Strain-Modulated Bandgap and Piezo-Resistive Effect in Black Phosphorus Field-Effect Transistors

Latest Innovations in 2D Flexible Nanoelectronics

2D materials with dangling-bond-free surfaces and atomically thin layers have been shown to be capable of being incorporated into flexible electronic devices. The electronic and optical properties of 2D materials can be tuned or controlled in other ways by using the intriguing strain engineering method. The latest and encouraging techniques in regard to creating flexible 2D nanoelectronics are condensed in this review. These techniques have the potential to be used in a wider range of applications in the near and long term. It is possible to use ultrathin 2D materials (graphene, BP, WTe2 , VSe2 etc.) and 2D transition metal dichalcogenides (2D TMDs) in order to enable the electrical behavior of the devices to be studied. A category of materials is produced on smaller scales by exfoliating bulk materials, whereas chemical vapor deposition (CVD) and epitaxial growth are employed on larger scales. This overview highlights two distinct requirements, which include from a single semiconductor or with van der Waals heterostructures of various nanomaterials. They include where strain must be avoided and where it is required, such as solutions to produce strain-insensitive devices, and such as pressure-sensitive outcomes, respectively. Finally, points-of-view about the current difficulties and possibilities in regard to using 2D materials in flexible electronics are provided.

Electronic Structure of Few-Layer Black Phosphorus from μ-ARPES

Black phosphorus (BP) stands out among two-dimensional (2D) semiconductors because of its high mobility and thickness dependent direct band gap. However, the quasiparticle band structure of ultrathin BP has remained inaccessible to experiment thus far. Here we use a recently developed laser-based microfocus angle resolved photoemission (μ-ARPES) system to establish the electronic structure of 2-9 layer BP from experiment. Our measurements unveil ladders of anisotropic, quantized subbands at energies that deviate from the scaling observed in conventional semiconductor quantum wells. We quantify the anisotropy of the effective masses and determine universal tight-binding parameters, which provide an accurate description of the electronic structure for all thicknesses.

Pseudo-heterostructure and condensation of 1D moiré excitons in twisted phosphorene bilayers

Heterostructures are not expected to form in a single homogeneous material. Here, we show that planar pseudo-heterostructures could emerge in a twisted bilayer of phosphorene (tbP), driving in-plane energy and charge transfer. The formation of moiré superlattices combined with electronic anisotropy in tbPs yields one-dimensional (1D) moiré excitons with long radiative and nonradiative lifetimes, large binding energies, and deep moiré potentials. Low-frequency moiré phonons and dynamic moiré potentials are revealed to be responsible for the in-plane energy/charge transfer and exciton dynamics. The 1D moiré excitons are predicted to exhibit Bose-Einstein condensation at high temperatures and may lead to exotic Tonks-Girardeau Bose gases.

Uniaxial Strain-Induced Tunable Mid-infrared Light Emission from Thin Film Black Phosphorus

Strain engineering is a powerful tool that can modulate semiconductor device performance. Here, we demonstrate that the bandgap of thin film (∼40 nm) black phosphorus (bP) can be continuously tuned from 2.9 to 3.9 μm by applying an in-plane uniaxial strain, as evidenced by mid-infrared photoluminescence (PL) spectroscopy. The deduced bandgap strain coefficients are ∼103 meV %^-1, which coincide with those obtained in few-layer bP. On the basis of first-principles calculations, the origin of the uniaxial tensile strain-induced PL enhancement is suggested to be due to the increase in both the effective mass ratio (m_e^*/m_h^*) and the bandgap, leading to the increment of the radiative efficiency. Moreover, the mid-infrared PL emission remains perfectly linear-polarized along the armchair direction regardless of tensile or compressive strain. The highly tunable bandgap of bP in the mid-infrared regime opens up opportunities for the realization of mid-infrared light-emitting diodes and lasers using layered materials.

Black phosphorous-based human-machine communication interface

Assistive technology involving auditory feedback is generally utilized by those who are visually impaired or have speech and language difficulties. Therefore, here we concentrate on an auditory human-machine interface that uses audio as a platform for conveying information between visually or speech-disabled users and society. We develop a piezoresistive tactile sensor based on a black phosphorous and polyaniline (BP@PANI) composite by the facile chemical oxidative polymerization of aniline on cotton fabric. Taking advantage of BP's puckered honeycomb lattice structure and superior electrical properties as well as the vast wavy fabric surface, this BP@PANI-based tactile sensor exhibits excellent sensitivity, low-pressure sensitivity, reasonable response time, and good cycle stability. For a real-world application, a prototype device employs six BP@PANI tactile sensors that correspond to braille characters and can convert pressed text into audio on reading or typing to assist visually or speech-disabled persons. Overall, this research offers promising insight into the material candidates and strategies for the development of auditory feedback devices based on layered and 2D materials for human-machine interfaces.

Strain-Enhanced Mobility of Monolayer MoS2

Strain engineering is an important method for tuning the properties of semiconductors and has been used to improve the mobility of silicon transistors for several decades. Recently, theoretical studies have predicted that strain can also improve the mobility of two-dimensional (2D) semiconductors, e.g., by reducing intervalley scattering or lowering effective masses. Here, we experimentally show strain-enhanced electron mobility in monolayer MoS₂ transistors with uniaxial tensile strain, on flexible substrates. The on-state current and mobility are nearly doubled with tensile strain up to 0.7%, and devices return to their initial state after release of the strain. We also show a gate-voltage-dependent gauge factor up to 200 for monolayer MoS₂, which is higher than previous values reported for sub-1 nm thin piezoresistive films. These results demonstrate the importance of strain engineering 2D semiconductors for performance enhancements in integrated circuits, or for applications such as flexible strain sensors.

