Phase‐Change Materials for Volatile Threshold Resistive Switching and Neuronal Device Applications

TL;DR

This paper reviews phase-change materials that can mimic neuronal behavior and fast switching for potential use in computing.

Contribution

The paper provides a review of recent advances in volatile resistive switching and neuronal oscillators using three phase-change materials.

Findings

VO2, 1T-TaS2, and BaTiS3 are highlighted for their phase transitions and potential in neuromorphic computing.

The materials show tunable and stochastic dynamics suitable for emulating neuronal behaviors.

Challenges in practical implementation and future research directions are emphasized.

Abstract

Volatile threshold resistive switching and neuronal oscillations in phase‐change materials, specifically those undergoing ‘metal‐to‐insulator’ transitions, offer unique attributes such as fast and low‐field volatile switching, tunability, and stochastic dynamics. These characteristics are particularly promising for emulating neuronal behaviors and solving complex computational problems. In this review, we summarize recent advances in the development of volatile resistive switching devices and neuronal oscillators based on three representative materials with coincident electronic and structural phase transitions, at different levels of technological readiness: the well‐studied correlated oxide VO2, the charge‐density‐wave transition metal dichalcogenide 1T‐TaS2, and the emerging phase‐change complex chalcogenide BaTiS3. We discuss progresses from the perspective of materials development and device implementation. Finally, we emphasize the major challenges that must be addressed for practical applications of these phase‐change materials and provides outlook on the future research directions in this rapidly evolving field.

Volatile threshold switching materials are an important pathway to simulate neuronal behavior. This review summarizes recent advances in the development of volatile resistive switching devices and neuronal oscillators based on three representative phase change materials, emphasizes the major challenges in this rapidly evolving field, and provides an outlook for future directions for basic research and applications.

Figures

a) Schematic illustration of the structure of a biological neuron. b) Representative tonic firing pattern of a single neuron showing spiking activity. c) Typical temperature‐dependence of electrical resistance of a phase‐change material showing electronic phase transitions. d) Typical I‐V characteristics of volatile threshold resistive switching in a phase change material driven by DC voltages. e,f) Representative circuit diagram for introducing voltage oscillations in a two‐terminal phase‐change volatile resistive switching device and the corresponding oscillation waveform. c–f) Figures adapted with permission from Ref.[34] Copyright 2023, John Wiley & Sons.

a) Schematic energy‐band diagrams of Mott‐Hubbard insulator (left) and charge‐transfer insulator (right). Figure adapted with permission from Ref.[40] Copyright 1998, American Physical Society. b) Schematic illustration of Peierls instability in 1D chains of atoms. Figure adapted with permission from Ref.[60] Copyright 2021, Springer Nature.

Coincident electronic and structural phase transitions. a,c,e) Representative temperature‐dependent electrical conductivity / resistivity of a) VO2 single crystal, c) 1T‐TaS2 single crystal, and e) BaTiS3 crystal along the c‐axis. Figures adapted with permission from Ref.[41] Copyright 1969, American Physical Society, Ref.[52] Copyright 1971, Elsevier, and Ref.[56] Copyright 2023, John Wile & Sons. b,d,f) Schematic illustration of the corresponding structural phase transitions in b) VO2, from tetragonal rutile phase to monoclinic phase at ≈340 K, d) 1T‐TaS2, from IC‐CDW to NC‐CDW phase at ≈350 K, and f) BaTiS3, from hexagonal semiconducting phase to trigonal CDW phase at ≈250 K.

Material synthesis. a) Schematic illustration of a PLD system for epitaxial thin‐film growth of VO2 using a V2O5 or V2O3 target. Figure adapted with permission from Ref.[99] Copyright 2023, Royal Society of Chemistry. b) Optical image (left) and a representative XRD scan (right) of VO2 thin films grown on sapphire substrates by hybrid‐MBE. Figures adapted with permission from Ref.[105] Copyright 2015, Springer Nature. c) Schematic illustration of 1T‐TaS2 single crystal growth using a CVT method. The schematic is adapted with permission from Ref.[91] Copyright 2013, Intech Open. d) Optical image (left) and the corresponding out‐of‐plane XRD scan (right) of a large‐sized 1T‐TaS2 single crystal. Figures adapted from wtih permission Ref.[108] Copyright 2015, Springer Nature. e) Schematic illustration of BaTiS3 single crystal synthesis using a vapor transport method. Figure adapted wtih permission from Ref.[109] Copyright 2022, John Wiley & Sons. f) Optical image (left) of representative as‐grown BaTiS3 crystals with needle‐like and plate‐like morphologies and out‐of‐plane XRD scan (right) of a BaTiS3 plate with a‐ and c‐axes in plane. Figures adapted with permission from Ref.[86] Copyright 2018, Springer Nature.

Device Fabrication. a) Cross‐sectional schematic of a two‐terminal planar VO2 thin film device. Figure adapted with permission from Ref.[130] Copyright 2011, Elsevier. b) Optical microscopic image of a four‐probe VO2 film device fabricated through dry etching. Figure adapted with permission from Ref.[126] Copyright 2008, AIP Publishing. c) Schematic illustration of an out‐of‐plane VO2 film device using TiN as the bottom electrode. Figure adapted wtih permission from Ref.[131] Copyright 2015, AIP Publishing. d) Optical microscopic images of few‐layer 1T‐TaS2 flakes showing the degradation progress in air. Figures adapted with permission from Ref.[108] Copyright 2015, Springer Nature. e) Optical microscopic images of device fabrication processes for mechanically exfoliated 1T‐TaS2 flakes on a SiO2/Si substrate, including hBN encapsulation (left) and metal deposition (right) steps. The inset to the right shows a cross‐sectional schematic of the device. Figures adapted with permission from Ref.[137] Copyright 2015, National Academy of Science. f) Schematic illustration of a multi‐terminal BaTiS3 bulk device fabricated through polymeric planarization and regular photolithography processes. Figure adapted with permission from Ref.[138] Copyright 2022, ACS Publications. g) Optical microscopic images of BaTiS3 bulk devices with a van der Waals (left) and a transmission line method (TLM, right) contact geometry. Figures adapted with permission from Ref.[56] Copyright 2023, John Wiley & Sons.

Transport properties. a) Schematic illustration of Hall measurements. (b) Temperature evolution of Hall mobility (left) and carrier concentration (right) across the MIT phase transition in VO2. Figures adapted with permission from Ref.[144] Copyright 1973, American Physical Society. c) Temperature dependence of Hall coefficient and carrier concentration across the transitions. Figure adapted wtih permission from Ref.[84] Copyright 1979, Elsevier. d) Temperature evolution of mobility and carrier concentration of a BaTiS3 crystal along the c‐axis. The associated temperature dependent electrical resistivity measurement is shown in Figure 3e. Figure adapted with permission from Ref.[56] Copyright 2023, John Wiley & Sons.

Electrically driven volatile threshold switching and mechanisms. a) I‐V characteristics of a VO2 thin film devices with active channel dimensions of 10 µm × 10 µm in both V‐mode (voltage sweeps) and I‐mode (current sweeps). Figure adapted with permission from Ref.[129] Copyright 2010, AIP Publishing. b) Optical microscopic images (bottom) and electrical characteristics (top) of filaments observed between the electrodes at different applied currents. Figures adapted with permission from Ref.[150] Copyright 2013, John Wiley & Sons. c) Spatiotemporal characterization of the electrically induced insulator‐to‐metal transition in VO2. Figures adapted with permission from Ref.[151] Copyright 2021, American Association for the Advancement of Science. d) Temperature dependent two‐probe resistance of a 11.8‐nm‐thick 1T‐TaS2 flake (left) and the associated Joule heating rate analysis. Figures adapted with permission from Ref.[63] Copyright 2018, ACS Publications. e) Cross‐sectional view of the simulated temperature distribution near a 1T‐TaS2 device channel, for applied current pulses of short (8 ns) and long (13.3 µs) durations. Figures adapted with permission from Ref.[152] Copyright 2021, AIP Publication. f) Temperature dependent four‐probe resistance of a bulk BaTiS3 device from 220 K to 240 K (left) and the associated thermal power analysis (right). g) Pulsed I‐V characterization of BaTiS3. (f) and (g) Figures adapted with permission from Ref.[34] Copyright 2023, John Wiley & Sons.

Self‐sustained voltage oscillations. a) Schematic diagram of the electrical circuit used for the generation of the MIT oscillation in a VO2 thin film device. b) Waveform of VD and ID of the device measured at room temperature. a,b) Figure adapted with permission from Ref.[129] Copyright 2010, AIP Publishing. c) I‐V characteristics of a 1T‐TaS2 flake device at room temperature and load lines of the series resistor at different VDC values. The oscillator circuit starts to oscillate across the threshold condition of VDC = 3.8 V. d) Voltage oscillations of a 1T‐TaS2 flake device under different VDC values. c,d) Figures adapted with permission from Ref.[62] Copyright 2016, Springer Nature. e) I‐V characteristics of a two‐terminal BaTiS3 device at 220 K. The dashed line represents a series resistor load line for stable voltage oscillations and the inset shows a schematic illustration of the oscillator measurement circuit. f) Oscillation waveforms of a BaTiS3 device operated at different temperatures. e,f) Figures adapted with permission from Ref.[34] Copyright 2023, John Wiley & Sons.

Device implementation of phase‐change neuronal oscillators. a) Circuit diagrams of a two‐channel artificial neuron to emulate the biological neuronal dynamics. b) Six representative biological neuron spiking behaviors experimentally demonstrated in VO2 neurons. a,b) Figures adapted wtih permission from Ref.[163] Copyright 2018, Springer Nature. c) Stochastic spiking of a VO2 oscillator due to cycle‐to‐cycle variations in threshold switching voltages. d) The associated spike probability that follows a sigmoidal pattern. c,d) Figures adapted with permission from Ref.[164] Copyright 2017, IEEE. e) Schematic illustration of an Ising Hamiltonian solver for combinatorial optimization problems using coupled stochastic VO2 oscillators. Figures adapted with permission from Ref.[165] Copyright 2021, Springer Nature. f) Schematic illustration of the process flow to solve the graph coloring problem using coupled VO2 oscillatory network. Figures adapted with permission from Ref.[166] Copyright 2017, Springer Nature.

Tables

Table 1. Selected list of phase‐change material candidates for resistive switching. Note that only the volatile switching and the associated neuronal oscillation applications are discussed in this review.

Material	Phase Transition Properties				Primary Mechanism	Device Demonstration		Ref.
	T C	Structural Transition	ρ / ρ0	Year		Resistive Switching	Electronic Devices
VO2	340 K	P42/mnm to P21/c	102–105	1959	Electron‐electron interactions (Mott‐Hubbard + Charge‐transfer)	Volatile	Oscillator	[35, 41]
V2O3	≈165 K	R 3¯ c to I 2/a	106	1959		Volatile	Oscillator	[35, 42, 43]
NbO2	≈1070 K	P42/mnm to I41/a	10	1966		Volatile	Oscillator	[44, 45]
PrNiO3	135 K	Pbnm to P21/n	103	1991		No	No	[46, 47, 48]
SmNiO3	403 K	Pbnm to P21/n	≈10			No	No
NbSe3	145 K	Displacement of Nb (III) column	≈1.2	1976	Electron‐phonon interactions (CDW)	No	No	[49, 50, 51]
	59 K	Displacement of Nb (I) column	≈2			Volatile	No
1T‐TaS2	350 K	NC‐CDW to IC‐CDW	≈2	1971		Volatile	Oscillator	[52, 53, 54]
	130–230 K	IC‐CDW to CDW	≈20			Non‐volatile	Memristor
1T‐TaSe2	473 K	IC‐CDW to CDW	3–4	1974		No	No	[55]
BaTiS3	250 K	Hexagonal to trigonal (CDW)	≈2	2023		Volatile	Oscillator	[56]
	150–190 K	Trigonal (CDW) to monoclinic	≈10			No	No

Table 2. Material synthesis and transport properties of VO2, 1T‐TaS2, and BaTiS3.

