Polymorphic phases in 2D In₂Se₃: fundamental properties, phase transition modulation methodologies and advanced applications

Abstract

Two-dimensional (2D) In₂Se₃, which is a multifunctional semiconductor, exhibits multiple crystallographic phases, each of which possesses distinct electronic, optical, and thermal properties. This inherent phase variability makes it a promising candidate for a wide range of applications, including memory devices, photovoltaics, and photodetectors. This review comprehensively explores the latest progress of various polymorphic phases of 2D In₂Se₃, emphasizing their unique properties, characterization methods, phase modulation strategies, and practical applications. Commencing with a rigorous examination of the structural attributes inherent in its various phases, we introduce sophisticated techniques for its characterization. Subsequently, modulation strategies, encompassing variations in temperature, application of electric fields, induced stress, and alterations in pressure, are explored, each exerting an influence on the phase transitions in 2D In₂Se₃. Finally, we highlight recent advancements and applications resulting from these phase transitions, including homoepitaxial heterophase structures, optical modulators, and phase change memory (PCM). By synthesizing insights into phase properties, modulation strategies, and potential applications, this review endeavours to provide a comprehensive understanding of the significance and prospects of In₂Se₃ in the semiconductor field.

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1. Introduction

The rapid advancement of semiconductor technology has led to an increasing demand for materials with superior performance characteristics. To meet the needs of efficient, low-power, and highly integrated devices, two-dimensional (2D) materials have garnered significant attention due to their unique electronic structures and exceptional physical properties.¹ Their ultrathin structure reduces electron interference during movement, resulting in higher electron mobility and lower energy consumption.^2–7 Additionally, 2D materials exhibit outstanding mechanical flexibility,^8–11 optical transparency,^12–15 and chemical stability,^16–19 opening up new opportunities for innovative semiconductor device designs. Among the various 2D materials, In₂Se₃ stands out by virtue of its unique phase transition behavior.^16,20–30 As a multifunctional semiconductor, In₂Se₃ can exist in multiple crystalline phases, including the well-established phases (α, β, and γ), as well as less common phases (α′, β′, β′′, γ′, δ, and κ). Each phase exhibits distinct electronic, optical, and thermal properties.^31–37 Notably, the ferroic properties of certain phases, such as α and β′ phases, have been applied in ultra-fast memory and neuromorphic computing.^38–41 The ability to modulate these phases offers significant advantages for tailoring In₂Se₃'s properties to specific applications.

This diverse phase behavior not only broadens the potential applications of In₂Se₃ but also underscores the complexity and dynamic nature of semiconductor materials.⁴² The phase transition behavior of In₂Se₃ enables dynamic control of its performance in response to external stimuli like temperature, electric fields, stress, and pressure.^35,43–48 Under these conditions, the material undergoes reversible transitions between different crystal structures, making it a tunable platform for controlling the electronic and optical properties. This dynamic behavior is particularly useful in applications ranging from memory devices to photodetectors. For example, manipulating In₂Se₃'s phase transitions can facilitate rapid writing and erasing in memory devices, improve photoelectric conversion efficiency in photovoltaic cells, and optimize the response speed and sensitivity of photodetectors.²⁹

Moreover, the 2D structure of In₂Se₃ allows for the formation of heterostructures with other 2D materials, further expanding its potential in semiconductor devices.^49–51 From memory devices to photovoltaic and photodetectors, the phase change behavior of In₂Se₃ offers unique opportunities for novel devices.^20,52–54 Therefore, 2D In₂Se₃'s remarkable phase-change characteristics represent a significant advancement in semiconductor technology. Understanding its phase transitions not only enhances our knowledge of the underlying physics and chemistry of semiconductor materials, but also provides insights into the development of novel materials and device designs for future applications. With its wide-ranging applications and potential for innovation, In₂Se₃ continues to be a promising material for ongoing research and development in the semiconductor field.^31,55–62

This review examines the intricate phase transitions of In₂Se₃, which are central to its material science and semiconductor applications. We explore the distinct structures of its various phases, particularly the three most common polymorphs (α, β, and γ), and highlight how their unique properties contribute to In₂Se₃'s versatility. Despite significant efforts to synthesize and study its phases,^63,64 there is still a lack of comprehensive reviews summarizing the developments and applications related to In₂Se₃'s phase transitions. Additionally, due to the similarities in crystal structures and the complex dependencies of phase transitions, accurate identification of In₂Se₃'s phases remains a challenge. This requires a combination of analytical techniques and standardized experimental conditions. Herein, we will focus on the latest progress of 2D phase transition In₂Se₃ from the perspective of unique properties, phase transition modulation and application scenarios. Fig. 1 illustrates the organization and key themes covered in this review. This paper begins by introducing the structures and characterization of In₂Se₃'s different phases, followed by a discussion of various methodologies for controlling its phase transitions. It will also review the current advancements in applications of these phase transitions. Finally, the paper will conclude with a summary and outlook on the future directions of In₂Se₃'s phase transition research.

Fig. 1 An overview of the themes discussed in this review.

2. Crystal structures of each phase of In₂Se₃

2.1 Crystal structures of each phase of In₂Se₃

In₂Se₃ currently exhibits three well-established phases: α, β, and γ, along with six less common phases (α′, β′, β′′, γ′, δ, and κ).^65–71 Fig. 2 provides an overview of the structural parameters for In₂Se₃'s common polymorphs and polytypes. Fig. 2a illustrates the crystal structure of the α(3R)-In₂Se₃ phase. The structure consists of Se–In–Se–In–Se sequences that are strongly bonded by covalent bonds, forming quintuple layers (QLs). These QLs are stacked vertically through weak van der Waals interactions. Fig. 2a provides a 3D view of the α(3R)-In₂Se₃ crystal, where ‘3R’ refers to its rhombohedral structure, with lattice parameters a = 4.03 Å, c = 28.73 Å, and Z = 3. In this structure, In1 forms octahedral coordination with 6-fold coordination, while In2 forms a tetrahedral coordination with 4-fold coordination. The central Se2 is tetrahedrally coordinated to 3 surrounding In1 atoms and 1 In2 atom. In addition, α-In₂Se₃ exhibits a 2H tetrahedral structure, wherein the bonding geometry of the equivalent In atoms is also tetrahedral. In the 2H phase, adjacent quintuple layers are rotated 60 degrees in-plane relative to each other, while in the 3R phase, the layers differ only by a translation along the ab plane. Both phases lack centrosymmetry and exhibit out-of-plane piezoelectricity. Fig. 2b illustrates the 3D structure of β(2H)-In₂Se₃, featuring lattice parameters a = 4.01 Å, c = 19.48 Å, and Z = 4. In the structure of β(2H)-In₂Se₃, the equivalent In1 atoms exhibit hexagonal coordination, and the surface Se1 atoms also exhibit hexagonal coordination. The structures of β(1T)-In₂Se₃ and β(3R)-In₂Se₃ are illustrated in Fig. 2g and h, respectively. The β(1T) structure adopts a trigonal symmetry with a simple repeating layer sequence (e.g., AA…), resulting in a single layer per unit cell, while the β(3R) structure exhibits a rhombohedral symmetry with a more complex stacking sequence (e.g., ABCBCACAB…) and three layers per unit cell. Furthermore, the structure of β′-In₂Se₃ is represented in Fig. 2f which is similar to β(2H)-In₂Se₃.^72–74 The structure of β′-In₂Se₃ can thus be understood as the parent β-In₂Se₃ structure modified by the nano striped superstructure with antiferroelectric ordering.⁴¹ In contrast, the 2H structure has a hexagonal symmetry with a two-layer stacking sequence (e.g., ABAB…). The structure of β′′-In₂Se₃ is shown in Fig. 2g, which consists of zig-zag nanostripes with canted dipoles, a smaller dielectric constant, and is more stable at low temperatures, and they also show different domain switching behaviors. In the structure of γ-In₂Se₃, the bonding geometry of atoms is tetrahedral, with unequal diatomic and triatomic Se shown in Fig. 2i.⁷⁵ As shown in Fig. 2h, the van der Waals ordered superstructure framework (VOSF) phase of γ-In₂Se₃ has a space group with a = 7.35 Å, c = 20.02 Å, and Z = 6.

