Phosphorene Allotropes Research Articles

Blue-Green-Black phosphorene allotropes conversion: Energetically easy and potentially promising

Three allotropic forms of phosphorene (Blue, Green and Black) are studied from both structural and electronic points of view. P–P bonds orientation change from vertical to lateral directions is behind the change from Blue to Black forms via Green one. The energetic profile shows that this conversion could take place easily. The rippling mode of the phosphorene sheet is rationalized using the naturel bond orbital (NBO) analysis. We present the landforms of these sheets as a result of MOs interaction depending on the kind (σ, σ∗ and/or LP), on the mode (lateral or axial), and on the position (geminal, vicinal or remote) of these MOs leading to an electronic delocalization phenomenon called hyperconjugation. The conversion Blue-Green-Black phosphorenes is accompanied by a change of properties; for example, from natural band gap (Blue form) to a sizable and tunable one (Green and Black forms). This change would confer to the phosphorene the ability to be involved in the electronics and optoelectronics manufacturing. The geometrical optimization and the hyperconjugative rationalization were undertaken at B3LYP/6-311+G(d,p) level of theory and NBO partitioning scheme respectively.

Allotropes of Phosphorus with Remarkable Stability and Intrinsic Piezoelectricity

In this letter, we show that a new class of two-dimensional phosphorus allotropes can be constructed via assembling the previously proposed ultrathin metastable phosphorus nanotube into planar structures in different stacking orientations. Based on first-principles method, the structures, stabilities and fundamental electronic properties of these new two-dimensional phosphorus allotropes are systematically investigated. These two-dimensional phosphorus allotropes possess remarkable stabilities due to the strong inter-tube van der Waals interactions, which cause an energy release of about 30-70 meV/atom depending on their stacking manners. Our results show that most of these two-dimensional van der Waals phosphorene allotropes are energetically more favorable than the experimentally viable black alpha-P and blue beta-P. Three of them showing relatively higher probability to be synthesized in future are further confirmed to be dynamically stable semiconductors with strain-tunable band gaps and remarkable piezoelectricity, which may have potential applications in nano-sized sensors, piezotronics, and energy harvesting in portable electronic nano-devices.

Reactive molecular dynamics simulations of the mechanical properties of various phosphorene allotropes

Although various phosphorene allotropes have been theoretically predicted to be stable at 0 K, the mechanical properties and fracture mechanism at room temperature remain unclear for many of them. We investigate through reactive molecular dynamics simulations at room temperature the mechanical properties of phosphorene allotropes including: five sheets with hexagonal structures (β-, γ-, δ-, θ-, and α-phosphorene), one sheet with 4-8 membered rings (4-8-P), and two sheets with 5-7 membered rings. High, moderate and slight anisotropies in their mechanical properties are observed, depending on their crystal structures. Their Young’s moduli and tensile strength are approximately in the range from 7.3% through 25%, and from 8.6% through 22% of those of graphene, respectively. At the early stage of fracture, eye-shaped cracks are formed by local bond breaking and perpendicular to the tensile direction in hexagonal and 4-8-P sheets. Complete fractures take place with straight cracks in these hexagonal sheets under tension along the zigzag direction and under tension along the square edge direction in the 4-8-P sheet. Crack meandering and branching are observed during the tension of α-, β-, and γ-phosphorene along the armchair direction; and along the square diagonal direction in the 4-8-P sheet. Under uniaxial tension of two phosphorene sheets with 5-7 atom rings, 12 and 10 membered rings are formed by merging two neighbor heptagons, and a heptagon and its neighbor pentagon, respectively. These 12 and 10 membered rings coalesce subsequently, causing the failure of these two sheets. The results are of great importance in the design of these novel phosphorene allotropes.

Effects of Temperature and Strain Rate on Mechanical Behaviors of Stone–Wales Defective Monolayer Black Phosphorene

The mechanical behaviors of monolayer black phosphorene (MBP) are explored by molecular dynamics (MD) simulations using reactive force field. It is revealed that the temperature and strain rate have significant influence on mechanical behaviors of MBP, and they are further weakened by SW (Stone-Wales) defects. In general, the tensile strength for both of the pristine and SW defective MBP decreases with the increase of temperature or decreasing of strain rate. Surprisingly, for relatively high temperature and low strain rate, phase transition from the black phosphorene to a mixture of {\beta}-phase ({\beta}-P) and {\gamma}-phase ({\gamma}-P) is observed for the SW-2 defective MBP under armchair tension, while self-healing of the SW-2 defect is observed under zigzag tension. A deformation map of SW-2 defective MBP under armchair tension at different temperature and strain rate is established, which is useful for the design of phosphorene allotropes by strain. The results presented herein yield useful insights for designing and tuning the structure, and the mechanical and physical properties of phosphorene.

Thermal conductivities of phosphorene allotropes from first-principles calculations: a comparative study

Phosphorene has attracted tremendous interest recently due to its intriguing electronic properties. However, the thermal transport properties of phosphorene, especially for its allotropes, are still not well-understood. In this work, we calculate the thermal conductivities of five phosphorene allotropes (α-, β-, γ-, δ- and ζ-phase) by using phonon Boltzmann transport theory combined with first-principles calculations. It is found that the α-phosphorene exhibits considerable anisotropic thermal transport, while it is less obvious in the other four phosphorene allotropes. The highest thermal conductivity is found in the β-phosphorene, followed by the δ-, γ- and ζ-phase. The much lower thermal conductivity of the ζ-phase can be attributed to its relatively complex atomic configuration. It is expected that the rich thermal transport properties of phosphorene allotropes can have potential applications in the thermoelectrics and thermal management.