Material	Material Synthesis			Transport Properties			Year	Ref.
	Synthesis Method	Substrate	Growth Temperature	Transition Temperature	Resistivity Change	Hysteresis Window
VO2	Flux (single crystal)		1000°C	340 K	105	0.5–1 K	1969	[41, 90]
	Sputtering	Sapphire	400°C	340 K	103	10 K	1967	[94]
	PLD	Sapphire (101¯0)	630°C	328 K	105	< 1 K	1994	[96]
	PLD	TiO2 (001)	370 °C	300 K	103	10 K	2002	[110]
	Sol‐gel	Sapphire (101¯0)	400–500°C	340 K	104	10 K	2005	[103]
1T‐TaS2	CVT (single crystal)		950°C	350 K	≈2	5 K	1971	[52]
	CVD	h‐BN	850°C	345 K	≈2	30 K	2018	[112]
BaTiS3	CVT (single crystal)		1050°C	250 K	2	10 K	2023	[56]
	Flux (single crystal)		1050°C	230 K	2–3	20 K	2024	[113]
	PLD	SrTiO3	700°C	N/A	N/A	N/A	2024	[114]

Table 3. Performance of phase‐change volatile switching and oscillator devices of VO2, 1T‐TaS2, and BaTiS3.

Material	Device Geometry			Temp.	Threshold Switching		Oscillator Device			Ref.
	Device Config.	Electrode	Channel Length		V th	I th	V S or I S	f	Year
VO2	Planar crystal	N/A	2 mm	RT	16 V	N/A	N/A	5 kHz	1975	[149]
	Planar film	Ti/Au	10 µm	RT	7 V	≈1 mA	≈10 V	>550 kHz	2008	[126]
	Planar film	Ti/Au	5 µm	RT	3 V	0.5 mA	10 V	0.8 MHz	2011	[130]
	Vertical film	Ti/Au	130 nm	RT	0.8 V	0.6 mA	1 mA	300 kHz	2014	[155]
	Vertical film	TiN	200 nm	RT	1.8 V	80 µA	13 V	9 MHz	2015	[131]
1T‐TaS2	Planar flake	Pd/Au	0.5–1 µm	RT	≈0.8 V	3 mA	≈4 V	2 MHz	2016	[62]
	Planar flake	Cr/Au	0.7 µm	RT	0.78 V	2.8 mA	≈3.9 V	1.1 MHz	2018	[63]
								0.8 MHz w. light
BaTiS3	Planar crystal	Ti/Au	80 µm	220 K	7 V	≈1 mA	≈ 20 V	16 Hz	2023	[34]
			10 µm	130 K	N/A	N/A	1.23 mA	0.9 kHz

Table 4. Technological readiness of VO2, 1T‐TaS2, and BaTiS3 for practical electronic device applications.

Material	Form	Device Processing		Device Operation			Integration	Tech. Readiness
		Fabrication Method	Air / thermal stability	Temp.	Best Performance	Channel Size	CMOS Compatibility
VO2	Thin film	lithography	Excellent	RT	9 MHz	200 nm (film thickness)	High	High
1T‐TaS2	Cleaved flakes	Mechanical exfoliation + ebeam lithography	Poor at thin limit	RT	2 MHz	0.5–1 µm	Medium	Low
BaTiS3	Bulk crystals	Polymeric planarization + lithography	Good	Cryogenic	≈0.9 kHz	10 µm	Low	Very low

Full text

Introduction

1

Due to the recent slowdown in Moore's law and the increasing computational demands of artificial intelligence applications,^[^ 1, 2, 3 ^]^ the development of novel “post‐complementary metal‐oxide‐semiconductor (CMOS)” hardware that is both energy‐efficient and capable of handling complex tasks has become highly sought after.^[^ 4, 5 ^]^ Neuromorphic computing, a paradigm that interconnects networks of artificial synapses and neuronal devices, can physically emulate the structure and function of the human brain, offering remarkably low power consumption and intrinsic learning capabilities.^[^ 6, 7, 8, 9, 10 ^]^ Figure 1a illustrates a biological neuron specialized for processing and transmitting cellular signals, whereas Figure 1b shows a typical tonic firing pattern of single neuron exhibiting rhythmic spiking activity.^[^ 11 ^]^ Early attempts to mimic the neuronal and synaptic behavior of brain used non‐von Neumann architectures based on conventional CMOS circuits and metal‐oxide memristors, enabling the demonstration of millions of programmable spiking neurons constructed from billions of transistors.^[^ 12, 13 ^]^ However, such systems remain far away from true brain‐like operation, primarily due to its low energy efficiency and limited system complexity.

a) Schematic illustration of the structure of a biological neuron. b) Representative tonic firing pattern of a single neuron showing spiking activity. c) Typical temperature‐dependence of electrical resistance of a phase‐change material showing electronic phase transitions. d) Typical I‐V characteristics of volatile threshold resistive switching in a phase change material driven by DC voltages. e,f) Representative circuit diagram for introducing voltage oscillations in a two‐terminal phase‐change volatile resistive switching device and the corresponding oscillation waveform. c–f) Figures adapted with permission from Ref.[34] Copyright 2023, John Wiley & Sons.

Alternatively, researchers have pursued novel materials and device architectures that leverage intriguing physical phenomena to emulate synaptic and neuronal functionalities. A range of non‐volatile devices, including memristors,^[^ 14, 15, 16 ^]^ phase change memory,^[^ 17, 18 ^]^ ferroelectric memory,^[^ 19, 20, 21 ^]^ and magnetic tunnel junctions,^[^ 22, 23, 24 ^]^ have been developed as synaptic components in integrated neuromorphic systems. Meanwhile, materials exhibiting volatile threshold switching mechanisms, such as metallic filament type,^[^ 25, 26 ^]^ thermal feedback,^[^ 27, 28 ^]^ ferroelectric,^[^ 29, 30 ^]^ and electronic phase transitions,^[^ 31, 32, 33, 34 ^]^ are often employed as neuronal devices. Among these, phase‐change materials with coincident structural and electronic phase transitions are especially promising for mimicking the oscillatory and dynamic features of biological neurons. Upon varying temperature, such materials often undergo well‐defined jumps in their electrical resistivity across the transition, as illustrated in Figure 1c. Oftentimes, volatile resistive switching is electrically triggered in simple two‐terminal devices when operating below the transition temperature (Figure 1d). By further integrating such phase‐change devices into various oscillatory circuits (Figure 1e), self‐sustained voltage oscillations (Figure 1f), or even more complex neuron‐like dynamic behaviors such as tonic firing pattern (Figure 1b) can be realized. Table 1 shows a selected list of phase‐change material candidates, primarily transition metal (V, Ti, Ni, Ta, etc.) oxides and chalcogenides, that are promising in realizing such electronic functionalities, despite the varying transition temperatures and mechanisms.

Notably, there have been a long history and extensive research interests in studying metal‐to‐insulator transitions (MIT) of various correlated binary and complex oxides. In a pioneering work in late 1950s, Morin observed that the resistance of certain binary transition metal oxides, such as vanadium oxides (VO_2_, V_2_O_3_) and titanium sesquioxide (Ti_2_O_3_), increased by several orders of magnitude upon crossing a critical temperature (T C).^[^ 35 ^]^ As sister compounds of vanadium oxides, niobium oxides (e.g., NbO_2_) also undergo similar transitions, albeit at much higher transition temperatures.^[^ 36, 37 ^]^ These phenomena are predominantly attributed to Mott‐Hubbard transitions.^[^ 38, 39, 40 ^]^ As illustrated in Figure 2a (left), the gap arises from electrons hopping between d‐bands of adjacent anions and is associated with the Coulomb interaction U (or Hubbard correlation energy).^[^ 38, 39, 40 ^]^ Later, rare‐earth nickelate perovskites, LnNiO_3_ (where Ln = Pr, Nd, Sm), were reported to exhibit metal‐to‐insulator transitions, in both bulk form and strained thin films, where the gap openingpotentially originated from the excitation from the anion p level to the metal d level with the charge‐transfer energy Δ, as illustrated in Figure 2a (right).^[^ 48, 57 ^]^ A theoretical framework describing Mott‐Hubbard and charge‐transfer insulators can be understood using the Zaanen‐Sawatzky‐Allen scheme.^[^ 40, 58 ^]^

a) Schematic energy‐band diagrams of Mott‐Hubbard insulator (left) and charge‐transfer insulator (right). Figure adapted with permission from Ref.[40] Copyright 1998, American Physical Society. b) Schematic illustration of Peierls instability in 1D chains of atoms. Figure adapted with permission from Ref.[60] Copyright 2021, Springer Nature.

Charge‐density‐wave (CDW) materials belong to another class of promising candidates to host metal‐to‐insulator transitions due to the gap opening from strong electron‐phonon interactions.^[^ 59 ^]^ According to Peierls’ picture, a 1D atomic chain is inherently unstable at low temperatures, resulting in a spontaneous periodic lattice distortion and gap opening at the zone boundary, as illustrated in Figure 2b.^[^ 59, 60 ^]^ Such transition is energetically favorable as the decrease in electronic energy due to gap opening outweighs the increase in elastic energy due to lattice reconstruction.^[^ 59 ^]^ However, only a handful of real CDW materials manifest pronounced resistivity jumps across transitions, which is a critical ingredient for potential device applications.^[^ 61 ^]^ The 1T phase of the transition metal dichalcogenide TaS_2_ (1T‐TaS_2_) happens to exhibit such metal‐to‐insulator transitions, as first observed by Thompson et al. in the early 1970s.^[^ 52 ^]^ With recent advances in 2D device fabrication and testing, interest in utilizing 1T‐TaS_2_ for neuronal applications has grown substantially since the mid‐2010s.^[^ 54, 62, 63 ^]^ Moreover, emerging chalcogenide crystals, such as BaTiS_3_ and EuTe_4_, have also shown to host both CDW order and metal‐to‐insulator transitions,^[^ 34, 56, 64, 65 ^]^ rendering them promising candidates to demonstrate resistive switching for emulating synaptic or neuronal functionalities. Note that due to the large thermal hysteresis, EuTe_4_ tends to demonstrate non‐volatile resistive switching and memory effects when operating at temperatures within the hysteresis window.^[^ 65 ^]^

In this work, we focus explicitly on phase‐change oxides and chalcogenides that exhibit metal‐to‐insulator transitions and volatile resistive switching, as well as their potential for neuronal device applications. Among all the candidates that have demonstrated such functionalities, we choose three archetypal phase‐change materials – namely the correlated binary oxide VO_2_ and the CDW chalcogenides 1T‐TaS_2_ and BaTiS_3_ – and discuss their similarities and differences in intrinsic structural and electrical properties, material synthesis and device fabrication methods, and electronic device implementation and characteristics. These materials represent two different categories of underlying mechanisms such as electron correlation and electron‐lattice interaction. Considering that there have been several comprehensive reviews on metal‐to‐insulator transitions in correlated oxides and their applications for neuromorphic computing,^[^ 66, 67, 68 ^]^ only one representative oxide material, VO_2_, was chosen from that category, as a benchmark to compare the similarities and differences with the other two phase‐change compounds.

Importantly, these materials are at three very different levels of technological readiness: for instance, after being studied for more than 60 years, VO_2_ is closest to a ‘technologically ready’ status with well‐established thin‐film synthesis and device fabrication processes that are ideal for large‐scale device applications; 1T‐TaS_2_ has been actively studied at the individual‐device level in research‐laboratories over the past 10–15 years, however, such mechanical exfoliation‐based processes are natural bottleneck to fully realize circuit‐level and large‐scale implementation of 1T‐TaS_2_ devices; as for BaTiS_3_, it represents the class of newly developed phase‐change materials and hence, has the lowest level of technological readiness. With only bulk single crystals being used for probing intrinsic physical properties and prototype device demonstration at cryogenic temperatures, BaTiS_3_‐based devices are still far away from achieving optimized individual device performance, let alone any practical higher‐level device integration at the moment.

Coincident Electronic and Structural Phase Transitions

2

Electronic phase transitions often coincide with structural phase transitions in these phase‐change materials (Table 1), as well documented in the literature.^[^ 69, 70 ^]^ Because these well‐defined structural phase transitions are directly tied to the changes of electrical characteristics, elucidating the structural transitions and understanding the associated mechanisms are crucial for developing phase‐change‐based electronic devices. In the correlated oxide VO_2_, a monoclinic‐to‐tetragonal structural transition occurs alongside a pronounced change in resistivity across the metal‐to‐insulator transition.^[^ 41, 69 ^]^ Meanwhile, in low‐dimensional CDW chalcogenides such as 1T‐TaS_2_ and BaTiS_3_, the underlying periodic lattice distortions such as star‐of‐David structural transition (1T‐TaS_2_)^[^ 53 ^]^ and in‐plane unit cell doubling (BaTiS_3_)^[^ 56 ^]^ coincide with the abrupt changes in the electrical properties.