Fig. 2 3D unit cell views and the crystal structure diagrams of common In₂Se₃ polytypes: (a) α(3R)-In₂Se₃, (b) α(2H)-In₂Se₃, (c) β(2H)-In₂Se₃, (d) β(1T)-In₂Se₃, (e) β(3R)-In₂Se₃, (f) β′-In₂Se₃, (g) β′′-In₂Se₃, and (h) and (i) γ-In₂Se₃. Reprinted with permission from ref. 30. Copyright 2021 American Chemical Society. Reprinted with permission from ref. 73. Copyright 2023 American Chemical Society. Reprinted with permission from ref. 76. Copyright 2023 The Japan Society of Applied Physics.^30,73,76

The observed structural differences arise from variations in stacking sequences, bonding geometries of In/Se atoms, and the distribution of vacancies within the In₂Se₃ structure.^{31,33,77–79} These variations lead to distinct electrical and optical properties. For example, due to its non-centrosymmetric crystal structure, α-In₂Se₃ exhibits 2D ferroelectricity at room temperature. Similarly, β′-In₂Se₃ and γ-In₂Se₃ also exhibit ferroelectric properties, which are discussed further below.

2.2 Band structures of each phase of In₂Se₃

The band structure serves as a fundamental determinant in dictating the electronic and optical behaviors of materials.^77,80 It provides a profound understanding of how electrons move, interact, and respond to external stimuli, thereby governing crucial properties like conductivity, absorption, and emission spectra.^81,82 In₂Se₃ has various phases, mainly including α, β, and γ phases, exhibiting distinct structural characteristics. Importantly, these phase differences translate into significant variations in the band structure. In the context of applications, such as in photodetectors, the unique bandgap and energy band dispersion of each phase can directly influence the device's sensitivity and spectral response range, due to pronounced quantum confinement,⁸³ as the thickness alters from 95 to 3.1 nm.⁸⁴ Moreover, for bulk and multilayer α-In₂Se₃, the band gap is of a direct nature at a value of 1.453 eV.⁸⁵ Single-crystal β-In₂Se₃ bulk is metastable, while 2D β-In₂Se₃ layers are stable at room temperature and ambient pressure.⁸⁵ β-In₂Se₃, an n-type semiconductor, has a direct bandgap of 1.3 eV in bulk or few-layer form, but an indirect bandgap of 1.55 eV in monolayers.^82,83 Although α-In₂Se₃ and β-In₂Se₃ have similar bandgaps, their band structures and intrinsic defect levels differ, leading to distinct electronic properties. In β-In₂Se₃, intrinsic defects act as shallow levels, enhancing conductivity, whereas in α-In₂Se₃, they likely act as deep levels, contributing little. Thus, α-In₂Se₃ behaves like a semiconductor,⁸⁶ while β-In₂Se₃ exhibits metal-like characteristics. β′-In₂Se₃ is an n-type indirect semiconductor with strong two-dimensional characteristics, showing minimal variation perpendicular to the layers. Its maximum direct band gap is ∼1.77 eV, increasing to 2.5 eV in monolayer form.⁸⁷ The Fermi surface in the conduction band exhibits strong in-plane dispersion around M̄, suggesting high electron mobility. Additionally, β′-In₂Se₃ has significantly lower resistance than β-In₂Se₃. γ-In₂Se₃ functions as an n-type semiconductor, featuring a direct bandgap that varies with thickness, typically between 2.05 and 2.55 eV.^26,88 Its electronic conductivity is extremely low, resembling that of an insulator.⁸⁹

3. Preparation methodologies and characterization of In₂Se₃ polymorphism

3.1 Synthesis and preparation techniques for In₂Se₃

From an application standpoint, developing a reliable strategy for synthesizing two-dimensional In₂Se₃ nanosheets with precise thickness control and uniformity across large areas is crucial. Several synthesis methods have been proposed to produce In₂Se₃, each with varying levels of quality and scalability. These methods primarily include chemical vapor deposition (CVD), molecular beam epitaxy (MBE), and mechanical exfoliation. Among these, CVD stands out as the most commonly used technique for growing high-quality In₂Se₃ films. It offers precise control over the film thickness and phase, making it a preferred method for fabricating In₂Se₃ with the desired properties.⁹⁰ Unlike mechanical exfoliation, which can introduce defects at the edges of transferred materials and make precise thickness control difficult, CVD can produce high-quality single-layer or few-layer In₂Se₃ materials under relatively mild conditions.⁵⁷ CVD can offer the advantage of a larger growth area and more uniform material properties.³⁰

In a typical CVD process, In₂Se₃ samples are grown in a furnace with three independent temperature zones within a quartz tube. The polymorphs and crystal structures of the resulting In₂Se₃ primarily depend on factors such as growth temperature, heating position, and substrate choice.^64,91 The selection of substrates is crucial in the CVD process.⁵⁷ Selenium pellets, indium(III) oxide (In₂O₃) and hydrogen (H₂) were used as reactants. Usually, selenium, In₂O₃ and the growing substrate were placed in the upstream, middle and downstream zones respectively. During the growth process, a mixture of argon (with a flow rate of 15–30 standard cubic centimeters per minute) and hydrogen (with a flow rate of 4 standard cubic centimeters per minute) was used as the carrier gas. A schematic illustration of the CVD growth is shown in Fig. 3a.⁹² For instance, when growing α-In₂Se₃ on an SiO₂/Si substrate, selenium, In₂O₃, and the substrate are heated to 270 °C, 850 °C, and 750 °C, respectively, within 30 minutes, and held at these temperatures for 5 minutes. Fig. 3b exhibits an optical image of few-layer In₂Se₃ on mica, and the AFM images in Fig. 3c exhibit high spatial homogeneity and a film thickness of ∼7 nm. For synthesizing 2H β-In₂Se₃ on highly oriented pyrolytic graphite (HOPG), the heating temperatures for selenium, In₂O₃, and the substrate are set to 270 °C, 750 °C, and 640 °C, respectively. When growing γ-In₂Se₃ on an SiO₂/Si substrate, the same temperatures and substrate are used as for α-In₂Se₃, except the substrate is positioned further downstream.⁹³

Fig. 3 (a) Schematic illustration of the CVD growth set-up using In₂O₃ and Se powder. (b) Optical microscope images of In₂Se₃ on mica substrate after growth. (c) Atomic force microscope image of In₂Se₃. (d) Schematic diagram of the MBE system utilized for the synthesis of 2D In₂Se₃. (e) The mechanisms of molecular behaviors during epitaxial growth, and the optical microscope images and TEM image. (f) Schematic illustration of the different growth conditions required to selectively grow the different binary phases of InSe. (g) AFM topography of the as-grown InSe, the mixed InSe and In₂Se₃, and α-In₂Se₃. (h) Schematic illustration of the PLD growth. (i) AFM images for the In₂Se₃ thin films grown at (i) 1 mT, (ii) 10 mT and (iii) 100 mT deposition pressures by PLD. Reprinted with permission from ref. 92. Copyright 2022 Wiley-VCH GmbH.⁹² Reprinted with permission from ref. 94. Copyright 2018 American Chemical Society 2024 The Authors.⁹⁴ Reprinted with permission from ref. 95. Copyright 2018 American Chemical Society.⁹⁵ Reprinted with permission from ref. 96. Copyright 2022 Published by Elsevier B.V.⁹⁶

