Single-layer Black Phosphorus Research Articles

Single-layer black phosphorus-enhanced narrowband perfect absorber in the terahertz range

In this paper, a narrowband absorber based on black phosphorus (BP) is proposed. By utilizing a single-layer BP, a Si structure with four etched holes, and a perfectly electrically conductive (PEC) plate, multi-band absorption can be achieved in the range of 3.8 THz to 5.0 THz. The location and absorbance of the three peaks are 4.32 THz (99.7 %), 4.53 THz (95.6 %), and 4.69 THz (56.7 %), respectively. The anisotropy of the BP structure leads to different absorption spectra when illuminated by TE and TM polarized light sources. Altering the electron doping in BP allows control over the position and intensity of absorption peaks. Upon examining the electric field distribution of the absorber, it is evident that the dominant physical mechanism is the localized surface plasmon resonance (LSPR). Overall, the monolayer BP absorber designed in this study can be utilized to construct a polarimetric sensor for infrared wavelengths. Additionally, it provides a valuable reference for 2D anisotropic plasma devices.

Nonlinear dynamic behavior of single-layered black phosphorus with an attached mass

The investigation of black phosphorus-based (BP)-based mass sensors provides theoretical support for the development of mass-detection devices. This study examines the non-linear dynamic behavior of a rectangular single-layered BP (SLBP) with an attached mass through the utilization of molecular dynamics (MD) simulations and a nonlinear orthotropic plate model (NOPM) with a concentrated mass. The results indicate that significant deformation of an SLBP with an attached mass necessitates consideration of geometric nonlinearity, although the attached mass does not affect the deformation. Additionally, this paper discusses the impact of the attachment mass and the amplitude of harmonic force on the non-linear forced vibration of the SLBP. It is observed that as the attachment mass increases, the nonlinear vibration resonance frequency decreases, while the peak amplitude increases. Furthermore, the thermal nonlinear vibration of SLBP with an attached mass has been investigated, revealing that an increase in the attached mass leads to a decrease in the nonlinear vibration frequency but an increase in the amplitude of the nonlinear vibration of SLBP with an attached mass. Overall, comparison with MD simulation results, this investigation suggests that NOPM with a concentrated mass effectively describes the nonlinear vibration behavior of an SLBP with an attached mass, providing theoretical support for designing such devices to detect attached masses.

Synthesis of Black Phosphorene/P-Rich Transition Metal Phosphide NiP3 Heterostructure and Its Effect on the Stabilization of Black Phosphorene

Black phosphorus (BP), as a direct band gap semiconductor material with a two-dimensional layered structure, has a good application potential in many aspects, but the surface state of it is extremely unstable, especially that of single-layer black phosphorus. In this study, BP crystals and two-dimensional black phosphorus (2D BP) are prepared by a mechanical ball-milling–liquid-phase exfoliation method. The X-ray diffraction (XRD) spectrum and high-resolution transmission electron microscopy (HRTEM) results showed that red phosphorus (RP) successfully turned to BP by the mechanical ball-milling method. The spectrophotometric analysis has detected absorption peaks at 780 nm, 915 nm, and 1016 nm, corresponding to single, double, and three-layer BP bandgap emission. A simple solvothermal strategy is designed to synthesize in-plane BP/P-rich transition metal phosphide (TMP) heterostructures (BP/NiP3) by defect/edge-selective growth of NiP3 on the BP nanosheets. HRTEM analysis indicates that the metal ions are preferentially deposited on the defects of 2D BP such as edges and unsaturated sites, forming a 2D BP/NiP3 in-plane heterojunction.

Negative Poisson's ratio effect of P2/m phosphine

Negative Poisson's ratio materials have the advantages of good shear resistance, dent resistance, and fracture resistance. Thus, they have great application potential in the manufacturing field with high requirements for material mechanical flexibility. However, negative Poisson's ratio materials are relatively rare. In this paper, the first principles calculation is used to study the single-layer P2/m-P phosphorene. It is found that when −5% to 5% strain is applied along the zigzag (Y) direction, there is a negative Poisson's ratio effect along the Z direction, and Poisson's ratio is −0.288, which is about ten times that of the single-layer black phosphorus (the negative Poisson's ratio of the single-layer black phosphorus is −0.027). Compared with black phosphorene, it has more potential applications in wearable and impact resistant equipment.