Strain-induced multigap superconductivity in electrene Mo2N: a first principles study

Superconductivity in low dimensional materials and 2D electrides are topics of great interest with possible applications in next generation electronic devices. Using density functional theory (DFT) associated with Migdal-Eliashberg approach and maximally localized Wannier functions this study shows how biaxial strain affects superconductivity in a monolayer of Mo₂N. Results indicate that 2D Mo₂N presents strong electron-phonon coupling with large anisotropy in the superconducting energy gap. It is also proposed that, at low temperatures, a single layer of Mo₂N becomes an electride with localized electron gas pockets on the surface, resembling anions adsorbed on an atomic sheet. Calculations point to T_c = 24.7 K, a record high transition temperature for this class of material at ambient pressure. Furthermore, it is shown that when biaxial strain is applied to a superconducting Mo₂N monolayer, a new superconductivity gap starts at 2% strain and is enhanced by continuum strain, opening additional coupling channels.

Anomalous non-equilibrium response in black phosphorus to sub-gap mid-infrared excitation

The competition between the electron-hole Coulomb attraction and the 3D dielectric screening dictates the optical properties of layered semiconductors. In low-dimensional materials, the equilibrium dielectric environment can be significantly altered by the ultrafast excitation of photo-carriers, leading to renormalized band gap and exciton binding energies. Recently, black phosphorus emerged as a 2D material with strongly layer-dependent electronic properties. Here, we resolve the response of bulk black phosphorus to mid-infrared pulses tuned across the band gap. We find that, while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance. With the support of DFT calculations, we tentatively ascribe this experimental evidence to a non-adiabatic modification of the screening environment. Our work heralds the non-adiabatic optical manipulation of the electronic properties of 2D materials, which is of great relevance for the engineering of versatile van der Waals materials.

Here, the authors investigate the optical response of bulk black phosphorus to mid-infrared pulses, and find that while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance.

One-dimensional quantum channel in bent honeycomb nanoribbons

The directionality of steering charge carriers is of great importance for the application of two-dimensional (2D) materials. Using the generalized Bloch theorem coupled with the self-consistent charge density-functional tight-binding method, we theoretically propose an approach to construct a one-dimensional (1D) quantum channel in honeycomb nanoribbons (NR) via in-plane bending deformation. Bending-induced pseudo-magnetic fields lead to Landau quantization and localize the electronic states along both edges of bent NR. These localized states form robust 1D quantum channels, whose energies can be linearly modulated through the bending angle. Our findings give new inspiration for the realization of transverse magnetic focusing (TMF) under zero magnetic fields and pave the way for the design of 2D material-based nano-devices via strain-engineering.

Revealing the Anisotropic Structural and Electrical Stabilities of 2D SnSe under Harsh Environments: Alkaline Environment and Mechanical Strain

As a promising thermoelectric and semiconducting material, the stability of two-dimensional tin selenide (SnSe) under harsh environments is significant for its practical applications. Here, focusing on the key procedures in the device fabrication process, we report the anisotropic structural and electrical stabilities of SnSe under an alkaline environment and mechanical strain. Due to the anisotropic mechanical properties, the SnSe flakes can naturally form long-straight {011} edge planes during the mechanical exfoliation process. Such a cleavage tendency provides an effective crystal orientation identification method to uncover the orientation-dependent properties. We find that the single-crystalline SnSe flakes experience an anisotropic degradation process with the preferable {011} dissolution planes in the alkaline environment and can be gradually transformed to be polycrystalline consisting of SnSe₂, Sn, and Se nanocrystals. SnSe flakes present an anisotropic electromechanical response with a gauge factor value that reaches ∼-460 under the uniaxial strain along the ⟨011⟩ directions. Our revealed structural and electrical stability of SnSe under harsh environments can provide guidance for the device design, fabrication, and performance evaluation.

Multi-scale modeling of 2D GaSe FETs with strained channels

Electronic devices based on bidimensional materials (2DMs) are the subject of an intense experimental research, that demands a tantamount theoretical activity. The latter must be hold up by a varied set of tools able to rationalize, explain and predict the operation principles of the devices. However, in the broad context of multi-scale computational nanoelectronics, there is currently a lack of simulation tools connecting atomistic descriptions with semi-classical mesoscopic device-level simulations and able to properly explain the performance of many state-of-the-art devices. To contribute to filling this gap we present a multi-scale approach that combines fine-level material calculations with a semi-classical drift-diffusion transport model. Its use is exemplified by assessing 2DM field effect transistors with strained channels, showing excellent capabilities to capture the changes in the crystal structure and their impact into the device performance. Interestingly, we verify the capacity of strain in monolayer GaSe to enhance the conduction of one type of carrier, enabling the possibility to mimic the effect of chemical doping on 2D materials. These results illustrate the great potential of the proposed approach to bridge levels of abstraction rarely connected before and thus contribute to the theoretical modeling of state-of-the-art 2DM-based devices.

