Long-range propagation of protons in single-crystal VO₂ involving structural transformation to HVO₂

Abstract

Vanadium dioxide (VO₂) is a strongly correlated electronic material with a metal-insulator transition (MIT) near room temperature. Ion-doping to VO₂ dramatically alters its transport properties and the MIT temperature. Recently, insulating hydrogenated VO₂ (HVO₂) accompanied by a crystal structure transformation from VO₂ was experimentally observed. Despite the important steps taken towards realizing novel applications, essential physics such as the diffusion constant of intercalated protons and the crystal transformation energy between VO₂ and HVO₂ are still lacking. In this work, we investigated the physical parameters of proton diffusion constants accompanied by VO₂ to HVO₂ crystal transformation with temperature variation and their transformation energies. It was found that protons could propagate several micrometers with a crystal transformation between VO₂ and HVO₂. The proton diffusion speed from HVO₂ to VO₂ was approximately two orders higher than that from VO₂ to HVO_2. The long-range propagation of protons leads to the possibility of realizing novel iontronic applications and energy devices.

Introduction

Controlling the properties of strongly correlated electronic materials via carrier and impurity doping has gained significant attention over the past years. Doping has an impact on 3d-band filling, which often results in dramatic modification of the orbital states. This results in large changes of electronic properties, such as the metal-insulator transition (MIT). For example, a shift of the MIT temperature (T_MI) of VO₂ via doping with a variety of elements, such as W, Mo, and Nb has been reported^{1,2,3,4,5,6,7,8}. This is caused by charge transfer from the impurity ions to the vanadium ions through the oxygen ions, which displaces an integral number of 3d¹ electrons in V⁴⁺ that are Mott insulating states to 3d^1+δ, resulting in the formation of more stable metallic states. When using impurity elements with large atomic numbers of W, Mo and Nb, however, it is impossible to dynamically control the number of mobile carriers because of solid-state materials determined by an initial doping level. On the other hand, protons having strongly reductive activity in oxide materials can dynamically move via external fields and function as an electron donor. Recent work has demonstrated that dynamic proton-intercalation results in a large, reversible resistance modulation in oxide thin films, such as SrTiO₃, NdNiO₃, and VO₂ via a catalytic effect^{9,10,11,12,13}, a non-catalytic effect^14,15, or an electric field^{16,17,18,19,20}. In general, the intercalation of protons in the insulating VO₂ state decreases its resistivity and it approaches a metallic state with a pseudo rutile structure^{11,19,21,22,23,24}. According to Yoon et al.¹³, heavy doping with protons using Pt catalytic nano-particles transforms VO₂ into HVO₂ under an H₂ + Ar gas atmosphere. HVO₂ has a different crystal structure from the tetragonal VO₂, and it demonstrates typical-insulating behavior that follows the Arrhenius equation with a higher resistivity than that of VO₂. Moreover, a reversible structural deformation is possible between VO₂ in air and HVO₂ in the H₂ + Ar gas atmosphere. This reversible resistance change has the potential to lead to the realization of novel ionic and/or electronic applications. However, there is lack of information regarding essential physical parameters in this system, such as the diffusion constant of the intercalated protons in VO₂ and the crystal transformation energy between VO₂ and HVO₂.

In this work, we demonstrated the long-range propagation of protons in VO₂. This was accomplished by investigating the transient electronic transport properties during proton intercalation in VO₂ and the associated structural transformation to HVO₂ under H₂ + Ar gas atmosphere. This was followed by a return to VO₂ from HVO₂ after proton desorption under an N₂ gas atmosphere. The results showed that the diffusion constants and crystal transformation energies differed for the two states.

