Thin-film growth of VO₂

Moving from the frontier of fundamental research in VO₂ electronics toward their realization in commercial products, a method to deposit high-quality and ultrathin VO₂ films on wafer scale is needed. For example, memory devices based on MITs have the advantage of compact node sizes down to a few nm and VO₂ films must preserve their MIT properties during the scaling process, e.g., maintaining at least four orders of magnitude change in resistivity across the MIT.^[ Reference Zhou and Ramanathan ^{44 ]} However, the MIT properties in VO₂ thin films has long been recognized to be highly sensitive to deposition conditions including substrate temperature, background oxygen pressure, as well as deposition technique. This delicate nature of VO₂ results from its complex phase diagram as shown in Fig. 4(a). The VO₂ phase is not a line compound, and, thus, is intrinsically susceptible to point defect formation if growth conditions deviate slightly from the ideal ratio. Long-range order of these defects can occur forming distinctive phases.^[ Reference Kang ^{45 ]} In the oxygen deficient case, VO_2−δ , the so-called Magnéli phases, V _n O_2n−1, with n = 3–7 form a homologous series with one oxygen layer missing after every nth vanadium (211) plane of the VO₂ rutile structure. Similarly, the oxygen-rich VO_2+δ Wadsley phases, V _n O_2n+1 are known with n = 2, 3, and 6.^[ Reference Hirotsu and Sato ^{46 ,} Reference Katzke, Tolédano and Depmeier ^{47 ]}

Figure 4. (a) Phase diagram of vanadium oxide, adapted permission from Ref. Reference Katzke, Tolédano and Depmeier47. Copyrighted by the American Physical Society. (b) The Ellingham diagram for vanadium oxide phases.^[ Reference Barin ^{48 ,} Reference Moshfegh and Ignatiev ^{49 ]} (c) Resistivity versus temperature for various V–O phases, with a MIT at different temperatures. While V₂O₃ exhibits the largest change in resistivity over eight orders of magnitude, but below room temperature, VO₂ has the largest resistivity ratio above room temperature of about five orders of magnitude.^[ Reference Morin ^{20 ,} Reference Feinleib and Paul ^{21 ,} Reference Chudnovskii, Terukov and Khomskii ^{30 ,} Reference Kachi, Kosuge and Okinaka ^{181 –} Reference Okinaka, Kosuge, Kachi, Nagasawa, Bando and Takada ^{183 ]}

The rich phase diagram, the different polymorphs and the ability to easily accommodate defects that can order and dramatically affect the MIT properties, makes the growth of a targeted vanadium oxide phase particularly challenging.^[ Reference Kang ^{45 ]} Figure 4(b) shows the Ellingham diagram calculated from the enthalpy of reaction for selected vanadium oxide phases tabulated in Refs. Reference Barin48, Reference Moshfegh and Ignatiev49. Because entropy data were not available for all of these phases, ∆S of the reactions was assumed to be zero. All lines represent thermodynamic phase equilibria of the oxidation reaction ${\rm VO}_{x(s)} + (y/2){\rm O}_{2(g)} \rightleftharpoons {\rm VO}_{x + y(s)} $ , where higher temperature and lower oxygen partial pressure stabilizes a vanadium oxide phase with a lower vanadium oxidation state. While V₂O₅ is the thermodynamically stable phase at ambient condition, thin-film deposition in vacuum and at elevated temperature are ideally suited to stabilize the desired VO₂ phase. Notably, with sample temperatures typically ranging between 300 and 600 °C, growth by pulsed-laser depostion (PLD) in varying oxygen partial pressures has shown that a minimum background oxygen pressure of 10⁻² Torr is required to avoid oxygen deficient VO₂ on sapphire substrates.^[ Reference Jeong, Aetukuri, Graf, Schladt, Samant and Parkin ^{42 ]} Similarly, for VO₂ grown by molecular-beam epitaxy (MBE) distilled ozone background pressures of 10⁻⁶ Torr with substrate temperatures in the 200–350 °C range,^[ Reference Tashman, Lee, Paik, Moyer, Misra, Mundy, Spila, Merz, Schubert, Muller, Schiffer and Schlom ^{50 –} Reference Paik, Moyer, Spila, Tashman, Mundy, Freeman, Shukla, Lapano, Engel-Herbert, Zander, Schubert, Muller, Datta, Schiffer and Schlom ^{52 ]} or an oxygen plasma pressure^[ Reference Fan, Chen, Wu, Chen, Chu, Chen, Zou and Wu ^{53 ]} of (1–3)  × 10⁻⁵ Torr at a substrate temperature of 550 °C were used.^[ Reference Paik, Moyer, Spila, Tashman, Mundy, Freeman, Shukla, Lapano, Engel-Herbert, Zander, Schubert, Muller, Datta, Schiffer and Schlom ^{52 ,} Reference Fan, Chen, Wu, Chen, Chu, Chen, Zou and Wu ^{53 ]} According to the Ellingham diagram in Fig. 4(b) in all cases V₂O₅ is expected to form. The discrepancy between thermodynamic equillibrium calculations and experimental conditions used for the growth of high-quality VO₂ films suggests that the growth kinetics play an important role as well. A kinetic barrier to the oxidation of vanadium at the low growth temperatures used to form VO₂ films has been observed in surface science experiments,^[ Reference Della Negra, Sambi and Granozzi ^{54 ]} necessitating oxidation conditions that fall in the V₂O₅ region of the Ellingham diagram for all growth techniques. Indeed, considering the growth conditions common to VO₂ films, it is plausible that some V₂O₅ does form during growth, but desorbs due to its high volatility^[ Reference Pak ^{55 ]} leaving behind a phase-pure film of VO₂ in conditions that thermodynamics indicates should be in the territory of V₂O₅. Growth at high substrate temperature to overcome the kinetic barrier to oxidation is not an option for two reasons: (1) the rapid interdiffusion of VO₂ into the underlying substrates^[ Reference Tashman, Lee, Paik, Moyer, Misra, Mundy, Spila, Merz, Schubert, Muller, Schiffer and Schlom ^{50 ,} Reference Paik, Moyer, Spila, Tashman, Mundy, Freeman, Shukla, Lapano, Engel-Herbert, Zander, Schubert, Muller, Datta, Schiffer and Schlom ^{52 ,} Reference Della Negra, Sambi and Granozzi ^{54 ]} and (2) if the entire film is oxidized to V₂O₅, it will all evaporate due to the high vapor pressure of V₂O₅.^[ Reference Pak ^{55 ]}

Despite the many challenges involved in the growth of VO₂ films, significant advances have been achieved in its deposition using PLD,^[ Reference Jeong, Aetukuri, Graf, Schladt, Samant and Parkin ^{42 ,} Reference Koo, Yoon, Kwon, Ko, Shin, Bae, Chang and Park ^{56 –} Reference Lee, Meyer, Park, Egami and Lee ^{63 ]} MBE,^[ Reference Paik, Moyer, Spila, Tashman, Mundy, Freeman, Shukla, Lapano, Engel-Herbert, Zander, Schubert, Muller, Datta, Schiffer and Schlom ^{52 ,} Reference Fan, Chen, Wu, Chen, Chu, Chen, Zou and Wu ^{53 ,} Reference Zhang, Zhang, Mukherjee, Zheng, Haislmaier, Alem and Engel-Herbert ^{64 ,} Reference Zhang, Eaton, Ye and Engel-Herbert ^{65 ]} sputtering,^[ Reference Cui and Ramanathan ^{66 –} Reference Zhang, Wang, Fan, Liu, Guo, Zou, Wang, Qian, Ibrahim, Yan, Xu and Wu ^{73 ]} electron-beam deposition,^[ Reference Hood and DeNatale ^{74 ]} ion-beam depostion,^[ Reference West, Lu and Yu ^{75 ]} metalorganic chemical vapor deposition (MOCVD),^[ Reference Kim, You, Chiarello, Chang, Zhang and Lam ^{61 ,} Reference Maruyama and Ikuta ^{76 ]} chemical solution deposition^[ Reference Ji, Pan, Bi, Liang, Zhang, Zeng, Wen, Zhang, Chen, Jia and Lin ^{77 ]} and atomic layer deposition (ALD).^[ Reference Dagur, Mane and Shivashankar ^{78 ,} Reference Rampelberg, Schaekers, Martens, Xie, Deduytsche, De Schutter, Blasco, Kittl and Detavernier ^{79 ]} Using the resistivity ratio across the MIT as a benchmark for film quality, Fig. 5 shows a comparison of VO₂ films grown by different techniques from the aforementioned references. Since strain affects the resistivity ratio across the MIT as well, only fully relaxed films grown on sapphire substrates were selected here. Two general trends are observed: (1) For thick films well above 100 nm, high-quality VO₂ films with MIT ratio more than four orders of magnitude are commonly achieved. (2) With decreasing film thickness, the MIT ratios deteriorate to less than two orders of magnitude. Interestingly, recent progress in PLD has demonstrated high-quality VO₂ films with an MIT ratio: >5000 at film thicknesses as small as ~20 nm.^[ Reference Jeong, Aetukuri, Graf, Schladt, Samant and Parkin ^{42 ]} Also, growth of high quality VO₂ thin films on large silicon wafers has been demonstrated using sputtering.^[ Reference Savo, Zhou, Castaldi, Moccia, Galdi, Ramanathan and Sato ^{80 ]} In addition, a combinatorial approach for the growth of VO₂ has been developed using a thermal source for V and the metalorganic precursor vanadium-oxo-triisopropoxide to supply vanadium in a much higher valence state, which demonstrated the potential to combine high-quality VO₂ at a dramatically reduced film thickness on wafer scale, while keeping a high resistivity change across the MIT intact.^[ Reference Paik, Moyer, Spila, Tashman, Mundy, Freeman, Shukla, Lapano, Engel-Herbert, Zander, Schubert, Muller, Datta, Schiffer and Schlom ^{52 –} Reference Della Negra, Sambi and Granozzi ^{54 ,} Reference Zhang, Zhang, Mukherjee, Zheng, Haislmaier, Alem and Engel-Herbert ^{64 ]} High-quality VO₂ films are a key enabler for electrical engineers to exploit the opportunities offered by electronic PCMs in general and VO₂ in particular in proof-of-principle photonic and electronic devices, which are described in detail next.