Actively variable-spectrum optoelectronics with black phosphorus

Room-temperature optoelectronic devices that operate at short-wavelength and mid-wavelength infrared ranges (one to eight micrometres) can be used for numerous applications^1-5. To achieve the range of operating wavelengths needed for a given application, a combination of materials with different bandgaps (for example, superlattices or heterostructures)^6,7 or variations in the composition of semiconductor alloys during growth^8,9 are used. However, these materials are complex to fabricate, and the operating range is fixed after fabrication. Although wide-range, active and reversible tunability of the operating wavelengths in optoelectronic devices after fabrication is a highly desirable feature, no such platform has been yet developed. Here we demonstrate high-performance room-temperature infrared optoelectronics with actively variable spectra by presenting black phosphorus as an ideal candidate. Enabled by the highly strain-sensitive nature of its bandgap, which varies from 0.22 to 0.53 electronvolts, we show a continuous and reversible tuning of the operating wavelengths in light-emitting diodes and photodetectors composed of black phosphorus. Furthermore, we leverage this platform to demonstrate multiplexed nondispersive infrared gas sensing, whereby multiple gases (for example, carbon dioxide, methane and water vapour) are detected using a single light source. With its active spectral tunability while also retaining high performance, our work bridges a technological gap, presenting a potential way of meeting different requirements for emission and detection spectra in optoelectronic applications.

Strong Modulation of Band Gap, Carrier Mobility and Lifetime in Two-Dimensional Black Phosphorene through Acoustic Phonon Excitation

Black phosphorene (BP) has been attracting intense attention due to its high charge mobility and potential applications in electronic, optical and optoelectronic devices. We demonstrate by ab initio molecular dynamics and nonadiabatic quantum dynamics simulations that the excitation of out-of-plane acoustic phonon (ZA) provides strong modulation of the band gap, carrier lifetime and carrier mobility in BP. A 1% tensile strain can significantly enhance ZA mode excitation at room temperature, distinctly reducing the band gap, carrier mobility, and lifetime. These electronic properties can be tuned easily by influencing the excitation amplitude of the ZA mode. Unique to the family of two-dimensional materials, the ZA mode plays an essential role in controlling the electronic properties of BP. The results of our study provide valuable guidelines for design of functional nanodevices based on 2D BP.

Mechanics of free-standing inorganic and molecular 2D materials

The discovery of graphene has triggered a great interest in inorganic as well as molecular two-dimensional (2D) materials. In this review, we summarize recent progress in the mechanical characterization of free-standing 2D materials, such as graphene, hexagonal boron nitride (hBN), transition metal-dichalcogenides, MXenes, black phosphor, carbon nanomembranes (CNMs), 2D polymers, 2D metal organic frameworks (MOFs) and covalent organic frameworks (COFs). Elastic, fracture, bending and interfacial properties of these materials have been determined using a variety of experimental techniques including atomic force microscopy based nanoindentation, in situ tensile/fracture testing, bulge testing, Raman spectroscopy, Brillouin light scattering and buckling-based metrology. Additionally, we address recent advances of 2D materials in a variety of mechanical applications, including resonators, microphones and nanoelectromechanical sensors. With the emphasis on progress and challenges in the mechanical characterization of inorganic and molecular 2D materials, we expect a continuous growth of interest and more systematic experimental work on the mechanics of such ultrathin nanomaterials.

Highly tunable anisotropic co-deformation of black phosphorene superlattices

Controlling mechanical deformation is one of the state-of-the-art approaches to tune the electronic properties of 2D materials. We report a new mechanism for tuning a phosphorene superlattice with intercalated amphiphiles by its strong anisotropic co-deformation. Anisotropic co-deformation of a phosphorene superlattice is found to follow tunable sinusoidal and Gaussian functions, which exhibit adjustable mechanical actuation, curvature and layer separations. We analysed the controlling mechanism and tuning strategy of co-deformation as a function of amphiphile assembly topology, van der Waals interactions, interlayer separation and global deformation based on Euler-beam theory. Our first-principles calculations demonstrate that the co-deformation mechanism can be used to achieve a theoretical bandgap tunability of 0.7 eV and a transition between direct and indirect bandgaps. The reported tuning mechanisms pave new ways for designing a wide range of tunable functional electronics, sensors and actuators.

From Anomalous to Normal: Temperature Dependence of the Band Gap in Two-Dimensional Black Phosphorus

The temperature dependence of the band gap is crucial to a semiconductor. Bulk black phosphorus is known to exhibit an anomalous behavior. Through optical spectroscopy, here we show that the temperature effect on black phosphorus band gap gradually evolves with decreasing layer number, eventually turns into a normal one in the monolayer limit, rendering a crossover from the anomalous to the normal. Meanwhile, the temperature-induced shift in optical resonance also differs with different transition indices for the same thickness sample. A comprehensive analysis reveals that the temperature-tunable interlayer coupling is responsible for the observed diverse scenario. Our study provides a key to the apprehension of the anomalous temperature behavior in certain layered semiconductors.

Giant Piezoresistive Effect and Strong Bandgap Tunability in Ultrathin InSe upon Biaxial Strain

The ultrathin nature and dangling bonds free surface of 2D semiconductors allow for significant modifications of their bandgap through strain engineering. Here, thin InSe photodetector devices are biaxially stretched, finding, a strong bandgap tunability upon strain. The applied biaxial strain is controlled through the substrate expansion upon temperature increase and the effective strain transfer from the substrate to the thin InSe is confirmed by Raman spectroscopy. The bandgap change upon biaxial strain is determined through photoluminescence measurements, finding a gauge factor of up to ≈200 meV %-1. The effect of biaxial strain on the electrical properties of the InSe devices is further characterized. In the dark state, a large increase of the current is observed upon applied strain which gives a piezoresistive gauge factor value of ≈450-1000, ≈5-12 times larger than that of other 2D materials and of state-of-the-art silicon strain gauges. Moreover, the biaxial strain tuning of the InSe bandgap also translates in a strain-induced redshift of the spectral response of the InSe photodetectors with ΔE cut-off ≈173 meV at a rate of ≈360 meV %-1 of strain, indicating a strong strain tunability of the spectral bandwidth of the photodetectors.