Results

Device structures and basic transport properties

For VO₂ microwire devices prepared on TiO₂ (001) substrates, the width (w) was fixed at 2 μm and the distance between catalytic Pt electrodes (d) was from 2 μm to 10 μm, as shown in the schematic in Fig. 1a. The optical image on the right of Fig. 1a shows a VO₂ microwire with Pt electrodes as an example. Figure 1b shows the temperature dependence of the resistivity curves in a VO₂ microwire with d = 4 μm. The pristine VO₂ shows typical electronic transport properties with hysteresis due to the MIT in a N₂ gas atmosphere (solid black dots). Continuous annealing under H₂(5%) + Ar(95%) gas at 380 K for ~5 h resulted in a marked change to the insulating phase that followed the Arrhenius equation (solid red dots). The resistivity increased by ~5 orders of magnitude, which is in agreement with ref. ¹³. They determined that the heavily hydrogenated VO₂ had a structural deformation to HVO₂, which resulted in a ~10% expansion in the [100] direction of the rutile VO₂ structure and opened a band gap calculated by a first-principle method¹³. The band gap (E_g) of the hydrogenated HVO₂ was 0.71 eV, as derived from the inset of Fig. 1b using the equation as a pure semiconductor $\mathrm{ln}\,\sigma =-\frac{{E}_{g}}{2{k}_{B}}\frac{1}{T}+\,\mathrm{ln}\,{\sigma }_{0}$, where σ, σ₀, and k_B are the conductivity of the thin film, a constant, and the Boltzmann constant, respectively. The E_g takes the half value with the calculated bandgap of the HVO₂ with 2 electron doping unit cell in ref. ¹³. Furthermore, these results indicate that the VO₂ microwires also become fully hydrogenated VO₂ in the 4 μm gap between the Pt source and drain catalytic electrodes. Figure 1c shows the reversibility of the transport properties under H₂+Ar or N₂ gases at 380 K. The VO₂ microwire was initially metallic at 380 K in a N₂ atmosphere. As soon as H₂ gas was introduced into the measurement cell, the resistivity promptly increased with the intercalation of protons into VO₂. Eventually, the H₂ gas annealing resulted in the heavily hydrogenated VO₂, i.e., it formed the insulating HVO₂ phase. Compared with the time required for the transformation from VO₂ to HVO₂, the HVO₂ phase returned to the initial metallic VO₂ more quickly on N₂ gas annealing. This trend was in agreement with the data from ref. ¹³. The results of this experiment revealed the micro-scale diffusion of protons with a crystal change from VO₂ to HVO₂. Regarding repeatability of electronic property of VO₂ thin films after N₂ annealing at 380 K from HVO₂, the temperature dependence of resistance curves is almost same as the pristine curve, keeping the framework of VO₂ (Please see the section E in Supplementary Information in detail).

Figure 1

VO₂ microwire device with Pt electrode with catalytic effect and Basic transport properties of VO₂ and heavily proton intercalated VO₂. (a) A schematic illustration (left) and an optical microscope image (right) of a VO₂ microwire for the proton intercalation experiment. (b) Temperature dependence of the resistivity curves of a pristine 4-μm-length VO₂ wire (the black solid dots) and of hydrogenated VO₂ (HVO₂) (the red solid dots). The inset shows the 1/T dependence of ln σ for the Arrhenius plots (c) The reversibility of the transport properties under H₂ + Ar or N₂ gases at 380 K.

Analysis of the transient resistance behavior

Based on the H₂ or N₂ atmosphere dependent reversible reaction, the evolution of the proton concentration in VO₂ with time was investigated. As a boundary condition between the Pt and VO₂ interface, the chemical reaction rate as a differential equation with respect to time (t) was introduced according to:

$$\frac{d{n}_{{\rm{inter}}}}{dt}={k}_{1}{n}_{{\rm{H}}+}-{k}_{2}{n}_{{\rm{inter}}}$$

(1)

where k₁ and k₂ are the forward and reverse reaction rate constants, respectively, n_H+ is the proton concentration at the contact area between the Pt catalytic electrodes and VO₂, and n_inter is the proton concentration at the VO₂ interface. From Eq. (1), the behavior of Fig. 1c can be understood. In the beginning, protons are intercalated into VO₂ at the contact points between Pt, VO₂, and the H₂ + Ar gas phase, as seen in an upper illustration of Fig. 2a, because k₁n_H+ > k₂n_inter, and n_inter = 0 during the initial stage. The value of k₂n_inter gradually approaches that of k₁n_H+, until the two values are finally equal and reach the equilibrium state. As the H₂ + Ar gas is changed to N₂, n_H+ approximately becomes zero, thus the protons in VO₂ are removed and the insulating HVO₂ returns to the metallic VO₂ form. This dynamic reaction at the interface was taken as a boundary condition with a dynamic time-dependence in the simulation below.