Figure 5. Change in resistivity across the MIT, Δρ/ρ (indicated by various symbol) reported for completely relaxed VO₂ films grown on sapphire with different thickness.^[ Reference Jeong, Aetukuri, Graf, Schladt, Samant and Parkin ^{42 ,} Reference Paik, Moyer, Spila, Tashman, Mundy, Freeman, Shukla, Lapano, Engel-Herbert, Zander, Schubert, Muller, Datta, Schiffer and Schlom ^{52 ,} Reference Fan, Chen, Wu, Chen, Chu, Chen, Zou and Wu ^{53 ,} Reference Koo, Yoon, Kwon, Ko, Shin, Bae, Chang and Park ^{56 –} Reference Maruyama and Ikuta ^{76 ]} The dotted line indicates the thickness at which VO₂ is completely relaxed. The data are grouped into the different thin-film deposition techniques, arranged from left to right with increasing scalability. Note that in general a larger film thickness results in a larger Δρ/ρ.

Augmenting field effect transistors (FETs) with VO₂

In CMOS technology, the backbone of the current computing hardware, the strategy to realize low-power, high-performance computation is to reduce the total energy necessary to switch a FET from an OFF-state to an ON-state. The FET is switched by changing the gate voltage V _GS to modulate the drain-to-source current I _DS by orders of magnitude. The associated energy contains a dynamic contribution $E_{{\rm dyn}} = (\alpha /2)CV_{dd}^2 $ , with the intrinsic transistor gate capacitance C charged to turn the device into the ON state, the supply voltage V _dd , and dimensionless activity factor α to account for the fraction of clock cycles the transistor is switched. The static contribution is given by E _stat = I _leak V _dd τ, with I _leak the leakage current between source and drain in the OFF-state and τ the switching period, i.e., the clock speed of the processor. Switching the transistor from OFF to ON is achieved by changing the gate voltage, and along with that the surface potential and band bending Ψ_S in the channel, reducing the energy barrier between source and channel thus modulating the source–drain current I _DS.

Even in the OFF-state thermally excited carriers can overcome this barrier, captured by the Boltzmann factor exp^{−Δ/k _B T} with k _B the Boltzmann constant, T the absolute temperature, and Δ the barrier height relative to the Fermi level. The resulting energy dissipation is approximately E _stat = E _leak ∝ V _dd e ^{−V _dd / S} with S is the subthreshold slope.^[ Reference Ionescu and Riel ^{81 ]} To ideally balance both contributions to the switching energy per cycle an optimal supply voltage V _dd , typically close to the transistor threshold voltage is chosen; see Fig. 6. While the transistor would suffer energy losses due to the high leakage energy E _stat for too small operation voltages V _dd , too high V _dd values would unnecessarily increase the dynamic contribution E _dyn.

Figure 6. (a) Energy per cycle and (b) source–drain current I _DS versus gate voltage V _GS in units of the supply voltage V _dd for transistors with two different subthreshold slopes S of 60 meV/dec. (limit of the Boltzmann switch), and strongly correlated Landau switch with S = 30 meV/dec.

Aside from the supply voltage, another key parameter of transistor performance is the subthreshold slope S. It describes the required change in gate voltage to achieve an order of magnitude change in the source–drain current^[ Reference Jain and Alam ^{82 ]}

$$S = \displaystyle{{\partial V_{{\rm GS}}} \over {\partial ({\rm log}I_{{\rm DS}} )}} = \displaystyle{{\partial V_{{\rm GS}}} \over {\partial \psi _{\rm S}}} \cdot \displaystyle{{\partial \psi _{\rm S}} \over {\partial (logI_{{\rm DS}} )}} = \eta \cdot \upsilon, $$

which can be separated into the two contributions η and ν: The body factor η describes the coupling of the gate voltage V _GS to the band bending Ψ_S in the channel η = ∂V _GS/∂ψ_S = 1 + (C _s /C _ox ), with C _s and C _ox the semiconductor and gate oxide capacitances, respectively. The transport factor ν relates band bending Ψ_S to the source–drain current I _DS. In conventional semiconductor materials, the transport factor ν is intrinsically limited by the carrier statistics through the Boltzmann factor 10^{−Δ/k _B T} . Modulating the source–drain current through changes in the gate voltage entails the subthreshold slope as conversion factor $I_{{\rm DS}}\sim 10^{ - \Delta /k_{\rm B}T}\sim 10^{ - {\rm \psi }_{\rm S}/S}$ with subthreshold slope S ≥ (q/k _B T), where q is the elemental charge. In other words, a minimum requirement of ~60 mV change in Ψ _S is needed to modulate the source–drain current at room temperature by one order of magnitude: the famous 60 mV/decade limit of conventional FETs.^[ Reference Sze and Ng ^{83 ]} This further implies that for a suitably large distinction between the OFF-state and the ON-state current, the supply voltage must be several times this limit. Consequently, the Boltzmann factor constrains supply voltage scaling, and, therefore, the switching energy of a conventional FET.

Reducing the operating voltage and energy while maintaining performance, i.e., the switching delay and a specific ON/OFF ratio, transistors with a subthreshold slope <60 mV/decade, referred to as steep-slope transistors,^[ Reference Ionescu and Riel ^{81 ,} Reference Zhirnov and Cavin ^{84 ,} Reference Lu and Seabaugh ^{85 ]} is therefore demanded. To achieve a subthreshold slope S < 60 mV/decade with η < 1 the integration of a ferroelectric layer into the gate stack to augment the linear gate dielectric has been proposed and is currently being explored.^[ Reference Salahuddin and Datta ^{86 –} Reference Catalan, Jiménez and Gruverman ^{90 ]} The ferroelectric capacitor in series with the dielectric gate capacitor is designed to stabilize an otherwise energetically disfavored reversal pathway that entails an overall negative gate oxide capacitance effect, reversing the sign of C _ox and resulting in a body factor, η, smaller than unity.

Another approach to achieve subthreshold slopes smaller than 60 mV/decade is to harness transport phenomena to directly beat the Boltzmann limit, hence improving the transport factor ν. Within the realm of conventional semiconductors, interband tunneling across semiconductor heterojunction [tunnel field effect transistor (TFETs)]^[ Reference Pandey, Madan, Liu, Chobpattana, Barth, Rajamohanan, Hollander, Clark, Wang, Kim, Gundlach, Cheung, Suehle, Engel-Herbert, Stemmer and Datta ^{91 ]} and carrier multiplication via impact ionization^[ Reference Gopalakrishnan, Griffin and Plummer ^{92 ,} Reference Gopalakrishnan, Woo, Jungemann, Griffin and Plummer ^{93 ]} in metal oxide semiconductor structures (I-MOS) offer opportunities toward steep-slope switching. The I-MOS concept relies on impact ionization in an ungated intrinsic region between the source region and the channel to induce carrier amplification, which subsequently enables a larger change in current in comparison with conventional CMOS transistors for a given change in gate voltage. Scaling the supply voltage to reduce the energy per cycle, however, is not possible for I-MOS, which along with its disadvantages, namely dead region in the output region precluding inverter operation, reliability issues due to hot carrier formation potentially damaging the dielectric, renders this design unsuitable for high-performance low-power transistors. TFETs utilize a gate tunable tunnel junction in which the conduction and valence band alignment across the heterojunction is modulated, which results in steep turn-ON characteristics for carriers entering the channel from the source.^[ Reference Ionescu and Riel ^{81 ,} Reference Theis, Solomon, Dennard, Gaensslen, Rideout, Bassous, LeBlanc, Haensch, Banerjee, Richardson, Coleman, Chatterjee, Appenzeller, Lin, Knoch, Avouris, Salahuddin, Datta, Li, Kopp, Mannhart, Mannhart and Schlom ^{94 ]} Relying on tunneling phenomenon as injection mechanism limits the source–drain current I _DS in the ON state and thus its suitability for high-performance computing where high ON currents are required.