Commensurate stacking-induced ultrahigh yet discontinuous bending stiffness of the double-layer black phosphorus

Black phosphorus (BP) has a considerable prospect in flexible electronics due to its atomic thickness and excellent photoelectric properties. Notably, their unique puckered surface makes flexible devices with highly adjustable bending performance possible. Here, a novel computational method for predicting the bending property of 2D materials is proposed based on molecular dynamics, focusing on the bending behavior of single- and double-layer BP. The results indicate that the bending stiffness of single-layer BP exhibits a significant chiral dependence. For double-layer BP, the bending stiffness varies from 6.35 to 54.77 eV, which depends on the stacking order and bending amplitude. The ultrahigh bending stiffness is about 10∼13 times larger than that of single-layer BP, but it will undergo an abrupt reduction when the bending angle exceeds the critical value. The mechanism of the abrupt change is attributed to the interfacial structural transition from commensurability-induced self-locking to unlocking by analyzing the cooperative adjustment between the interlayer spacing, characteristic size and interlayer structures. This work reveals that the number of layers, stacking order and bending amplitude are vital factors affecting the bending stiffness of multi-layer 2D materials. Thus, 2D structural design provides an effective strategy for preparing on-demand flexible devices.

Anisotropic thermal conductivity and corrugated patterns in single-layer black phosphorus nanoribbon subjected to shear loading: a molecular dynamics study

Single-layer black phosphorus (SLBP) also known as phosphorene is a recently introduced two-dimensional material with unique structure and promising physical properties that has drawn considerable attention in the field of nanodevices. This structure demonstrates a high anisotropy in mechanical and thermal behavior along zigzag (ZZ) and armchair (AC) principal in-plane directions. Here in this study, it is shown that implementing shear strain on 10 nm × 50 nm SLBP nanoribbons (SLBPNRs) along ZZ and AC directions, the anisotropy leads to different corrugated patterns on the pristine structure. Applying non-equilibrium molecular dynamics under a parameterized Stillinger–Weber potential for modelling SLBP, thermal conductivity (TC) behavior of the sheared SLBPNRs with corrugated patterns are examined. The results show a higher amplitude and wavelength of the corregations on the ZZ-aligned SLBPNRs, which is around two times higher than that of AC-aligned counterparts. Although, it is also shown that unlike some other 2D materials, such as graphene, the wrinkling does not have such a significant effect on TC of SLBP. The phonon density of states results obtained in this work as well as phonon dispersion curves by first-principle calculations in other works concrete this finding. The results show small frequency shifts in both high- and low-frequency phonons, which are not strong enough to affect TC in SLBPNRs. This interesting thermal property of SLBP under shear strain suggests the great potential application of these corrugated structures in nanodevices without any loss of TC abilities.

Behaviour of induced states of substitutional and adatom impurity doping on electronic transport properties of single-layer black phosphorus

Substitutional and adatom impurity doping can be considered quite effective or even better for modulating the electronic transport coefficients. Herein, we have studied the impact of substitutional doping by Al and Cl multi atoms and adatom adsorption by O, Cu, K, and Ag atoms on the electronic transport properties of single-layer black phosphorus using the first-principles method based density functional theory framework in conjunction with Boltzmann transport equation at room temperature. We found that these impurity atoms introduce new donor and acceptor induced eigenstates and flat bands within the fundamental bandgap. We have calculated the scattering rates and relaxation time by solving the Boltzmann transport equation with the ab-initio calculated electron-phonon interactions. The electron-phonon coupling matrix elements are computed through maximally localized Wannier functions and density functional perturbation theory using Wannier-Fourier interpolation on a fine sampling of the Brillouin zone . The binding energies illustrated the structural stability of all doped systems and found that phosphorene showed a stronger adsorption capability as compared with the graphene and MoS 2 sheet. Moreover, binding energy for the substitutionally doped system is found to decrease with the increasing atomic number. Furthermore, the achieved electron mobility, electrical conductivity ( σ ), and Seebeck coefficient (S) of pristine single-layer black phosphorus are ~279 cm 2 V −1 s −1 , 6.1 × 10 6 Ω −1 m −1 and 1.4 mV/K respectively. The calculated values of carrier mobility , electrical conductivity and Seebeck coefficient have found a rich diversity in each impurity doped layer, and the negative differential behaviour is observed. These results provide comprehensive information about chemical functionalization and bandgap tunability for modelling of phosphorene based devices. • Substitutional and adatom impurity doping are effective for modulating the electronic transport coefficients of phosphorene. • We have studied the impact of substitutional doping by Al and Cl multi atoms and adatom adsorption by O, Cu, K, and Ag atoms. • We have calculated the scattering rates and relaxation time by solving the Boltzmann transport equation. • The binding energies illustrated the structural stability and found that phosphorene showed a stronger adsorption capability. • The calculated values of carrier mobility, electrical conductivity and Seebeck coefficient have found a rich diversity.