Figure 2

Transient electronic transport behaviors of VO₂ microwires in 4-μm-, 6-μm- and 10-μm-length. (a) Illustration of the chemical kinetics with forward (k₁) and reverse (k₂) reaction rate constants with the Pt catalytic effect (upper) and the serial resistor model via the FMD simulation. (b) Experimental and simulation results for the time dependence of the resistivity in 4-μm-, 6-μm-, and 10-μm-length VO₂ wires after starting hydrogen intercalation under the H₂(5%) + Ar(95%) gas atmosphere at 380 K. The inset shows the spatiotemporal map of the proton ratio for the case of D_HVO2 = 150 nm²/s, which was the fitting value for the doted lines of the 4-μm-, 6-μm-, and 10-μm-length VO₂ wires in Fig. 2b. (c) Spatial maps of the proton ratio using D = 150 nm²/s in the 4-μm-, 6-μm-, and 10-μm-length VO₂ wires for 4 h after start from hydrogen intercalation.

Next, we consider how the intercalated protons diffuse in VO₂. Theoretically, for ion diffusion, the ionic fluxes likely arise from a gradient in the ion concentration in the solid-state material. Thus, since n_HVO2 is the proton ratio in a VO₂ unit cell, the hydrogen ion flux (J_HVO2) can be described as:J_HVO2 = −D∇n_HVO2, where D is the diffusion coefficient. To conduct the transient state analysis, we use Fick’s second law in the one dimensional case, namely, $\frac{\partial {n}_{HVO2}}{\partial t}=-\frac{\partial {J}_{HVO2}}{\partial x}$, which predicts the spatiotemporal evolution of the ion concentration. With this the following equation was obtained:

$$\frac{\partial {n}_{HVO2}}{\partial t}=-\,D\frac{{\partial }^{2}{n}_{HVO2}}{\partial {x}^{2}}\cdot $$

(2)

To evaluate the spatiotemporal evolution of the proton concentration in VO₂, numerical analysis using the finite difference method (FDM) was carried out based on the boundary condition of Eq. (1) and the transient diffusion equation of Eq. (2) (see Section A in Supplementary Information).

The inset of Fig. 2b shows the spatiotemporal mapping of the proton density in VO₂ from the simulation with D = 150 nm²/s. Here, x = 0 represents the interface of the VO₂ contacted with the Pt electrodes. We divided the 2-μm-length VO₂ wire by 100 in the FDM calculation, thus the integral i goes from 1 to 100 and the divided length (Δx) is 20 nm (further details in Section A of the Supplementary Information). The inset of Fig. 2b represents the proton diffusion behavior of a 4-μm-length VO₂ wire because the intercalation and diffusion behavior becomes symmetric at a 2 μm distance from the Pt electrodes. Through this analysis, we can clearly understand the transient behavior of proton diffusion in the VO₂ wires.

For conversion of the proton concentration in VO₂ to resistivity, a serial resistor model was used as shown in the lower illustration of Fig. 2a, which is represented by the following equation:

$$\rho (T)=\frac{1}{100}{\sum }_{i=1}^{100}{\rho }_{i}(T)$$

(3)

The ρ_i(T) can be simply defined as $(1-{n}_{HVO2}){\rho }_{i}^{VO2}+{n}_{HVO2}{\rho }_{i}^{HVO2}(T)$, where ${\rho }_{i}^{VO2}$ is the resistivity of metallic VO₂ and ${\rho }_{i}^{HVO2}(T)$ is the temperature dependent resistivity of the insulating HVO₂.

The ${\rho }_{i}^{VO2}$ was fixed at 0.0008 Ω cm between 300 K and 380 K because of its nearly constant value with reference to the VO₂ resistivity curve in Fig. 1c, while ${\rho }_{i}^{HVO2}(T)$ varies with temperature. The experimental values of ${\rho }_{i}^{HVO2}(T)$ were taken at the required temperature by referring to the temperature vs resistance curve of HVO₂ in Fig. 1b. Figure 2b shows the transient resistivity behavior with time for the 4-μm-, 6-μm-, and 10-μm-length VO₂ wires at 380 K. The red dot curves show the simulation results using Eqs. (1) to (3) with the appropriately selected diffusion constant for the proton that transforms the crystal structure from VO₂ to HVO₂; D_HVO2 =150 nm²/s at 380 K determined by the wire lengths of VO₂ with 4 μm, 6 μm, and 10 μm. The simulation curves could fit to the experimental curves well in their lengths. The diffusion value was compared with proton diffusion in the [001] direction of rutile-type TiO₂ without a structural transformation²⁵. It is considered that the slower diffusion constant of VO₂ [110] than that of TiO₂ [001] would be due to difference of two oxygen distance (d_o-o) in [001] and [110] directions, respectively, because the diffusion constant of protons hopping to next oxygen sites is dependent on square length of d_o-o. The d_o-o in TiO₂ [001] direction is approximately 1.48 Ų⁵, whereas the d_o-o in VO₂ [110] and HVO₂ [110] are approximately 2.66 Å and 2.68 Ź³, respectively. Figure 2c shows the spatial mapping of the proton ratio using D_HVO2 = 150 nm²/s with 4-μm-, 6-μm-, and 10-μm-length VO₂ wires for 4 h after the start of proton intercalation. The occupancy of the protons was high at >80%/unit cell, even at the center of the 4-μm-length VO₂ wire, while the center of the 10-μm-length wire was still unoccupied by protons. The spatial density of HVO₂ clearly reflects the resistance behavior shown in Fig. 2b.