Nevertheless, the modulation of the band alignments at the heterojunction is a powerful concept, which suggests an alternative pathway to overcome the Boltzmann limit by employing materials exhibiting electronic phase transitions, as schematically shown in Fig. 7. In contrast to conventional semiconductors, where the electronic bands are only shifted with respect to the Fermi level by an electric field, carriers in correlated electron system can change their character from localized to itinerant and the entire band structure is altered in the vicinity of the Fermi level. Rather than a Boltzmann switch in case of conventional FETs, the concept is best coined as a “Landau switch” in the sense that switching characteristics is not governed by carrier statistics anymore, but rather by the free energy of the competing phases with different electronic ground states. Materials exhibiting strong correlations are therefore uniquely suited to overcome the intrinsic limit of conventional Boltzmann switches by harnessing electronic phase transition. The external perturbation triggering the electronic phase transformation between different ground states does not necessarily have to be an electric field, but could be strain, magnetic field, optical excitation, or other thermodynamic variables, such as temperature or pressure,^[ Reference Inoue and Rozenberg ^{95 ,} Reference Hwang, Iwasa, Kawasaki, Keimer, Nagaosa and Tokura ^{96 ]} all of those offering novel opportunities toward steep-slope-transistor functionalities.

Figure 7. A comparison of the properties of the currently employed Boltzmann switch as FETs (left), which switch state by changing the Fermi level E _F relative to the band structure unaltered by the electric field. The concept of a Landau switch is shown on the right, which is envisioned to operate by changing the DOS at the Fermi level by triggering an electronic phase transition through various external stimulations. Such functionality could overcome the 60 mV/dec. limit intrinsic to conventional FETs semiconductors, enabling low-power, high-performance computing with ultrascaled supply voltages.

The Mott-FET^[ Reference Newns, Misewich, Tsuei, Gupta, Scott and Schrott ^{97 –} Reference Kim, Chae, Youn, Maeng, Kim, Kang and Lim ^{100 ]} is a concept in which the semiconducting channel of a conventional transistor is replaced by a phase transition material, for example VO₂. The operating principles are as follows: the transistor is initially OFF when the phase transition material is in the high-resistance insulating state. When a sufficient gate field is applied accumulation of free carriers at the dielectric/Mott-material interface screens the Coulomb repulsion among the localized carriers in the insulating state of VO₂. Consequently, the electric field triggers an abrupt carrier delocalization inducing the low resistance metallic state. The abrupt liberation of all carriers previously localized to atomic sites enables the transistor to exhibit a sharp turn-on characteristics with S < 60 mV/decade. Attempts to reverse the phase transition by applying an electric field to recapture the insulating ground state and to turn the transistor OFF only had limited success. The external field cannot effectively penetrate into the channel material with metallic-like carrier concentration due to the short Angstrom-scale screening length.^[ Reference Martens, Jeong, Aetukuri, Rettner, Shukla, Freeman, Esfahani, Peeters, Topuria, Rice, Volodin, Douhard, Vandervorst, Samant, Datta and Parkin ^{101 ]} The switching has to be bidirectional. The combination of ultrathin films und large field strengths using an ionic liquid gate exhibited very slow switching characteristics,^[ Reference Nakano, Shibuya, Okuyama, Hatano, Ono, Kawasaki, Iwasa and Tokura ^{41 ,} Reference Zhou and Ramanathan ^{102 ]} hinting that unintentional ionic exchange reactions affecting the channel stoichiometry might be at play as well.^[ Reference Jeong, Aetukuri, Graf, Schladt, Samant and Parkin ^{42 ]} The straight forward strategy of a Mott-FET to simply replace the semiconductor material in the channel with a strongly correlated material exhibiting an MIT is thwarted by these roadblocks.

To nevertheless harness the abrupt changes of electronic phase transition materials (EPTMs) while circumventing the field effect requirement, the concept of the Hyper-FET has been proposed and demonstrated using VO₂.^[ Reference Shukla, Thathachary, Agrawal, Paik, Aziz, Schlom, Gupta, Engel-Herbert and Datta ^{103 ]} Rather than using the MIT material in the channel, the conventional FET is augmented by integrating VO₂ directly into the source of the conventional MOSFET, as schematically shown in Fig. 8(a). The device design of the Hyper-FET concept ideally integrates abrupt switching phenomenon of VO₂ with the superior transport characteristics of a semiconductor channel material, while circumventing the problem of bidirectional electric field switching of VO₂. The operation of the Hyper-FET can be described as follows. Initially, at gate voltage V _GS = 0 V, the transistor is in the OFF state with a small channel current I _DS that is further reduced by the high resistance state of VO₂. Increasing gate voltage as V _GS increases I _DS until a critical value is reached, which switches VO₂ into the metallic state, thereby lowering the series resistance and abruptly increasing I _DS; see Fig. 8(b). Similarly, as V _GS is reduced, the channel current decreases until a lower critical current is reached at which VO₂ transitions back into the high resistance state. The Hyper-FET exhibits a feedback enhanced gate field controlled abrupt switching characteristics due to the phase transition in VO₂ with the switching slope of 12 mV/decade at room temperature.^[ Reference Shukla, Thathachary, Agrawal, Paik, Aziz, Schlom, Gupta, Engel-Herbert and Datta ^{103 ]} The steep switching slope enables this hybrid phase-transition-FET to achieve higher ON current at matched OFF currents in comparison with conventional MOSFETs. The Hyper-FET primarily enables steep slope operation by achieving a transport factor ν = [∂ψ_S/∂(logI _DS)] less than 60 mV/decade at room temperature due to orders of magnitude abrupt change in resistance in the source, and, thus, providing a much larger current change ∂(logI _DS) for an infinitesimally small increment in the channel potential ∂ψ_S.

Figure 8. (a) Schematic representation of the Hyper-FET wherein an electronic PCM exhibiting an electronically induced abrupt change in resistivity (such as VO₂) is integrated in series with the source of a conventional MOSFET. (b) Transfer characteristics (I _DS–V _GS) of the VO₂-based Hyper-FET at room temperature. (c) Switching slope S of the Hyper-FET as a function of drain-to-source current I _DS demonstrating a sub-k _B T/q switching-slope (i.e., <60 mV/dec) at room temperature [panels (a) and (b) are adapted from Ref. Reference Shukla, Thathachary, Agrawal, Paik, Aziz, Schlom, Gupta, Engel-Herbert and Datta103].

The EPTM integrated into the source of the FET is not restricted to VO₂, the device design is scalable and has also been demonstrated using In_0.7Ga_0.3As quantum-well multi-channel FinFETs for n-MOS and complimentary p-MOS using a Ge quantum-well multi-channel FinFETs.^[ Reference Shukla, Thathachary, Agrawal, Paik, Aziz, Schlom, Gupta, Engel-Herbert and Datta ^{103 ]}

While proof-of-principle has been demonstrated, technological challenges to implement this device concept into mainstream technology remains to be addressed. First, it needs to be demonstrated that aggressive scaling of the Hyper-FET design to below 10 nm can be achieved with maintaining a sizeable, (i.e., few orders of magnitude) resistivity change across the MIT of VO₂; this then favorably reflects into transfer characteristics with much larger source–drain current for a fixed, small gate voltage modulation. Further, given that the MIT in VO₂ is affected by temperature, a potential sensitivity of transfer characteristics to the chip temperature when implemented in portable electronics, and more under heavy computation loads when large amounts of heat are being dissipated, are additional practical concerns to be addressed in the future. While VO₂ might not be an ideal materials solution for the application, the task for material scientists will be to find a better suited electronic PCM that allows for scaling and for a more seamless integration into the existing fabrication process. The concept of the Hyper-FET uniquely combines the abrupt collective carrier response from phase transition materials arising from strong electron correlation present in small band width material with the superior carrier transport characteristics in semiconductor materials stemming from the small carrier effective mass enabled by a large band width, while avoiding the need to directly induce the phase transition by an electric field. It therefore represents an ideal symbiosis of the two entirely different material classes of semiconductors and electronic PCMs.

Non-Boolean computing using charge coupled VO₂ oscillators

While in the Hyper-FET concept the MIT material has merely the role to augment, it dramatically improved the conventional FET characteristics dominated by the semiconductor channel by utilizing the abrupt resistivity change of VO₂. A completely different aspect of computation, namely associative computing, has been explored and can be potentially harnessed if the attention is focused back on the two-terminal VO₂ device as the active element and simplifying the function of the FET in series to that of a tunable resistor R _s, as shown in Fig. 9(a). The abrupt and hysteretic evolution of current passing through VO₂ as a function of applied voltage encompasses the fundamental instability of the first order phase transition, separating the insulating from the metallic state. In the case of a negligible series resistance R _S the insulator-to-metal transition (IMT), i.e., the transition from the insulating to the metal state of VO₂ is triggered at a critical field strength of E ₂ = V ₂/L, determined from the voltage drop V ₂ across VO₂ and the electrode distance L; see Fig. 9(b). The applied voltage has to then be reduced to E ₁ = V ₁/L to reverse the transition, i.e., going from the metallic back to the insulating state (MIT) to obtain the high resistance state again. Small series resistances will merely affect this hysteretic switching behavior. However, the abrupt reduction of the VO₂ resistance at the critical field E ₂ will redistribute the voltage drops across the series resistor R _S and the VO₂ device. Triggering the metallic state in VO₂ results in an instantaneous current increase and reduction of the voltage across the VO₂ device, thus acting as a negative differential resistance. For a series resistance above the critical value R _C the change in voltage drop across the VO₂ device is so high that the remaining field strength is less than the critical field E ₁ required to stabilize the metallic state. Under these conditions and even though the metallic state was nucleated at the critical field value E ₂, the high resistance state in VO₂ cannot be completely annihilated. Rather, the low electric field now favors the insulating state of VO₂, reversing the transition. This in turn increases the device resistance, and, with it the voltage drop across VO₂ device, again favoring the metallic state. The sufficiently large series resistance stabilizes VO₂ into a non-hysteretic phase coexistence regime, defined within the bounds of the critical field values E ₂ and E ₁, which are strongly temperature dependent; see Fig. 9(c). The waveform of the oscillation induced by a DC signal is shown in Fig. 9(d), which has been measured by probing the voltage drop V _R across the series resistor [Fig. 9(a)]. An increase in V _R is found upon decreasing the VO₂ resistance (IMT), while a reduction of V _R is associated with a resistance increase of VO₂ (MIT). The associated time constants for the IMT and the MIT of τ ₁ (0.35 µs) and τ ₂ (0.65 µs), respectively, were dominated by parasitic resistances and capacitances present in the simple experimental setup, and thus orders of magnitude larger than the intrinsic time constants of the VO₂ phase transition.^[ Reference Wen, Guo, Barnes, Lee, Walko, Schaller, Moyer, Misra, Li, Dufresne, Schlom, Gopalan and Freeland ^{104 ]} Reducing the series resistance R _S increased the frequency of the VO₂ oscillation, Fig. 9(e). A continuous change in the R _S can be achieved by replacing R _S with a transistor and adjusting its channel resistance using the gate voltage V _GS, Fig. 9(f).

