On the Field-Induced Insulator–Metal Transition in VO₂ Films

Serge Luryi and Boris Spivak

Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY, 11794, USA

Department of Physics, University of Washington, Seattle, WA, 98195, USA

1 Introduction

First-order metal–insulator transitions (MITs) in crystalline materials have been known for many years¹ and correspond to a transformation between states with a dielectric (semiconductor) and a metallic types of conductivity. These transitions occur under the influence of certain external parameters, such as temperature and pressure, as well as with varying material composition. Materials exhibiting these phenomena include many transition metal oxides, of which over 40 are known to possess MITs.^{2 3}

Among the best-known MIT materials are vanadium oxides. Being able to combine with oxygen in 2-, 3-, 4-, and 5-valent states, vanadium forms a series of oxides of which at least eight exhibit MITs.⁴ Phase transition in V₂O₃ occurs at a critical temperature T_C = 150 K and in VO₂ at T_C = 340 K, with the electrical conductivity changing by up to 10 and 5 orders of magnitude, respectively. The MIT in vanadium oxides is also accompanied by a discontinuous variation of other than electrical properties, such as optical and magnetic. Vanadium dioxide, VO₂, is of particular interest for technology because its transition occurs near room temperature and furthermore its T_C is tunable over a wide range by doping with impurities such as tungsten. A recent review of vanadium oxide electronics⁵ exhaustively cites the relevant literature. Another recent review⁶ has a somewhat different focus and perspective.

Despite numerous attempts, no commercially viable applications of VO₂ have been found thus far. One known application, in infrared-vision systems, employs a closely related but nontransitioning, nonstoichiometric VO_x rather than VO₂. The reason for choosing VO_x over VO₂ had to do with a difficulty of dealing with the hysteretic nature of a transition in VO₂. A recently proposed VO₂ sensor for infrared-vision systems utilizes a spectacular bolometric effect that is of nonhysteretic nature,⁷ even though it is within the hysteretic loop of the transition. This proposal has not found commercial use either.

The dramatic difference in the electronic spectrum on the metallic and the dielectric side of the transition opens the possibility for switching applications triggered by an external electric field applied to a thin transitioning film in a gated structure. Since the field penetrates very differently into the dielectric and metallic phases, the field energy in the two phases is different (a possibility to the best of our knowledge first suggested by Valiev et al.⁸). As a result, application of an external electric field shifts the critical temperature of the transition.^8–21

We had previously estimated¹⁴ such a shift δT_C for a transistor-like structure with a thin VO₂ film sandwiched between two metallic plates insulated from the film by dielectric layers (cf. Fig. 1). One of these plates is the ground plane and to the other a gate voltage V_G is applied, resulting in

1

where S_M and S_D denote the entropy densities and C_M and C_D the electrostatic capacitances per unit area of the film in the metallic and the dielectric phase, respectively. In this estimate, it is assumed that the entire film undergoes the transition. As suggested in Ref. 14, this may be “true for a thin enough film, where the formation of in-plane transition boundary is energetically unfavorable.” The negative sign in Eq. (1) implies that application of a gate voltage drives the system into its metallic state.¹ For an applied voltage V_G = 1 V in an exemplary gated structure, we found δT_C ≈ −1 K. This is a substantial shift, but it is hardly adequate for switching applications.

The electrostatic effect of Eq. (1) is based on thermodynamics and is independent of a physical origin of the MIT. However, this mechanism is rather weak, as it allows shifting T_C by at most several degrees. A much stronger effect, albeit model-dependent, is introduced in the next section and will form the basis for our subsequent discussion. Here we wish to stress that the idea of inducing insulator-to-metal transition in a thin vanadium oxide film by applying an external electric field is a sound idea. The effect surely exists!

Nevertheless, despite multiple reports that observe such an effect and the sound theoretical reasons for its existence (see Refs 8–21 and above-cited reviews^{5 6}), the status of this problem is unsatisfactory and we offer our reflections on the reason why. We believe that for a sufficiently large applied field the transition indeed occurs, but it is confined to an infinitesimal sliver at the surface of the sample. In its “insulator” phase, the VO₂ sample is, in fact, a semiconductor with a relatively narrow bandgap and a rather high conductivity at typical experimental temperatures. As a result, the field-induced transition is never observed in a gated bulk sample. The transition has been reported only in double-gated films, but even there the effect is rather weak because most of the film remains semiconducting and shunts the emergent metallic sliver.