In contrast, MBE, which involves the chemical reaction of precursor species in an ultra-high vacuum, allows for epitaxial growth of high-quality, ultrathin 2D In₂Se₃ layers with atomic-scale precision. Wu et al. achieved the growth of large-area, atomic layer flatness, and pure-phase β-In₂Se₃ using MBE and a detailed diagram of the MBE system is shown in Fig. 3d, which is for growing a series of 2-inch β-In₂Se₃ nano thin films. The growth temperature was carefully set at 480 °C, and the selenium to indium flux ratio (R_Se/In) was systematically varied from 1 to 100. The mechanisms of molecular behaviors during epitaxial growth, and the optical microscope images and TEM image are shown in Fig. 3e. Fig. 3f shows a hypothetical model of samples with different Se/In flux ratios. A lower chemisorption energy is beneficial for horizontal growth, while a higher one results in smaller 2D flake sizes. To achieve large-scale two-dimensional van der Waals growth, it is necessary to control the chemisorption energy and maintain an appropriate physisorption potential energy. Increasing the proportion of selenides may help achieve this. The selected area electron diffraction (SAED) pattern shown in Fig. 3e was collected to investigate the crystallographic planes at the β-In₂Se₃ and sapphire interface. The regular diffraction points indicate that the β-In₂Se₃ film has a single crystal structure epitaxially grown on a C-plane sapphire substrate. Poh et al. successfully grew centimeter-sized monolayer α-In₂Se₃ films using the Frank–van der Merwe growth mode, employing the co-evaporation of In₂Se₃ and Se powders as the starting materials.⁹⁵ Fig. 3f shows a schematic diagram of the MBE system used for synthesizing 2D In₂Se₃. This method resulted in highly crystalline, uniform, and continuous monolayers at a temperature of around 250 °C, which is significantly lower than that required for typical CVD processes. Fig. 3g analyzes the morphology of the films grown under different conditions using AFM. Compared to InSe, the nucleation density of α-In₂Se₃ is much lower and its grains are larger, better-faceted, and highly oriented. However, the AFM of the mixed-phase indium selenide shows a similar grain size to that of pure InSe. It is notable that there is buckling of grain boundaries in the mixed-phase indium selenide, which may be due to the lateral lattice mismatch of InSe and α-In₂Se₃. They also reported the non-layered growth of γ-In₂Se₃ on the SiO₂/Si substrate using the same growth parameters, which further confirms the incompatibility between SiO₂ and In₂Se₃.⁹⁷ MBE, with its ability to produce high-purity, defect-free films, is particularly well-suited for research and high-performance applications, offering precise control over film quality and thickness at the atomic scale.

Mechanical exfoliation from the bulk crystal using adhesive tape is the most well-known method for producing high-quality atomically thin 2D flakes.^98–101 The adhesive force between the tape and the top layers of In₂Se₃ is strong enough to overcome the weak van der Waals (vdW) interaction between two adjacent layers in a bulk crystal, thus achieving layer-by-layer separation. In contrast, the ionic-covalent (IP) bonds within each layer remain intact and the crystallinity is preserved, which is highly attractive for fundamental research on intrinsic properties and for achieving excellent device performance. However, the limited lateral dimensions, uncontrolled thickness uniformity, and extremely low yield of the exfoliated flakes hinder their applications in large-scale device development and array integrations.¹⁰²

Pulsed laser deposition (PLD), schematically illustrated in Fig. 3h, is a versatile thin-film synthesis technique that utilizes high-energy pulsed laser ablation of a target material to deposit stoichiometric films on a substrate. Chanchal et al. employed PLD to synthesize phase-defined In₂Se₃ thin films by precisely controlling the deposition pressure (1–100 mTorr) in a nitrogen ambient.⁹⁶ The AFM images of the as-grown In₂Se₃ films are shown in Fig. 3i. At 1 mTorr (Fig. 3i(i)), the Se-deficient environment facilitated the growth of layered 3R α-In₂Se₃, while higher pressures (10 mTorr) induced the formation of β-In₂Se₃ with excess Se due to increased Se flux which is shown in Fig. 3i(ii). At 100 mTorr (Fig. 3i(iii)), non-layered γ-In₂Se₃ dominated under Se-rich conditions. Jeengar et al. demonstrates the fabrication of a high-performance NO₂ gas sensor using bilayer α-In₂Se₃ thin films grown via PLD.¹⁰³ The results highlight PLD's capability to produce ultrathin, high-quality α-In₂Se₃ films for low-power gas-sensing applications. Zheng et al. indicates that photodetectors made using centimeter-scale, high-quality In₂Se₃ films grown on various substrates via a PLD technique exhibit outstanding photoresponses.¹⁰⁴ In conclusion, compared to CVD, PLD offers precise stoichiometry and uniformity. MBE provides high crystallinity but requires ultra-high vacuum and slow growth, while PLD operates at lower Torr with faster rates. Unlike mechanical exfoliation, PLD enables large-area films with tunable thickness, essential for optoelectronic devices.

Moreover, flash-within-flash (FWF) Joule heating is a novel synthesis technique developed in recent years. The FWF method enables gram-scale synthesis of α-In₂Se₃ crystals by overcoming the conductivity limitations of precursors through indirect Joule heating. Shin et al. successfully achieved the production of high-purity, single-phase α-In₂Se₃ by FWF for neuromorphic computing applications.¹⁰⁵

3.2 Characterization of In₂Se₃ polymorphism

Given the complex polymorphism of In₂Se₃, it is essential to distinguish between its various crystal structures using nondestructive characterization and imaging techniques. Key methods typically employed for this purpose include transmission electron microscopy (TEM), Raman spectroscopy, and X-ray diffraction (XRD). These techniques provide valuable insights into the material's structural properties without compromising its integrity.

2D In₂Se₃ can be precisely characterized in terms of its nanoscale crystal structure, lattice defects, and crystal orientations using TEM, a high-resolution technique that transmits an electron beam through the sample. High-angle annular dark-field (HAADF) imaging, a mode of TEM, enhances contrast based on electron scattering angles, providing valuable insights into elemental distribution. Both TEM and HAADF are essential for characterizing 2D In₂Se₃. The α and β polymorphs exhibit distinct intralayer quintuple atomic arrangements, as shown in Fig. 2, making them identifiable through cross-sectional TEM imaging. To distinguish α- and β-In₂Se₃ more clearly, it is necessary to analyze the layer stacking sequences, as illustrated by TEM. As shown in Fig. 4a, the α(3R)-In₂Se₃ features a unit cell with no mirror symmetry among its layers, with each layer undergoing a lateral translation relative to its predecessor. For β(2H)-In₂Se₃, shown in Fig. 4d, the unit cell consists of two quintuple layers, with alternating mirrored layers that form a zigzag pattern. In contrast, γ-In₂Se₃, as delineated in Fig. 4g, displays a van der Waals ordered superstructure framework (VOSF) configuration, with a periodic length of 20.02 Å corresponding to the d spacing of ss planes in the γ-In₂Se₃ crystal lattice,¹⁰⁶ rather than following a conventional layered structure.⁷⁷

Fig. 4 Characterization of In₂Se₃. (a) TEM, (b) Raman and (c) XRD of α(3R)-In₂Se₃. (d) TEM, (e) Raman and (f) XRD of α(2H)-In₂Se₃. (g) TEM, (h) Raman and (i) XRD of β(2H)-In₂Se₃. (j) TEM, (k) Raman and (l) XRD of γ-In₂Se₃. Reprinted with permission from ref. 107. Copyright 2024 American Chemical Society. Reprinted with permission from ref. 108. Copyright 2018 WLEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Reprinted with permission from ref. 5. Copyright 2022 Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature. Reprinted with permission from ref. 109. Copyright 2021 Elsevier Ltd. Reprinted with permission from ref. 75. Copyright 2023 Wiley-VCH GmbH. Reprinted with permission from ref. 93. Copyright 2019 American Chemical Society.^{5,75,93,107–109}

In addition, Raman spectroscopy is a primary characterization technique for phase identification of In₂Se₃, leveraging its sensitivity to high-frequency modes that inherently reflect the phase-dependent characteristics. Fig. 4b showcases the micro-Raman spectrum of α(3R)-In₂Se₃, unveiling prominent Raman peaks at 90, 102, 180, and 196 cm⁻¹, corresponding to the E², A¹₁, E⁴ and A²₁ vibration modes, respectively.^{85,106,110–112} α(2H)-In₂Se₃ was confirmed by the Raman spectrum,¹¹³ which reveals vibration peaks at 88, 105, 179, and 194 cm⁻¹ and is depicted in Fig. 4e.^32,113 The Raman spectrum can be utilized to discern the difference between these two structures. Specifically, one of the Raman peak values of α-In₂Se₃, which is 90 cm⁻¹ (E²), is conspicuously observable in the hexagonal structure (2H), whereas it is less distinct in the rhombohedral structure (3R), likely making the intensity ratio between the E² and A¹₁ modes a distinguishing fingerprint for 2H and 3R α-In₂Se₃. Conversely, β(2H)-In₂Se₃ presents a distinct triad of characteristic peaks at 109, 175 and 205 cm⁻¹ depicted in Fig. 4h, which are different from those of α(3R)-In₂Se₃.^93,114 β′-In₂Se₃ is typically considered a derivative of the β phase,⁷⁴ so they have few differences in their Raman spectra. What is worth mentioning is that distinguishing among 1T, 2H and 3R β-In₂Se₃ crystals in the Raman spectra at room temperature is challenging. In contrast, γ-In₂Se₃, characterized by a non-layered crystal structure, lacks additional polytypes, rendering its identification relatively straightforward among the common polymorphs. It exhibits a singular principal Raman peak at 150 cm⁻¹ as shown in Fig. 4k.⁷⁵

