Effect of inhomogeneities and substrate on the dynamics of the metal-insulator transition in ${\mathrm{VO}}_2$ thin films

We study the thermal relaxation dynamics of ${\mathrm{VO}}_2$ films after the ultrafast photoinduced metal-insulator transition for two ${\mathrm{VO}}_2$ film samples grown on ${\mathrm{Al}}_2{\mathrm{O}}_3$ and ${\mathrm{TiO}}_2$ substrates. We find two orders of magnitude difference in the recovery time (a few nanoseconds for the ${\mathrm{VO}}_2/{\mathrm{Al}}_2{\mathrm{O}}_3$ sample versus hundreds of nanoseconds for the ${\mathrm{VO}}_2/{\mathrm{TiO}}_2$ sample). We present a theoretical model to take into account the effect of inhomogeneities in the films on the relaxation dynamics. We obtain quantitative results that show how the microstructure of the ${\mathrm{VO}}_2$ film and the thermal conductivity of the interface between the ${\mathrm{VO}}_2$ film and the substrate affect long time-scale recovery dynamics. We also obtain a simple analytic relationship between the recovery time-scale and the film's parameters.

Figure 1

Relative change in reflectivity ($\mathrm{\Delta }R/R$) for the ${\mathrm{VO}}_2$ film on (a) ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrate and (b) ${\mathrm{TiO}}_2$ substrate as a function of time after the MIT is induced at time $t=0$ by a strong ultrafast pump pulse. The values of the pump fluence are shown in the legend, and the sample temperature is set to (a) 311 and (b) 280 K, which correspond to approximately 30 K below the critical temperature $T_c$ for thermally induced MIT for each sample.

Figure 2

Schematic of the ultrafast pump-probe setup. BS is an $80/20$ beam splitter.

Figure 3

Schematic of the experimental setup using a continuous-wave probe laser.

Figure 4

Dependence of metal state decay constant $\tau$ on the laser pump fluence and substrate temperature. Dots represent experimental data and lines correspond to the results of the theoretical calculations. The initial temperature $T_s$ for both sample substrates was approximately 30 K below their respective MIT critical temperatures.

Figure 5

Evolution of the reflectivity across the thermally induced MIT for the case of sapphire and rutile substrates normalized to the average critical transition temperature. The open circles (red) correspond to the measured reflectivity in the heating branch, the solid circles (blue) correspond to the measured reflectivity in the cooling branch, and the solid curve corresponds to the theoretical result. For rutile substrate $\langle T_c\rangle =314.0$ K, and for the sapphire substrate $\langle T_c\rangle =340.1$ K.

Figure 6

(a) and (b) show the grain size distributions normalized to the average grain size for sapphire ($\langle D\rangle =64.7\mathrm{nm}$) and rutile ($\langle D\rangle =17.4$ nm) substrates, respectively. (c) and (d) show the critical temperature distribution normalized to the average critical temperature for sapphire ($\langle T_c\rangle =340.1$ K) and rutile ($\langle T_c\rangle =314.0$ K), respectively. The bulk critical temperature is taken to be $T_c^{\left(\mathrm{bulk}\right)}=355$ K.

Figure 7

Evolution of the insulating partial volume ${\eta }_I$ across the thermally induced MIT for case of (a) sapphire and (b) rutile substrates. For rutile, $\langle T_c\rangle =314.0$ K and for sapphire $\langle T_c\rangle =340.1$ K.

Figure 8

Sketch of the heterostructure considered in this work. It is composed of a vanadium dioxide (${\mathrm{VO}}_2$) thin film deposited on top of a substrate. The substrates considered in this work are titanium dioxide (${\mathrm{TiO}}_2$), and aluminum oxide $({\mathrm{Al}}_2{\mathrm{O}}_3$). For ${\mathrm{VO}}_2/{\mathrm{TiO}}_2$, $d=110\mathrm{nm}$ while for ${\mathrm{VO}}_2/{\mathrm{Al}}_2{\mathrm{O}}_3$, $d=80\mathrm{nm}$. For both substrates, $L=0.5$ mm.

Figure 9

Full numerical calculation of the dependence of metal state decay constant $\tau$ on ${\sigma }_{T_c}$ for two different values of the sample average critical temperature $\langle T_c\rangle$, and $T_s\left(L\right)=280$ K. The initial temperature $T_0=360$ K is such that the sample is initially fully metallic, and $(T_0-\langle T_c\rangle )/\left(\sqrt{2}{\sigma }_{T_c}\right)\approx 9$.

Figure 10

${\mathrm{VO}}_2/{\mathrm{Al}}_2{\mathrm{O}}_3$ metal state decay time $\tau$ dependence on the Kapitza constant ${\sigma }_k$ for $\langle D\rangle =64.7$ nm, ${\sigma }_D=38.5$ nm, substrate temperature $T_s\left(L\right)=310$ K, and fluence $\varphi =8{\mathrm{mJ}/\mathrm{cm}}^2$. The red dots correspond to numerical calculations, and the dashed line is given by $\tau \propto {\sigma }_K^{-1}$.

Figure 11

(a) Time evolution of reflectivity after the photoinduced MIT for ${\mathrm{VO}}_2/{\mathrm{TiO}}_2$ for three different $T_s\left(L\right)$ and $\varphi =9\text{mJ}/{\mathrm{cm}}^2$. The solid curves correspond to the theoretical results, and the dashed curves correspond to the experimental results. For the three theory curves, we use ${\sigma }_K=1100\mathrm{W}/(\mathrm{K}{\mathrm{cm}}^2$). (b) shows the corresponding insulating fraction time evolution.

Figure 12

Dependence of the ${\mathrm{VO}}_2/{\mathrm{TiO}}_2$ metal state decay time constant $\tau$ on ${\sigma }_D$ for two values of $\langle lnD\rangle$, as defined in Eq. (5), Kapitza constant ${\sigma }_K=1100\mathrm{W}/(\mathrm{K}{\mathrm{cm}}^2$), substrate temperature $T_s\left(L\right)=280$ K, and initial fluence $\varphi =9\text{mJ}/{\mathrm{cm}}^2$.

Figure 13

${\mathrm{VO}}_2/{\mathrm{Al}}_2{\mathrm{O}}_3$ reflectivity time evolution after photoinduced MIT for $\varphi =7.5\text{mJ}/{\mathrm{cm}}^2$. The red dots correspond to the experimental result. The dotted curve correspond to the theory with ${\sigma }_K=1100\mathrm{W}/(\mathrm{K}{\mathrm{cm}}^2$), and the solid curve corresponds to ${\sigma }_K=13000\mathrm{W}/(\mathrm{K}{\mathrm{cm}}^2$).

Figure 14

Film and substrate temperature time evolution. For sapphire (a), $T_s\left(L\right)=310$ K, and for rutile (b), $T_s\left(L\right)=280$ K.

Figure 15

Dependence of metal state decay constant $\tau$ on fluence and substrate temperature for ${\mathrm{VO}}_2/{\mathrm{TiO}}_2$.