Systematic competition between strain and electric field stimuli in tuning EELS of phosphorene

The strongly anisotropic properties of phosphorene makes it an attractive material for applications in deciding the specific direction for different purposes. Here we have particularly reported the competition between strain and electric field stimuli in evaluating the band gap and electron energy loss spectrum (EELS) of single-layer black phosphorus using the tight-binding method and the Kubo conductivity. We construct possible configurations for this competition and evaluate the interband optical excitations considering the corresponding band gap variations. The band gap increases with the individual electric field, while it increases (decreases) with tensile (compressive) uniaxial in-plane strain. Contrary to the in-plane strains, the uniaxial out-of-plane strain shows a critical strain at which the system suffers from a phase transition. Furthermore, the presence of these stimuli simultaneously results in an extraordinary band gap engineering. Based on the EELS response in the electromagnetic spectrum, the armchair (zigzag) direction is classified into the infrared and visible (ultraviolet) region. We report that the electric field gives rise to the blue shift in the interband optical transitions along the armchair direction, while the compressive/tensile (tensile/compressive) in-plane/out-of-plane strain provides a red (blue) shift. Moreover, we observe an inverse behavior of EELS response to the individual and combined effects of electric field and strains compared to the band gap behavior except at critical out-of-plane strain for which the physical theory of interband excitation is simply violated. Our results provide a new perspective on the applicability of phosphorene in stimulated optical applications.

Critical role of the bending stiffness of the monolayer black phosphorus in its mechanical behaviors: molecular dynamics simulation

Black phosphorus (BP) is a novel two-dimensional nanostructure with wide potential applications in such areas as nanoresonators and nanosensors. In this study, we concentrate on the role of the bending stiffness of the BP monolayer in its mechanical performances, including tension, compression, buckling and bending. Firstly, the stress–strain curve and Young’s modulus of the single layer black phosphorus (SLBP) nanoribbon with different chiral structures are obtained in the tension process via the molecular dynamics (MD) simulation. Next, the loading behavior of the SLBP nanoribbon during compression is simulated via MD. It was found that the bending stiffness of the nanoribbon has an essential effect on its postbuckling behaviors, and an empirical formula is proposed which can accurately depict the postbuckling process. Eventually, the bending properties of chiral SLBP nanoribbons are explored via the MD simulation, and the modified expression of the bending stiffness can better predict its large deflection. These findings are beneficial for us to fully understand mechanical responses of BP, which hold implications in engineering new materials and devices at nanoscale.

Studies on covalent functionalization of single layer black phosphorus from GW calculations based on the many body perturbation theory

The major challenge of black phosphorus (BP) is its fast-oxidative degradation in air. Organic covalent chemical modification of BP flakes could suppress the chemical degradation. Here we focus on the effects of covalent chemical modification on the electronic structures of single layer BP. We employed the state-of-the-art first principles GW method, which is based on the many body green functions, to study the covalent modification of single layer BP by forming P–C bonds. Our results show that the functional group chemisorbed at perfect lattice site results in deep in-gap state, which may deteriorate its performance, while the P–C bonds forming at single vacancies are electrically inactive. In addition, our results show that functional groups at low concentration would be preferably chemisorbed at single vacancies. At high concentration, functional groups would lead to the breaking of P–P bonds, and hence, oxygen impurity will easily insert in the interstitial position. Finally, we propose that functional groups at low concentration would protect BP from deterioration, and at high concentrations, functional groups would accelerate the deterioration of BP performance.

Lithium intercalation drives mechanical properties deterioration in bulk and single-layered black phosphorus: a first-principles study

It is of critical importance to understand the mechanical properties change of electrode materials during lithium intercalation in the mechanical design of Li-ion batteries (LIBs), for the purpose of the high reliability and safety in their applications. Here, we investigated the mechanical properties of both bulk and single-layered black phosphorus (BP) during the lithium intercalation process by using the first-principles calculations. Our results show that the Young’s modulus of bulk and single-layered phosphorus strongly depends on the lithium intercalation. The mechanical bearing capacities, such as critical strain and stress, are significantly reduced by several times after lithium intercalation in both bulk and single-layered BP, which may reduce the reliability of LIBs. Our findings suggest that this notable mechanical properties deterioration during lithium intercalation should be considered carefully in the mechanical design of LIBs, in order to keep the work reliable and safe in the charge-discharge process.