Strain-Sensitive Magnetization Reversal of a van der Waals Magnet

By virtue of the layered structure, van der Waals (vdW) magnets are sensitive to the lattice deformation controlled by the external strain, providing an ideal platform to explore the one-step magnetization reversal that is still conceptual in conventional magnets due to the limited strain-tuning range of the coercive field. In this study, a uniaxial tensile strain is applied to thin flakes of the vdW magnet Fe₃ GeTe₂ (FGT), and a dramatic increase of the coercive field (H_c ) by more than 150% with an applied strain of 0.32% is observed. Moreover, the change of the transition temperatures between the different magnetic phases under strain is investigated, and the phase diagram of FGT in the strain-temperature plane is obtained. Comparing the phase diagram with theoretical results, the strain-tunable magnetism is attributed to the sensitive change of magnetic anisotropy energy. Remarkably, strain allows an ultrasensitive magnetization reversal to be achieved, which may promote the development of novel straintronic device applications.

Proposal for an electrostrictive logic device with the epitaxial oxide heterostructure

The possible use of electrostrictive materials for information processing devices has been widely discussed because it could allow low-power logic operation by overcoming the fundamental limit of subthreshold swing greater than 60 mV/decade in conventional MOSFETs. However, existing proposals for electrostrictive FET applications typically adopt approaches that are entirely theoretical and simulative, thus lacking practical insights into how an electrostrictive material can be best interfaced with a channel material. Here we propose an electrostrictive FET device, involving the epitaxial oxide heterostructure as an ideal material platform for maximum strain transfer. The ON/OFF switching occurs due to a stress-induced concentration change of oxygen vacancies in the memristive oxide channel layer. Based on finite-element simulations, we show that the application of a minimal gate voltage bias can induce stress in the channel layer as high as 10⁸ N/m² owing to the epitaxial interface between the electrostrictive and memristive oxide layers. Conductive AFM experiments further support the feasibility of the proposed device by demonstrating the stress-induced conductivity modulation of a perovskite oxide thin film, SrTiO₃, that is well known to serve as the substrate for epitaxial growth of other functional oxide layers.

Strain-Engineered Anisotropic Optical and Electrical Properties in 2D Chiral-Chain Tellurium

Atomically thin materials, leveraging their low-dimensional geometries and superior mechanical properties, are amenable to exquisite strain manipulation with a broad tunability inaccessible to bulk or thin-film materials. Such capability offers unexplored possibilities for probing intriguing physics and materials science in the 2D limit as well as enabling unprecedented device applications. Here, the strain-engineered anisotropic optical and electrical properties in solution-grown, sub-millimeter-size 2D Te are systematically investigated through designing and introducing a controlled buckled geometry in its intriguing chiral-chain lattice. The observed Raman spectra reveal anisotropic lattice vibrations under the corresponding straining conditions. The feasibility of using buckled 2D Te for ultrastretchable strain sensors with a high gauge factor (≈380) is further explored. 2D Te is an emerging material boasting attractive characteristics for electronics, sensors, quantum devices, and optoelectronics. The results suggest the potential of 2D Te as a promising candidate for designing and implementing flexible and stretchable devices with strain-engineered functionalities.

Recent Advances in Strain-Induced Piezoelectric and Piezoresistive Effect-Engineered 2D Semiconductors for Adaptive Electronics and Optoelectronics

The development of two-dimensional (2D) semiconductors has attracted widespread attentions in the scientific community and industry due to their ultra-thin thickness, unique structure, excellent optoelectronic properties and novel physics. The excellent flexibility and outstanding mechanical strength of 2D semiconductors provide opportunities for fabricated strain-sensitive devices and utilized strain tuning their electronic and optic-electric performance. The strain-engineered one-dimensional materials have been well investigated, while there is a long way to go for 2D semiconductors. In this review, starting with the fundamental theories of piezoelectric and piezoresistive effect resulted by strain, following we reviewed the recent simulation works of strain engineering in novel 2D semiconductors, such as Janus 2D and 2D-Xene structures. Moreover, recent advances in experimental observation of strain tuning PL spectra and transport behavior of 2D semiconductors are summarized. Furthermore, the applications of strain-engineered 2D semiconductors in sensors, photodetectors and nanogenerators are also highlighted. At last, we in-depth discussed future research directions of strain-engineered 2D semiconductor and related electronics and optoelectronics device applications.

Strain-engineering the Schottky barrier and electrical transport on MoS2

Strain provides an effective means to tune the electrical properties while retaining the native chemical composition of the material. Unlike three-dimensional solids, two-dimensional materials withstand higher levels of elastic strain making it easier to tune various electrical properties to suit the technology needs. In this work we explore the effect of uniaxial tensile-strain on the electrical transport properties of bi-and few-layered MoS₂, a promising 2D semiconductor. Raman shifts corresponding to the in-plane vibrational modes show a redshift with strain indicating a softening of the in-plane phonon modes. Photoluminescence measurements reveal a redshift in the direct and the indirect emission peaks signaling a reduction in the material bandgap. Transport measurements show a substantial enhancement in the electrical conductivity with a high piezoresistive gauge factor of ∼321 superior to that for Silicon for our bi-layered device. The simulations conducted over the experimental findings reveal a substantial reduction of the Schottky barrier height at the electrical contacts in addition to the resistance of MoS₂. Our studies reveal that strain is an important and versatile ingredient to tune the electrical properties of 2D materials and also can be used to engineer high-efficiency electrical contacts for future device engineering.