Furthermore, XRD is commonly used to characterize the different phases of In₂Se₃, as it relies on the lattice parameters of a crystalline material to produce diffraction patterns that are unique to each phase. However, as shown in Fig. 4c and f, the differences in lattice parameters between α- and β-In₂Se₃ are minimal, making XRD less effective for distinguishing between these phases. In contrast, TEM offers superior phase identification.^106,109 XRD can, however, reliably identify γ-In₂Se₃, with characteristic peaks observed at 2θ values of 25° and 27.5° for the (110) and (006) facets, respectively, as shown in Fig. 4i.⁷³

4. Comparative properties of In₂Se₃ polymorphism

4.1 Electrical properties of In₂Se₃ polymorphism

The three prevalent phases of In₂Se₃ exhibit distinct electrical properties and optoelectronic characteristics due to structural discrepancies previously delineated. Zheng et al. investigated the electrical properties of 2D In₂Se₃ devices by applying continuous, milder bias/current using the in situ TEM technique.¹¹⁵ The schematic of the devices is shown in Fig. 5a. They measured the I–V characteristics across different phases of In₂Se₃ using point-like contacts, as illustrated in Fig. 5b. The results indicate superior conductivity in α-In₂Se₃ and β′-In₂Se₃ compared to γ-In₂Se₃. Subsequent cyclic biasing across the different phases revealed distinct behaviors. Notably, resistive hysteresis was observed in α-In₂Se₃ after multiple I–V cycles during the electroforming process, as shown in Fig. 5c and d, and further detailed in Fig. 5g. In contrast, β′-In₂Se₃ (Fig. 5e) and γ-In₂Se₃ (Fig. 5f) did not exhibit the resistive memory effect observed in α-In₂Se₃. This absence of resistive switching in β′-In₂Se₃ and γ-In₂Se₃ is likely due to their weaker ferroelectric polarization compared to α-In₂Se₃, despite the confirmed ferroelectric properties of all three materials.

Fig. 5 (a) A schematic of the In₂Se₃ FET. (b) I–V curves of the three common phases of In₂Se₃. (c) and (d) The electroforming process of α-In₂Se₃. (e) I–V cycles of β′-In₂Se₃. (f) I–V cycles of γ-In₂Se₃. Reprinted with permission from ref. 115. Copyright 2022 The Authors.¹¹⁵

4.2 Ferroelectric polarization

Ferroelectric polarization is a critical property of In₂Se₃ that significantly influences its electrical and optoelectronic behavior. Cui et al. investigated this phenomenon in α- and β-In₂Se₃ flakes using piezoresponse force microscopy (PFM).¹¹⁶ The PFM amplitude signifies the local piezoelectric contrast's strength, while the phase reveals the ferroelectric polarization's direction. As shown in Fig. 6a, the AFM image indicates α-In₂Se₃ flakes range from 2–6 nm in thickness. Upon scrutinizing the out-of-plane (OOP) images, as depicted in Fig. 6b (amplitude) and Fig. 6c (phase), alongside the in-plane (IP) counterparts portrayed in Fig. 6d (amplitude) and Fig. 6e (phase), the discernment of singular ferroelectric domains within each terrace for α-In₂Se₃ emerged conspicuously. Such observations suggest that α-In₂Se₃ can spontaneously achieve a singular domain state devoid of external electric field perturbations, with the notable finding that its IP polarization magnitude surpassed its OOP counterpart. In non-volatile memory applications like ferroelectric field-effect transistors (FeFETs), the polarization states of ferroelectric properties can represent “0” and “1” in binary data. For example, upward polarization can denote “1”, and downward polarization represents “0”. When applying appropriate voltage pulses, the polarization direction of the In₂Se₃ material can be changed to achieve data writing.^106,117

Fig. 6 AFM and PFM images of thin flakes for different In₂Se₃ phases: (a) AFM image of α-In₂Se₃ flakes with the corresponding OOP PFM images showing (b) amplitude and (c) phase, as well as IP PFM images depicting (d) amplitude and (e) phase. Similarly, for β-In₂Se₃: (f) AFM image, (g) OOP PFM amplitude, (h) OOP PFM phase, (i) IP PFM amplitude, and (j) IP PFM phase. For γ-In₂Se₃: (k) AFM image, (l) OOP PFM amplitude, (m) OOP PFM phase, (n) IP PFM amplitude, and (o) IP PFM phase.^116,118 Reprinted with permission from ref. 116. Copyright 2018 American Chemical Society. Reprinted with permission from ref. 118. Copyright 2021 Elsevier B.V.

Moving forward, Cui et al. examined the ferroelectric response of α-In₂Se₃ when subjected to electric fields, as well as the duration of its ferroelectric state.¹¹⁶ They discussed the stability of this state and its switchability under an external electric field, which is essential for memory applications.¹¹⁹ As shown in Fig. 7, it is evident that after applying −6 V and +6 V stripes, the PFM image of a 6 nm α-In₂Se₃ distinctly reveals high and low current states, corresponding to opposing polarization states.^31,120 What is more, the voltage-induced domain states in 6 nm flakes persist for up to 3 hours. Fig. 6g–i provide further insight into how the polarization within α-In₂Se₃ is manipulated by an external electric field. This modulation significantly impacts the current and conductance of the channel, showcasing nonvolatile memory effects. In Fig. 6h, α-In₂Se₃ resets at 1.75 V during the initial positive I–V cycle and sustains the reset state upon subsequent cycles, indicating its potential for nonvolatile memory. This can be recovered under negative bias (Fig. 6i).¹²⁰

Fig. 7 The stability of the as-written domains on 6 nm thick α-In₂Se₃ (scale bar: 1 μm).¹¹⁶ Reprinted with permission from ref. 116. Copyright 2018 American Chemical Society.

However, Bai et al. recently suggested that the in-plane ferroelectricity of α-In₂Se₃ may have been overestimated.¹²¹ Through experimental characterization and symmetry analysis, they refute previous claims of in-plane ferroelectricity in single-domain α–α-In₂Se₃. Additionally, deep-learning-assisted molecular dynamics simulations reveal that the vertical polarization switching mechanisms in monolayer α-In₂Se₃ differ fundamentally from those in bulk ferroelectrics. Angle-resolved PFM shows the in-plane response stems from out-of-plane signal crosstalk, not intrinsic piezoelectric effects. Their findings clarify misunderstandings about α-In₂Se₃'s ferroelectric properties and provide quantitative insights into domain wall behavior in 2D ferroelectric α-In₂Se₃.

γ-In₂Se₃ has a non-centrosymmetric structure.^{41,74,122,123} Rashid et al. determined the ferroelectric properties of γ-In₂Se₃ in both IP and OOP directions by PFM, which is relatively shown in Fig. 6l–o.¹¹⁸ Conversely, the absence of ferroelectric behavior was ascertained for β-In₂Se₃. This assertion was corroborated by the absence of discernible phase contrast distinctions in either IP (Fig. 6i and j) or OOP (Fig. 6g and h) orientations, attributable to the intrinsic lack of a ferroelectric phase in β-In₂Se₃. This conclusion harmonizes with the known structural attributes of β-In₂Se₃, characterized by centrosymmetric arrangements that preclude ferroelectricity. Notably, β′-In₂Se₃, as a typically derivative of β-In₂Se₃, has additional structural modulation in the form of 1D nano stripes. By virtue of second-harmonic generation, four-dimensional STEM, and in-plane piezoresponse force microscopy, the long-range inversion-breaking symmetry, uncompensated local polarization, and net polarization domains are unambiguously verified, revealing β′-In₂Se₃ as an in-plane ferrielectric layered material.^{41,74,122,123}

4.3 Optoelectronic characteristics

2D materials have garnered significant attention in optoelectronics due to their unique light–matter interaction and high carrier mobility.¹²⁴ In₂Se₃ stands out as a promising 2D semiconductor with effective light absorption and carrier generation properties. The different phases of In₂Se₃, α, β, and γ, exhibit distinct bandgaps, ranging from 1.39–1.45 eV for α and β-In2Se₃, and 2–2.52 eV for γ-In₂Se₃, making them suitable for broadband photodetection across ultraviolet (UV) to near-infrared (NIR) wavelengths.¹²⁵ Notably, phase transitions in In₂Se₃ play a significant role in modulating its optical characteristics, thereby influencing its optoelectronic performance. This section explores the optoelectronic properties of these phases, providing crucial insights into their potential applications in various optoelectronic devices.