Figure 9. (a) Schematic representation of the VO₂-based relaxation oscillator: a two-terminal VO₂ device in series with a resistor R _S. (b) Current versus voltage characteristics of the VO₂ device: no R _S (black), R _S < R _C (red load line 2), and with R _S > R _C (blue load line 1). While hysteretic transition and abrupt change in current is found for R _S < R _C, a non-hysteretic transition with oscillations is observed for R _S > R _C. (c) Temperature dependence of the critical electric-fields E ₂ and E ₁ for VO₂ devices grown on (001) TiO₂. An intermediate region of phase coexistence of both, the insulating and metallic phases was accessible, enabling the oscillatory behavior of VO₂. (d) Typical time-domain wave form of the VO₂-based relaxation oscillator. Inset shows the one oscillation period with the two time constants (τ ₁ = 0.35 and τ ₂ = 0.651 µs) associated with the IMT and the MIT. (e) Effect of input voltage V _in and series resistor R _S on the operating frequency of the oscillator. (f) Frequency versus gate voltage V _GS characteristics of a voltage-controlled VO₂ oscillator constructed by replacing R _S with a MOSFET; allowing to tune the series resistance using V _GS [panels (b), (c), (e), and (f) are adapted from Ref. Reference Shukla, Parihar, Freeman, Paik, Stone, Narayanan, Wen, Cai, Gopalan, Engel-Herbert, Schlom, Raychowdhury and Datta184, and (d) is adapted from Ref. Reference Shukla, Parihar, Cotter, Barth, Li, Chandramoorthy, Paik, Schlom, Narayanan, Raychowdhury and Datta110].

Coupling these highly scalable, inductor-free voltage controlled charge oscillator devices and investigating the synchronization dynamics of those coupled devices could open up opportunities to realize a simple hardware platform for a specific class of computing problems, referred to as associative computing.^[ Reference Türel, Lee, Ma and Likharev ^{105 ]} Compared with sequential algorithms developed for conventional CMOS hardware the synchronization dynamics of coupled oscillators, an inherently parallel process, could be potentially used to solve computationally hard problems more efficiently. Such tasks range from combinatorial optimization problems like graph coloring^[ Reference Wu ^{106 ]} or the traveling salesman problem,^[ Reference Lawler, Lenstra, Rinnooy Kan and Shmoys ^{107 ]} and include associative computating problems related to image and pattern recognition,^[ Reference Hölzel and Krischer ^{108 –} Reference Shukla, Parihar, Cotter, Barth, Li, Chandramoorthy, Paik, Schlom, Narayanan, Raychowdhury and Datta ^{110 ]} as well as scene segmentation and saliency detection problems using the concept of oscillatory locally excitatory globally inhibitory networks^[ Reference Wang and Terman ^{111 ]} required in computer vision systems.

To investigate the coupling behavior of VO₂ oscillators, two devices were stabilized at different frequencies of 48.43 and 37.27 kHz by choosing different values of R _S (38 and 47 kΩ). Figure 10(a) schematically shows how both elements were linked using a capacitor (C _C = 680 pF) as the coupling element. The different operating frequencies of each oscillator prior to coupling shown in Fig. 10(b) indicated that the oscillators were completely independent. After pairing them with the coupling capacitor, the oscillators synchronized to a common resonant frequency. A narrowing of the spectral line width further corroborated the locking of the two oscillators and the presence of a mutual feedback stabilizing the synchronized oscillator pair against noise. Figure 10(c) shows the time evolution of the coupled resistance states of both oscillators, 1 and 2. Tracing the trajectory in the phase diagram by using the voltage drops V _R,1 and V _R,2 across both series resistances R _S,1 and R _S,2 allowed one to determine the metallic-to-insulating phase ratio in the individual devices. As device-1 transitioned from the insulating toward the metallic phase, device-2 changed from the metallic to the insulating state [Section  “Strong electron correlations in V-based oxides” of the phase space trajectory in Fig. 10(c)]. Conversely, when device-1 was in a more metallic and device-2 was in a more insulating state, charge was exchanged through the coupling capacitance and moved from device-1 to device-2, represented by the Section  “Ternary oxide vanadates” of the trajectory in Fig. 10(c).

Figure 10. (a) Schematic of the capacitively coupled VO₂ oscillators. (b) Spectral characteristics of the oscillators before and after capacitive coupling. The individual oscillators synchronize to a common resonant frequency when coupled. (c) Simulated phase space trajectory of the coupled oscillators. The evolution of phase composition in the coupled VO₂ devices is determined from V _R,1 and V _R,2. Coupled oscillators predominantly show out of phase locking with one oscillator in the metallic state, while the other is in the insulating state. (d) Schematic representation of a pair of voltage tunable coupled VO₂ oscillators wherein R _S is replaced by a transistor with gate voltage tunable channel resistance. (e) Phase space trajectory of the coupled VO₂ oscillators as function of gate voltage difference V _GS,2–V _GS,1. As the degree of similarity between the inputs decreases V _GS2–V _GS1 becomes larger (inputs are similar when V _GS,2–V _GS,1 = 0) and the oscillators exhibit increased in-phase locking behavior (shaded area in the V _R,1–V _R,2 phase space). (f) Simulated time average XOR output of the coupled oscillators, and (g) L _1/2 distance norm as a function of V _GS,1 and V _GS,2. The qualitative match between the XOR output and the L _1/2 distance norm indicates that the XOR output of the coupled oscillators resembles the nonlinear distance norm of the Euclidean space [panels (b) and (c) are adapted from Ref. Reference Shukla, Parihar, Freeman, Paik, Stone, Narayanan, Wen, Cai, Gopalan, Engel-Herbert, Schlom, Raychowdhury and Datta184, and (e)–(g) are adapted from Reference Shukla, Parihar, Cotter, Barth, Li, Chandramoorthy, Paik, Schlom, Narayanan, Raychowdhury and Datta110].

The precise shape of phase space trajectories of the coupled oscillator pair has been found strongly dependent on the difference of the series resistances R _S,1 and R _S,2. Therefore, as shown in Fig. 10(d), replacing the resistors by conventional MOSFETs and using the gate voltages V _GS,1 and V _GS,2 as input parameter, their degree of match is decoded into a specific shape of the trajectory in the V _R,1–V _R,2 phase space. While for large differences in the input voltages V _GS,1 and V _GS,2 no stable trajectory was formed—the oscillator pair did not sychronize—smaller differences ΔV = V _GS,2–V _GS,1 dramatically altered the trajectory, as schematically depicted in Fig. 10(e). To analyze these changes and form a simple output value from the coupled oscillator pair an average exclusive-OR (XOR) measure applied to V _R,1 and V _R,2 was used; a time-equivalent metric to quantify how long the coupled oscillators remained in the gray-shaded area in phase space during an oscillation period, as indicated in Fig. 10(e). While the XOR values were small for ΔV ≈ 0, the nonlinear increase with ΔV shown in Fig. 10(f) closely resembled the Euclidean norm L _1/2 = (X ₁ ² + X ₂ ²)^1/2 shown in Fig. 10(g).

This sensitivity of the coupled oscillators’ phase space orbit to the difference in the input parameters forms the basic computational hardware building block of the coupled oscillators. A non-linear distance norm^[ Reference Parihar, Shukla, Datta and Raychowdhury ^{112 ]} that can be used to determine how closely the two analog voltage input values resemble each other is realized by the simple hardware building block of capacitively coupled two-terminal electronic PCM, allowing for fast and energy-efficient computation of tailored non-linear degree-of-match-type analysis.^[ Reference Shukla, Parihar, Cotter, Barth, Li, Chandramoorthy, Paik, Schlom, Narayanan, Raychowdhury and Datta ^{110 ,} Reference Parihar, Shukla, Datta and Raychowdhury ^{112 ]} This task will play a critical role in the paradigm shift from precise computing on small data sets to approximate computing on large data sets, which has already occurred in future application areas, such as machine learning, augmented reality, and data base search.^[ Reference Watts and Strogatz ^{113 ]} A dramatically increasing demand to solve this task elegantly in a fast, computationally inexpensive, and thus, energetically efficient way, is projected for data analysis generated from massive sensor arrays in the dawning IOT (internet-of-things) era. Two-terminal devices made from electronic PCM exhibiting current-controlled resistive switching have been identified as key in neuristors^[ Reference Pickett, Medeiros-Ribeiro and Williams ^{114 ]} to mimic biological functionality of neural networks using solid-state electronic circuitry, a further evidence of the critical role of these types of materials to meet future computation demands.