Piezoelectricity in Multilayer Black Phosphorus for Piezotronics and Nanogenerators

Recently, piezoelectric characteristics have been a research focus for 2D materials because of their broad potential applications. Black phosphorus (BP) is a monoelemental 2D material predicted to be piezoelectric because of its highly directional properties and non-centrosymmetric lattice structure. However, piezoelectricity is hardly reported in monoelemental materials owing to their lack of ionic polarization, but piezoelectric generation is consistent with the non-centrosymmetric structure of BP. Theoretical calculations of phosphorene have explained the origin of piezoelectric polarization among P atoms. However, the disappearance of piezoelectricity in multilayer 2D material generally arises from the opposite orientations of adjacent atomic layers, whereas this effect is limited in BP lattices due to their spring-shaped space structure. Here, the existence of in-plane piezoelectricity is experimentally reported for multilayer BP along the armchair direction. Current-voltage measurements demonstrate a piezotronic effect in this orientation, and cyclic compression and release of BP flakes show an intrinsic current output as large as 4 pA under a compressive strain of -0.72%. The discovery of piezoelectricity in multilayer BP can lead to further understanding of this mechanism in monoelemental materials.

Two-Dimensional Pnictogen for Field-Effect Transistors

Two-dimensional (2D) layered materials hold great promise for various future electronic and optoelectronic devices that traditional semiconductors cannot afford. 2D pnictogen, group-VA atomic sheet (including phosphorene, arsenene, antimonene, and bismuthene) is believed to be a competitive candidate for next-generation logic devices. This is due to their intriguing physical and chemical properties, such as tunable midrange bandgap and controllable stability. Since the first black phosphorus field-effect transistor (FET) demo in 2014, there has been abundant exciting research advancement on the fundamental properties, preparation methods, and related electronic applications of 2D pnictogen. Herein, we review the recent progress in both material and device aspects of 2D pnictogen FETs. This includes a brief survey on the crystal structure, electronic properties and synthesis, or growth experiments. With more device orientation, this review emphasizes experimental fabrication, performance enhancing approaches, and configuration engineering of 2D pnictogen FETs. At the end, this review outlines current challenges and prospects for 2D pnictogen FETs as a potential platform for novel nanoelectronics.

Nanoelectromechanical Sensors Based on Suspended 2D Materials

The unique properties and atomic thickness of two-dimensional (2D) materials enable smaller and better nanoelectromechanical sensors with novel functionalities. During the last decade, many studies have successfully shown the feasibility of using suspended membranes of 2D materials in pressure sensors, microphones, accelerometers, and mass and gas sensors. In this review, we explain the different sensing concepts and give an overview of the relevant material properties, fabrication routes, and device operation principles. Finally, we discuss sensor readout and integration methods and provide comparisons against the state of the art to show both the challenges and promises of 2D material-based nanoelectromechanical sensing.

2D BeP2 monolayer: investigation of electronic and optical properties by driven modulated strain

Recently, the two-dimensional (2D) material beryllium diphosphide (BeP₂) has attracted significant attention for potential device applications due to its Dirac semimetal state, dynamic and thermal stability, and high carrier mobility. In this work, we investigated its electronic and optical properties under biaxial Lagrangian strain using density functional theory (DFT). Electronic band gaps and effective charge carrier mass were highly sensitive to the Lagrangian strain of BeP₂ monolayer. The bandgaps of BeP₂ varied from 0 eV to 0.30 eV for 2% to 8% strain, where the strain range is based on the final stable condition of the system. The absorption spectra for the dielectric properties show the highest absorption peaks in the infrared (IR) region. These abundant strain-dependent studies of the BeP₂ monolayer provide guidelines for its application in infrared sensors and devices.

BeP₂ monolayer is a promising material for the novel IR optical device.

Strain engineering of the electronic and transport properties of monolayer tellurenyne

Two-dimensional (2D) materials exhibiting quality electronic properties such as suitable band gap, giant Rashba effect and high carrier mobility are essential for promising applications in electronics and spintronics. Strain engineering has been recognized as an effective strategy to engineer the atomic and electronic properties of 2D materials. Herein, based on density functional theory, we demonstrate that the electronic properties of tellurenyne can be tuned well by using uniaxial strain. We find that tellurenyne retains the unique noncovalent bond structure and exhibits good stability under the uniaxial strain. Meanwhile, the band gap of tellurenyne can be tuned to a large scale (0.33-1.18 eV and 0.73-1.27 eV under the uniaxial strain along and perpendicular to the chain direction, respectively). Under 10% tension strain along the chain direction, the Rashba constant reaches 2.96 eV Å, belonging to giant Rashba systems. More importantly, the hole mobility of tellurenyne along the chain direction reaches 1.1 × 105 cm2 V-1 s-1 under 10% tension strain along the chain direction, which is one order of magnitude larger than that of phosphorene. Therefore, these remarkable electronic properties of tellurenyne engineered by using strain indicate its potential applications in electronics and spintronics.