Figure 3a shows a representative temperature‐dependent conductivity measurement of a VO_2_ single crystal, which exhibits a resistivity of ≈10 Ω⋅cm at room temperature and drops to below 10^−4^ Ω⋅cm at high temperatures, resulting in a change up to five orders of magnitude across the transition.^[^ 41 ^]^ As illustrated in Figure 3b, VO_2_ adopts a monoclinic crystal structure at room temperature (a = 5.75 Å, b = 4.52 Å, c = 5.38 Å, α = γ = 90°, β = 122.6°) with a space group of P2_1_/c. Above the transition temperature (T c = 340 K, or 67 °C), the structure becomes tetragonal (a = b = 4.55 Å, c = 2.85 Å, α = β = γ = 90°) with a space group of P4_2_/mnm, analogous to rutile TiO_2_.

Coincident electronic and structural phase transitions. a,c,e) Representative temperature‐dependent electrical conductivity / resistivity of a) VO2 single crystal, c) 1T‐TaS2 single crystal, and e) BaTiS3 crystal along the c‐axis. Figures adapted with permission from Ref.[41] Copyright 1969, American Physical Society, Ref.[52] Copyright 1971, Elsevier, and Ref.[56] Copyright 2023, John Wile & Sons. b,d,f) Schematic illustration of the corresponding structural phase transitions in b) VO2, from tetragonal rutile phase to monoclinic phase at ≈340 K, d) 1T‐TaS2, from IC‐CDW to NC‐CDW phase at ≈350 K, and f) BaTiS3, from hexagonal semiconducting phase to trigonal CDW phase at ≈250 K.

Despite the clear observations of both structural and metal‐to‐insulator transitions in VO_2_, the underlying mechanism has been highly debated. In early days, Goodenough suggested that an antiferroelectric distortion and the formation of V‐V zigzag bonds below T c are responsible for the gap opening and metal‐to‐insulator transition in VO_2._ ^69^ Several experimental observations such as optical phonon softening at the R point of the Brillouin zone also supports this scheme.^[^ 70 ^]^ However, the Peierls’ picture does not account for features such as the relatively large bandgap (0.6 eV) and the appearance of additional intermediate phases. Later in 1975, Zylbersztejn and Mott argued that the metal‐to‐insulator transition in VO_2_ is triggered when the Hubbard energy (U) becomes comparable to the band width.^[^ 71 ^]^ The Mott's criterion for the electronic transition is given as (*n_c_ *)^1/3^α_ H _ ≈ 0.25, where *n_c_

• denotes the critical carrier density and α_ H _ is the Bohr radius. In 2000, Stefanovich et al. found that the insulator‐to‐metal transition in VO_2_ can be induced by injecting excessing carriers without heating up the lattice to T c, which they construed as strong evidence for the electronic Mott‐Hubbard scenario.^[^ 72 ^]^ More importantly, from the perspective of theoretical calculations, phenomena such as broad band gap and the emergence of intermediate phases can only be properly described by introducing an additional Hubbard energy, through either DFT + U or GW methods.^[^ 73, 74, 75 ^]^

Indeed, there has not been a universal understanding of the VO_2_ phase transition mechanism, although both Peierls and Mott mechanisms seem to contribute. In 2005, the switching of orbital occupancy across the transition in VO_2_ was experimentally observed to be directly connected with both the delocalization of electrons and the lattice distortion, and hence, an orbital‐assisted ‘collaborative’ Mott‐Peierls transition picture was proposed.^[^ 76 ^]^ Moreover, in 2014, Morrison et al. reported a photoinduced metal‐like monoclinic phase of VO_2_ from the insulating phase, suggesting that the photoexcitation was only able to rearrange the occupancy of d orbitals but insufficient to alter the underlying lattice distortion.^[^ 77 ^]^ More detailed discussions on the mechanism debate of VO_2_ can be found in several other reviews.^[^ 78, 79 ^]^ Note that in Table 1, we label the electron‐correlation as the primary mechanism for the metal‐to‐insulator transition in VO_2_, as well as in many other correlated oxides.

Charge density waves have been reported in various layered transition metal dichalcogenides (TMDCs) such as 1T‐TaS_2_, 2H‐TaSe_2_, and 1T‐TiSe_2_, in addition to classic quasi‐1D metals.^[^ 80 ^]^ The 2D compound TaS_2_ belongs to the family of TMDCs and crystalizes in different layered structures, including the 1T and 2H polytypes.^[^ 52, 81 ^]^ In 1T‐TaS_2_, tantalum (Ta) atoms, octahedrally coordinated by surrounding sulfur atoms, are hexagonally arranged in plane. In 1975, Scruby et al. carried out temperature‐dependent electron and X‐ray diffraction studies^[^ 53, 82 ^]^ to reveal three metastable phases in 1T‐TaS_2_.

The material exhibits a metallic phase at high temperatures (a = b = 3.36 Å, c = 5.90 Å, α = β = 90°, γ = 120°) with the P 3¯ m1 space group, and it switches to an incommensurate CDW (ICCDW) phase below 550 K. The diffraction pattern of the ICCDW phase is dominated by diffuse spots with an incommensurate wave vector q IC = 0.283a**.^[^ 53 ^]^ Upon further cooling to ≈350 K, the wave vector rotates by about 12° toward q NC = 0.245a** + 0.068b**,^[^ 53 ^]^ giving rise to a nearly commensurate CDW (NCCDW) phase. Finally, below 180 K, a commensurate CDW (CCDW) phase with a 13a×13b×13c supercell dominates, which corresponds to a commensurate wave vector of q C = (3a** + b*)/13 = 0.231a** + 0.077b**.^[^ 53 ^]^

Accordingly, 1T‐TaS_2_ exhibits two pronounced discontinuities in resistivity below 400 K, as illustrated in Figure 3c. Near 350 K, the NCCDW‐to‐ICCDW transition occurs with minimal thermal hysteresis. In contrast, the low‐temperature transition at ≈200 K between the CCDW and NCCDW phases exhibits a roughly 20‐fold increase in resistivity and a large hysteresis spanning tens of kelvins.^[^ 52 ^]^

In the CCDW phase, the star‐of‐David clusters form as twelve surrounding Ta atoms displace inward toward a central thirteenth Ta atom within each layer. In 1979, Fazekas and Tosatti proposed that out of the thirteen 5d ^1^ electrons, twelve become paired in ‘star‐bonding’ orbitals, leaving the thirteenth electron localized near the cluster center.^[^ 83 ^]^ As a result, only these central electrons contribute to electrical conduction and magnetism. Therefore, a Mott‐type localization may occur within the sub‐band of these central electrons due to their large separations, which explains the drop in conductivity below 200 K. This electron localization scenario is further supported by Hall measurements performed by Inada et al. in 1979,^[^ 84, 85 ^]^ which demonstrated that the charge carrier density in the CCDW state is an order of magnitude lower than what would be expected from CDW‐induced band gaps alone. As illustrated in Figure 3d, the NCCDW phase also contains star‐of‐David clusters, albeit arranged in a less uniform pattern. Notably, the structural transition between the NCCDW and ICCDW phases is highly relevant for electrically induced threshold switching and voltage oscillations in 1T‐TaS_2_ devices operating at room temperature.

Unlike conventional metallic CDW materials, the recently discovered quasi‐1D chalcogenide BaTiS_3_ is a small bandgap d ^0^ semiconductor with an bandgap of ≈0.3 eV.^[^ 86 ^]^ At room temperature, BaTiS_3_ adopts a hexagonal crystal structure (a = b = 11.7 Å, c = 5.83 Å, α = β = 90°, γ = 120°) with a space group of P6_3_ cm.^[^ 56 ^]^ In 2018, Niu et al. reported a giant optical anisotropy with a record‐high birefringence in single crystals of BaTiS_3_, sparking significant research interest in this material.^[^ 86 ^]^ Because of its nominally empty conduction band, no phase transition was initially expected for BaTiS_3_, even though its d ^1^ counterpart, BaVS_3_, is considered an archetypical CDW system with a magnetic transition.^[^ 87, 88 ^]^ In 2023, Chen et al. experimentally demonstrated the presence of a CDW phase and a series of transitions in BaTiS_3_ using electrical transport measurements and temperature‐dependent synchrotron X‐ray diffraction.^[^ 56 ^]^ Upon cooling from room temperature to ≈240 K, a structural transition takes place with titanium atoms displacing in a‐b plane, which leads to a lattice unit cell doubling (a = b = 23.3 Å, c = 5.84 Å, α = β = 90°, γ = 120°) and hence a new CDW phase with a space group of P3c1, as illustrated in Figure 3f. Key evidence for the CDW includes the emergence of weak superlattice reflections in the diffraction pattern and the corresponding resistivity anomalies observed from transport measurements.^[^ 56 ^]^ Further cooling to 130 K causes these superlattice peaks to disappear while a new set of reflections associated with a smaller 23×23 unit cell (a = b = 13.4 Å, c = 5.82 Å, α = β = 90°, γ = 120°) emerges. This observation indicates a suppression of the CDW phase via the structural transition from P3c1 to P2_1_. Consistently, transport measurements reveal two hysteretic transitions in the 150–190 K and 245–255 K ranges, respectively, as shown in Figure 3e.^[^ 56 ^]^

The underlying mechanisms driving these phase transitions in a gapped semiconductor such as BaTiS_3_ can be complicated and are not fully understood yet. Because its Fermi level lies within the bandgap, these is no conventional concept of Fermi surface; thus, the nesting mechanism associated with quasi‐1D CDW metals does not apply.^[^ 56 ^]^ Hall measurements reveal a low carrier concentration of ≈1.1 × 10^18^ cm^−3^ at room temperature, which further drops to less than 10^15^ cm^−3^ at 100 K.^[^ 56 ^]^ In such a non‐degenerate system with dilute concentration of electrons, the role of electron‐electron interaction in BaTiS_3_ can be nontrivial, unlike most metallic or semi‐metallic CDW compounds. Therefore, Chen et al. suggested that both electron‐lattice coupling and non‐negligible electron‐electron interactions could contribute to the observed CDW order and phase transitions in semiconducting BaTiS_3_.^[^ 56 ^]^

Materials Synthesis

3

This section provides an overview of the synthesis routes employed for the three phase‐change material systems covered in this review (VO_2_, 1T‐TaS_2_, and BaTiS_3_). Owing to their distinct chemistries, physical properties, and different levels of research focus since their initial discoveries, the methods used to synthesize these materials vary significantly. In general, single‐crystal forms of materials are being used in early days of research for studying their intrinsic physical properties and the demonstration of prototype devices. By contrast, large‐area, high‐quality thin film growth is usually crucial for realizing any practical electronic device applications. Table 2 summarizes details of representative material synthesis methods for each material and the associated transport properties.