As for optoelectronic applications,¹²⁵ α-In₂Se₃ can be seamlessly integrated with 3D materials. For instance, Jia et al. introduced a device incorporating a hybrid-dimension α-In₂Se₃/Si vertical heterojunction, illustrated schematically in Fig. 8a.¹²⁶ This innovative setup resulted in a photodetector, showcased in Fig. 8b, exhibiting exceptional sensitivity to incident light. Fig. 8b illustrates that within the 405–980 nm spectral range, the α-In₂Se₃/Si heterojunction demonstrates remarkable photoresponse, surpassing an I_on/I_off ratio of 10⁵ and a fast response to rapidly switching optical signals about the μs level. Additionally, it is suggested that the ferroelectric modulation of α-In₂Se₃ also contributes synergistically to its photoelectric properties. Fig. 8c illustrates the wavelength-dependent responsivity and enhancement photoresponsivity ratio (R_up/R_down), demonstrating the discrepancy in light response to various wavelengths between the P_up and P_down states. Clearly, the photoresponsivity of the photodetector varies significantly across different ferroelectric polarization states.

Fig. 8 α-In₂Se₃/n-Si ferroelectric heterojunction. (a) A schematic diagram. (b) The time response under different wavelength illumination. (c) The responsivity ratio as a function of incident light wavelength. β-In₂Se₃/n-Si ferroelectric heterojunction: (d) A schematic. (e) The time response under different wavelength illumination. (f) The wavelength dependent responsivity and EQE curves. γ-In₂Se₃/n-Si ferroelectric heterojunction: (g) A schematic. (h) The time response, measured at bias voltages of 0 and −1 V, under 808 nm light illumination. (i) The wavelength dependent responsivity. Reprinted with permission from ref. 126. Copyright 2023, The Authors, published by American Chemical Society. Reprinted with permission from ref. 127. Copyright 2017 American Chemical Society. Reprinted with permission from ref. 128. Copyright 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.^126–128

β-In₂Se₃ also demonstrates considerable potential for optoelectronic applications. For instance, Guo et al. successfully fabricated a high-speed, broad-spectrum β-In₂Se₃/Si p–n photodetector utilizing the pulsed laser deposition (PLD) technique, as shown in Fig. 8d.^109,127 The β-In₂Se₃/Si photodetector demonstrated outstanding device performance, featuring a wide response broadband spectrum spanning from 265 to 1300 nm as depicted in Fig. 8e, a high responsivity up to 6.4 A W⁻¹ shown in Fig. 8f (by the red line), and a high response speed approaching 2.2 μs at zero bias. Notably, these characteristics surpass those of many previous III–VI/Si based photodetectors and certain 2D TMDCs/Si heterojunctions.¹²⁴

As for γ-In₂Se₃, Chen et al. fabricated a high-quality γ-In₂Se₃/Si heterojunction photodiode,¹²⁸ as illustrated schematically in Fig. 8g. The photodiode demonstrates exceptional responsivity and detectivity across a wide range of wavelengths, making it a compelling candidate for highly efficient photodetectors. Fig. 8i shows the device's performance under dark conditions and various light intensities (380, 680, and 880 nm) from Xenon lamps. Notably, the photoresponsivity peaks at 5.67 A W⁻¹ at 820 nm, far exceeding the typical 0.8 A W⁻¹ of commercial Si-based photodetectors. Fig. 8h presents time-resolved photoresponse curves under 808 nm laser illumination at 0 and −1 V bias, demonstrating the heterojunction's rectifying nature and confirming its functionality as a photodiode.

The three types of In₂Se₃-based photodetectors exhibit exceptional optoelectronic characteristics, highlighting their potential in a wide range of photonic applications. Each detector demonstrates high photoresponsivity, indicating their sensitivity to light, especially in the UV to near-infrared spectrum. Overall, these In₂Se₃-based photodetectors, in their different phases (α, β, and potentially γ), offer diverse and complementary properties, making them attractive candidates for a wide range of photonic applications where sensitivity, speed, and broadband response are critical.

Table 1 consolidates a comprehensive summary of the properties and applications of the various phases of In₂Se₃. It succinctly outlines the distinctive characteristics and potential utilizations of each common phase, namely α, β, β′, and γ, highlighting their differences in terms of structural, ferroelectric, and optical properties. Through a comparative analysis of these properties, a more profound comprehension can be attained regarding the potential utilization of the different phases of In₂Se₃ for specific technological applications, including but not limited to optoelectronics, photodetectors, and data storage systems.

Table 1 Summary of properties and applications of different phases of In₂Se₃

Phase	Morphologies	Ferroelectric	Optoelectronic	Application	Ref.
α	Monolayer	IP and OOP	Wavelength: 405–1550 nm	Photodetector, memory, synaptic transistor	39, 93 and 129
	2H (bulk)	Layer dependence	Responsivity: 347 A W^−1
	3R (bulk)	IP and OOP	For 520 nm, 0.49 mW cm^−2
β	Monolayer	None	Wavelength: 265–1300 nm	Photodetector	62, 93 and 109
	1T	None	Responsivity: 6.4 A W^−1
	2H	None	For 850 nm, 0.14 mW cm^−2
β′	Monolayer	IP	None	Memory	41, 130 and 131
γ	P61	IP and OOP	Wavelength: 300–1100 nm	Photodetector, memory	75, 118 and 128
			Responsivity: 5.67 A W^−1
			For 820 nm

---

The intense optical absorption within the visible to near-infrared wavelength range, the phase-dependent direct bandgap, and the moderate mobility render In₂Se₃ a potential candidate for photodetection. Additionally, by taking advantage of its ferroelectric properties, the amplitude of the photocurrent can be modulated. Li et al. mentioned that a systematic exploration on the atomic structures and optical properties of polymorphic In₂Se₃ through density functional theory (DFT) calculations,⁴³ revealing critical insights into its phase-dependent electronic behavior and stability. For the α state, the calculated optical bandgap was determined to be 1.44 eV, while its fundamental indirect bandgap was 1.34 eV.¹³² The extinction coefficient (k) of it decreased sharply beyond 800 nm. Regarding the β state, the optical bandgap was 1.27 eV, and its fundamental indirect bandgap was significantly smaller, being 0.46 eV, and the value of k gradually decreased from 800 nm to 1400 nm and was less than 10⁻⁵ at 1550 nm.¹³² To ensure transparency at telecommunication wavelengths, both optical bandgaps exceeded 0.8 eV. These differences in bandgaps serve as the foundation for the phase transition applications of In₂Se₃, enabling a significant refractive index contrast in optoelectronic devices.