Suppression of Electron-Hole Recombination by Intrinsic Defects in 2D Monoelemental Material

The Shockley-Read-Hall (SRH) model, in which the deep trap defect states in the band gap are proposed as nonradiative electron-hole (e-h) recombination centers, has been widely used to describe the nonradiative e-h recombination through the defects in semiconductor. By using the ab initio nonadiabatic molecular dynamics method, we find that the SRH model fails to describe the e-h recombination behavior for defects in 2D monoelemental material such as monolayer black phosphorus (BP). Through the investigation of three intrinsic defects with shallow and deep defect states in monolayer BP, it is found that, surprisingly, none of these defects significantly accelerates the e-h recombination. Further analysis shows that because monolayer BP is a monoelemental material, the distinct impurity phonon, which often induces fast e-h recombination, is not formed. Moreover, because of the flexibility of 2D material, the defects scatter the phonons present in pristine BP, generating multiple modes with lower frequencies compared with the pristine BP, which further suppresses the e-h recombination. We propose that the conclusion can be extended to other monoelemental 2D materials, which is important guidance for the future design of functional semiconductors.

Strain-Engineered van der Waals Interfaces of Mixed-Dimensional Heterostructure Arrays

van der Waals (vdWs) heterostructures have provided a platform for nanoscale material integrations and enabled promise for use in optoelectronic devices. Because of the ultrastrength of two-dimensional materials, strain engineering is considered as an effective way to tune their band structures and further tailor the interface performance of vdWs heterostructures. However, the less-constrained vdWs interfaces make the traditional strain technique via lattice-mismatched growth infeasible. Here, we report a strategy to construct mixed-dimensional heterostructure arrays with periodically strain-engineered vdWs interfaces utilizing one-dimensional semiconductor-induced nanoindentation. Using monolayer MoS₂ (1L-MoS₂)/ZnO heterostructure arrays as a model system, we demonstrate inhomogeneous built-in strain gradient at the heterointerfaces ranging from 0 to 0.6% tensile. Through systematic optical characterization of the hybrid structures, we verify that strain can improve the interfacial charge transfer efficiency. Consequently, we observe that the photoluminescence (PL) emission of 1L-MoS₂ at strained interfaces is dramatically quenched more than 50% with respect to that at unstrained interfaces. Furthermore, we confirm that the strain-optimized interfacial carrier behavior is attributed to the reduction of interfacial barrier height, which originated from the strain-dependent Fermi level of 1L-MoS₂. These results demonstrate that strain provides another degree of freedom in tuning the vdWs interface performance and our method developed here should enable flexibility in achieving more sophisticated vdWs integration via strain engineering.

Two-dimensional layered materials: from mechanical and coupling properties towards applications in electronics

With the increasing interest in nanodevices based on two-dimensional layered materials (2DLMs) after the birth of graphene, the mechanical and coupling properties of these materials, which play an important role in determining the performance and life of nanodevices, have drawn increasingly more attention. In this review, both experimental and simulation methods investigating the mechanical properties and behaviour of 2DLMs have been summarized, which is followed by the discussion of their elastic properties and failure mechanisms. For further understanding and tuning of their mechanical properties and behaviour, the influence factors on the mechanical properties and behaviour have been taken into consideration. In addition, the coupling properties between mechanical properties and other physical properties are summarized to help set up the theoretical blocks for their novel applications. Thus, the understanding of the mechanical and coupling properties paves the way to their applications in flexible electronics and novel electronics, which is demonstrated in the last part. This review is expected to provide in-depth and comprehensive understanding of mechanical and coupling properties of 2DLMs as well as direct guidance for obtaining satisfactory nanodevices from the aspects of material selection, fabrication processes and device design.

Strain-tunable van der Waals interactions in few-layer black phosphorus

Interlayer interactions in 2D materials, also known as van der Waals (vdWs) interactions, play a critical role in the physical properties of layered materials. It is fascinating to manipulate the vdWs interaction, and hence to "redefine" the material properties. Here, we demonstrate that in-plane biaxial strain can effectively tune the vdWs interaction of few-layer black phosphorus with thickness of 2-10 layers, using infrared spectroscopy. Surprisingly, our results reveal that in-plane tensile strain efficiently weakens the interlayer coupling, even though the sample shrinks in the vertical direction due to the Poisson effect, in sharp contrast to one's intuition. Moreover, density functional theory (DFT) calculations further confirm our observations and indicate a dominant role of the puckered lattice structure. Our study highlights the important role played by vdWs interactions in 2D materials during external physical perturbations.

The Opposite Anisotropic Piezoresistive Effect of ReS2

Mechanical strain induced changes in the electronic properties of two-dimensional (2D) materials is of great interest for both fundamental studies and practical applications. The anisotropic 2D materials may further exhibit different electronic changes when the strain is applied along different crystalline axes. The resulting anisotropic piezoresistive phenomenon not only reveals distinct lattice-electron interaction along different principle axes in low-dimensional materials but also can accurately sense/recognize multidimensional strain signals for the development of strain sensors, electronic skin, human-machine interfaces, etc. In this work, we systematically studied the piezoresistive effect of an anisotropic 2D material of rhenium disulfide (ReS₂), which has large anisotropic ratio. The measurement of ReS₂ piezoresistance was experimentally performed on the devices fabricated on a flexible substrate with electrical channels made along the two principle axes, which were identified noninvasively by the reflectance difference microscopy developed in our lab. The result indicated that ReS₂ had completely opposite (positive and negative) piezoresistance along two principle axes, which differed from any previously reported anisotropic piezoresistive effect in other 2D materials. We attributed the opposite anisotropic piezoresistive effect of ReS₂ to the strain-induced broadening and narrowing of the bandgap along two principle axes, respectively, which was demonstrated by both reflectance difference spectroscopy and theoretical calculations.

