase on the oxygen-vacancy mobility, and thereby on the conductivity of the filament, leads to a self-acceleration of the set process.

Figure 1

(a) Geometry of the $(100\times 100){\mathrm{nm}}^2$ crossbar devices composed of $\mathrm{Pt}/8\mathrm{nm}$ ${\mathrm{SrTiO}}_3/\mathrm{TiN}$. All voltages are given with respect to the bottom electrode. (b) Current-voltage characteristics of the forming (red line) and switching (blue lines) of a typical $\mathrm{Pt}/\mathrm{STO}/\mathrm{TiN}$ cell. The dashed markings indicate the forming, set, and reset voltages.

Figure 2

Measurement schemes for the pulse measurements with set pulse lengths (a) below 1 s and (b) above 1 s. Voltage and current transients showing two set events on different time scales are shown in (c) and (d). (c) For a $10\mu \mathrm{s}$ pulse at a $-1.2\mathrm{V}$ amplitude, the set occurs after $5.8\mu \mathrm{s}$. (d) A constant voltage of $-0.8\mathrm{V}$ is applied to the cell. Before the set event after 511 s, the current increases linearly. The solid black line represents the linear fit used to quantify the pre-set-slope. (Inset) Definition of the transition time.

Figure 3

(a) Transient current during a paused measurement at $-0.85\mathrm{V}$, with pauses at 0 V of 1 s duration every 10 s. The enlargement in the inset demonstrates that the cell resistance does not relax during the pauses. (b) Resistance degradation due to an applied voltage of $-0.88\mathrm{V}$ (blue line) with intermediate read pulses (red lines) at $-0.5\mathrm{V}$.

Figure 4

(a) Current transient of a $-0.84\mathrm{V}$ pulse applied to a $(25\times 25)\mu {\mathrm{m}}^2$ $\mathrm{Pt}/{\mathrm{TaO}}_x/\mathrm{Ta}$ cell (the same stack as was used in Refs. [24, 27]); the pre-set-slope is very prominent.

Figure 5

Equivalent circuit diagram representing the electrical model of the $\mathrm{TiN}/\mathrm{STO}/\mathrm{Pt}$ device. As in the measurements, the voltage is applied to the bottom electrode.

Figure 6

(a) set time as a function of the applied voltage. As expected, the dependency is highly nonlinear. (b) The voltage dependence of the pre-set-slope (absolute values), which ranges over 10 orders of magnitude. (c) The transition time $t_{\text{trans}}$ as a function of the applied voltage is also highly nonlinear. Experimental data is shown as blue dots and the simulation result as a red line.

Figure 7

The pre-set-slope (absolute values) plotted against $1/t_{\mathrm{SET}}$ shows the direct correlation of both parameters. The solid red line represents the simulation and the dashed black line a hyperbolic fit of the measurement.

Figure 8

The pre-set-slope (absolute values) measured on the ${\mathrm{TaO}}_x$ device has a similar voltage dependence to that measured on the STO nanocrossbars.

Figure 9

(a) Simulated current transients of applied voltage pulses with amplitudes ranging from $-0.8$ to $-1.5\mathrm{V}$ and a rise time of 10 ns. (b) Current transient with criteria marked to determine the slope of the plateau and the set time. The slope of the current, i.e. the pre-set-slope, is fitted linearly between the beginning of the plateau and the point for which $[\partial I(t)/\partial t]/[\mathrm{\Delta }I(t)/\mathrm{\Delta }t]=2$ holds. To visualize the fitted slope, a line with the calculated slope is also plotted. The set time $t_{\mathrm{SET}}$ is determined by the point in time with a ratio $[\partial I(t)/\partial t]/[\mathrm{\Delta }I(t)/\mathrm{\Delta }t]=100$. (c) The four current transients with the highest slopes are normalized with respect to the current value at the beginning of the plateau.

Figure 10

Transients of current, temperature, and disc concentration of oxygen vacancies for (a) $V_{\text{pulse}}=-0.8\mathrm{V}$ and (b) $V_{\text{pulse}}=-1.5\mathrm{V}$. (c) Current transients for applied voltages ranging from $-0.8$ to $-1.5\mathrm{V}$, with the current normalized to the start value at the beginning of the current plateau and the time normalized to the set time of each pulse.

Figure 11

Analysis of the contribution of Joule heating on the switching process, for (a) $V_{\text{pulse}}=-1.5\mathrm{V}$ current transients and (b) $[\partial I(t)/\partial t]/[\mathrm{\Delta }I(t)/\mathrm{\Delta }t]$ modeled with Joule heating in blue and with the temperature held constant at $T_0$ in green. Without any thermal feedback, the set transition is highly gradual.