Discussion of the physical picture

Next, we estimated the activation energy (E_HVO2) for the structural transformation from VO₂ to HVO₂ using the experimental results of the 4-μm-length VO₂ wire and simulation fittings. Figure 3a–d show the time dependence of the resistivity behaviors in the 4-μm-length VO₂ wire at 320 K, 340 K, 260 K, and 380 K, respectively. The simulation curves (red dot curves) were fitted by appropriately selecting the D_HVO2 values. The dashed blue lines in Fig. 3a–d indicate the resistivity of HVO₂ with the measurement temperature taken from the 4-μm-length VO₂ wire in Fig. 1b. The values of the experimental resistivity at each temperature were used as the simulation values of ${\rho }_{i}^{HVO2}(T)$. From these fittings, we estimated the D_HVO2 values, which are 5 nm²/s at 320 K, 10 nm²/s at 340 K, 50 nm²/s at 360 K, and 150 nm²/s at 380 K, respectively. In general, the variation of the diffusion constant (D) with temperature takes the form of a thermally activated-type equation as below:

$$D(T)={D}_{0}\exp (-\frac{{E}_{{\rm{D}}}}{{k}_{B}T})\cdot $$

(4)

where E_D is the diffusive activation energy and D₀ is the frequency factor.

Figure 3

Transient electronic transport behaviors of the 4-μm-length VO₂ microwire at a variety of temperatures. (a–d) Time dependence of the resistivity behaviors in the 4-μm-length VO₂ wire at 320 K, 340 K, 360 K and 380 K, respectively. (e) the red dots represent experimental D_HVO2 values in the VO₂ wire with structural transformation to HVO₂, estimated from the simulated fitting in Fig. 3a–d (the red dot lines). The red line is the fitting curve using Eq. (4). In comparison with the experimental D_HVO2, the proton diffusion constant of the parallel direction along the c axis of TiO₂ as a function of temperature in ref. ²¹ (black line). The inset shows the 1/T dependence of ln D_HVO2 for the Arrhenius plots.

Figure 3e shows temperature dependence of D_HVO2. The red dots represent the experimental D_HVO2 values in the VO₂ wire with structural transformation to HVO₂, estimated from the simulated red dot lines in Fig. 3a–d. The red line is the fitting curve using Eq. (4). Compared with our experimentally determined D_HVO2 values, the diffusion constant of protons in the direction parallel to the c axis of rutile-TiO₂ (black line)¹⁸ are reasonably similar. Considering the diffusion constant of protons in TiO₂²⁵, which is same crystal structure as VO₂, and the direct observation of proton diffusion in VO₂ by a microscope¹⁵. In addition, at the section D in Supplementary Information, resistance once insulating monoclinic-state of VO₂ at 290 K decreases in an insulating monoclinic-state of VO₂ at 290 K under a H₂(5%) + Ar(95%) gas atmosphere. This is due to carrier doping from OH group without crystal transformation, that is, carrier density increases keeping the tetragonal VO₂ structure. With further developing proton-intercalation, the heavy proton dopants promote transformation to the different crystal structure of insulating HVO₂¹³. This transient response appears in Fig. S4. Thus, the origin of resistance changes in Figs. 2b, 3a–d and 4a can be more reasonably explained as proton diffusion in VO₂ than formation of contact resistance and/or small fractions having proton-puddles. The inset shows the 1/T dependence of ln D_HVO2 for the Arrhenius plots. Figure 3e shows 1/T dependence of the D_HVO2 values derived from the fitting curves using Eq. (4). The solid red line was obtained by the least-square method. From the slope, we determined that the diffusive activation energy for transformation from VO₂ to HVO₂ was 0.61 eV. For the diffusive activation energy for the reverse transformation from HVO₂ to VO₂, we estimated the diffusion coefficients (D_VO2(T)). Figure 4a shows the transient normalized-resistance curves for the reverse HVO₂ to VO₂ transformation in a N₂ atmosphere at 300 K, 320 K, 340 K, 360 K, and 380 K, respectively. Simulation curves using the FDM calculations could be well fitted to the experimental curves by incorporating the temperature-dependent coverage of hydrogen adatoms on Pt surface²⁶ (Section B of the Supplementary Information provides further details). The D_VO2 was 4600 nm²/s at 300 K, 10000 nm²/s at 320 K, 20000 nm²/s at 340 K, 45000 nm²/s at 360 K, and 90000 nm²/s at 380 K, which were more than two orders higher than those of D_HVO2. From the fitted D_VO2 at various temperatures, the activation energy for the transformation from HVO₂ to VO₂ (E_VO2) was determined to be 0.37 eV, as obtained from the slope in Fig. 4b. Figure 4(c) shows the transformation energy between VO₂ and HVO₂ derived from the above data. VO₂ structure is more stable than that in HVO₂ structure.