VO₂ as RF switch

Currently state-of-the-art switches can be categorized into MEMS and solid-state devices, both of which enable switching between a high-impedance (OFF) state and a low-impedance (ON) state for RF frequency signals. One of the key performance parameter of an RF switch is the cut-off frequency, f _CO, at which the ratio of impedance of the ON state and OFF state is unity, thus defining the maximum operating frequency

$$f_{{\rm CO}} = (2\pi R_{{\rm ON}} C_{{\rm OFF}} )^{ - 1}, $$

with R _ON is the ON state resistance, and C _OFF is the OFF state capacitance.While solid-state semiconductor-based RF switches are limited to f _CO at least 2–3 orders lower than MEMS switches due to their comparably high R _ON and high C _OFF, their low drive voltage, high switching speed, and excellent reliability due to no moving mechanical parts render them a highly competitive solution. Near zero power consumption, high electrical isolation in the OFF state, very low insertion losses, high cut-off frequencies, and highly linear performance make MEMS switches attractive, compensating for their low switching speeds, high voltage, or current drive needed to actuate the switch despite their higher fabrication costs and lower reliability. The ideal RF switch would be a combination of both approaches, a simple solid-state design exhibiting a fast-switching characteristics along with a MEMS-like high frequency of operation and low insertion loss.

One approach to realize such an RF switch is to harness the change in resistivity across the MIT in TMOs such as VO₂. Demonstrations and benchmarking of VO₂-based RF switches have been done using films grown by pulse laser deposited (PLD)^[ Reference Dumas-Bouchiat, Champeaux, Catherinot, Crunteanu and Blondy ^{115 ]} and sputtering.^[ Reference Ha, Zhou, Fisher, Ramanathan and Treadway ^{116 ]} While these deposition techniques produce films with varying degree of crystallinity and strain, a relatively low R _OFF/R _ON ratio and increase in device capacitance due to grain boundaries causing undesirable parasitic contributions and reducing C _OFF are expected to detrimentally affect device performance. For the best performance single-crystalline VO₂ films with a large change in the resistivity across the MIT grown on a low loss substrate using a scalable deposition technique is desired. Figure 11(a) shows a false-colored secondary electron micrograph of a solid-state RF switch. A ground-signal-ground (GSG) pad structure consisting of 24 parallel two-terminal VO₂ devices with 1 µm width and 100 nm length was fabricated from a 30-nm-thick single-crystalline VO₂ film with resistivity ratios larger than 10⁴ grown on sapphire using a combinatorial growth approach.^[ Reference Zhang, Zhang, Mukherjee, Zheng, Haislmaier, Alem and Engel-Herbert ^{64 ]} Similar to the Hyper-FET concept, the transition to the low impedance metallic state was triggered by applying a DC current. A critical current of 5 mA was needed to destabilize the high impedance state. An attenuation change due to the MIT in VO₂ for a 1 GHz signal from 35 dB in the OFF state (I _DC = 0 mA) to 0.55 dB in the ON state (I _DC = 25 mA) was measured. Figure 11(b) shows the switching response of the device for a 50 MHz RF signal and a 250 ns pulse of 2 V amplitude to activate the switch. A fast turn-on characteristic of 25 ns was found along with an excellent endurance without observing device breakdowns after cycling between ON and OFF states for more than 10⁸ times, shown in Fig. 11(c).

Figure 11. (a) False-colored scanning electron micrograph (SEM) of a VO₂-based solid-state RF switch, a two-terminal GSG structure made up of 24 parallel channels, each with a width of 1 µm and length of 100 nm. (b) Turn ON characteristics of the VO₂-based RF switch with a DC activating pulse (black) and 50 MHz RF signal (green). The output pulse (red) shows that the switch can be turned ON in <25 ns. (c) Endurance test of the solid-state VO₂ RF switch. Stable R _ON/R _OFF ratio (normalized to the first cycle) is observed for close to one billion cycles. (d) Performance benchmarking of various RF switch technologies, comparing the typical OFF-state capacitance (C _OFF) at a specified ON-state resistance (R _ON);^[ Reference Howell, Stewart, Freitag, Parke, Nechay, Harlan, King, Gupta, Hartman, Borodulin, Snook, Wathuthanthri, Ralston, ReNaldo and Henry ^{119 –} Reference Mennai, Bessaudou, Cosset, Guines, Blondy and Crunteanu ^{126 ]} the color scale represents the cut-off frequency f _co. PCMs and EPTMs, such as VO₂, ideally combine the superior performance of MEMS with the reliable and fast switching characteristics of solid-state switches [panels (a)–(d) are adapted from Ref. Reference Madan, Zhang, Jerry, Mukherjee, Alem, Engel-Herbert and Datta118].

These testaments of fast response and reliability of the VO₂-based solid-state RF switch are ideally complemented by a high cut-off frequency of 26.5 THz, enabled by the low insertion loss of metallic VO₂ in the ON state and a large OFF state capacitance due to excellent microstructural properties of the grown VO₂ films. Compared with a state-of-the-art GaN based solid-state RF switch using a superlattice structure with a castellated three-dimensional (3D) gate^[ Reference Nechay, Howell, Stewart, Parke, Freitag, Cramer, King, Gupta, Hartman, Borodulin, Snook, Wathuthanthri, Renaldo and Henry ^{117 ]} a 10 dB improvement in the switching ratios for a 20 GHz signal highlights the potential of VO₂-based RF switches for high-frequency signal operation, outperforming conventional solid-state FET designs, and III–V-based high-electron-mobility transistors (HEMTs).^[ Reference Madan, Zhang, Jerry, Mukherjee, Alem, Engel-Herbert and Datta ^{118 ]} Figure 11(d) compiles cut-off frequencies of several MEMs and solid-state RF switching technologies with PCM and VO₂.^[ Reference Howell, Stewart, Freitag, Parke, Nechay, Harlan, King, Gupta, Hartman, Borodulin, Snook, Wathuthanthri, Ralston, ReNaldo and Henry ^{119 –} Reference Mennai, Bessaudou, Cosset, Guines, Blondy and Crunteanu ^{126 ]} While VO₂ devices were also operated using local heating, which revealed a higher cut-off frequency of f _CO = 44 THz, the turn-on characteristics is expected to be not as competitive due to the necessity to integrate an in-line resistive heater. While the technology for integrated local heater elements have been developed and demonstrated for PCMs such as GeTe,^[ Reference El-Hinnawy, Borodulin, Jones, Wagner, King, John Mason, Bain, Paramesh, Howell, Lee and Young ^{122 ]} which also suffer from the requirement of a continuous DC power during the ON-state, longer switching times and isolation challenges due to RF leakage through the resistive heater in the OFF state are avertible complications of this design. Thus, EPTMs in general and VO₂ on sapphire in particular provide a viable path toward realization of high-performance RF switches, ideally combining the MEMS-like high frequency of operation with reliability and fast switching characteristics of a solid-state design, harnessing the favorable properties of a MIT in this application.