Bright Mid-Infrared Photoluminescence from Thin-Film Black Phosphorus

Recently rediscovered layered black phosphorus (BP) provides rich opportunities for investigations of device physics and applications. The band gap of BP is widely tunable by its layer number and a vertical electric field, covering a wide electromagnetic spectral range from visible to mid-infrared. Despite much progress in BP optoelectronics, the fundamental photoluminescence (PL) properties of thin-film BP in mid-infrared have rarely been investigated. Here, we report bright PL emission from thin-film BP (with thickness of 4.5 to 46 nm) from 80 to 300 K. The PL measurements indicate a band gap of 0.308 ± 0.003 eV in 46 nm thick BP at 80 K, and it increases monotonically to 0.334 ± 0.003 eV at 300 K. Such an anomalous blueshift agrees with the previous theoretical and photoconductivity spectroscopy results. However, the observed blueshift of 26 meV from 80 to 300 K is about 60% of the previously reported value. Most importantly, we show that the PL emission intensity from thin-film BP is only a few times weaker than that of an indium arsenide (InAs) multiple quantum well (MQW) structure grown by molecular beam epitaxy. Finally, we report the thickness-dependent PL spectra in thin-film BP in mid-infrared regime. Our work reveals the mid-infrared light emission properties of thin-film BP, suggesting its promising future in tunable mid-infrared light emitting and lasing applications.

Investigating the interlayer electron transport and its influence on the whole electric properties of black phosphorus

Two-dimensional (2D) nanomaterials have attracted great attention in next generation electronic and optoelectronic technologies due to the unique layered structure and excellent physical and chemical properties. However, the mechanism of transmission along the vertical direction of 2D semiconductor materials has not been investigated. Here, we use first-principles calculations to explore the bandgap energies along different directions, and fabricate a vertical, a lateral and a mixture-structured black phosphorus field effect transistor (BPFET) to study the electrical characteristics along different directions under variable temperatures. The variable temperature test indicates that the mixture-structured device performs more like a lateral device, while the conductance along the vertical direction is hard to be tuned by temperature and electrical field. The unchanged conductance under electric field and variable temperatures allows the vertical device to act as a fixed resistor, promising possible application for the prospective electronic and optoelectronic devices.

Off-Plane Dielectric Screening of Few-Layer Graphdiyne and Its Family

We performed first-principles calculations on few-layer graphdiyne (GDY) and its family, sp-sp² hybrid carbon atomic layers, for an off-plane, static dielectric screening. The vertical dielectric constants of semiconducting GDY structures are finite and independent of the thickness. However, unlike the widely accepted wisdom that the static metallic screening is infinite, those of metallic GDY structures are finite and dependent on their thickness. Furthermore, the vertical dielectric screening can be tuned by varying the interlayer distance. We also studied the dielectric properties of heterostructures of GDY/its family; the vertical dielectric constant has an equivalent value from the two distinct values of the two distinct monostructures. The dielectric screening behaviors are well described by the uniform dielectric slab model. In addition, the band gaps can be widely tuned from 0 to 0.8 eV, by varying the thickness and electric field. Our results provide a method for engineering the dielectric constant and band gap of GDY and its family for applications of supercapacitors and nanodevices.

Anisotropic Thermal Conductivity of Suspended Black Phosphorus Probed by Opto-Thermomechanical Resonance Spectromicroscopy

Atomic layer semiconducting black phosphorus (P) exfoliated from its bulk crystals offers excellent properties and promises for emerging two-dimensional (2D) electronics, photonics, and transducers. It also possesses unique strong in-plane anisotropy among many 2D semiconductors, stemming from its corrugated crystal structure. As an important thermophysical aspect, probing the anisotropic thermal conductivity of black P is essential for device engineering, especially for energy dissipation and thermal management. Here, we report on measurement and analysis of anisotropic in-plane thermal conductivity of black P crystal, in a mechanically suspended device platform, by exploiting a novel opto-thermomechanical resonance spectromicroscopy (OTMRS) technique. With spatially resolved heating effects and thermomechanical resonance motions of suspended structures, anisotropic in-plane thermal conductivity (κ_AC and κ_ZZ) is determined for black P crystals of 10-100 nm thick. This study validates a new noninvasive approach to determining anisotropic thermal conductivity without any requirement of preknowledge of crystal orientation or specific configurations of structure and electrodes according to the anisotropy.

Two-dimensional black phosphorus: its fabrication, functionalization and applications

Phosphorus, one of the most abundant elements in the Earth (∼0.1%), has attracted much attention in the last five years since the rediscovery of two-dimensional (2D) black phosphorus (BP) in 2014. The successful scaling down of BP endows this 'old material' with new vitality, resulting from the intriguing semiconducting properties in the atomic scale limit, i.e. layer-dependent bandgap that covers from the visible light to mid-infrared light spectrum as well as hole-dominated ambipolar transport characteristics. Intensive research effort has been devoted to the fabrication, characterization, functionalization and application of BP and other phosphorus allotropes. In this review article, we summarize the fundamental properties and fabrication techniques of BP, with particular emphasis on the recent progress in molecular beam epitaxy growth of 2D phosphorus. Subsequently, we highlight recent progress in BP (opto)electronic device applications achieved via customized manipulation methods, such as interface, defect and bandgap engineering as well as forming Lego-like stacked heterostructures.

