Figure 1

(a) Four-probe measurement of thermally induced IMT. (b) Two-probe nonequilibrium transport measurements of the $10\mu \mathrm{m}$ (open symbols) and $20\mu \mathrm{m}$ channels for various set temperatures $T_{\mathrm{set}}$ set by the Peltier heater under the sample. The schematic circuit used is presented in Fig. 2b. The dc voltage applied across the channel is obtained by subtracting the dc voltage drop across both resistances placed in series to the generator dc applied voltage. The dc current in the circuit is measured by acquiring the dc voltage drop across a $55\mathrm{k}\Omega$ resistance placed in series. Above $V_{\mathrm{threshold}}$ [identified as an example by a vertical arrow on one of the curves in (b)], in the low resistance state of ${\mathrm{VO}}_2$, the dc current flowing in the circuit is limited by the 123 and $55\mathrm{k}\Omega$ resistances placed in series.Reuse & Permissions

Figure 2

(a) $20\mu \mathrm{m}$ channel before, during, and after positioning the micron-wide rare-earth fluorescent particle (from left to right). Right-hand image: The four gold electrodes identified were used in the four-probe measurements ($I+$, $V+$, $V-$, $I-$ from left to right); the indicated “source” and “probe” gold electrodes were used in the two-probe measurements. (b) Description of the experimental optical and electrical setup.Reuse & Permissions

Figure 3

Equivalence between fluorescent temperature and peak area ratio using Eq. (1) and both calibration points (room temperature $27°\mathrm{C}$ and thermally induced IMT $66°\mathrm{C}$, error bars of these points are $\pm 0.5°\mathrm{C}$, which are smaller than the symbols used). Inset: Fluorescent 520 and 550 nm lines (normalized to equalize all 520 nm peak heights for clarity) as a function of set temperature $T_{\mathrm{set}}$ (only 4 spectra shown out of 18 for clarity) set by a Peltier heater under the sample.Reuse & Permissions

Figure 4

Local temperature versus dc voltage [(a), (c)] and local temperature versus resistance [(b), (d)] for the 10 and $20\mu \mathrm{m}$ channels. Starting from $T_{\mathrm{set}}$, the temperature rise due to Joule heating brings the ${\mathrm{VO}}_2$ sample above the onset of the thermally induced IMT, i.e., inside the dashed regions (the thermal induced transition region). All curves are measured up to the dc voltage induced IMT. For local temperature after the switching at higher dc voltages, see discussion in the text and Fig. 5 for the data. Note that the power used by the Peltier device to heat the sample holder to $T_{\mathrm{set}}$ was maintained constant during each dc voltage sweep. Panels (b) and (d) also show the equilibrium $R(T)$ and nonequilibrium $R(T)$ data as explained in the main text. Panels (a) and (c) also show the Ohmic Joule heating model [22, 23] $T_{\mathrm{model}}=T_{\mathrm{set}}+\alpha IV$ fitting the measured temperature rise.Reuse & Permissions

Figure 5

dc switching hysteresis loops (paths 1–5) of transport (a) and thermal heating (b) of the $20\mu \mathrm{m}$ channel as a function of dc voltage (applied across the channel). Color code: Black as generator dc voltage rises and gray (red) as it goes down. (b) Inserted images of the channel above and below (top and bottom) $V_{\mathrm{threshold}}$. The fluorescent particle and the conducting path are indicated for clarity. As dc voltage is applied (path 1) temperature rises from $T_{\mathrm{set}}$ ($54.3°\mathrm{C}$) to $65°\mathrm{C}$ [as already presented or discussed previously in Figs. 4a, 4c]. After the dc switching (path 2), the temperature drops by a few degrees to $58°\mathrm{C}$. A conducting path is created (see narrow horizontal dark line in top image of (b)]. As the dc voltage generator reaches its maximum and starts ramping down (path 3), inverse dc switching occurs (path 4) from metallic back to insulating (the channel aspect transfers back to the lower image of the channel without conducting path). The transport falls back to the initial level, as does the temperature of the channel (path 5).Reuse & Permissions