Correlation effects in d ¹-filled SrVO₃ and CaVO₃

Both SrVO₃ and CaVO₃ are correlated metals with a nominal 3d ¹ configuration. The strong correlation properties are seen by a reduced band width compared with density functional theory calculations, as measured by angle-resolved photoemission spectroscopy.^[ Reference Yoshida, Tanaka, Yagi, Ino, Eisaki, Fujimori and Shen ^{134 ,} Reference Yoshida, Kobayashi, Yoshimatsu, Kumigashira and Fujimori ^{135 ]} As schematically shown in Fig. 2, the spectral weight transfer feature from the coherent quasi-particle peak to incoherent side bands has been experimentally observed in photoemission experiments,^[ Reference Fujimori, Hase, Namatame, Fujishima, Tokura, Takegahara and de Groot ^{136 –} Reference Mossanek, Abbate, Yoshida, Fujimori, Yoshida, Shirakawa, Eisaki, Kohno and Vicentin ^{138 ]} a precursor to a Mott-insulating state with a lower and upper Hubbard band separated by a sizeable Mott gap. The Ca²⁺ ions have a smaller ionic radii (1.34 Å) than Sr²⁺ ions (1.44 Å) driving the structural distortion from the a ⁰ a ⁰ a ⁰ cubic structure of SrVO₃ (with a = 3.842 Å)^[ Reference Goodenough, Longo, Hellwege and Hellwege ^{139 ]} to the a ⁻ a ⁻ c ⁺ orthorhombic structure of CaVO₃ (with orthorhombic lattice parameters a = 5.326, b = 5.352, c = 7.547 Å, and pseudocubic lattice constant of a = 3.775 Å). The orthorhombic distortion reduces the V–O–V bond angle from the ideal 180° in SrVO₃ to ~160° in CaVO₃, accompanied with a reduced orbital overlap between neighboring V 3d orbitals mediated by oxygen 2p orbitals and therefore resulting in a decreased bandwidth (W) by a factor of ~cos²(θ), i.e., about 6%.^[ Reference Yoshida, Hashimoto, Takizawa, Fujimori, Kubota, Ono and Eisaki ^{140 ,} Reference Pavarini, Biermann, Poteryaev, Lichtenstein, Georges and Andersen ^{141 ]} The Sr _x Ca_1−x VO₃ solid solution system has been investigated to explore how the structural distortion couples to band width, and thus correlation effects, since this compound interpolates between the a ⁰ a ⁰ a ⁰ and a ⁻ a ⁻ c ⁺ structures while maintaining the 3d ¹ electronic configuration. Furthermore, the V 3d bands were well separated from O 2p band, minimizing complex hybridization and thus charge transfer effects. The spectral weight transfer of ~2 eV below the Fermi level was determined from UPS [ultraviolet (UV) photoemission spectroscopy] measurement by systematically decreasing the composition of Sr (x) in the polycrystalline Sr _x Ca_1−x VO₃ system.^[ Reference Inoue, Hase, Aiura, Fujimori, Haruyama, Maruyama and Nishihara ^{142 ]} However, despite the large spectral transfer that confirmed photoemission results, only a moderate increase of m*/m _b from 2.9 to 3.1 was observed when going from SrVO₃ to CaVO₃, as determined from magnetic susceptibility measurement,^[ Reference Makino ^{143 ]} which suggests minute changes in the carrier renormalization Z _k through enhancement of the electron correlation. A more detailed photoemission study using a tunable UV laser source in vacuum where samples were prepared by fracturing in situ to ensure a pristine surface confirmed the suppression of spectral weight near the Fermi edge (~50%) for CaVO₃ single-crystal samples compared with SrVO₃.^[ Reference Eguchi, Kiss, Tsuda, Shimojima, Mizokami, Yokoya, Chainani, Shin, Inoue, Togashi, Watanabe, Zhang, Chen, Arita, Shimada, Namatame and Taniguchi ^{144 ]} The differences between SrVO₃ and CaVO₃ being relatively small inside the bulk changed when shifting from bulk to surface sensitive characterization conditions, which was attributed to the lifting of the t _2g orbital degeneracy on the surface by breaking the orbital degeneracy.^[ Reference Yoshida, Tanaka, Yagi, Ino, Eisaki, Fujimori and Shen ^{134 ,} Reference Eguchi, Kiss, Tsuda, Shimojima, Mizokami, Yokoya, Chainani, Shin, Inoue, Togashi, Watanabe, Zhang, Chen, Arita, Shimada, Namatame and Taniguchi ^{144 ]} Despite the considerably enhanced correlation effect on the surface, which is more pronounced for CaVO₃, it is generally accepted that no MIT can be observed in the bulk-like form of SrVO₃ and CaVO₃ at all temperatures.^[ Reference Zhang, Zhou, Guo, Zhao, Barnes, Zhang, Eaton, Zheng, Brahlek, Haneef, Podraza, Chan, Gopalan, Rabe and Engel-Herbert ^{133 ]} This may stem from the fact that the distortion away from a 180° bond angle of is partially compensated by a contraction in the lattice parameter, as well as the less sensitive nature of the orbital overlap of the t _2g orbitals compared with the e _g orbitals for materials such as rare-earth nickelates. Other means to engineer the structure in materials accessible in epitaxial thin films, namely dimensional confinement and epitaxial strain, can be used to further enhance correlations effects in d ¹ vanadates to drive these systems closer to their Mott-insulator phase.

Thin-film growth of AVO₃ perovskites

As already discussed in section  “MIT in binary vanadium compounds: VO₂ and V₂O₃” for the growth of binary vanadium oxides there are many techniques to deposit epitaxial thin films. Despite the challenge in binary oxides to stabilize vanadium in a particular oxidation state by ensuring the incorporation of vanadium and oxygen in a stoichiometric ratio, the growth of ternary vanadates presents additional challenges. In particular, an extra level of control is needed to achieve a 1:1 cation ratio, i.e., the cation occupying the A-site to V at the B-site. Employing target ablation techniques, such as PLD,^[ Reference Sheets, Mercey and Prellier ^{145 –} Reference He, Sanders, Gray, Wong, Mehta and Suzuki ^{152 ]} sputtering, ion beam and (pulsed) electron beam evaporation^[ Reference Ishiwara and Jyokyu ^{153 –} Reference Gu, Laverock, Chen, Smith, Wolf and Lu ^{155 ]} this problem is approached by using cation stoichiometric targets and adjusting oxygen partial pressure and substrate temperature during deposition. While the film's composition is mainly set by the target's composition, achieving stoichiometric transfer from the target to the substrate has been proved difficult. The high-energy bombardment of species ablated from the target impinging on the film with large kinetic energies can cause resputtering of more volatile components or cause point defect formation from high-energy impacts of ablated species. In fact, the majority of AVO₃ films studied in the literature have been grown by PLD. Although film deposition can be controlled down to the monolayer (ML) level, therefore enabling studies of dimensional controlled MITs, thicker AVO₃ films were found to have low residual resistivity ratios (RRR) of around ~2,^[ Reference Sheets, Mercey and Prellier ^{145 ,} Reference Kim, Kim, Kang, Noh, Lee, Lee and Lee ^{148 ,} Reference Koinuma, Yoshimoto, Nagata and Tsukahara ^{156 ]} indicating that electron transport is limited by defect scattering, being of the same order of magnitude than phonon scattering at room temperature. Therefore disorder effects are dominant, preventing to study the intrinsic electronic properties of AVO₃.

In contrast, molecular beam epitaxy uses low-energy thermal evaporation to supply individual elements with low incident energies limited to thermal agitation when evaporated from the effusion cell. They are typically of the order of 0.1 eV therefore limiting the formation of unintentional defects in the film upon impact on the growth front. However, unlike in the case of MBE growth of compound semiconductors, such as in the archetypical case of GaAs, where the stoichiometry is self-regulated due to the volatility of As,^[ Reference Tsao ^{157 ]} AVO₃ compounds do not contain a volatile component and cannot be grown in a self-regulated manner. Therefore film stoichiometry is limited by the precision of flux calibration and the stability of fluxes during film growth, typically about 1%. Recently, the hybrid MBE (hMBE) growth scheme^[ Reference Jalan, Engel-Herbert, Wright and Stemmer ^{158 ,} Reference Engel-Herbert ^{159 ]} has been expanded to vanadates by employing the metal-organic precursor vanadium oxytriisopropoxide (VTIP) to overcome this challenge. Here, the elements occupying the A-site effused from conventional thermal evaporation sources are supplied together with a flux of highly volatile VTIP molecule, which are directed at the substrate using a gas injector. The low defect density achieved in SrVO₃ films grown of hMBE films have resulted in RRR values larger than 220, with a low temperature resistivity ~0.1 µΩ cm, and a room temperature resistivity of ~20 µΩ cm.^[ Reference Moyer, Eaton and Engel-Herbert ^{160 ]} An adsorption controlled growth window was accessed for SrVO₃,^[ Reference Brahlek, Zhang, Eaton, Zhang and Engel-Herbert ^{161 ]} CaVO₃,^[ Reference Eaton, Zhang, Brahlek, Lapano and Engel-Herbert ^{162 ]} and LaVO₃,^[ Reference Zhang, Dedon, Martin and Engel-Herbert ^{163 ,} Reference Zhang, Brahlek, Ji, Lei, Lapano, Freeland, Gopalan and Engel-Herbert ^{164 ]} and recently even for the quaternary compound La_1−x Sr _x VO₃,^[ Reference Brahlek, Zhang, Zhang, Lapano, Dedon, Martin and Engel-Herbert ^{165 ]} in which defect concentrations were found minimal and physical properties were independent of growth conditions, offering the possibility of reliable, and scalable growth.

A route to enhanced correlation effects: thickness-driven MIT

Driving a thin film from a correlated metal into insulating phases is of great interest for novel device functionalities that are based on electronic phase transition. Even though electron correlation strength existing in bulk SrVO₃ and CaVO₃ are not sufficient to induce an MIT, lowering the dimensionality breaks the orbital degeneracy and can enhance the correlations strength, which may be sufficient to trigger an MIT.^[ Reference Gu, Wolf and Lu ^{154 ,} Reference Gu, Laverock, Chen, Smith, Wolf and Lu ^{155 ,} Reference Yoshimatsu, Horiba, Kumigashira, Yoshida, Fujimori and Oshima ^{166 ,} Reference Yoshimatsu, Okabe, Kumigashira, Okamoto, Aizaki, Fujimori and Oshima ^{167 ]} Normally, three V 3d t _2g orbitals (d _xy , d_xz, d_yz ) are degenerate in the bulk case. As thickness is reduced, bonding normal to the surface is interrupted and orbitals with projection normal to the surface shift to higher energy and become gradually depopulated. This orbital selective quantum confinement is unique to TMOs and density functional theory + dynamical mean-field theory calculation have shown that even though two layers of SrVO₃ on SrTiO₃ substrate were insulating, they are at the very verge of an MIT and sensitive to external parameters, such as pressure, temperature or electrical field.^[ Reference Zhong, Wallerberger, Tomczak, Taranto, Parragh, Toschi, Sangiovanni and Held ^{168 ]}

