Estimation of the energy barrier responsible for hysteresis and multilevel nonvolatile resistance states in ${\mathrm{VO}}_2$ thin films

We propose a model to estimate the energy barrier responsible for the hysteresis of the thermally driven Mott phase transition. The fitting results are in good agreement with experimental data, where the associated barrier values for ${\mathrm{VO}}_2$ films with various hysteretic behavior are determined. For heating to a fixed temperature in the hysteresis, the electric pulse $(\sim 100\mathrm{V}/\mathrm{cm})$ induced responses exhibit steps of the resistance in ${\mathrm{VO}}_2$ thin films, forming multiple nonvolatile states, whereas no remarkable changes occur for the cooling case. We propose that the memory ability can be attributed to the barrier in the hysteresis regime and the multilevel resistances induced electrically are associated with the configuration of the metal and insulator domains.

Figure 1

(a) Schematic illustration for the model of free energy in the hysteresis temperature range. The arrows show the transition from insulator to metal phase during heating. For the reversal process, from metal to insulator, the transition temperature will be different due to the existence of the barrier $U$. (b) The temperature-dependent order parameter ${\eta }_s$ at the extremum of the free energy for different energy barriers around the phase transition.

Figure 2

(a) Temperature-dependent order parameter $\eta \left(T\right)$ around the phase transition with $T_c^0=340\mathrm{K}$ and a hysteresis width $W=T_c^{+}-T_c^{-}$. (b) The schematic illustration for the calculated temperature-dependent resistance with various energy barrier $U$, based on Eqs. (2) and (3) and the relation $T_c^{+}-T_c^0=W/2=\left|2p\right|\sqrt{-3p}/\left(9h\right)$.

Figure 3

Fitting results of the temperature-dependent resistance of ${\mathrm{VO}}_2$ film deposited on (a) ${\mathrm{Al}}_2{\mathrm{O}}_3$ [$R_m=16.26 \mathrm{\Omega }, R_i=11.2exp(3068/T) \mathrm{\Omega }$]—the data were captured from Ref. [45]—and (b) ${\mathrm{TiO}}_2$ [$R_m=0.0011 \mathrm{\Omega }\mathrm{cm}, R_i=0.00187exp(1535.2/T)\mathrm{\Omega }\mathrm{cm}$], around the MIT [46].

Figure 4

(a) Fitting results of the temperature-dependent resistivity of ${\mathrm{VO}}_2$ film measured in our experiments, using $R_m=165 \mathrm{\Omega }$ and $R_i=2.36exp(3576/T)\mathrm{\Omega }$. The arrows indicate the states at which the pulsed induced responses were measured. (b)–(d) The relaxation of the resistance of ${\mathrm{VO}}_2$ film with $T=328\mathrm{K}$, 340.9 K, and 336.9 K, respectively. Note that the temperature remains stable after no more than 30 s [shown by $\downarrow$ in (b)] from the small overshoot. The dotted lines in (c) and (d) are the fitting results by the logarithm relation: $R\left(t\right)=18850-917.9\text{ln}(t-39.8)$ and $R\left(t\right)=6668.4+198.5\text{ln}(t-80.3)$, respectively.

Figure 5

(a) Relaxation of the metallic-phase fraction of ${\mathrm{VO}}_2$ film at $T=340.9\mathrm{K}$ and $T=336.9\mathrm{K}$. (b) The resistance response of ${\mathrm{VO}}_2$ film after excited by electric pulses with duration 20 $\mu \mathrm{s}$, at $T=340.9\mathrm{K} (\mathrm{heating}+\mathrm{hold})$ and $T=336.9\mathrm{K} (\mathrm{cooling}+\mathrm{hold})$. The arrows indicate the eventual resistance values ($R_E$) after pulsed electrically.

Figure 6

(a) Normalized resistance changes ($\mathrm{\Delta }R/R_0$) of ${\mathrm{VO}}_2$ film excited by electric pulses [duration 20 $\mu \mathrm{s}$; amplitude 2, 5, 8, 10, and 12 V; see Fig. 5] for $\mathrm{heating}+\mathrm{hold}$ at various temperatures in the hysteresis range. (b) Similar to (a), but for the $\mathrm{cooling}+\mathrm{hold}$ case. (c) The eventual resistance change excited by electric pulses corresponding to different fractions of the metallic phase. (d) The schematic illustration of free energy around the transition temperature to explain the resistance change by excitations.