In 1959, Morin conducted the first electrical transport study of various oxides showing MIT, such as Ti_2_O_3_, VO, V_2_O_3_, and VO_2_.^[^ 35 ^]^ In his work, single crystals of vanadium oxides were synthesized via a hydrothermal process. The details of the crystal growth using this method can be found in a subsequent book chapter by Laudise and Nielsen.^[^ 89 ^]^ At that time, however, the single‐crystal samples were on the order of 0.1 mm in size, which were too small for standard four‐point measurements. Consequently, the observed electrical conductivity change across the MIT in VO_2_ was limited to merely two orders of magnitude,^[^ 35 ^]^ likely due to significant contact resistances in two‐probe geometry. Thereafter, a variety of advanced synthesis methods have been developed to produce high‐quality and large‐sized VO_2_ single crystals. For instance, in 1969, Ladd and Paul employed a molten‐flux technique to grow millimeter‐scale VO_2_ single crystals using V_2_O_5_ as flux.^[^ 90 ^]^ These crystals showed a 10^5^‐fold change in resistivity near 340 K, which is widely considered the benchmark performance for VO_2_.^[^ 41, 90 ^]^ In 1971, Nagasawa adopted a chemical vapor transport (CVT) method^[^ 91 ^]^ to obtain single crystals of vanadium oxides using TeCl_4_ as a transport agent,^[^ 92 ^]^ and in 1972, Reyes et al. succeeded in synthesizing doped VO_2_ single crystals via an iso‐thermal flux evaporation method.^[^ 93 ^]^

Research efforts on synthesizing VO_2_ thin films have been predominantly centered on using reactive magnetron sputtering^[^ 94, 95 ^]^ and pulsed laser deposition (PLD),^[^ 96, 97, 98, 99 ^]^ although other methods including molecular beam epitaxy (MBE),^[^ 100, 101 ^]^ metal‐organic chemical vapor deposition (MOCVD),^[^ 102 ^]^ and sol‐gel routes^[^ 103, 104 ^]^ have also been investigated. In 1967, Fuls et al. synthesized VO_2_ thin films by reactive sputtering from a vanadium target in an argon atmosphere with a controlled oxygen partial pressure.^[^ 94 ^]^ These films, grown at 400°C on sapphire substrates, exhibited a highly orientated monoclinic phase at room temperature.^[^ 94 ^]^ From late 1980s, PLD emerged as a versatile technique for synthesizing high‐quality oxide thin films (Figure 4a). Its compatibility with relatively high oxygen pressures makes it particularly suitable for depositing stoichiometric oxides. In 1994, Kim and Kwok demonstrated high‐quality VO_2_ thin films on (0001) and (101¯0) sapphire substrates by PLD, using pressed V_2_O_3_ powder as the target.^[^ 96 ^]^ More recently, Zhang et al. reported wafer‐scale VO_2_ growth on sapphire substrates (Figure 4b, left) with a large resistance jump of ≈10^4^ through a hybrid‐MBE approach. The right panel of Figure 4b shows a representative XRD scan of such a VO_2_ film.^[^ 105 ^]^

Material synthesis. a) Schematic illustration of a PLD system for epitaxial thin‐film growth of VO2 using a V2O5 or V2O3 target. Figure adapted with permission from Ref.[99] Copyright 2023, Royal Society of Chemistry. b) Optical image (left) and a representative XRD scan (right) of VO2 thin films grown on sapphire substrates by hybrid‐MBE. Figures adapted with permission from Ref.[105] Copyright 2015, Springer Nature. c) Schematic illustration of 1T‐TaS2 single crystal growth using a CVT method. The schematic is adapted with permission from Ref.[91] Copyright 2013, Intech Open. d) Optical image (left) and the corresponding out‐of‐plane XRD scan (right) of a large‐sized 1T‐TaS2 single crystal. Figures adapted from wtih permission Ref.[108] Copyright 2015, Springer Nature. e) Schematic illustration of BaTiS3 single crystal synthesis using a vapor transport method. Figure adapted wtih permission from Ref.[109] Copyright 2022, John Wiley & Sons. f) Optical image (left) of representative as‐grown BaTiS3 crystals with needle‐like and plate‐like morphologies and out‐of‐plane XRD scan (right) of a BaTiS3 plate with a‐ and c‐axes in plane. Figures adapted with permission from Ref.[86] Copyright 2018, Springer Nature.

It is important to note that the transport properties of VO_2_ such as the transition temperature, magnitude of resistivity change, and the width of the hysteresis loop depend strongly on the material synthesis method and growth conditions, as detailed in Table 2. For instance, a typical VO_2_ thin film grown by RF sputtering exhibits a three‐order‐of‐magnitude resistivity changes and a 10 K hysteresis.^[^ 106 ^]^ In contrast, high‐quality VO_2_ thin films synthesized via pulsed laser deposition can attain a resistivity change of up to five orders of magnitude with a hysteresis of 1 K,^[^ 96 ^]^ comparable to that observed in bulk single crystals,^[^ 90, 107 ^]^ yet its transition temperature is reduced to ≈330 K. Moreover, it has been reported that in the thin film limit of VO_2_ (10‐15 nm thick), the epitaxial strain, which is induced by the differences of the lattice constants between the film and the TiO_2_ (001) substrate, could dramatically reduce the transition temperature to ≈300 K.^[^ 110 ^]^

Single crystals of 1T‐TaS_2_ are commonly obtained by the CVT technique, like many other layered TMDCs, as illustrated in Figure 4c.^[^ 91 ^]^ A comprehensive review of this method can be found in the book by Schäfer (1964).^[^ 111 ^]^ By 1969, Wilson and many other researchers had succeeded in synthesizing TMDCs single crystals (including TaS_2_) with dimensions up to a centimeter.^[^ 81 ^]^ Iodine (I_2_) serves as the most widely used transport agent, although bromine and chlorine are also occasionally employed. Typically, ≈1 mg cm^−3^ of I_2_ is placed in a sealed quartz ampule to balance an efficient reaction rate with minimal unintentional iodine incorporation. Figure 4d (left) displays an optical image of a representative bulk 1T‐TaS_2_ crystal (2 mm × 3 mm), with the right panel illustrating an XRD scan of the same sample.^[^ 108 ^]^ In 1971, Thompson et al. obtained 1T‐TaS_2_ crystals by quenching sealed ampules from ≈950°C, following a CVT crystal growth process using pre‐reacted 2H‐TaS_2_ powder as the starting materials and I_2_ as the transport agent.^[^ 52 ^]^ Notably, the 1T polymorph of TaS_2_ is thermodynamically stable at temperatures above 777°C (≈1050 K) in its phase diagram, and therefore, growths with slow cooling will lead to 2H‐TaS_2_, which is metallic and becomes superconducting below 0.8 K.^[^ 83 ^]^ With sufficiently large crystal sizes, Thompson et al. further performed transport measurements up to 400 K using a van der Pauw geometry, revealing the intrinsic electrical transport behavior of bulk 1T‐TaS_2_ featuring two metal‐to‐insulator phase transitions.^[^ 52 ^]^ Those two transitions were later assigned as the CCDW‐to‐NCCDW and NCCDW‐to‐ICCDW transitions, respectively. Due to the upper limit of the measurement temperature, the higher‐temperature metallic phase was not captured in that study.^[^ 52 ^]^

Thus far, most existing thin 1T‐TaS_2_ devices have been fabricated by mechanically exfoliating bulk crystals. While this method yields high‐quality flakes, it restricts both sample size and fabrication throughput. As a result, establishing large‐area, controllable, and high‐quality thin‐film synthesis of 1T‐TaS_2_ is crucial for advancing both fundamental studies – especially at the thin limit – and practical device applications. In 2016, Fu et al. demonstrated a chemical vapor deposition (CVD) approach to grow 1T‐TaS_2_ thin flakes of varying thickness on SiO_2_/Si substrates, using TaCl_5_ and sulfur powder as precursors under an H_2_/Ar atmosphere at 1093 K.^[^ 115 ^]^ Later in 2018, Wang et al. reported the electrical measurements from CVD‐grown 1T‐TaS_2_ thin films on hBN, where the NCCDW‐to‐ICCDW transition features a pronounced thermal hysteresis of 30 K and the low‐temperature CCDW‐to‐NCCDW transition is largely suppressed, deviating from the transport properties of 1T‐TaS_2_ crystals.^[^ 112 ^]^ Alternatively, Lin et al. developed an MBE growth method for TaS_2_ on graphene‐terminated 6H‐SiC (0001) substrates.^[^ 116 ^]^ At a growth temperature of ≈700°C, both 1T and 2H phases of TaS_2_ were obtained, and the authors suggested that higher substrate temperatures favor the formation of the 1T phase, however, no transport properties were reported.^[^ 116 ^]^ It is worth noting that, despite the necessity for circuit‐level device integration, the synthesis of 1T‐TaS_2_ film with quality comparable to that of exfoliated single‐crystal flakes remains challenging, which is potentially attributed to the lack of suitable substrates, the propensity to forming defects during growth, and the susceptibility of phase transitions to these defects.

In stark contrast to VO_2_ and 1T‐TaS_2_, BaTiS_3_ has received far less attention as a phase‐change material, and its single‐crystal form was not available prior to 2018, despite the synthesis and structural characterization of BaTiS_3_ powders dating back to 1957.^[^ 117 ^]^ In 1996, Imai et al. measured the specific heat of pressed BaTiS_3_ powder from 1.4 K to 300 K, but they did not observe any anomaly indictive of phase transitions.^[^ 118 ^]^ The absence of observable transitions remains puzzling; one plausible hypothesis is that powders of BaTiS_3_ contain significantly more point and extended defects than single crystals, thereby suppressing the transitions. Further thermodynamic studies of large, high‐quality BaTiS_3_ single crystals are expected to clarify this issue.

In 2018, Niu et al. reported the first successful growth of BaTiS_3_ single crystals using a vapor‐phase growth approach with I_2_ as the transport agent.^[^ 86 ^]^ Unlike many conventional CVT processes where source materials are transported toward the other end of the ampule, clusters of needle‐like BaTiS_3_ crystals (typically < 50 µm in both width and thickness) were observed to directly grow out of BaTiS_3_ powder,^[^ 86 ^]^ as subsequently confirmed by Yang et al. in 2022^109^ (Figure 4e). Beyond these needle‐like morphologies, Niu et al. also obtained thin platelets of BaTiS_3_ with a‐ and c‐ axes in plane that are suitable for optical studies, as shown in Figure 4f (left). The right panel of Figure 4f illustrates a representative out‐of‐plane X‐ray diffraction scan of such a plate‐like BaTiS_3_ crystal. These samples facilitated the full characterization of BaTiS_3_’s giant optical anisotropy, with a record‐high birefringence of up to 0.76 in the mid‐ to long‐infrared range.^[^ 86 ^]^ Subsequently, Zhao et al. synthesized thin flakes of 001‐type BaTiS_3_ flakes with a‐ and b‐axes in plane through a similar CVT route, albeit with slightly modified conditions.^[^ 119 ^]^ Recently, Chen et al. developed a molten‐flux approach using either potassium iodide (KI) or a mixture of barium chloride (BaCl_2_) and barium iodide (BaI_2_) to grow BaTiS_3_ crystals.^[^ 113 ^]^ The KI‐based flux approach yielded crystals of dimensions up to a centimeter in length and 500 µm in both width and thickness, whereas the BaCl_2_‐BaI_2_ flux method produced plate‐like, (001)‐oriented BaTiS_3_ crystals up to 200 µm thick. These flux‐grown crystals exhibit substantially larger volumes than those obtained via vapor transport, while preserving the material's intrinsic optical and electronic properties.^[^ 113 ^]^

Similar to that of 1T‐TaS_2_, the development of high‐quality thin‐film growth of BaTiS_3_ still faces substantial challenges. Despite the successful demonstration of BaTiS_3_ thin films using magnetron sputtering^[^ 120 ^]^ and solution processing^[^ 121 ^]^ for optoelectronic applications, efforts toward realizing epitaxial thin films growth of BaTiS_3_ for leveraging its intrinsic optical anisotropy and phase‐change properties have, to date, been attempted exclusively via PLD approaches developed for complex chalcogenides.^[^ 114, 122, 123 ^]^ In 2022, Surendran et al. demonstrated the quasi‐epitaxial synthesis of BaTiS_3_ on single‐crystalline SrTiO_3_ substrates at ≈700°C, using an Ar/H_2_S (5%) background atmosphere.^[^ 114 ^]^ X‐ray diffraction measurements revealed a pronounced out‐of‐plane texture in these films, although no clear in‐plane epitaxial relationship between thin film and the substrate was observed.^[^ 114 ^]^ More recently, Surendran et al. developed a hybrid PLD strategy that employs an organosulfur precursor as the background sulfur source, substituting the chemically aggressive Ar/H_2_S environment.^[^ 122 ^]^ BaTiS_3_ films grown on SrTiO_3_ using this hybrid PLD method exhibited substantially improved surface and interface smoothness, while retaining crystallinity/texture comparable to that achieved by conventional PLD using Ar/H_2_S.^[^ 122 ^]^ It is worth noting that proper defect control in growth condition optimization, particularly of sulfur vacancies, can be critical in realizing high‐quality epitaxial BaTiS_3_ thin films, as has been demonstrated on another ternary chalcogenide BaZrS_3_.^[^ 124, 125 ^]^ The scarcity of lattice‐matched and chemically compatible substrates can be another limiting factor. At the moment, regular perovskite oxide substrates such as SrTO_3_, LaAlO_3_, and SrLaAlO_4_ are still the only few available options for complex chalcogenide synthesis.^[^ 114, 122, 123 ^]^ Therefore, achieving wafer‐scale complex chalcogenide single crystals through advanced synthesis techniques such as top‐seeded solution growth or Bridgeman method, represents a vital step toward realizing high‐quality chalcogenide thin films and their heterostructures in the future.