4.4 Layer-dependent properties of In₂Se₃

The electronic and optical properties of 2D In₂Se₃ vary significantly with the number of layers, making it highly versatile for optoelectronic applications.⁹⁷

For α-In₂Se₃, the thickness-dependent bandgap is particularly advantageous for applications like photodetectors, as it allows for the selection of the desired photonic energy window by simply adjusting the material thickness. Atomically thin α-In₂Se₃ crystals exhibit a substantial quantum confinement effect, which influences their optical properties. Quereda et al. demonstrated that as the thickness of α-In₂Se₃ varies from 3.1 nm (approximately 3 layers) to 95 nm (more than 90 layers), the optical transmittance decreases monotonically at a fixed illumination wavelength.^84,133 In fact, the band gap variation observed in atomically thin In₂Se₃ due to the effect of quantum confinement is among the largest reported to date in 2D semiconductor materials, and is comparable to that of atomically thin black phosphorus (as shown in Fig. 9a). For γ-In₂Se₃, the direct bandgap ranges from approximately 2.05 eV to 2.55 eV depending on the layer thickness.¹³⁴

Fig. 9 (a) Comparison of the band gap values for different van der Waals semiconductor crystals. The horizontal bars spanning a range of energies indicate that the band gap can be tuned over that range by changing the number of layers. (b) Thickness-dependent transmittance spectra of the γ-In₂Se₃ layered crystals. The lower inset shows an energy window of about 0.4 eV for the band gap difference between 6 μm and 125 μm thick samples. (c) The ratios of >30 deg phase area in the different layers. Reprinted with permission from ref. 84. Copyright 2016 Wiley-VCH GmbH.⁸⁴ Reprinted with permission from ref. 134. Copyright 2013 Royal Society of Chemistry.¹³⁴ Reprinted with permission from ref. 4. Copyright 2014 Royal Society of Chemistry.⁴

In terms of optical absorption, the absorption coefficient of In₂Se₃ is also thickness-dependent. According to the Tauc model, the optical band gap strongly depends on the flake thickness, increasing from 1.45 eV for thicker flakes to 2.8 eV for the thinnest studied.¹³⁵ The inset in Fig. 9b indicates that the optical gap energy window for two samples with different thicknesses (6 mm and 125 mm) is approximately 0.4 eV, which implies that γ-In₂Se₃ layers can be used to fabricate an optical-logic switch for a common 532 nm laser for communication purposes.

In addition to optical properties, ferroelectric polarization also exhibits significant dependence on the number of layers. Through analysing the phase area from PFM, the ratios of >30 deg phase area in the different layers were obtained and displayed in Fig. 9c. In 2H-stacked α-In₂Se₃ nanoflakes, the magnitude and reversal of polarization show this oscillation. For odd layers (OL), the IP polarization is larger than for even layers (EL), and when IP is reversed, OL's OOP polarization exceeds that of the ELs. Samples with aligned OOP polarization also show IP polarization's odd–even dependence. This property is due to the IP anti-parallel arrangement of adjacent layers in 2H stacking and the strong coupling between OOP and IP.⁴ Using odd and even layers as different storage units can store more information by controlling polarization states. In addition, utilizing the negative differential resistance (NDR) characteristic is another important application advantage brought about by the odd–even layer-dependent ferroelectric polarization phenomenon, which can realize multifunctional logic circuits.^136,137

The electrical properties of In₂Se₃ including ferroelectric, thermoelectric, and optoelectronic characteristics, are all influenced by the number of layers. For instance, multilayer β-In₂Se₃ can exhibit enhanced light absorption, making it more suitable for high-performance photodetectors. The ability to tune these properties by adjusting the layer number offers flexible solutions for designing next-generation optoelectronic devices, making In₂Se₃ a promising material for a variety of advanced electronic applications.

5. Phase transition modulation methodologies

The potential for fabricating controllable phase-change devices is appealing, given the rich array of physical and material characteristics exhibited by the various common phases of materials. However, despite these inherent attributes, the effective control of reversible phase transitions between them still remains a significant challenge.¹³⁸ Therefore, it becomes imperative to comprehend the existing reversible phase transition methodologies applicable to In₂Se₃, with a view to refining and innovating upon them. This imperative is underscored by its pivotal role in advancing the development of non-volatile integrated photonic devices. To enhance the controllability and quality of phase transitions in In₂Se₃, a comprehensive understanding of the underlying phase switching techniques and mechanisms is indispensable.

5.1 Temperature-dependent modulation of phase transitions

Temperature can serve as an effective tool for modulating the phase transitions of In₂Se₃. Many studies have observed distinct phase transitions in In₂Se₃ as it undergoes thermal treatment.^{25,42,64,77,85,139–145} For example, Hsu et al. investigated the phase transition behavior of In₂Se₃ by annealing as-deposited thin films (approximately 35 nm in thickness) at various temperatures.⁶⁴ Their findings, shown in Fig. 10e, revealed four distinct stages of phase transition: amorphous, γ-phase, β-phase, and α-phase. Specifically, amorphous In₂Se₃ transformed into γ-In₂Se₃ at around 400 °C, followed by a transition to the β-phase at 700 °C. Interestingly, they also observed that the transition from the β-phase to the α-phase occurred at room temperature once the sample was removed from the furnace, as depicted in Fig. 10f. The phase of as-deposited In₂Se₃ annealed at different temperatures can be classified into amorphous/α/β/γ-In₂Se₃, each characterized by distinct Raman peaks, as shown in Fig. 10a–d.

Fig. 10 Raman spectra of In₂Se₃ annealed at various temperatures and at room temperature: (a) amorphous structure, (b) γ-In₂Se₃, (c) β-In₂Se₃, and (d) α-In₂Se₃. (e) Schematic phase transition of In₂Se₃ with a thickness of 35 nm. (f) Phase transition of In₂Se₃ after annealing at 700 °C for 1 h which was observed by an optical microscope at room temperature. Raman spectra of In₂Se₃ at various temperatures and various environments (g) measured in the atmosphere, and (h) in 99% purity argon. Reprinted with permission from ref. 64. Copyright 2024 The Authors, published by Wiley-VCH GmbH. Reprinted with permission from ref. 145. Copyright 2023 The Authors, published by Wiley-VCH GmbH.^64,145

This temperature-induced phase modulation highlights the critical role of thermal treatment in controlling the structural properties of In₂Se₃, which is essential for tailoring its optoelectronic and electronic behaviors across various applications. Ignaci et al. investigated the α–β phase transformation in layered In₂Se₃, induced under varying environmental conditions, temperatures, and encapsulation methods.¹⁴⁵ As shown in Fig. 10g and h, the α–β transformation was triggered by thermal excitations between 200 and 350 °C, irrespective of whether the samples were exposed to ambient air or an inert atmosphere. This transformation was identified by the A₁(LO) phonon mode at 204 cm⁻¹.^63,93,110 Notably, during the cooling process, significant differences were observed: β-In₂Se₃ reverted to the α-phase in ambient air, while exhibiting stability in an inert environment. This suggests that the transition from β to α is facilitated by oxidative conditions. To mitigate this phase transition, the research team applied an encapsulating layer, such as graphene or hexagonal boron nitride (hBN).⁸⁵ Their findings demonstrated that these encapsulation layers effectively prevented the transition from β to α phase.

5.2 Electrical stimuli modulation of phase transitions

While temperature-dependent modulation offers a primary means of inducing phase transitions in In₂Se₃, there are still limitations of using temperature alone for phase control in 2D In₂Se₃. For instance, elevating the temperature from room temperature to either 220 °C¹²² or 290 °C⁸⁵ can induce a transition of 2D α-In₂Se₃ to β′-In₂Se₃. Nonetheless, once the temperature returns to room temperature, β′-In₂Se₃ does not revert to α-In₂Se₃.

Recent studies have shown that electrical stimuli can also play a significant role in modulating its phase behavior. Zheng et al. explored alternative methods for phase modulation, suggesting that electrical stimuli could offer a more versatile and dynamic approach for controlling the phase transitions of 2D In₂Se₃.¹¹⁵ In particular, they discovered that an applied electric field can trigger a reversible phase shift between the β′ and non-layered γ phases of In₂Se₃, which shows promise for memristor applications. Through comprehensive in situ TEM analysis, Zheng et al. demonstrated that both electrical and mechanical stimuli could effectively manipulate the phases of 2D In₂Se₃, as shown in Fig. 11a and b. The influence of electrical stimuli on the material is attributed to both the electric field and the thermal effect. Fig. 11a presents the in situ electrical TEM setup used in their study. The experimental procedure reveals that with a low current, about 5 × 10⁻⁵ A, a phase transition from α-In₂Se₃ and β′-In₂Se₃ occurs. Increasing the current to ∼8 × 10⁻⁵ A results in a direct transformation from α-In₂Se₃ to γ-In₂Se₃.¹⁴⁶ These results highlight how electrical current-induced heating can trigger phase transitions in 2D α-In₂Se₃, which offer valuable new insights into the phase manipulation of 2D materials. Wu et al. ulteriorly investigated the ferroelectric polarization switching mechanisms and phase transition behaviors of two-dimensional ferroelectric material α-In₂Se₃ under different stacking orders (2H and 3R) through in situ electrical STEM experiments and density functional theory (DFT) calculations.¹⁴⁷

Fig. 11 (a) Electrical TEM and experimental procedure diagrams. (b) Strain-induced reversible phase transition. (c) High-pressure Raman spectra of α-In₂Se₃. (d) Atomic scheme of the phase transitions of In₂Se₃.^115,148 Reprinted with permission from ref. 115. Copyright 2022 The Authors. Reprinted with permission from ref. 148. Copyright 2014 AIP Publishing.