Motivated by these predictions Yoshimatsu et al. probed ultrathin SrVO₃ films grown on Nb:SrTiO₃ and provided the spectroscopic evidence for a thickness-driven MIT.^[ Reference Yoshimatsu, Okabe, Kumigashira, Okamoto, Aizaki, Fujimori and Oshima ^{167 ]} Figure 13(a) shows the evolution of the DOS measured from photoemission spectra as a function of SrVO₃ thickness in unit cells. The spectra have been symmetrized with respect to E _F, which enables tracking the energy gap as the thickness is reduced. In the ultrathin limit, i.e., a film thickness between 1 and 5 ML a pseudogap (PG) was present, the DOS at the Fermi level was suppressed and transferred into the incoherent side peak that emerged at a binding energy of ~1.6 eV. The spectral weight transfer with decreasing thickness along with the energy gap formation was interpreted as resulting of an increased correlation strength. These spectroscopic data suggested that a Mott-insulator phase emerged out of the correlated metal phase in the ultrathin limit. The trends in the position of coherent quasi-particle and incoherent side peak as well as intensity of the coherent quasi-particle intensity with thickness are summarized in Fig. 13(b). While the position of the side peaks remained unaltered with thickness, suggesting a constant Coulomb repulsion energy U, the coherent quasi-particle peak shifts away from the Fermi level in the PG region along with an intensity reduction.^[ Reference Yoshimatsu, Okabe, Kumigashira, Okamoto, Aizaki, Fujimori and Oshima ^{167 ]} These spectral features have been confirmed by transport measurements performed on SrTiO₃–SrVO₃–SrTiO₃ structures grown on (001) (La_0.3Sr_0.7) (Al_0.65Ta_0.35)O₃ by hybrid MBE; see Figs. 13(c) and 13(d). Here the 15-nm-thick SrTiO₃ buffer and cap layer were kept constant, which imposed the dimensional confinement over the SrVO₃ layer with thicknesses of a few perovskite unit cells. For large SrVO₃ thicknesses the conductivity monotonically decreased with increasing temperature, which is characteristic of metallic conduction. While for a SrVO₃ thickness of 8 ML the metallic behavior was still dominant, despite the fact the electrical conductivity was reduced due to an enhanced surface scattering effect in the ultrathin limit. The transport characteristics of the 3-ML-thick SrVO₃ film was dramatically different. Here, the temperature dependent conductivity had a positive slope indicating the formation of a fully gapped insulating phase. Carrier concentration extracted from Hall effect measurements are shown in Fig. 13(d) and revealed a 100× reduction in the bulk carrier density of the 3-ML-thick SrVO₃ layer compared with the samples with metallic conduction. The orders-of-magnitude reduction in the number of delocalized carriers is temperature independent, consistent with the picture of a complete DOS transfer away from E _F. The large nominal sheet carrier concentration of ~2 × 10¹⁵ cm⁻², expected for a 3-ML-thick SrVO₃, would require a similar defect concentration to trap nearly all delocalized carriers, an unlikely scenario given the perfection of the material demonstrated by hybrid MBE,^[ Reference Moyer, Eaton and Engel-Herbert ^{160 ,} Reference Son, Moetakef, Jalan, Bierwagen, Wright, Engel-Herbert and Stemmer ^{169 ]} thus precluding disorder-related extrinsic effects and supporting the spectroscopic results.^[ Reference Yoshimatsu, Okabe, Kumigashira, Okamoto, Aizaki, Fujimori and Oshima ^{170 ]}

Figure 13. (a) Photoemission spectra from SrVO₃ thin films with thickness indicated in ML. (b) Intensity (blue circles) and position (green triangles) of the coherent quasi-particle peak and the incoherent peak (red squares) relative to the Fermi level E _F, extracted from the photoemission data shown in (a), revealing a transition from the SrVO₃ metal phase at a large layer thickness (>8 ML) to a gapped insulating phase (MI) in the ultrathin limit between 3 and 1 ML. (c) Temperature-dependent conductivity of SrTiO₃–SrVO₃–SrTiO₃ heterostructures with varying SrVO₃ layer thickness. (d) Free-carrier density n of samples measured in (c) as a function of SrVO₃ layer thickness with a two orders of magnitude reduction for the 3-ML-thick SrVO₃, evidence for a pronounced carrier localization effect in the ultrathin limit of SrVO₃ [panel (a) and (b) are reprinted from Ref. Reference Yoshimatsu, Okabe, Kumigashira, Okamoto, Aizaki, Fujimori and Oshima167. Copyrighted by the American Physical Society].

Correlated metals as TCs

Although bulk SrVO₃ and CaVO₃ are far from the Mott transition and the Mott gap can only be opened in the ultrathin limit, the strong electron–electron correlation alters the electrical and optical properties in ways that makes them interesting for the application as thin-film TC materials.^[ Reference Zhang, Zhou, Guo, Zhao, Barnes, Zhang, Eaton, Zheng, Brahlek, Haneef, Podraza, Chan, Gopalan, Rabe and Engel-Herbert ^{133 ]} TC materials are a key component for virtually any modern electro-optical devices, from flat-panel screens in smart phones and televisions, to photovoltaic devices. The properties of high optical transparency and high electrical conductivity are mutually exclusive—the large amount of free carriers required to effectively conduct electricity will also cause to reflect the visible light, which presents a distinct challenge at a fundamental materials design level.

The two effects relevant to optical transmission are reflection at low energies, caused by the free carrier response to light, and absorption at higher energies due to interband transitions. Minimizing these effects are the cornerstones for the design strategy of TCs. This has been achieved in the past by choosing a wide band gap semiconductors to avoid interband transitions in the visible spectrum, and to degenerately dope it to make it sufficiently conducting. While the low-energy cut-off for high transmission is determined by the reflection edge due to the free carrier response, quantified by the screened plasma frequency, a sufficiently large band gap ensured that interband transitions occurred at photon energies above the visible spectrum, opening a transmission window over the entire visible range of photon energies from 1.75 to 3.25 eV. The trade-off between the mutually exclusive properties of optical transparency and electrical conductivity can be best seen by comparing the screened plasma frequency $\omega _{\rm p} = (q/\sqrt {\varepsilon _0 \varepsilon _{\rm r}} )\sqrt {n/m*} $ where q is the electron charge, ε ₀ and ε _r are the vacuum and relative permittivity, respectively, n is the charge carrier concentration, and m* is the effective carrier mass, to the conductivity σ = q ² τ _s (n/m*) where τ _s is the mean scattering time of the free carriers. Doping the semiconductor increases n, which increases σ and simultaneously pushes the reduced plasma energy E _p = ħω _p toward the onset of the visible spectrum. For the current work-horse material, Sn-doped indium oxide (ITO), electrical conductivities up to ~1 × 10⁴ S/cm were achieved with E _p ≈ 0.77 eV. This is well below the low-energy onset of the visible spectrum thus leaving room to further increase conductivity, which was not possible because the maximum carrier concentration of ~3 × 10²¹/cm³ in ITO marks the solubility limit of dopants. In addition, pronounced charged impurity scattering from the dopant atoms occurred at these dopant concentrations, detrimentally affecting the room temperature carrier mobility reducing the electrical conductivity.^[ Reference Ellmer ^{171 ]} For the application as a TC both phenomena mark the intrinsic limits of degenerately doped wide band semiconductors in general, and ITO in particular.

This fundamental limit can be overcome when focusing the attention to materials with a sizeable electron correlation. The effective carrier mass of materials with negligible electron–electron interaction, such as conventional semiconductors with bands derived from s- and p-orbitals, is solely determined by the band effective mass. In contrast, materials exhibiting strong electron–electron correlation provide an additional design DOF: modulation of carrier effective mass m* through electron correlation. Therefore, ω _p and σ can not only be modified by changing the carrier concentration n, as in the case of conventional semiconductors, but also by engineering the correlation strength. In particular, materials with a metal-like high-carrier concentration and strong correlation resulting in a renormalized and thus heavier electron effective mass can meet the requirements of a sufficiently small ω _p despite a large σ. The key factor to balance conductivity and plasma frequency is n/m*, but rather than finding semiconductors with a small effective mass m* to compensate for the limited n, in case of correlated metals the high-carrier concentration n is compensated by a large carrier effective mass m*. While the high carrier concentration renders normal metals, such as aluminum, copper, gold, and silver unsuitable as TCs, exhibiting reduced plasma frequencies within or even beyond the visible range, the reduced plasma energy for a correlated metal with large carrier effective mass can be below the visible range, yet higher than the plasma energy of ITO. As shown in Fig. 14(a), correlated metals SrVO₃ and CaVO₃ with a carrier concentration of ~2 × 10²²/cm³ have proven this hypothesis with an experimentally determined screened plasma frequencies as low as 1.33 and 1.29 eV, well below the critical value of 1.75 eV and larger than E _p of ITO of 0.77 eV. A one order of magnitude higher electrical conductivity of SrVO₃ and CaVO₃ compared with ITO are testaments of the tremendous potential of correlated metals to push the carrier reflection edge closer to the 1.75 eV.

Figure 14. (a) Optimization of electrical conductivity σ of correlated metals while keeping reflection edge, represented by the screened plasma frequency ω _p, below the visible spectrum, indicated by the rainbow. (b) The electrical conductivity as a function of film thickness of Ag, Au, polycrystalline ITO, pulsed laser deposition (PLD)-grown ITO and epi-ITO, SrVO₃, and CaVO₃ (adapted from Ref. Reference Zhang, Zhou, Guo, Zhao, Barnes, Zhang, Eaton, Zheng, Brahlek, Haneef, Podraza, Chan, Gopalan, Rabe and Engel-Herbert133).