Device Fabrication

4

This section provides an overview of the recent advancements in electrical contact and device fabrication processes for three phase‐change materials – VO_2_ (thin films), 1T‐TaS_2_ (mechanically cleaved thin flakes), and BaTiS_3_ (micro‐scale bulk crystals). Owing to the different susceptibilities of these materials’ phase transitions to external factors such as oxidation and strain, researchers have developed and implemented various strategies to preserve intrinsic transport properties and achieve the desired device performance.

Fabrication processes for VO_2_ tend to be the most matured and well understood among the three materials, largely owing to its excellent air / thermal stability and the well‐developed processes for synthesizing high‐quality thin films whose monoclinic‐to‐tetragonal phase transition is well‐preserved.^[^ 94, 96 ^]^ Hence, conventional cleanroom micro‐fabrication techniques, such as photolithography, etching and metal deposition, can be readily applied. Device geometries of VO_2_ such as multi‐terminal Hall bars or linear bars are often patterned through dry etching approaches such as reactive ion etching (RIE) or ion milling for proper transport measurements.^[^ 126, 127, 128 ^]^ Simpler two‐terminal geometries are generally sufficient for neuronal oscillator devices (Figure 5a,b), where a short channel length proves crucial to achieving low switching voltages and high oscillation frequencies.^[^ 126, 129, 130 ^]^ When device dimensions must be reduced beyond the limits of standard lithography techniques, an out‐of‐plane VO_2_ device geometry, where the channel dimension is equivalent to the film thickness (on the order of tens of nanometers), is often employed.^[^ 131, 132 ^]^ In such configurations, VO_2_ films are typically deposited on high‐temperature‐compatible conductive substrates, including Pt, TiN, and SrRuO_3_, before putting down top electrodes.^[^ 97, 131, 132 ^]^ In 2015, Mian et al. reported a record‐high oscillation frequency of 9 MHz from a VO_2_/TiN vertical device,^[^ 131 ^]^ as illustrated in Figure 5c. Additional optimization of metal‐to‐VO_2_ contacts is expected to further improve the device performance.

Device Fabrication. a) Cross‐sectional schematic of a two‐terminal planar VO2 thin film device. Figure adapted with permission from Ref.[130] Copyright 2011, Elsevier. b) Optical microscopic image of a four‐probe VO2 film device fabricated through dry etching. Figure adapted with permission from Ref.[126] Copyright 2008, AIP Publishing. c) Schematic illustration of an out‐of‐plane VO2 film device using TiN as the bottom electrode. Figure adapted wtih permission from Ref.[131] Copyright 2015, AIP Publishing. d) Optical microscopic images of few‐layer 1T‐TaS2 flakes showing the degradation progress in air. Figures adapted with permission from Ref.[108] Copyright 2015, Springer Nature. e) Optical microscopic images of device fabrication processes for mechanically exfoliated 1T‐TaS2 flakes on a SiO2/Si substrate, including hBN encapsulation (left) and metal deposition (right) steps. The inset to the right shows a cross‐sectional schematic of the device. Figures adapted with permission from Ref.[137] Copyright 2015, National Academy of Science. f) Schematic illustration of a multi‐terminal BaTiS3 bulk device fabricated through polymeric planarization and regular photolithography processes. Figure adapted with permission from Ref.[138] Copyright 2022, ACS Publications. g) Optical microscopic images of BaTiS3 bulk devices with a van der Waals (left) and a transmission line method (TLM, right) contact geometry. Figures adapted with permission from Ref.[56] Copyright 2023, John Wiley & Sons.

1T‐TaS_2_ exhibits a layered structure bonded via weak van der Waals interactions, and hence, it can be mechanically exfoliated down to a few tens of nanometers or thinner for device fabrication. Notably, there has been a long history of research on exfoliation and transfer of layered TMDCs,^[^ 81, 133 ^]^ dating back well before the discovery of single‐layer graphene in 2004.^[^ 134, 135 ^]^ For instance, in 1962, Frindt and Yoffe produced ultra‐thin molybdenum disulfide (MoS_2_) flakes (< 10 nm) by mechanical cleavage for optical and electron diffraction studies.^[^ 133 ^]^ By 1969, Wilson and Yoffe were able to prepare thin specimens (<100 nm) of various TMDCs by repeated cleaving on adhesive tapes.^[^ 81 ^]^ More recently, atomically thin 1T‐TaS_2_ has re‐attracted enormous research interest, revealing novel phenomena such as gate‐tuned phase transition,^[^ 108 ^]^ electrical oscillations,^[^ 62, 63 ^]^ and memristive switching.^[^ 54, 136 ^]^ These advances have been facilitated by the fast‐evolving developments of exfoliation and transfer techniques for 2D materials, wherein thin flakes of 1T‐TaS_2_ with thickness down to monolayer can be isolated and integrated into devices. E‐beam lithography is often adopted to pattern fine features at the micrometer scale or smaller, and to accommodate the specific alignment requirement for each flake. However, due to high processing temperatures of most ebeam resists (e.g., ≈180°C baking temperature for PMMA), additional care needs to be taken to avoid material degradation when fabricating 1T‐TaS_2_ based devices, particularly at their thin limits.

In 2015, Yu et al. observed that below 10 nm, the CCDW‐to‐NCCDW transition in 1T‐TaS_2_ is suppressed, whereas the higher‐temperature NCCDW‐to‐CCDW transition at ≈350 K persists till ≈4 nm, below which it also disappears.^[^ 108 ^]^ Debate arises regarding whether the apparent absence of CDW phase transitions in ultrathin, unprotected 1T‐TaS_2_ flakes arises from intrinsic dimensional effects or extrinsic factors such as oxidation, considering the thin material's propensity to degradation in air (Figure 5d). Soon after Yu's work, Tsen et al. demonstrated that ultrathin 1T‐TaS_2_ flakes, protected by hexagonal boron nitride (hBN), retained the NCCDW‐to‐CCDW transition at thickness down to 4 nm through both electron diffraction and transport measurements (Figure 5e).^[^ 137 ^]^ Further, they showed evidence of the NCCDW phase in the 2 nm sample using electron diffraction, although the transition to the CCDW was not observed at this thin limit.^[^ 137 ^]^ These findings suggest that oxidization, rather than purely dimensional effects, may be responsible for the absence of charge order in ultrathin, unprotected 1T‐TaS_2_ flakes.^[^ 137 ^]^ Therefore, hBN encapsulation strategy is usually employed to preserve the intrinsic device performance of 1T‐TaS_2_ when working with ultrathin samples.^[^ 108, 137 ^]^ On the other hand, although mechanical exfoliation and hBN encapsulation strategies are suitable for laboratory‐scale research, it is not practical for large‐area device fabrication. Consequently, further efforts need to be made on high‐quality thin‐film synthesis and device encapsulation of 1T‐TaS_2_, where intrinsic electrical switching properties can be well‐preserved.^[^ 115, 116 ^]^

For BaTiS_3_, like many other small, non‐exfoliable crystals, establishing high‐quality multiterminal electrodes on them has proven challenging due to their limited size. Although Niu et al. has demonstrated the synthesis of large, thin BaTiS_3_ platelets with lateral dimensions of several millimeters via a vapor transport method in his original optical anisotropy study in 2018,^[^ 86 ^]^ the yield of such large samples suitable for manual bonding remains low, due to the large number of nucleation sites during growth. Indeed, most BaTiS_3_ crystals grown by CVT methods exhibit a needle‐like shape that is typically tens of microns in thickness and width, and up to several millimeters along the chain axis, as confirmed by several recent reports.^[^ 86, 109 ^]^ In 2022, Chen et al. addressed this challenge by adapting a polymeric planarization technique, initially developed for handling micro‐scale GaAs‐based devices,^[^ 139, 140 ^]^ to fabricate multiterminal electrical contacts on small, bulk BaTiS_3_ crystals for electrical transport studies.^[^ 138, 141 ^]^ As depicted in Figure 5f, the crystals are first embedded in a low‐stress polymeric matrix (e.g., polyimide) to achieve a planar top surface, enabling direct application of standard lithography and microfabrication processes for forming electrodes with desired geometries.^[^ 138 ^]^ The choice of a low‐stress polymer minimizes extrinsic thermal strain effects at low temperatures, which preserves intrinsic transport characteristics of BaTiS_3_ that are highly susceptible to strains.^[^ 56, 138 ^]^ These prototype BaTiS_3_ single‐crystal devices (Figure 5g) exhibited clear signatures of phase transitions and enabled proof‐of‐concept demonstrations of electrical resistive switching and voltage oscillations.^[^ 34, 56 ^]^ Further research and development on high‐quality BaTiS_3_ thin‐film synthesis that features intrinsically robust or tunable phase transitions, will help streamline its device fabrication and pave the way toward practical electronic devices applications of this emerging phase‐change material.

Transport Properties

5

Temperature‐dependent electrical transport measurements are among the most important characterizations for phase‐change materials. Upon varying the temperature, anomalies in electrical resistivity such as metal‐to‐insulator transitions can emerge near specific transition temperatures, typically reflecting an underlying structural transition and corresponding modification in the electronic structure. In addition to the classic metal‐to‐insulator transitions observed in the correlated oxide VO_2,_ ^[^ 35 ^]^ both the CDW systems 1T‐TaS_2_ and BaTiS_3_ display pronounced resistivity changes across the transitions.^[^ 52, 56 ^]^ It is important to note, however, that the metal‐to‐insulator transition is not a universal feature in all real CDW materials, despite the prediction of Peierls’ theory for ideal 1D metals.^[^ 142, 143 ^]^ Detailed temperature‐dependent Hall measurements (Figure 6a), which probe the evolution of carrier concentration and mobility, further provide important insights into the mechanisms governing these phase transitions.

Transport properties. a) Schematic illustration of Hall measurements. (b) Temperature evolution of Hall mobility (left) and carrier concentration (right) across the MIT phase transition in VO2. Figures adapted with permission from Ref.[144] Copyright 1973, American Physical Society. c) Temperature dependence of Hall coefficient and carrier concentration across the transitions. Figure adapted wtih permission from Ref.[84] Copyright 1979, Elsevier. d) Temperature evolution of mobility and carrier concentration of a BaTiS3 crystal along the c‐axis. The associated temperature dependent electrical resistivity measurement is shown in Figure 3e. Figure adapted with permission from Ref.[56] Copyright 2023, John Wiley & Sons.