5.3 Strain-induced reversible phase transition modulation

Strain-induced reversible phase transition can also effectively modulate the phase transition in In₂Se₃.^112,149,150 A schematic graph of the strain-induced reversible phase transition is shown in Fig. 11b. Zheng et al. used in situ TEM techniques to load or unload the mechanical strain on the In₂Se₃ samples.¹¹⁵ During the compression process, the β′-In₂Se₃ remains unchanged. When the tip is pulled back in the reverse direction, the transition from β′-In₂Se₃ to α-In₂Se₃ occurs due to strain relaxation. The reason why strain can cause the phase transition is that upon the TEM manipulation, when the tip moves away from the β′-In₂Se₃, the delamination between β′-In₂Se₃ and the substrate occurs with strain relaxation in β′-In₂Se₃. In this way, the tensile strain originally restored in β′-In₂Se₃ applied by the substrate is released, which results in the phase transition from β′-In₂Se₃ to α-In₂Se₃.⁴⁷

Similar to the strain-induced method, the application of pressure serves as a potent controlling factor for driving transformations.^48,151–154 Ke et al. reported an anomalous phase transition in compressed In₂Se₃.¹⁴⁸ Fig. 11c displays the high-pressure Raman spectra of In₂Se₃, revealing a clear transformation from rhombohedral to a new R3̄m structure at 0.8 GPa. This is evidenced by the emergence of new peaks at approximately 205 cm⁻¹, which are attributed to β-In₂Se₃. The article states that this transition occurs due to a pressure-induced interlayer slide. The phase transition of In₂Se₃ can be achieved through various pathways, and the schematic diagram (Fig. 11d) encapsulates most of the current methods.

In addition, theoretical research to explain the crystal conversion principle of In₂Se₃ is also an important aspect. Modi et al. synthesized β′′-In₂Se₃ nanowires through experiments.¹⁵⁵ Under a direct current bias, the electrical and microscopic structures of the nanowires changed. The varied I–V curve is illustrated in Fig. 12(f), in which amorphization occurs at 20 V and is preceded by a rapid decrease in current with time. What is more, the TEM characterization revealed the crystal-amorphous transformation and related structural changes, which are shown in Fig. 12(a) and (b). The contrast from the crystal-amorphous interface can be seen at the left side of the nanowire, where a part of the interface is shown in the TEM image in Fig. 12(c). Electron diffraction and HR-TEM images are shown in Fig. 12(d) for the paraelectric crystalline phase and in Fig. 12(e) for the amorphous regions of the nanowire device. The amorphization was affected by multiple factors rather than just heating, also involving the interaction of multiple factors such as the electric field and carrier force. The in situ TEM analysis observed the correlation between strain and current fluctuations and the dynamic process of amorphization.

Fig. 12 (a) The TEM image of a pristine nanowire device before applying any electrical stimuli. (b) The TEM image of the nanowire after amorphization. (c) The TEM image of part of the crystal-amorphous interface. (d) Electron diffraction from the paraelectric crystalline phase. (e) HR-TEM image of the amorphous regions of the nanowire device. (f) Evolution of current in the nanowire device with time when the device is held at different fixed dc voltages.¹⁵⁵ Reprinted with permission from ref. 155. Copyright 2024 The Author, under exclusive license to Springer Nature Limited.

6. Phase change applications of polycrystalline In₂Se₃

6.1 Hetero-phase junction

As mentioned above, 2D In₂Se₃ is attractive for its polymorphism. Also, hetero-phase junctions, also referred to as homoepitaxial heterojunctions, are composed of the same chemical elements or compounds. However, they exhibit significantly different physical and chemical properties due to variations in their internal atomic arrangements, spatial structures, or crystal forms.¹⁵⁶ Hetero-phase junctions play a critical role in both material science and device applications, offering avenues for innovative materials and device performance enhancements.

By forming hetero-phase junctions, novel properties emerge that are absent in the single phase.^{130,157–160} In₂Se₃, featuring an out-of-plane ferroelectric (FE) α phase and antiferroelectric (AFE) β′ phase, has substantial promise for electronic applications. The β′-state of In₂Se₃ is renowned for its room-temperature in-plane ferroelectricity¹²³ and high carrier mobility.¹³¹ Han et al. adopted the method of strain-induced reversible phase transition, which is shown in Fig. 13a, to build up the α–β′ hetero-phase junction.¹³⁰ The synthetic processes are clearly shown in Fig. 13a and b, and the corresponding Raman spectra are shown in Fig. 13c. As a junction interfacing two phases, the α–β′ junction benefits from both band alignment in conventional semiconductor heterojunctions and the degree of freedom in polarization control under external electric fields, leading to wider hysteresis windows and superior non-volatile memory properties compared to single-phase devices. Fig. 13d shows hysteresis loops widening with increasing gate voltage sweeps.

Fig. 13 (a) Schematic of the controlled synthesis of β-, β′- and α-In₂Se₃ films. (b) Schematic of the α–β′ hetero-phase junction. (c) Raman spectra of β-, β′- and α-In₂Se₃. (d) Hysteresis transfer characteristic loops of α–β′ junction devices during double sweeping with various V_gs sweep ranges. (e) Schematic direct-laser-writing procedure.^130,159 Reprinted with permission from ref. 130. Copyright 2022, The Author, under exclusive license to springer Nature limited. Reprinted with permission from ref. 159. Copyright 2019 American Chemical Society.

Similarly, Igo et al. fabricated β–α In₂Se₃ hetero-phase junctions utilizing laser writing which demonstrate rectifying electrical behaviors and short-circuit photocurrent, indicating potential applications as ultrathin nanoscale photodiodes and photovoltaics, which are shown in Fig. 13e.¹⁵⁹ Li et al. developed a vdW heterophase homojunction and tuned the electronic characteristics between n-type α-phase and p-type β-phase semiconductors by alloying Sb into In₂Se₃ and controlling the Sb concentration. This structure exhibited excellent broadband photovoltaic performance,¹⁶⁰ high open circuit voltage (∼400 mV), a high on/off current ratio (∼10⁶), and a high-speed response time (∼102 μs), with reconfigurable performance via polarization switching. These studies undoubtedly inspire the idea that by combining the correlated phases and ferroelectric (FE) properties of In₂Se₃, along with the realized polarizable hetero-phase junction, numerous opportunities can be opened up in developing novel structures and concepts for future FE electronics as well as logic-in-memory devices.¹⁵⁹

6.2 Phase change memory

Phase change memory (PCM) is another important application of the crystalline–crystalline phase transitions.^161–164 Reversible polymorphic layered materials provide an alternative atomic transition mechanism for low-energy electronic and photonic nonvolatile memories. Previously, Ge₂Sb₂Te was commonly utilized as the phase change material for PCM, achieving the transition between amorphous and crystalline states through heating.¹⁶⁵ However, this process consumed a significant amount of energy and led to a long response time for PCM. In contrast, In₂Se₃, with its non-melting phase transition, can effectively reduce the phase transition temperature and set/reset time which are demonstrated in Fig. 14a, thereby achieving efficient and high-performance PCM.^166,167

Fig. 14 (a) Phase transition devices response. (b) Comparison of the performance matrix of PCMs between crystalline and amorphous states and a polymorphic layered In₂Se₃ (red part). (c) The In₂Se₃ phase change device: the relationship between resistance and excitation optical power at 1550 nm wavelength.^43,168 Reprinted with permission from ref. 168. Copyright 2024 The Author, published by De Gruyter, Berlin/Boston. Reprinted with permission from ref. 43. Copyright 2022 Wiley-VCH GmbH.