Quantum Hall Effect in Electron-Doped Black Phosphorus Field-Effect Transistors

The advent of black phosphorus field-effect transistors (FETs) has brought new possibilities in the study of two-dimensional (2D) electron systems. In a black phosphorus FET, the gate induces highly anisotropic 2D electron and hole gases. Although the 2D hole gas in black phosphorus has reached high carrier mobilities that led to the observation of the integer quantum Hall effect, the improvement in the sample quality of the 2D electron gas (2DEG) has however been only moderate; quantum Hall effect remained elusive. Here, we obtain high quality black phosphorus 2DEG by defining the 2DEG region with a prepatterned graphite local gate. The graphite local gate screens the impurity potential in the 2DEG. More importantly, it electrostatically defines the edge of the 2DEG, which facilitates the formation of well-defined edge channels in the quantum Hall regime. The improvements enable us to observe precisely quantized Hall plateaus in electron-doped black phosphorus FET. Magneto-transport measurements under high magnetic fields further revealed a large effective mass and an enhanced Landé g-factor, which points to strong electron-electron interaction in black phosphorus 2DEG. Such strong interaction may lead to exotic many-body quantum states in the fractional quantum Hall regime.

Two-dimensional transistors beyond graphene and TMDCs

Two-dimensional semiconductors (2DSCs) have attracted considerable attention as atomically thin channel materials for field-effect transistors. Each layer in 2DSCs consists of a single- or few-atom-thick, covalently bonded lattice, in which all carriers are confined in their atomically thin channel with superior gate controllability and greatly suppressed OFF-state current, in contrast to typical bulk semiconductors plagued by short channel effects and heat generation from static power. Additionally, 2DSCs are free of surface dangling bonds that plague traditional semiconductors, and hence exhibit excellent electronic properties at the limit of single atom thickness. Therefore, 2DSCs can offer significant potential for the ultimate transistor scaling to single atomic body thickness. Earlier studies of graphene transistors have been limited by the zero bandgap and low ON-OFF ratio of graphene, and transition metal dichalcogenide (TMDC) devices are typically plagued by insufficient carrier mobility. To this end, considerable efforts have been devoted towards searching for new 2DSCs with optimum electronic properties. Within a relatively short period of time, a large number of 2DSCs have been demonstrated to exhibit unprecedented characteristics or unique functionalities. Here we review the recent efforts and progress in exploring novel 2DSCs beyond graphene and TMDCs for ultra-thin body transistors, discussing the merits, limits and prospects of each material.

Grain Boundaries Are Benign and Suppress Nonradiative Electron-Hole Recombination in Monolayer Black Phosphorus: A Time-Domain Ab Initio Study

Using time-domain density functional theory combined with nonadiabatic molecular dynamics, we demonstrate that both symmetrical (GB_s) and asymmetrical grain boundaries (GB_a) significantly extend charge-carrier lifetime compared with monolayer black phosphorus. Boundaries create no deep trap states, which decrease electron-phonon coupling. As a result, GB_s increases carrier lifetime by a factor of 22, whereas GB_a extends the lifetime by a factor of 4. More importantly, the interplay between the immobile electron localized at the boundaries in the GB_s and extended excited-state lifetime facilitates a chemical reaction, which is beneficial for photocatalysts. In contrast, GB_a separates electron and hole spatially in different locations, which forms a long-lived charge-separated state and is favorable for photovoltaics. Our simulations demonstrate that grain boundaries are benign and retard nonradiative electron-hole recombination in monolayer black phosphorus, suggesting a route to reduce energy losses via rational choice of defect to realize high-performance photovoltaic and photocatalytic devices.

Largely Tunable Band Structures of Few-Layer InSe by Uniaxial Strain

Because of the strong quantum confinement effect, few-layer γ-InSe exhibits a layer-dependent band gap, spanning the visible and near infrared regions, and thus recently has been drawing tremendous attention. As a two-dimensional material, the mechanical flexibility provides an additional tuning knob for the electronic structures. Here, for the first time, we engineer the band structures of few-layer and bulk-like InSe by uniaxial tensile strain and observe a salient shift of photoluminescence peaks. The shift rate of the optical gap is approximately 90-100 meV per 1% strain for four- to eight-layer samples, which is much larger than that for the widely studied MoS₂ monolayer. Density functional theory calculations well reproduce the observed layer-dependent band gaps and the strain effect and reveal that the shift rate decreases with the increasing layer number for few-layer InSe. Our study demonstrates that InSe is a very versatile two-dimensional electronic and optoelectronic material, which is suitable for tunable light emitters, photodetectors, and other optoelectronic devices.

Strain-engineering the electronic properties and anisotropy of GeSe2 monolayers

As a new two-dimensional (2D) material, GeSe₂ has attracted significant attention recently due to its distinctive in-plane anisotropic properties originated from the in-plane anisotropic crystal structure, high air stability and excellent performance in polarization-sensitive photodetection. However, no systematic study of the strain effect on the electronic properties and anisotropy of GeSe₂ has been reported, restricting the relevant applications such as mechanical-electronic devices. Here we investigate the change of the electronic properties and anisotropy of GeSe₂ monolayer under strains along x and y directions through first-principle calculations. The electronic band structure and effective mass of charge carriers are highly sensitive to the strain. Notably, through appropriate x or y directional strain, the anisotropy of the hole effective mass can even be rotated by 90°. These plentiful strain-engineering properties of GeSe₂ give it many opportunities in novel mechanical-electronic applications.

GeSe₂ has attracted significant attention recently due to its distinctive in-plane anisotropic properties originated from the in-plane anisotropic crystal structure and excellent performance in polarization-sensitive photodetection.

2D library beyond graphene and transition metal dichalcogenides: a focus on photodetection

Two-dimensional materials beyond graphene and TMDs can be promising candidates for wide-spectra photodetection.