As detailed in Figure 3a, single crystals of VO_2_ undergo dramatic change in resistivity of up to five orders of magnitude across the transition.^[^ 41 ^]^ In 1973, Rosevear and Paul investigated magneto‐transport properties of both semiconducting and metallic phases in VO_2_ single crystals using an oscillating AC magnetic field,^[^ 144 ^]^ as shown in Figure 6b. At the insulator‐to‐metal transition, the carrier concentration extracted from the Hall measurements increased by roughly a factor of 5 × 10^4^, whereas the Hall mobility changed from about 0.5 to 0.35 cm^2^ (V⋅s) ^−1^.^[^ 144 ^]^

1T‐TaS_2_ exhibits two pronounced hysteretic transitions in resistivity below 400 K, as illustrated in Figure 3c. The exact hysteresis width varies among samples, which is presumably associated with impurities, structural defects or other forms of disorder. In fact, the earliest electrical transport study on 1T‐TaS_2_ by Thompson et al. in 1971 reported hysteresis width as large as 100 K for the CCDW‐to‐NCCDW transition.^[^ 52 ^]^ In 1980, Inada et al. found an even larger resistivity hysteresis of 150 K in 1T‐TaS_1.2_Se_0.8_ single crystals, which was attributed to the increased disorder from selenium alloying.^[^ 85 ^]^ Moreover, a substantial rise in resistivity is often observed at temperatures below ≈50 K. In 1977, Di Salvo and Graebner attributed this low‐temperature increase in resistivity to an extrinsic Anderson localization effect due to random impurities or defect potentials.^[^ 145 ^]^ Hall measurements of 1T‐TaS_2_ provide further insights into its transport processes by revealing both the carrier type and concentrations, as demonstrated by Inada et al. in 1979 (Figure 6c).^[^ 84 ^]^ The high‐temperature metallic phase transforms into the ICCDW phase, where the Fermi surface is broken into fragments as a result of CDW formation. In this ICCDW phase, the residual Fermi surface fragments still give rise to a high carrier concentration of ≈10^22^ cm^−3^ and the majority carriers are electrons.^[^ 84 ^]^ Upon crossing the NCCDW transition near 350 K, the carrier concentration drops by about 30%, and continues to decrease to ≈3 × 10^21^ cm^−3^ down to ≈200 K. At the NCCDW‐to‐CCDW transition upon cooling, a discontinuous change in resistivity accompanies a sign reversal of the Hall coefficient (R H).^[^ 84 ^]^ The system enters a semimetallic or semiconducting region with its majority carrier type switched to p‐type at carrier concentrations of ≈10^19^ cm^−3^. A characteristic peak of R H ≈30–50 K is further postulated that, below that temperature range, the material becomes a semiconductor of the impurity type.^[^ 84 ^]^

Moreover, by simply reducing the thickness of 1T‐TaS_2_, researchers have significantly modulated its transport characteristics compared to bulk samples. In 2015, Yu et al. systematically investigated 1T‐TaS_2_ thin flakes with varying thicknesses down to ≈2 nm, observing a pronounced broadening in the hysteresis width of the low‐temperature NCCDW‐to‐CCDW transition as the thickness decreased from ≈100 to ≈10 nm, alongside a less abrupt overall resistivity change.^[^ 108 ^]^ Below 10 nm, the CCDW‐to‐NCCDW transition is suppressed, whereas the higher‐temperature NCCDW‐to‐CCDW transition at ≈350 K persists till ≈4 nm, below which it also disappears.^[^ 108 ^]^ Notably, Tsen et al. demonstrated that, by simply encapsulating ultrathin 1T‐TaS_2_ flakes with hexagonal boron nitride (hBN), NCCDW‐to‐CCDW transition can be retained in samples with thicknesses down to 4 nm, suggesting that oxidization plays an important role in suppressing the charge order in ultrathin, unprotected 1T‐TaS_2_ flakes.^[^ 137 ^]^

In contrast, BaTiS_3_ was not known to exhibit any phase transition until recently. In 2023, Chen et al. identified two distinct transitions in single‐crystal BaTiS_3_ from its non‐monotonic, hysteretic transport behavior,^[^ 56 ^]^ as shown in Figure 3e. Upon cooling, the system undergoes a transition from the ambient semiconducting phase to the CDW phase at ≈240 K (“Transition II”) with a clear resistivity jump. On further cooling, the resistivity continues to rise till ≈150 K, whereupon another transition (“Transition I”) drives the system into a high‐conductivity state (or high‐mobility state), marked by a sharp resistivity drop. The hysteresis spans over 40 K for Transition I and about 10 K for Transition II.^[^ 56 ^]^ Structural characterizations revealed weak superlattice reflections indictive of a periodic lattice distortion emerging below Transition II, and these are subsequently suppressed at Transition I.^[^ 56 ^]^ Below 100 K, the resistivity increases rapidly and becomes too large to measure reliably using standard AC transport techniques.

Hall measurements of BaTiS_3_ single crystals further clarify its transport mechanisms.^[^ 56 ^]^ With electron as majority carrier, BaTiS_3_ has a room‐temperature carrier concentration of ≈1.1 × 10^18^ cm^−3^, which is among the lowest reported for known CDW compounds, confirming its nondegenerate nature.^[^ 56 ^]^ As illustrated in Figure 6d, the carrier concentration decreases monotonically upon cooling, reaching ≈10^15^ cm^−3^ by 100 K, without any abrupt changes in magnitude or sign across either transition.^[^ 56 ^]^ Instead, Hall mobility undergoes a significant drop and then a substantial rise at Transition II and I, respectively, suggesting that the modulation of BaTiS_3_’s resistance stems largely from changes in mobility.^[^ 56 ^]^ This contrasts notably with VO_2_ and 1T‐TaS_2_, where large carrier concentration changes are responsible for the resistance jumps across phase transitions.^[^ 84, 144 ^]^

Electrically Driven Volatile Threshold Switching and Mechanisms

6

In addition to varying system temperature, adjacent phases in phase‐change materials can be switched electrically by applying either voltages or currents.^[^ 32, 33, 34, 146 ^]^ Such electrically controlled resistive switching holds unique advantages over other modulating parameters such as temperatures, high pressure, and optical pulses, owning to the relative ease of implementation in electronic devices. Depending on the nature of the transition and specific testing conditions, these materials may exhibit either volatile or non‐volatile resistive switching. Here, we focus on volatile threshold switching of these materials that are promising in demonstrating neuronal oscillator devices, although non‐volatile multi‐level resistive switching has also been reported when operating under different conditions (within hysteretic transition window) for both VO_2_ and 1T‐TaS_2_.^[^ 54, 136, 147 ^]^

VO_2_ crystals and thin films undergo a structural and insulator‐to‐metal transitions upon heating to about 340 K, exhibiting a resistivity drop of several orders of magnitude, as shown in Figure 3a. Resistive switching induced by applying voltage or current above a critical threshold, with negative differential resistance (NDR) often observed in current sweeping measurements, has been widely observed in both single crystals^[^ 148, 149 ^]^ and thin films^[^ 129 ^]^ of VO_2_, as illustrated Figure 7a. In 1980, Mansingh et al. systematically investigated the current‐voltage (I‐V) characteristics of a VO_2_ single crystal at varying temperatures from 220 to 325 K, while tracking the crystal temperature through a thermocouple attached to the sample surface.^[^ 32 ^]^ They observed that lowering the ambient temperature increased the threshold voltage (V th) upon switching but decreased the corresponding current (I th) at V th, resulting in a nearly constant threshold power (V th × I th).^[^ 32 ^]^ Notably, the measured crystal surface temperature rose just above the ambient, remaining well below the bulk transition temperature of 340 K.^[^ 32 ^]^ On this basis, they proposed a model involving a conducting channel of finite width arising from local heating, where switching is initiated once the channel temperature reaches the transition threshold of VO_2_.^[^ 32 ^]^ More recently, Kumar et al. utilized black‐body emission mapping to spatially resolve the temperature distribution of a VO_2_ thin film under varying applied currents, as shown in Figure 7b.^[^ 150 ^]^ Similarly, Valle et al. employed spatiotemporal optical reflectivity measurements (Figure 7c) to characterize the growth and percolation dynamics of the metallic phase in VO_2_, suggesting that the electrically driven insulator‐to‐metal transition can be explained just by considering the effect of Joule heating.^[^ 151 ^]^ These results revealed the emergence and growth of a filament‐shaped hot channel bridging the electrodes, further supporting the thermal nature of the switching.

Electrically driven volatile threshold switching and mechanisms. a) I‐V characteristics of a VO2 thin film devices with active channel dimensions of 10 µm × 10 µm in both V‐mode (voltage sweeps) and I‐mode (current sweeps). Figure adapted with permission from Ref.[129] Copyright 2010, AIP Publishing. b) Optical microscopic images (bottom) and electrical characteristics (top) of filaments observed between the electrodes at different applied currents. Figures adapted with permission from Ref.[150] Copyright 2013, John Wiley & Sons. c) Spatiotemporal characterization of the electrically induced insulator‐to‐metal transition in VO2. Figures adapted with permission from Ref.[151] Copyright 2021, American Association for the Advancement of Science. d) Temperature dependent two‐probe resistance of a 11.8‐nm‐thick 1T‐TaS2 flake (left) and the associated Joule heating rate analysis. Figures adapted with permission from Ref.[63] Copyright 2018, ACS Publications. e) Cross‐sectional view of the simulated temperature distribution near a 1T‐TaS2 device channel, for applied current pulses of short (8 ns) and long (13.3 µs) durations. Figures adapted with permission from Ref.[152] Copyright 2021, AIP Publication. f) Temperature dependent four‐probe resistance of a bulk BaTiS3 device from 220 K to 240 K (left) and the associated thermal power analysis (right). g) Pulsed I‐V characterization of BaTiS3. (f) and (g) Figures adapted with permission from Ref.[34] Copyright 2023, John Wiley & Sons.

Similar resistive switching behavior has also been reported in 1T‐TaS_2_. In 2015, Hollander et al. demonstrated electrically driven, reversible switching between the insulating CCDW phase and metallic NCCDW/ICCDW phases in mechanically exfoliated 1T‐TaS_2_ flakes at cryogenic temperatures, which was interpreted as a result of a carrier‐assisted collapse of the Mott gap.^[^ 33 ^]^ Later, Liu et al. exploited the unique transport properties of ultrathin 1T‐TaS_2_ (6 to 9 nm in thickness), where the low‐temperature insulator‐to‐metal transition between the CCDW and NCCDW phases is suppressed, to demonstrate volatile resistive switching devices based on the NCCDW‐to‐ICCDW transition, which operated at a wide temperature range from 78 K to 320 K.^[^ 62 ^]^ To evaluate the contributions of Joule heating to the resistive switching in 1T‐TaS_2_, Zhu et al. carried out temperature‐dependent I‐V measurements and estimated the local temperature rise due to Joule heating by establishing a simple analytical thermal model, as illustrated in Figure 7d.^[^ 63 ^]^ The threshold Joule heating power required for switching reduces as the ambient temperature approaches T C, consistent with a thermally driven picture.^[^ 63 ^]^

Pulsed I‐V measurements also provide insights into the switching mechanism by deconvoluting the thermal and electric‐field contributions that can otherwise be conflated in conventional DC measurements. In a pulsed I‐V measurement, an arbitrary waveform generator produces a single or a series of pre‐programmed voltage/current pulses and sends them to the device under test, while the response is recorded by an oscilloscope or other high‐speed measurement instrument. effects.^[^ 153 ^]^ In 2021, Mohammadzadeh et al. studied the NCCDW‐to‐ICCDW switching in exfoliated 1T‐TaS_2_ flakes using electrical pulses ranging from 8 ns to ≈13 µs.^[^ 152 ^]^ They found that the reconstructed pulsed I‐V characteristics exhibited no hysteresis for pulse durations below ≈200 ns, whereas longer pulses induced pronounced hysteresis that peaks at some particular value of pulse duration.^[^ 152 ^]^ COMSOL‐based simulations show that the heating is insufficient to drive the NCCDW‐to‐ICCDW transition for 8‐ns pulse duration (Figure 7e, top), while the local temperature of the 1T‐TaS_2_ channel rises well above 350 K with a 13.3 µs duration (Figure 7e, bottom).^[^ 152 ^]^ Mohammadzadeh et al. further suggested that, despite the thermal origins of the switching, GHz‐level switching speed are still feasible in thin 1T‐TaS_2_ devices by optimizing device geometry and thermal resistance.^[^ 152 ^]^

First observation of electrically driven reversible resistive switching in BaTiS_3_ was reported in 2023, shortly after the initial discovery of phase transitions in this material.^[^ 34 ^]^ BaTiS_3_ exhibits a transition from a semiconducting room‐temperature phase to a CDW state near 250 K, featuring a resistance jump of two‐ to threefold and a thermal hysteresis of ≈10 K,^[^ 56 ^]^ as illustrated in Figure 3e. Electrically, BaTiS_3_ exhibits a threshold switching behavior below its transition temperature T c: the I‐V characteristics show an abrupt switching to a conductive state above a threshold voltage (V F) during forward scan, and a return to its original high‐resistance state below another critical voltage (V R) during reverse scan, forming a characteristic hysteresis window,^[^ 34 ^]^ similar to those reported for both VO_2_ and 1T‐TaS_2_. When driving the device with a current source, an “S‐type” NDR regime is also observed.^[^ 34 ^]^