Figure 4

Transient electronic transport behaviors returned from HVO₂ to VO₂. (a) Time dependence of normalized-resistive behaviors from HVO₂ to VO₂ under a N₂ gas atmosphere in the 4-μm-length wire at 300 K, 320 K, 340 K, 360 K, and 380 K, respectively. The red dot lines show simulation curves derived by Eqs. Eq. (1–4) including the inhabitant effect in Section B of Supplementary Information. (b) The 1/T dependence of ln D_VO2 for the Arrhenius plots. (c) Schematic of the crystal transformation energies between VO₂ and HVO₂.

Discussion

We clarified the physical parameters of heavily proton-intercalated VO₂ through investigation of proton diffusion. Single-crystal VO₂ thin films with a layer-by-layer growth were used to describe the crystal transformation energies from VO₂ to HVO₂ and from HVO₂ to VO₂. This was accomplished through investigation of the proton diffusion using the basic equations listed in Eq. (1) to Eq. (3). Data from in-plane poly-crystalline VO₂ thin films with grains on Al₂O₃ (0001) substrates²⁷ were not well-fitted to the ideal simulations using these equations. This was because a different crystal direction in-plane and grain boundaries disturb the ideal proton diffusion (Section C in Supplementary Information provides further details). It was found that the proton diffusion speed from HVO₂ to VO₂ was approximately two orders higher than that for VO₂ to HVO₂. The long-range micro-meter proton propagation, differences in the proton diffusion constants, and the asymmetry transformation energy between HVO₂ and VO₂ offer opportunity for the realization of novel iontronic applications and for energy devices, such as hydrogen storage.

Methods

Microwire preparation

Single crystal VO₂ thin films were epitaxially grown on TiO₂ (001) substrates using the pulsed laser deposition technique (ArF excimer laser, λ = 193 nm), with a substrate temperature of 420 °C, an oxygen pressure of 0.95 Pa, a laser repetition rate of 2 Hz, and with an energy fluency of 10 mJ/cm². A V₂O₅ pellet was used as the target. The deposition rate was ~0.3 nm/min. The thickness of the VO₂ thin films were fixed at ~10 nm. VO₂ grown on the TiO₂ (001) substrate had a tetragonal (001) plane, which could be verified by the X-ray diffraction pattern and SEM images of the VO₂ thin films prepared under the same fabrication conditions in Ref. ^28,29,30. The films and Pt catalytic electrodes were patterned via photolithography. A 40-nm-thick Pt electrode was deposited on the patterned VO₂ microwires. The width (w) was fixed at 2 μm and the Pt electrode distance (d) was from 2 μm to 10 μm, as shown in the schematic in Fig. 1(a). The right image in Fig. 1a shows a VO₂ microwire with Pt electrodes as an example.

Measurements

The electronic properties of the films were measured via a two-probe method using a current-voltage source meter (2614B, Keithley Instruments) under H₂(5%) + Ar(95%) or N₂ gas atmospheres. The current flow direction was [110] in the rutile VO₂ thin films.