Moreover, Fig. 14b depicts the comparison of PCM performance among four commonly used PCM materials, further indicating the superior performance of In₂Se₃ in PCM.^169–172 The optical transparency of In₂Se₃ in both states at telecommunication wavelengths guarantees low insertion loss, with both optical bandgaps of the material exceeding 0.8 eV, rendering it transparent.⁴³ It is more worth mentioning that the refractive index change in layered In₂Se₃ is only half of that in Ge₂Sb₂Te₅, a typical phase transition material used in PCM we mentioned before, but In₂Se₃'s figure of merit as an optical phase change material is among the highest of all optical PCM materials.

Li et al. demonstrated that a single nanosecond pulse with nearly double the energy can switch the material from the β-state to the α-state,⁴³ which is shown in Fig. 14a, and proved that the optical transparency of In₂Se₃ at telecommunication wavelengths enables low insertion loss and phase-only memory devices. Fig. 14c illustrates the relationship between device resistivity and light intensity at 1550 nm, further indicating the ability of In₂Se₃ to undergo phase transition under optical excitation, enabling PCM through resistivity changes. Choi et al. firstly reported a novel PCM using a layered crystalline In₂Se₃ film on a graphene bottom electrode,⁴⁴ leveraging reversible phase changes between the crystalline β and γ phases for repeatable SET/RESET programming. The resulting change in configurational entropy is expected to be significantly smaller compared to the melting-induced RESET programming commonly seen in conventional In₂Se₃-based PCM. The unique phase change characteristics of polymorphic layered materials, specifically In₂Se₃, propel them to the forefront of future investigations aimed at developing photonic memory solutions that are energy-efficient, swift, and resilient.

6.3 Integrated photonic nonvolatile phase shifters

Light-sensitive phase-change materials are essential for integrated photonic devices as well. In₂Se₃, with its stable and tunable refractive index, exhibits excellent performance in nonvolatile phase shifters and post-fabrication phase trimming. This makes it highly valuable for photonic applications including programmable and reconfigurable photonic networks.^173,174 Wu et al. integrated micro-ring resonators (MRRs) with multi-layer In₂Se₃ sheets,¹⁷⁵ utilizing them as phase shifters. Fig. 15a shows the side view cartoon of atomic structures for α-In₂Se₃ and β′-In₂Se₃ that can be thermally driven. The Raman spectra of the α-In₂Se₃ flake at 20 °C before (α-In₂Se₃) and after (β′-In₂Se₃) thermal annealing in Fig. 15b further confirm the thermally driven reversible phase transitions between α and β′ phases. An optical microscope image of an MRR is shown in Fig. 15c. MMR is a type of ring-shaped resonant cavity that can achieve resonant amplification and filtering of light, and is widely used in optical sensors and communication systems. It is found that after thermal annealing at 300 °C, there is a red shift in the resonance wavelength from 1277.427 to 1277.470 nm, as depicted in Fig. 15d. This shift is attributed to the phase transition of In₂Se₃ from α to β′, with the refractive index of the material changing from 2.25 for α-In₂Se₃ to 2.47 for β′-In₂Se₃. This significant variation in refractive index plays a crucial role in integrated photonics applications.

Fig. 15 (a) Side-view cartoon of atomic structures for α-In₂Se₃ and β′-In₂Se₃. (b) Raman spectra of a 2H In₂Se₃ flake at 20 °C before (α-In₂Se₃) and after (β′-In₂Se₃) thermal annealing. (c) Optical microscope image of an MRR integrated with a 45 nm-thick In₂Se₃ flake. (d) Transmission spectra of the MRR (α and β′ phases). (e) Optical microscope image of an MZI integrated with a 90 nm-thick In₂Se₃. (f) Transmission spectra of the MZI (α and β′ phases).¹⁷⁵ Reprinted with permission from ref. 175. Copyright 2023 American Chemical Society.

The Mach–Zehnder interferometer (MZI) is widely used to measure optical path differences through interference effects. Its flexibility in terms of channel spacing and grid configuration makes it ideal for fabricating phase shifters, modulators, sensors, and other optical devices. Wu et al. integrated multilayer α-In₂Se₃ flakes into the MZI, with an optical image of the MZI shown in Fig. 15e.¹⁷⁵ The extinction ratio (ER), which measures optical wave loss in materials, was evaluated experimentally.¹⁷⁶ The original MZI exhibited an ER of approximately 34.1 dB, which decreased to 29.5 dB after integrating 90 nm thick α-In₂Se₃ flakes, and then increased to 32.6 dB following thermal annealing. This high ER indicates that multilayer In₂Se₃ is a low-loss optical material in the O-band. Additionally, a red shift of 206 pm was observed after thermal annealing, as shown in Fig. 15f. These results demonstrate the potential of utilizing In₂Se₃'s phase-change properties in low-loss phase shifters.

Wang et al. developed a novel photonic PCM-enabled reversible metalens on a standard silicon photonic platform by employing a fixed geometric design.¹⁷⁷ The unique refractive index combination of In₂Se₃ allows for nonvolatile tuning of the focusing length. These studies demonstrate the successful use of phase-change materials to achieve a tunable refractive index, which in turn facilitates the creation of photonic memory devices with reduced insertion loss and minimized power consumption. The layered In₂Se₃ prototype offers promising potential for integrated photonic devices, particularly in nonvolatile optical memory applications.^43,175,176

7. Summary and outlook

This review examines the phase transitions in In₂Se₃, highlighting their fundamental properties and potential applications. These transitions significantly affect key material properties such as electrical resistance, photo-responsivity, thermal conductivity, and refractive index. The ability to control phase transitions through external factors like temperature, mechanical stress, and electric fields offers versatile control over the material's properties, enabling its use in reconfigurable applications such as homojunctions, optical modulators, and phase change materials. The review provides a comprehensive overview of In₂Se₃, focusing on its structural characteristics, methods of characterization, performance comparisons, and the conditions necessary for phase transitions. This detailed analysis aims to enhance understanding of In₂Se₃'s phase transition behaviours and its potential for advancing future technologies.

Looking ahead, several future research directions can further advance the understanding of In₂Se₃. First, phase stabilization techniques should be prioritized. This involves developing novel methods, such as the use of specific dopants or the exploration of external conditions like pressure and annealing, to stabilize the desired phases of In₂Se₃ at room temperature. A deep understanding of the thermodynamic and kinetic factors involved is essential for improving device reliability by minimizing performance-degrading phase transitions. Second, layer engineering deserves attention. Investigating the effects of different layer stacking sequences and intercalation techniques on In₂Se₃ properties, with a focus on addressing growth-related challenges like precise control over layer numbers and phase uniformity can enable the tuning of bandgaps and carrier mobility for specific applications. This approach could lead to more efficient and versatile device designs by allowing for tailored responses to external stimuli. Crucially, we must prioritize the resolution of growth-related bottlenecks, such as precise layer number control in large-area samples and uniformity of phase distribution, while addressing cost, environmental sustainability, and process consistency for industrial scalability. Third, integration with other materials warrants further exploration. Examining the interfacial properties and electronic coupling when combining In₂Se₃ with other two-dimensional materials can enhance charge transfer and other critical characteristics. Optimizing heterostructure designs can facilitate the development of innovative, high-performance electronic and optoelectronic components. Finally, addressing the challenges of scaling up high-quality In₂Se₃ synthesis is crucial. It is important to tackle issues related to cost, uniformity, and environmental impact. Developing cost-effective methods, optimizing processes for consistency, and adopting sustainable practices will be essential for industrial applications of this material.

Author contributions

W. Liao proposed and supervised the project. W. Zheng wrote the manuscript with comments from W. Liao, Z. Liu, T. Liu, D. Wang, and L. Wang. All authors discussed the results and commented on the manuscript.

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

The work was partially supported by the financial support from the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515010693), partially by the Shenzhen Science and Technology Program (Grant No. ZDSYS20220527171402005), the Shenzhen University 2035 Program for Excellent Research (Grant No. 2023C008), the Shenzhen Strategic Emerging Industry Support Plan (Grant NO. F-2023-Z99-509043), and the National Natural Science Foundation of China (Grant No. 61904110 and No. 52302187). The authors also acknowledge the support from the Instrumental Analysis Center of Shenzhen University (Xili Campus).

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