To assess the contribution of Joule heating in BaTiS_3_ resistive switching, Chen et al. carried out thermal analysis based on four‐probe I‐V sweeps at various temperatures across the CDW transition, as shown in Figure 7f.^[^ 34 ^]^ They noted that the critical voltage (V th) required to switch the device increases with decreasing temperature, as does the threshold current (I th).^[^ 34 ^]^ The threshold thermal power (P th) generated by Joule heating was then estimated using P th = V th × I th for both forward and reverse scans at each temperature. Unlike VO_2_, where P th remains largely temperature‐independent and hence the switching is achieved through a conducting channel (or filament),^[^ 32 ^]^ P th in BaTiS_3_ was found to decrease linearly as the temperature approached T c. Two characteristic temperatures of 245 K and 258 K were extrapolated at which the threshold thermal power equals to zero, which aligns with the transition temperatures extracted from low‐field transport measurements.^[^ 34 ^]^ Moreover, pulsed I‐V measurements were carried out at 210 K with varying pulse widths ranging from 1 ms to 8 ms and a constant pulse period of 10 ms.^[^ 34 ^]^ The reconstructed I‐V curves with voltages swept between 0.8 and 1.8 V are displayed in Figure 7g. Decreasing the pulse width from 8 ms to 1 ms, while maintaining the same pulse period and voltage sweep ranges, reduced the contribution of Joule heating and in turn narrowed the hysteresis window and raised the threshold switching voltage.^[^ 34 ^]^ Notably, no hysteresis was observed at 1 ms pulse width. Therefore, Chen et al. suggested that the switching in BaTiS_3_ is primarily thermally driven, as reducing pulse width decreases Joule heating power without altering the applied electric field.^[^ 34 ^]^

Self‐Sustained Voltage Oscillations

7

This section surveys the development of the self‐sustained phase‐change oscillator devices of VO_2_, 1T‐TaS_2_, and BaTiS_3_, by leveraging the electrically driven volatile resistive switching in the systems. The detailed device geometries, the associated threshold switching behavior, and voltage oscillation performance are listed in Table 3.

Self‐sustained oscillations in VO_2_ were first reported in 1975 by Taketa et al., who employed a bulk crystal device (≈mm channel length) connected in series with a load resistor under an applied DC voltage.^[^ 149 ^]^ The oscillation frequency at room temperature was ≈5 kHz, and it decreases as the ambient temperature approached the transition temperature.^[^ 149 ^]^ In 2008, Sakai et al. achieved a substantially higher oscillation frequency of ≈550 kHz in a VO_2_ thin‐film device (10  µm × 10 µm × 0.22 µm), fabricated by PLD and subsequent dry etching.^[^ 126 ^]^ As shown in Figure 8a,b, similar device performance with oscillation frequency > 0.5 MHz was demonstrated by Kim and Lee et al. on sol‐gel prepared VO_2_ thin‐film devices with comparable lateral sizes (10  µm × 10 µm × 0.1 µm).^[^ 129, 154 ^]^ In 2011, Seo et al. experimentally investigated dimensional effects on VO_2_ oscillators in planar device geometries, demonstrating a decrease in oscillation frequency as either the channel length or width increased.^[^ 130 ^]^ This finding suggests that scaling the active device region could lead to higher oscillation frequencies, pending other limiting factors such as contact resistances or intrinsic capacitance.

Self‐sustained voltage oscillations. a) Schematic diagram of the electrical circuit used for the generation of the MIT oscillation in a VO2 thin film device. b) Waveform of VD and ID of the device measured at room temperature. a,b) Figure adapted with permission from Ref.[129] Copyright 2010, AIP Publishing. c) I‐V characteristics of a 1T‐TaS2 flake device at room temperature and load lines of the series resistor at different VDC values. The oscillator circuit starts to oscillate across the threshold condition of VDC = 3.8 V. d) Voltage oscillations of a 1T‐TaS2 flake device under different VDC values. c,d) Figures adapted with permission from Ref.[62] Copyright 2016, Springer Nature. e) I‐V characteristics of a two‐terminal BaTiS3 device at 220 K. The dashed line represents a series resistor load line for stable voltage oscillations and the inset shows a schematic illustration of the oscillator measurement circuit. f) Oscillation waveforms of a BaTiS3 device operated at different temperatures. e,f) Figures adapted with permission from Ref.[34] Copyright 2023, John Wiley & Sons.

Alternatively, in 2014, Beaumont et al. investigated out‐of‐plane VO_2_ devices (3  µm × 3 µm) integrated in crossbars geometry and realized oscillation frequencies of up to 300 kHz.^[^ 155 ^]^ They noted that such metal‐VO_2_‐metal configurations not only minimize the device footprint to enhance circuit integration, but also reduce the threshold voltage for triggering insulator‐to‐metal transition by shortening the conduction path to the film thickness (e.g., <100 nm).^[^ 155 ^]^ However, using regular Ti/Au/Ti bottom electrodes largely constrained the achievable VO_2_ film quality, likely due to limited growth temperatures or poor interfaces, resulting in low resistance jump across the transition.^[^ 155 ^]^ Similar limitations have been reported using SrRuO_3_ or Pt bottom electrodes, where resistance changes across the transition are often below one order of magnitude.^[^ 132 ^]^ In 2015, Mian et al. addresses these challenges by incorporating TiN as the bottom electrode, improving the interface and overall VO_2_ film quality in an out‐of‐plane device configuration.^[^ 131 ^]^ This approach yielded self‐oscillations of up to 9 MHz with low threshold switching voltages and currents.^[^ 131 ^]^ Further optimization of thin‐film deposition conditions and electrode‐integration strategies, aimed at minimizing contact resistances and active channel sizes, could further increase the oscillation frequencies of VO_2_ devices, thereby making them more attractive for practical high‐frequency applications.

It is also worth pointing out that, in the literature, some researchers adopted the concept of ‘endurance’ incorrectly for such phase‐change oscillators and reported erroneous and unusually high values of endurance.^[^ 156, 157 ^]^ For instance, Liu et al. directly regarded the >10^6^ switching cycles of a VO_2_ oscillator over ≈60 s’ operation time as its endurance,^[^ 156 ^]^ and similarly, Li et al. reported an exceptionally high endurance of ≈6.5 × 10^10^ in a NbO_2_‐based oscillator device by operating the device for over 96 min.^[^ 157 ^]^ Indeed, such device characteristics can be somewhat misleading in these scenarios, as the endurance of a resistive switching device, by definition, refers the number of writing/erasing cycles the device can undergo before it deviates outside of the operation window, whereas no such concepts of writing/erasing even exist in the context of volatile switching. Therefore, the ‘endurance’ is most commonly used in characterizing non‐volatile switching devices such as memories and memristors.^[^ 158, 159, 160 ^]^

As for 1T‐TaS_2_, despite extensive research on bulk crystals in the 1970s and 1980s, including several studies on CDW‐associated metal‐insulator transitions,^[^ 52, 84 ^]^ the phase‐change oscillator applications based on this material were not realized until the mid‐2010s.^[^ 62, 63 ^]^ Much of the current electrical studies of 1T‐TaS_2_ relies on mechanically exfoliated micro‐scaled flakes, whose lateral dimensions and production yield remain limited. In 2016, Liu et al. constructed the first room‐temperature CDW oscillator using thin 1T‐TaS_2_ flakes.^[^ 62 ^]^ Their device exploits the electrically driven NCCDW‐to‐ICCDW transition near 350 K, achieving a maximum oscillation frequency of ≈2 MHz in a simple oscillation circuit composed of a two‐terminal 1T‐TaS_2_ device in series with a load resistor,^[^ 62 ^]^ as shown in Figure 8c,d. They further integrated a top‐gated graphene field‐effect transistor (FET) with the 1T‐TaS_2_ device, enabling tunable oscillation frequencies through gate‐mediated adjustments of the load resistance.^[^ 62 ^]^ Although the 1T‐TaS_2_ flakes used for demonstration were only 6–9 nm thick, the same room‐temperature oscillation behavior could, in principle, be observed in thicker 1T‐TaS_2_ crystals, provided that the NCCDW‐to‐ICCDW transition persists. Suppressing the low‐temperature CCDW‐to‐NCCDW transition in such thin 1T‐TaS_2_ extends the oscillator's operation window to much lower temperature ranges without interference from the low‐temperature transition. This disappearance of the CCDW‐to‐NCCDW transition in sufficiently thin 1T‐TaS_2_ flakes is typically attributed to extrinsic surface oxidation effects, as discussed by Tsen et al. in 2015.^[^ 137 ^]^ Furthermore, Zhu et al. developed light‐tunable CDW oscillators based on 1T‐TaS_2_, whose oscillation frequency can be well modulated by varying the illumination intensity through the laser thermal effect.^[^ 63 ^]^

As discussed earlier, phase‐change oscillators have been experimentally demonstrated in both VO_2_ and 1T‐TaS_2_ with oscillation frequencies reaching the MHz regime, although the underlying switching mechanisms may differ. BaTiS_3_ undergoes a unique semiconductor‐to‐CDW transition near 250 K, resulting in a two‐to‐three‐fold resistivity jump and a thermal hysteresis window of ≈10 K.^[^ 34, 56 ^]^ The overall shape of this transition, in terms of temperature‐dependent resistivity, resembles that of the MIT in VO_2_ or the ICCDW‐to‐NCCDW transition in 1T‐TaS_2_, suggesting the feasibility of inducing voltage oscillations in BaTiS_3_. In 2023, Chen et al. reported the first phase‐change oscillator based on single‐crystal BaTiS_3_ operating at 220 K (≈30 K below its transition temperature), achieving an oscillation frequency of ≈16 Hz by connecting a two‐terminal BaTiS_3_ device in series with a load resistor (R S) under a DC bias,^[^ 34 ^]^ as shown in Figure 8e. The oscillation arises from volatile threshold resistive switching, a common feature of all three phase‐change materials discussed in this review, and reflects the periodic changes of electrical resistance triggered by repetitive local heating and cooling cycles across the phase transition boundary.^[^ 34 ^]^ When the voltage applied across the BaTiS_3_ channel exceeds the critical voltage (V F), a transition to the low‐resistance state is initiated due to Joule heating (P=VDC2(R+RS)2/R), resulting in a sudden increase in current and a subsequent increase in voltage across the load resistor.^[^ 34 ^]^ The Joule heating powder (P) is insufficient to maintain the temperature in the low‐resistance regime, because P decrease as R is reduced (for R < R S), driving BaTiS_3_ back to the CDW state. The cycle repeats and yields self‐sustained voltage oscillations.^[^ 34 ^]^

Despite this successful demonstration in a relatively new phase‐change material, the oscillation frequencies of BaTiS_3_ single‐crystal devices remain orders of magnitude lower than those reported for VO_2_ and 1T‐TaS_2_, due to combined effects of non‐ideal sample morphologies, device geometries, and thermal managements.^[^ 34 ^]^ Inspired by earlier efforts with VO_2_ single‐crystal oscillators,^[^ 149 ^]^ Chen et al. employed a thermal management strategy to enhance the oscillation frequencies of BaTiS_3_ devices.^[^ 34 ^]^ Figure 8f shows that the oscillation frequency of the same device increased from 67 Hz to 910 Hz by lowering the operating temperature from 200 K to 130 K, benefited from an enhanced cooling efficiency.^[^ 34 ^]^ However, maintaining stable CDW oscillations below ≈130 K proved challenging, as the low‐temperature structural transition in BaTiS_3_ starts to interfere with the switching behavior.^[^ 56 ^]^ Strategies that can suppress this low‐temperature transition could potentially improve the device performance but require further research investigations. Additionally, Chen et al. improved oscillation frequency by reducing the channel length, a method previously employed in other oscillating systems such as VO_2_.^[^ 130 ^]^ Both operating at 170 K, a BaTiS_3_ device with a 5 µm channel outperformed a 10 µm device by over a factor of three in oscillation frequency.^[^ 34 ^]^ This effect likely stems from more efficient local heating and cooling in smaller channels. Further reduction of the BaTiS_3_ channel dimensions, including thickness, is expected to oscillation frequency significantly. Consequently, synthesizing high‐quality BaTiS_3_ thin film with intrinsic phase‐change properties would be highly desired for their practical electronic device applications, benefiting from the precise thickness control and the fabrication scalability.