Effect of tensile and compression deformation on the electronic structure and optical properties of single-layer black phosphorus

Based on the first-principles method of density functional theory, the electronic structure and optical properties of single-layer black phosphorus under tensile and compression deformation were calculated. It is found that the overall trend of single-layer black phosphorus stability decreased with the increase of tensile and compression deformation; In the interval where the tensile deformation changes from 0% to 2.5%, the band gap of single-layer black phosphorus tends to increase first and then decrease. Under compression deformation, the band gap of single-layer black phosphorus decreased as the compression deformation increased; The highest absorption and reflection peaks of the light were blue-shifted first when the value of tensile deformation was small. Then, as the tensile deformation increased, both were red-shifted. Under compression deformation, as the compression deformation increased, the highest absorption and reflection peaks of the light were red-shifted gradually.

Synthesis of Black Phosphorus via a Facile Vapor Transfer Method

Single-layer black phosphorus (BP), known as phosphorene, has recently attracted interest in research due to its exceptional properties, similar to those of other 2D materials. BP is the most stable allotrope of phosphorus with high density. BP can be obtained from other phosphorus allotropes by a number of ways. Due to white phosphorus being highly reactive at ≥ 30 °C, researchers tend to work with red phosphorus (RP). In this work, RP powder was heated under an argon atmosphere inside a muffle furnace along with tin and iodine at sequential temperatures for different times. All elements were placed inside a quartz ampoule evacuated with a vacuum pump. The ampoule was sealed after substituting it with argon gas. This method, known as the vapor transfer method, allows to synthesize BP with a ribbon-like structure. FE-SEM analyses revealed that the morphological structure of BP comprised clearly-stacked sheets. The structural analysis of the as-synthesized BP, conducted by XRD, TEM and Raman, showed the successful transformation of RP into BP.

Thermal vibration of MoS2/Black phosphorus Bi-layered heterostructure

Thermal vibration is extremely crucial to nanostructure-based nanoresonators. In this paper, a laminated plate model (LPM) with the van der Waals (vdW) interactions between MoS2 and black phosphorus (BP) taken into consideration is proposed to explore the thermally induced vibration of a MoS2/BP heterostructure. The vdW coefficient between single-layered MoS2 and single-layered BP is calculated. The natural frequencies and the root-mean-squared (RMS) amplitudes of the MoS2/BP heterostructure are obtained from molecular dynamics (MD) simulations and the LPM. The natural frequencies and the RMS amplitudes of the MoS2/BP heterostructure calculated by the LPM and those obtained from the MD simulations coincide well. The LPM has in-phase vibrational modes and anti-phase vibrational modes. The natural frequencies of the in-phase vibrational modes are much lower than the frequencies of the anti-phase vibrational modes of the same order. In the thermal vibration of the MoS2/BP heterostructure, the RMS amplitudes of MoS2 and BP are obviously different. Compared with the natural frequencies and RMS amplitudes of the MoS2/BP heterostructure obtained from the MD simulations, the LPM can provide an accurate prediction of the thermal vibration of the MoS2/BP heterostructure.

Unique mechanical responses of layered phosphorus-like group-IV monochalcogenides

As interesting analog of black phosphorus, group-IV monochalcogenides MX (M = Ge, Sn; X = S, Se) are greatly expected to have potential applications in photodetectors, photovoltaics, thermoelectric, and piezoelectric devices. In this paper, we conduct a thorough investigation on the mechanical properties of four MX monochalcogenides, i.e., single- and multi-layered GeS, GeSe, SnS, and SnSe, including their ideal tensile strength, evolution of monolayer bulking height, and phase transition under uniaxial strain within the framework of density functional theory. The ultimate tensile strengths of the four monochalcogenides are found rather low, while the failure strains are remarkably high, showing ultrahigh mechanical flexibility. Meanwhile, the ideal strength demonstrates strong anisotropy, which may induce the exfoliated MX thin flakes showing an obvious in-plane cleavage tendency of much easier to crack along the zigzag orientation. In addition, it is found that all of them are potential auxetic materials with large negative Poisson's ratios, just like single-layer black phosphorus. Furthermore, we find all the monolayer monochalcogenides will demonstrate geometrical phase transition when uniaxial compressive strains are applied. It is expected that these newly found unique features of monolayer group-IV monochalcogenides and their derivatives make them attractive candidates for their incorporation in future mechanical, nanoelectronics, and thermal applications.

Improved Dreiding force field for single layer black phosphorus.