We discuss the conditions under which the transition can be induced in the entire film, rather than its top sliver. We show that this favorable situation can be realized when the film is sufficiently thin, so that the energy cost of converting the entire film into the metallic phase (which is “thermodynamically wrong” in the part of the film away from the surface) is smaller than the would-be cost of creating a domain boundary between the two phases. At this time, we cannot predict how thin the film should be for the proposed stabilization of the entire-film transition by the domain boundary energy, but we discuss the physical quantities that should be determined to make this prediction.

Finally, we discuss the need for the ground plane, which does not sit well with the technological reality that the best and thinnest VO₂ films are grown on insulating monocrystalline sapphire substrates. In large transistor-like structures with gate lengths of a micron and longer, the ground plane appears indispensible, for otherwise the field configuration would be accommodated with tiny domain boundaries across the film. The phase boundary must be comparable to the film area for its energy to count. Whether or not this can be accomplished with deep submicron gate lengths is an open question.

2 Electron concentration-induced transition

There is no definitive theory of the metal–insulator transition in vanadium oxides. Possible mechanisms under discussion are the electron–phonon or Peierls mechanism and electron correlation mechanism of Mott–Hubbard type.^{1 22, 23} Ultrafast experiments,^24–27 where the transition is excited by femtosecond optical pulses, support the electron correlation model, at least in VO₂. Nowadays, this seems to be the prevalent view of most practitioners.^{5 6, 28}

The correlation model naturally leads to the assumption that the transition is controlled by the concentration of mobile carriers. This implies a model of the transition triggered by the total electron concentration in the dielectric phase, irrespective of whether it results from doping, thermal excitation, photo excitation – or is induced by an applied electrostatic field. We are interested, of course, in the latter case. In an intrinsic semiconductor in the absence of an applied field, the chemical potential μ is approximately in the middle of the bandgap E_G. As the field F is applied, μ moves toward one of the allowed bands and the concentration of electrons (or holes) in the vicinity of the surface increases. At some critical concentration we can expect a transition to the metallic state.

Although there is yet no quantitative theory to describe such a transition, the very existence of induced concentration effect should be regarded as likely. The critical carrier concentration may be estimated to be of the order of the thermal carrier concentration that arises in the dielectric phase at the transition temperature T_C due to the thermal excitation across the gap. That concentration is of the order 10¹⁸ cm⁻³ and should be easily achievable by field effect. The induced-carrier effect is much “stronger” than the electrostatic field energy effect and should work in a wide range of temperatures. The expected “strong” effect is very attractive for switching applications.¹⁴

Qualitatively, we assume that the transition driven by electron concentration is controlled by the position of the chemical potential μ relative to the conduction band E_C (in a homogeneous system), see Fig. 2. We shall denote by ϕ(T) the critical position of μ at a given temperature T that corresponds to the transition. We regard the temperature as fixed and vary the concentration. Dielectric phase corresponds to μ < ϕ(T).

We shall continue describing the system by its dielectric diagram even when the semiconductor phase is unstable. This provides the meaning to μ > ϕ as the level of the chemical potential that would be present if the dielectric phase were stabilized externally.

For the difference ΔG in the free energy density per unit volume between the metallic and dielectric phases we assume the model illustrated in Fig. 3. Here in this diagram, the quantity Δ_D is the penalty the system pays for keeping a unit volume metallic in the region where μ < ϕ, that is, where the volume should be dielectric; similarly, Δ_M is the penalty for maintaining a dielectric unit volume in the region where it should be metallic. The sum of these quantities, Δ_D + Δ_M = Δ, is the total discontinuity in the free energy density upon transition, but their ratio is completely unknown at this time.

3 Field-induced transition in a film

Consider a dielectric VO₂ film of thickness d in an external electric field F. To determine what happens with the film, when part of it, a layer of thickness x, is subject to μ > ϕ (while stabilized in the dielectric phase), we must tally the penalties. The reason the layer may not transition to metal is associated with the boundary energy b between the two phases. The quantity b is per unit area and its value should be also considered unknown at this time. The value of x depends only on the electric field and increases with the field. There is a well-defined equation x = x(F) that is determined by electrostatics of the accumulation layer.

Three possible configurations are illustrated in Fig. 4. In the configuration (a), the film remains dielectric, paying the penalty xΔ_M.

In the configuration (b), a thin layer x_M goes metallic and screens the applied field. The remaining portion (x − x_M) is no longer under metallic condition. Since the field does not penetrate beyond x_M, the film underneath has μ < ϕ and no penalty is extracted except, of course, for the boundary energy b, which is the only penalty in this configuration.

We can safely assume that x_M is very small, on the order of where ≈ 10⁸ cm/s is the Fermi velocity of electrons in the metallic phase, and E_G ≈ 0.5 eV is the bandgap energy in the dielectric phase. The actual extent of x_M should be determined from the Ginzburg–Landau equation that describes the spatially inhomogeneous transition. The combination appears reasonable on dimensional considerations and gives x_M ≈ 10 Å.