For a material to be a promising TC material, a low optical absorption is mandatory. The band structure of the vanadates are favorable because the V3d band is energetically isolated from the higher lying V3d e _g bands and the lower lying valence bands derived from O 2p. In case of SrVO₃ a sizeable interband transition from O 2p to V 3d t _2g near the UV edge is present, while other interband transitions within the visible spectrum are largely suppressed, resulting in a compromised optical transmissivity compared with ITO. Nevertheless, the combination of very high electrical conductivities and acceptable optical transmission in the visible spectrum makes vanadates ideal TC candidates with competitive figure of merits (FOMs) on par with ITO, as shown in Fig. 15(a).

Figure 15. (a) Photographs from left to right are a bare (La_0.3Sr_0.7)(Al_0.65Ta_0.35)O₃ (LSAT) substrate, 4 nm SrVO₃ on LSAT, 12 nm SrVO₃ on LSAT, 12 nm CaVO₃ on SrLaAlO₄ (SLAO) substrate, 4 nm CaVO₃ on LSAO and a bare LSAO substrates on colored background, respectively. (b) FOM Φ_TC = T ¹⁰/R _S for free-standing transparent conducting film as a function of thickness with average transmittance in the visible spectrum and sheet resistance R _S (adapted from Ref. Reference Zhang, Zhou, Guo, Zhao, Barnes, Zhang, Eaton, Zheng, Brahlek, Haneef, Podraza, Chan, Gopalan, Rabe and Engel-Herbert133).

The film thickness scaling is another important aspect of a TC material in real-world applications: a decrease of electrical conductivity due to an enhanced film surface scattering occurs when film thickness approaches electron mean free path (EMFP) Γ = ℏ(3π ²)^1/3(τ _s/n ^2/3)(n/m*). While thinner films result in a higher optical transparency it in turn reduces electrical conductivity. The EMFP of SrVO₃ (Γ_SVO ≈ 5.6 nm) and CaVO₃ (Γ_CVO ≈ 3.9 nm) were found much shorter compared with conventional metals (Γ_Au ≈ 50 nm for gold, and Γ_Ag ≈ 52 nm for silver) or ITO^[ Reference Tahar, Ban, Ohya and Takahashi ^{172 ]} (Γ_ITO ≈ 17 nm for polycrystalline film). The favorable, while shorter, EMFP in correlated metals is a direct consequence of the larger effective mass and higher carrier concentration since Γ ~ n ^1/3/m*. Technologically, this shorter EMFP is beneficial, allowing not only thinner films, but also reduces the sensitivity to grain boundary scattering, making the electrical conductivity more tolerant to the film's microstructural effects. The thickness dependence of a material as TC can be quantified by a FOM, which is taken to be Φ_TC = T ¹⁰/R _S, where R _S is the sheet resistance and T is the transmission coefficient.^[ Reference Zhang, Zhou, Guo, Zhao, Barnes, Zhang, Eaton, Zheng, Brahlek, Haneef, Podraza, Chan, Gopalan, Rabe and Engel-Herbert ^{133 ]} As shown in Fig. 15(b), SrVO₃ and CaVO₃ have a comparable FOM a maximum value Φ_TC ≈ 4 × 10⁻³ 1/Ω for 10-nm-thick films striking the best balance between the mutually excluding properties of electrical conductivity and optical transparency. For comparison the maximum FOM for epi-ITO of Φ_TC ≈ 6 × 10⁻³ 1/Ω is on par, but achieved at a much larger film thickness of above 100 nm. This comparison exemplifies the economic advantage of correlated metals as TCs that can be achieved through faster manufacturing time and being composed out of earth abundant, less expensive starting materials. This holds true in particular for the main constituent of ITO, namely indium, being more than 30 times more expensive than the elements Sr and V. The much reduced film thickness and lower costs of the starting material provide a tremendous driving force toward overcoming the materials synthesis challenge to scaling up the growth of vanadate thin films toward high-throughput, low-temperature deposition processes needed to commercialize vanadates as novel transparent electrode material.

The Mott-insulating phase in rare-earth vanadates

The electronic configuration of rare-earth vanadates is different to alkaline earth vanadates, the trivalent rare-earth ions occupying the A-site leave vanadium in a 3⁺ state resulting in a d ² configuration. All rare-earth compounds exhibit orthorhombic distortion (space group Pbnm).^[ Reference Goodenough ^{11 ]} Despite the increase of the ionic radius of vanadium by about 20% being in a lower valence state; all rare-earth ions have a much larger radius. The carriers are localized, the d _xy orbital is lowered in energy compared with the two other t _2g orbitals d _yz and d _zx and a sizeable Mott gap is formed.^[ Reference Miyasaka, Okimoto and Tokura ^{173 ]} At low temperatures spin and orbital ordering effects occur that are coupled to the degree of orthorhombic distortion and thus the ionic radius of the A-site cation, as shown in Fig. 16. In moving from smaller (Yb) toward larger (La) cations, antiferromagnetic ordering of orbitals emerge  ~125 K with spins aligned in the G-type configuration (π, π, π) (indicating out of phase, hence π, along the x, y, and z).^[ Reference Sage, Blake, Marquina and Palstra ^{174 ]} The spins reorder in the C-type antiferromagnetic fashion (π, π, 0) below ~100 K, and finally below 80 K, orbital ordering switches to C-type as well. As the radius of the rare-earth ion is increased, thus increasing the bonding angle and reducing the orthorhombic distortion toward the cubic perovskite, the type of spin and orbital ordering and transition temperatures change accordingly. For the vanadate with the largest rare-earth ion occupying the A-site of the perovskite structure, LaVO₃, the orbital and spin ordering occur at nearly the same temperature with spin order emerging first, followed by the orbital order. These ordering as well as the slight ferromagnetic canting can be understood in the context of the Goodenough–Kanamori rules,^[ Reference Goodenough ^{175 ,} Reference Kanamori ^{176 ]} along with the evolution of the orthorhombic-to-monoclinic distortion dependent on the change in tolerance factor with increasing cation radius.

Figure 16. Temperature dependence of orbital ordering (subscript OO) and spin ordering (subscript N) versus ionic radius for the rare-earth vanadates (RVO₃). G and C indicated the two different ordering types schematically shown in the bottom panel (adapted with permission from Ref. Reference Sage, Blake, Marquina and Palstra174. Copyrighted by the American Physical Society).

While in the case of rare-earth vanadates the underlying physics and the complex interplay of spin and orbital ordering is rich, the aspect of application of these films has so far been pursued to a lesser degree. Interestingly LaVO₃ is well suited for photovoltaic applications, exhibiting the largest Mott gap of ~1.1 eV in the RVO₃ series formed between the d _xy and d _yz /d _zx bands.^[ Reference Assmann, Blaha, Laskowski, Held, Okamoto and Sangiovanni ^{177 ]} The transition is direct and in the optimum range of 1–1.5 eV for energy harvesting from the solar spectrum. Assmann et al. have proposed to utilize LaVO₃/SrTiO₃ oxide heterostructures for high-efficiency photovoltaic cells.^[ Reference Assmann, Blaha, Laskowski, Held, Okamoto and Sangiovanni ^{177 ]} While in SrTiO₃ Sr and Ti have nominal valence states of 2⁺ and 4⁺, and therefore alternating Sr²⁺O²⁻ and Ti⁴⁺O₂ ⁴⁻ planes are charge neutral, in LaVO₃ both La and V have nominal valence of 3⁺, rendering the LaO and VO₂ surfaces polar with alternating charge +1 and −1, respectively. The polar discontinuity formed at the LaVO₃/SrTiO₃ interface can be compensated by electrons transferred from the surface of LaVO₃ to the interface. Similar to the well-studied example LaAlO₃/SrTiO₃ ^[ Reference Ohtomo and Hwang ^{39 ]} this will set up an electrical field across LaVO₃.^[ Reference Hotta, Susaki and Hwang ^{149 ]} The large absorption coefficient of LaVO₃ causes effective electron–hole pair formation, which are separated by the imposed electric field and collected on the bottom electrode, the 2D electron gas formed at the LaVO₃/SrTiO₃ interface and a transparent electrode deposited on LaVO₃. The Mott gap of LaVO₃ is direct so that incident photons can effectively create electron–hole pairs. The high extraction efficiency due to the small distance to the electrodes makes this all-oxide solar cell design attractive. Wang et al.^[ Reference Wang, Li, Bera, Ma, Jin, Yuan, Yin, David, Chen, Wu, Prellier, Wei and Wu ^{178 ]} also pointed out that both, d–d transition between LHB and UHB and p–d transition from O 2p into the V 3d, give rise to light absorption in the visible and UV spectrum. Density functional theory has predicted that the absorption coefficient of LaVO₃ is even higher than that of CdTe,^[ Reference Assmann, Blaha, Laskowski, Held, Okamoto and Sangiovanni ^{177 ]} a conventional semiconductor dominating thin-film solar cells on the market.^[ Reference Mathew, Thompson, Singh, McClure, Velumani, Mathews and Sebastian ^{179 ]} The ability to epitaxially integrate structurally compatible, closely lattice-matched perovskite material with good TCs and absorbers with different band gaps, such as LaFeO₃,^[ Reference Scafetta, Cordi, Rondinelli and May ^{180 ]} could further boost the efficiency of these all-oxide multi-junction solar cells beyond commonly accepted limits.