We present an improved Dreiding force field for single layer black phosphorus (SLBP) obtained by first-principle calculations in conjunction with the particle swarm optimization algorithm and molecular dynamics (MD) simulations. The proposed Dreiding force field can describe material properties of the SLBP very well in comparison with first-principle calculations and the Stillinger-Weber potential, including Young's modulus, Poisson's ratio, shear modulus, bending stiffness and phonon spectrum. Through the improved Dreiding force field, the wetting of a water nanodroplet and the adsorption of a villin headpiece on SLBP under compressive deformation are also studied by MD simulations. The simulation results show that the microscopic contact angle increases with the level of compressive strain on the SLBP. Meanwhile, the compressive strain reduces disruption caused by SLBP to the structure of the villin headpiece. The proposed Dreiding force field shows great potential to describe the interaction between SLBP and water molecules. It can be further used to simulate the transport of water on SLBP, especially under mechanical deformation, and interactions between SLBP and biological systems.

Shell model extension to the valence force field: application to single-layer black phosphorus.

We propose an extension of the traditional valence force field model to allow for the effect of electronic polarization to be included in the inter-atomic potential. Using density functional theory as a reference, this model is parameterized for the specific case of single-layer black phosphorus by fitting the phonon dispersion relation over the entire Brillouin zone. The model is designed to account for the effect of induced dipole interaction on the long-wavelength (|q[combining right harpoon above]| → 0) modes for the case of homopolar covalent crystals. We demonstrate that the near Γ-point frequencies of the IR-active modes are substantially damped by the inclusion of the induced dipole interaction, in agreement with experiment. The fitting procedure outlined here allows for this model to be adapted to other materials, including but not limited to two-dimensional crystals.

Nonlinear vibrations of circular single-layer black phosphorus resonators

A strong nonlinear relationship between the displacement and the load in single-layer black phosphorus sheets (SLBPs) was observed under the large deflection by nanoindentation experiments. However, the nonlinear effect is rarely considered in the Nano-Electro-Mechanical-System (NEMS) resonators based on the SLBPs. In this letter, nonlinear static and dynamics behaviors of circular SLBPs (CSLBPs) are investigated using molecular dynamics (MD) simulations and a nonlinear orthotropic plate model (NOPM), respectively, where the geometrical nonlinearity is systematically considered in the NOPM. Our results show that the response-frequency curves of forced vibrations in CSLBPs meet clear hardening-type nonlinearity. The damping ratios of CSLBPs are proportional to the square of the vibration amplitude. In particular, the NOPM together with the law of energy equipartition is further utilized to study the nonlinear thermal vibrations of the CSLBPs. Checking against present MD calculations shows that the solution of the present NOPM has high accuracy. The present study should be of great help for designing NEMS resonators based on two-dimensional (2D) orthotropic materials.

Anisotropic magneto-thermoelectric properties of single-layer dilute charged impurity-infected black phosphorus

The continuum model, the Born approximation, and the Green's function approach are used to investigate thermoelectric properties of impurity-infected phosphorene subjected to a Zeeman magnetic field. We found that both disordered electrical and electronic thermal conductivities decrease (increase) with the magnetic field with (without) a threshold value in x−(y−)direction, stemming from the distributed charge with new potential. Furthermore, we found an anisotropic Drude weight at fairly low temperatures in the electrical conductivity. The opposite sign for low-temperature thermopower is captured by strong magnetic fields. Moreover, this information for the thermoelectric efficiency of disordered phosphorene tells us that the efficiency of the disordered phosphorene oscillates (increases) with the magnetic field in x−(y−)direction. Investigation of impurity configuration effects results in the significant differences. The efficiency regardless of the direction oscillates with high impurity concentrations and vanishes at low temperatures, whereas it does not change (oscillates) in x−(y−)direction with impurity scattering potential.

Thermal transport properties of single-layer black phosphorus from extensive molecular dynamics simulations

We compute the anisotropic in-plane thermal conductivity of suspended single-layer black phosphorus (SLBP) using three molecular dynamics (MD) based methods, including the equilibrium MD method, the nonequilibrium MD (NEMD) method, and the homogeneous NEMD (HNEMD) method. Two existing parameterizations of the Stillinger–Weber (SW) potential for SLBP are used. Consistent results are obtained for all the three methods and conflicting results from previous MD simulations are critically assessed. Among the three methods, the HNEMD method is the most and the NEMD method the least efficient. The thermal conductivity values from our MD simulations are about an order of magnitude larger than the most recent predictions obtained using the Boltzmann transport equation approach considering long-range interactions in density functional theory calculations, suggesting that the short-range SW potential might be inadequate for describing the phonon anharmonicity in SLBP.