Device Implementation of Phase‐Change Neuronal Oscillators

8

As for the device implementation aspect, phase‐change neuronal oscillators can be used individually or integrated into high‐level circuits to not only emulate both deterministic and stochastic dynamics of biological neurons, but also leverage the dynamics to solve various NP‐hard optimization tasks accurately and efficiently that are otherwise challenging using conventional von Neumann processors. In this section, we discuss potential neuronal device applications of these phase‐change materials at the circuit integration level. Note that due to distinctive differences in their technological readiness and literature availability, as illustrated in Table 4, the majority of the device application examples covered in this section are based on VO_2_ oscillators.

Electronic devices based on threshold resistive switching in phase‐change materials are promising candidates for emulating biological‐neuron‐like temporal dynamics at different levels of complexities. Based on the classification criterions proposed by Kumar et al., most selector‐type devices exhibiting volatile switching, either voltage controlled or current controlled, are categorized as first‐order, whose dynamical complexity arises from the changing of internal temperatures during the switching.^[^ 161 ^]^ This class includes the two‐terminal VO_2_, 1T‐TaS_2_, and BaTiS_3_ devices discussed in Section 6, even though the underlying operating mechanisms may vary. Second‐order neuronal complexity such as self‐sustained oscillations can be realized by integrating a first‐order device into a relaxation oscillator circuit, as shown in Section 7.^[^ 161 ^]^ The higher‐order complexity is achieved via two alternating dynamical processes: that is, the charging‐discharging dynamics of the capacitor and the internal thermodynamics of volatile switching.^[^ 161 ^]^ Standalone second‐order devices are also possible when their built‐in capacitance is sufficiently large to sustain the oscillations without the need for an external parallel capacitor, as demonstrated with NbO_2_.^[^ 162 ^]^

Achieving even higher‐order complexities often requires multiple coupled circuit elements. For instance, Yi et al. reported a non‐transistor fourth‐order neuronal system employing two volatile VO_2_ switching devices and a series of circuit elements to emulate the biologically accurate Hodgkin‐Huxley neuron model.^[^ 163 ^]^ This approach successfully reproduced all 23 neuronal functionalities, including spiking, bursting and mixed mode firing. Figure 9a illustrates the structure of a biological neuron membrane, highlighting Na^+^ and K^+^ channels. In the corresponding circuit diagram, two VO_2_ neuronal devices (*X_1_

• and X 2) are coupled with two capacitors (C 1 and C 2) and two series load resistors (R L1 and R L2). When driven by a steady DC current, this circuit can produce periodic bursts of spikes, a hallmark of tonically active neurons.^[^ 163 ^]^ By either replacing the load resistor R L1 with a capacitor C in, or by inserting C in before R L1 in the tonic neuron circuit, one can emulate another basic type of neurons, that is, phasically active neurons, characterized by a single spike fired upon the onset of a DC input followed by quiescence afterward.^[^ 163 ^]^ Moreover, by placing a capacitor C in in parallel with R L1, a mixed‐mode neuron can be simulated, which features a phasic burst followed by a series of tonic spiking upon applying the DC input. Figure 9b shows part of the 23 experimentally demonstrated biological neuron spiking behaviors. A detailed circuit design and neuron emulation results can be found in the original reference.^[^ 163 ^]^

Device implementation of phase‐change neuronal oscillators. a) Circuit diagrams of a two‐channel artificial neuron to emulate the biological neuronal dynamics. b) Six representative biological neuron spiking behaviors experimentally demonstrated in VO2 neurons. a,b) Figures adapted wtih permission from Ref.[163] Copyright 2018, Springer Nature. c) Stochastic spiking of a VO2 oscillator due to cycle‐to‐cycle variations in threshold switching voltages. d) The associated spike probability that follows a sigmoidal pattern. c,d) Figures adapted with permission from Ref.[164] Copyright 2017, IEEE. e) Schematic illustration of an Ising Hamiltonian solver for combinatorial optimization problems using coupled stochastic VO2 oscillators. Figures adapted with permission from Ref.[165] Copyright 2021, Springer Nature. f) Schematic illustration of the process flow to solve the graph coloring problem using coupled VO2 oscillatory network. Figures adapted with permission from Ref.[166] Copyright 2017, Springer Nature.

The stochastic dynamics represents another important aspect of neuronal complexities that plays key roles in signal and information processing.^[^ 167, 168 ^]^ Recently, several phase‐change materials,^[^ 164, 169, 170 ^]^ including VO_2_ and 1T‐TaS_2_, have been explored to demonstrate stochastic artificial neurons. For instance, VO_2_‐based devices show cycle‐to‐cycle variations in the threshold switching voltages, as illustrated in Figure 3c (left).^[^ 164 ^]^ Therefore, when the switching devices are integrated to construct neuronal oscillators, depending on where the electrical load line locates (controlled by V GS), the status of output waveforms vary (Figure 9c, right).^[^ 164 ^]^ The neuron sits in a resting state when the load line crosses the stable high‐resistance state (e.g., V GS = 1.8 V). As V GS increases (e.g., V GS = 1.92 V), the load line occasionally crosses both boundaries of hysteresis window (dashed lines) due to cycle‐to‐cycle V th variation, leading to probabilistic firing of oscillations. The spike probability follows a sigmoidal pattern, as shown in Figure 9d. Further increases in V GS (e.g., V GS = 2.04 V) give rise to varying amplitude of the oscillations (determined by the two threshold voltages), although the spike probability reaches 100%.^[^ 164 ^]^ Similar idea has been applied to 1T‐TaS_2_ stochastic neuronal oscillators later by Liu et al. to study detailed statistical characteristics of these artificial neurons.^[^ 170 ^]^

One of the most promising use cases of phase‐change neuronal oscillators is to effectively solve complex computational problems such as large‐scale combinatorial optimization. These problems belong to a so‐called non‐deterministic polynomial time (NP)‐hard complexity class and are important in various practical applications such as machine learning, route planning, and resource allocation, however, the computational resources required to find an optimal solution to them using conventional von Neumann computers increases rapidly with problem size, making them almost impractical to solve effectively and energy efficiently.^[^ 171 ^]^ In 2014, Lucas proposed that many NP‐hard optimization problems can be mapped into the problem of finding the ground state of an Ising model with the Ising Hamiltonian H (consisting of Ising spin σ and the coupling matrix J), offering a potential physical solution for such problems.^[^ 172 ^]^

In 2021, Dutta et al. constructed an Ising Hamiltonian solver based on a network of eight electrically coupled stochastic VO_2_ phase‐transition nano‐oscillators (PTNOs), as illustrated in Figure 9e.^[^ 165 ^]^ The artificial Ising spin σ is emulated by the binary degree of freedom in phases due to the second‐harmonic injection‐locking (SHIL) phenomenon, while the coupling matrix J is emulated by the capacitive coupling between VO_2_ neuronal oscillators with the matrix W. When the oscillator is perturbated with the injection‐locking signal (S inj) at the second harmonic (f inj ≈ 2f 0), the output waveform shows both in‐phase (40°, representing up‐spin) and out‐of‐phase (220°, representing down‐spin) injection‐locking configuration, while the first‐harmonic perturbation only gives rise to a constant 80° phase‐locking configuration.^[^ 165 ^]^ Dutta et al. further implemented this oscillator network to experimentally solve an NP‐hard MaxCut graph problem by minimizing the Ising Hamiltonian H. Note that this platform features an exceptionally high energy efficiency of 1.3 × 10^7^ solutions per second per watt for 100‐node problems, offering several orders of magnitude improvement over conventional approaches using CPUs or GPUs.^[^ 165 ^]^ Figure 9f illustrates another example of solving an NP‐hard problem (vertex graph coloring problem) using VO_2_ oscillators capacitively coupled in a network same as the input graph. The experimentally obtained order of oscillator phases is then correlated to the eigenvectors of the adjacency matrix of the input graph, which in turn are related to the solution of the graph coloring problem.^[^ 166 ^]^

It is worth noting that the device implementation examples discussed in this section are not exclusively limited to VO_2_‐based devices. One can certainly extend these applications to construct 1T‐TaS_2_ and BaTiS_3_‐based neuronal oscillatory circuits for biomimetic emulation and solving optimization problems, considering their similarities in demonstrated volatile threshold switching and oscillatory behaviors. However, unlike VO_2_, whose high‐quality thin‐film synthesis and large‐scale device integration are relatively well established, the scalable fabrication of 1T‐TaS_2_ microflakes and BaTiS_3_ bulk crystals remains challenging. Therefore, advancing the synthesis of 1T‐TaS_2_ and BaTiS_3_ thin films with pristine CDW phase transitions is essential to unlock energy‐efficient, chalcogenide‐based neuronal device applications in the future.

Summary and Discussion

9

In this review, we have surveyed recent research progresses on three representative phase‐change materials exhibiting metal‐to‐insulator transitions – specifically, the correlated oxide VO_2_, the transition metal dichalcogenide 1T‐TaS_2_, and the hexagonal complex chalcogenide BaTiS_3_ – and their potential applications in neuronal devices. Despite differences in chemical composition, morphology, underlying phase‐change mechanisms, and levels of technological readiness, these three materials display similar volatile threshold resistive switching across the associated transitions and exhibit self‐sustained voltage oscillations, making them promising candidates for neuronal device applications. From the perspective of material development and device implementation, we sequentially discussed their coincident electronic and structural phase transitions, material synthesis, device fabrication, transport characterization, resistive switching, sustained oscillation, and neuronal device integration.

Table 4 summarizes an overall assessment of the technological readiness of VO_2_, 1T‐TaS_2_, and BaTiS_3_ for practical electronic device applications, in terms of material development, device processing, operation, and integration. Despite these advances, there are still significant challenges for practical implementation of these volatile switching‐based phase‐change neurons in neuromorphic computing. For instance, to be compatible with the processing conditions for fabricating artificial synapses or CMOS‐based chips, the material deposition temperature must be maintained below 400°C, or alternative transfer‐based heterogeneous integration approaches must be developed. Among these three materials, VO_2_ is currently the only system demonstrating high‐quality thin‐film deposition processes that produce an metal‐to‐insulator transition comparable to that of a bulk crystals.^[^ 96 ^]^ Nonetheless, depositing at such reduced temperatures on non‐ideal substrates may compromise materials quality, leading to changes of transport behaviors such as a shift of transition temperature and a decrease in the amplitude of the resistance jump.^[^ 173 ^]^

In terms of device configuration, despite being well adopted for preliminary research studies, the planar resistive switching devices are not ideal for neuromorphic applications due to relatively large channel sizes ranging from several micrometers to millimeters (Table 3), which has resulted in limited oscillation frequencies and low integration density. It is worth noting that a record‐high 9 MHz oscillation frequency has been demonstrated on an out‐of‐plane VO_2_ vertical device, whose channel size equals to the film thickness (≈200 nm).^[^ 131 ^]^ Further employment of crossbar‐shaped vertical configuration, which has been widely adopted for metal/oxide/metal‐type memristor integration,^[^ 4, 12 ^]^ together with properly designed interconnections of VO_2_ devices, is promising in realizing high‐density oscillator network for handling various complex computational tasks.

As for the two CDW‐based materials, that is, 1T‐TaS_2_ and BaTiS_3_, more research is required to ultimately realize such high integration density for practical neuromorphic computing applications. Thus far, single crystals of 1T‐TaS_2_ and BaTiS_3_ are still being used to examine their intrinsic material properties and demonstrate proof‐of‐concept prototype devices. Although several back‐end‐of‐line (BEOL)‐compatible 2D and 3D integration approaches have been recently reported,^[^ 174, 175, 176 ^]^ such labor‐intense integration procedures and limited device packing density would inevitably increase the overall fabrication cost when dealing with 1T‐TaS_2_ and BaTiS_3_. The development of high‐quality thin‐film synthesis approaches for these materials is itself a demanding but rather challenging task, considering the susceptibility of external factors such as strain, defects, and doping on CDW phase transitions.^[^ 56, 83, 177 ^]^ Additionally, the development of chalcogenide thin‐film‐compatible device processes, such as lithography, etching, and high‐quality contact fabrication, are equally important to maximize the overall device performance.

Conflict of Interest

The authors declare no conflict of interest.