In the configuration (c), the entire film goes metallic and there is no boundary penalty. However, most of the film, (d − x), is in the regime μ < ϕ and hence pays the penalty for being metallic, Δ_D(d − x).

For thick enough films, only configurations (a) and (b) are competitive. The transition occurs in thick films at large enough fields, when x > b/Δ_M. Due to the smallness of x_M, the effect of the transition is not very strong and may be hard to see in resistance measurements. The reason is that the conductivity of a thick VO₂ film in its “dielectric” phase (where the intrinsic free-carrier concentration is considerable at room temperature, n ≈ 10¹⁸ cm⁻³) is rather high and it would not be much changed by the conversion to metal of a surface sublayer of thickness x_M.

The critical field F_C for the transition in thick films is defined by the electrostatic relation x_C = x(F_C) with a finite thickness of penetration x_C. For thick films, the critical field penetration thickness is given by x_C = b/Δ_M.

In the opposite limit of thin films, where dΔ_D < b, configuration (c) in Fig. 4 becomes competitive, Δ_D(d − x) < xΔ_M, and the entire film undergoes transition. This happens at large enough fields, x > dΔ_D/(Δ_D + Δ_M), and the critical field now corresponds to

2

Equation (2) together with the electrostatic relation x_C = x(F_C) determines the critical field for driving the transition in a thin film.

Note that in light of the dΔ_D < b condition for thin films, the thin-film critical field of Eq. (2) is smaller than the corresponding field, x_C = b/Δ_M, for thick films.

4 Need for a ground plane

The above estimates necessarily assume a double-gated structure (cf. Figs 1 and 4). In this case, the domain boundary is planar and the boundary energy per unit area may compete on equal footing with the phase energy densities corresponding to different configurations. However, the best thin films of VO₂ are produced on insulating crystalline substrates, such as sapphire. In these structures, a meaningful ground plane is hard to fabricate. The ground plane is “meaningful” if it attracts most of the field lines emanating from the gate electrode; therefore, it must be positioned close to the film, much closer than the source–drain spacing. Otherwise, instead of the configurations of Fig. 4, the electric field lines would terminate on the source and drain contacts and the domain walls would be “vertical” (across the film). Vertical walls may also tangibly contribute to the energy balance; thus, they possess enough energy to stabilize nonhysteretic branches in temperature excursions within the hysteresis loop of the metal–insulator transition in thin VO₂ films.⁷ However, for long gates (e.g., on the order of a micron or longer), the vertical-wall area would be negligible compared to the area of the film and the boundary energy would hence not be significant.

The situation may be more favorable for deep submicron gates. It seems reasonable that for short enough gates the vertical wall energy may be sufficient to stabilize the transition in the entire film. Philosophically, however, the short-gate quest seems to undermine perhaps the main advantage of the three-terminal switch based on a metal–insulator transition: namely, that its speed is independent of the gate length. As discussed earlier,¹⁴ unlike field-effect transistors, the speed of such a switch is not limited by carrier drift time under the gate.

Therefore, we believe the main research effort would be best deployed in the development of a viable technology for the deposition of a high-quality thin VO₂ film on a substrate that could incorporate a meaningful insulated ground plane.

5 Conclusion

First-order metal insulator phase transitions in thin VO₂ films can be controlled by an applied electric field. The effect can be used for the implementation of useful devices such as a three terminal ultrafast switch. For the successful development of such a switch, it is imperative that the thin film be double-gated and moreover be thin enough to transition as a whole, rather than separating into two planar domains, the metallic and the semiconducting. We have argued that in thin enough films, the entire-film transition can be stabilized by the domain boundary energy.

It would be very worthwhile to develop a quantitative theory that microscopically describes the spatially inhomogeneous first-order transition. Such a theory should be able to provide an estimate for the key quantities required to assess the needed film thickness. First and foremost, this is the domain boundary energy b, about which we presently know next to nothing, quantitatively. Another parameter one would like to know is the breakdown of the free-energy discontinuity upon transition, Δ = Δ_D + Δ_M, into its components describing the “penalties” on the metallic and the dielectric sides of the transition. While the Δ itself can be estimated from the transition latent heat data (about 1 kcal/mol, according to Ref. 1), nothing is known about its breakdown into Δ_D and Δ_M. Still another interesting (and unknown at this time) quantity is the thickness x_M of a metallic sliver that forms on the surface bulk (or thick-film) VO₂ in response to an applied electric field. The smallness of this quantity according to our estimate, , should account for the unsatisfactory status of the problem today.

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