Five low energy phosphorene allotropes constructed through gene segments recombination

Based on the crystal structures of the previously proposed low energy η-P and θ-P, five new phosphorene allotropes were predicted through gene segments recombination method. These five new phosphorene allotropes are confirmed dynamically stable and energetically more favorable than their parents (η-P and θ-P). Especially, the XX-XX type G1-P is confirmed energetically more favorable than most of all the previously proposed phosphorene allotropes, including black phosphorene and blue phosphorene, which is highly expected to be synthesized in future experiment through vapor deposition or epitaxial growth method like blue β-P. The calculated results also show that such a new promising phosphorene allotrope G1-P is a potential candidate for application in nano-electronics according to its middle band gap of about 1.491 eV from DFT-HSE06 calculation.

Van der Waals heterostructures based on allotropes of phosphorene and MoSe2.

The van der Waals heterostructures of allotropes of phosphorene (α- and β-P) with MoSe2 (H-, T-, ZT- and SO-MoSe2) are investigated in the framework of state-of-the-art density functional theory. The semiconducting heterostructures, β-P/H-MoSe2 and α-P/H-MoSe2, form anti-type structures with type I and type II band alignments, respectively, whose bands are tunable with an external electric field. α-P/ZT-MoSe2 and α-P/SO-MoSe2 form ohmic semiconductor-metal contacts while the Schottky barrier in β-P/T-MoSe2 can be reduced to zero by an external electric field to form ohmic contacts which is useful to realize high-performance devices. Simulated STM images of the given heterostructures reveal that α-P can be used as a capping layer to differentiate between various allotropes of underlying MoSe2. The dielectric response of the considered heterostructures is highly anisotropic in terms of lateral and vertical polarization. The tunable electronic and dielectric response of van der Waals phosphorene/MoSe2 heterostructures may find potential applications in the fabrication of optoelectronic devices.

ψ-Phosphorene: a new allotrope of phosphorene.

Based on the crystal structure prediction, we propose a new allotrope of phosphorene, ψ-phosphorene (ψ-P), with a porous structure, which is both thermally and dynamically stable in comparison with the previously reported allotropes. Due to its unique atom configuration, ψ-P has highly orientation-dependent mechanical properties and excellent flexibility. Calculations using the HSE functional predict that ψ-P is semiconducting with an indirect band gap of 1.57 eV and possesses anisotropic transport properties. Particularly, the electron mobility along the x-direction is up to 1.3 × 104 cm2 V-1 s-1, which is comparable with that of black phosphorene. Considering its intrinsic porous structure, the performance of monolayer ψ-P as a gas purification membrane was investigated. The calculation demonstrates that ψ-P could be used for hydrogen purification from the mixture of CH4, CO2, N2, CO, and H2 with high selectivity. Furthermore, combining a suitable band gap with high carrier mobility, a MoSe2/ψ-P van der Waals heterojunction is predicted to be a good solar cell material, whose power conversion efficiency is estimated up to 20.26%. Finally, we demonstrated that the Au(110) surface could be a suitable substrate for the synthesis of ψ-P.

Directional-dependent thickness and bending rigidity of phosphorene

The strong mechanical anisotropy of phosphorene combined with the atomic-scale thickness challenges the commonly employed elastic continuum idealizations. Using objective boundary conditions and a density functional based potential, we directly uncover the flexibility of individual $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ phosphorene allotrope layers along an arbitrary bending direction. A correlation analysis with the in-plane elasticity finds that although a monolayer thickness cannot be defined in the classical continuum sense, an unusual orthotropic plate with a directional-dependent thickness can unambiguously describe the out-of-plane deformation of $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$ allotropes. Such decoupling of the in-plane and out-of-plane nanomechanics might be generic for two-dimensional materials beyond graphene.

First‐principles prediction of a novel hexagonal phosphorene allotrope

Phosphorus prefers three‐connected configurations due to its inequivalent sp3‐hybridization. In the past year, many quasi two‐dimensional three‐connected networks were proposed as possible phosphorene allotropes. In this Letter, a new quasi two‐dimensional three‐connected network is proposed as a new potential phosphorene allotrope (Hex‐star). Based on first‐principles method calculations, the structure, stability and electronic properties of Hex‐star were systematically investigated. Our results indicate that Hex‐star is dynamically stable and it is a semiconductor with quasi‐direct band gap of 1.81 eV based on HSE06 method.Perspective top view (left) and Magen–David‐like orthographic top view (right) of Hex‐star phosphorene. magnified image(© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

New Phosphorene Allotropes Containing Ridges with 2- and 4-Coordination

In all of the phosphorus monolayers reported to date, phosphorus is 3-fold coordinated. However, flexible chemistry of phosphorus allows it to have varying coordination number up to 6. Here, we report three new phosphorus monolayers (labeled α-P6, β-P6, and 558-P6) having 2-, 3-, and 4-fold coordination, which can be observed in epitaxial growth where flakes merge forming ridges at the boundaries. On the basis of state-of-the-art theoretical simulations, we show that these three new monolayer allotropes are thermally and dynamically stable, and they have comparable energetic stability with some reported monolayers such as δ-P, γ-P, and ε-P. Because of their special atomic configurations, they exhibit exceptional properties, including extremely high electron mobility, anisotropic Young’s moduli, and optical absorbance in visible and ultraviolet regions. These findings can extend the family of phosphorenes with novel properties and potential for applications.

Thermal properties of black and blue phosphorenes from a first-principles quasiharmonic approach

Different allotropes of phosphorene are possible of which black and blue phosphorus are the most stable. While blue phosphorus has isotropic properties, black phosphorus is strongly anisotropic in its electronic and optical properties due to its anisotropic crystal structure. In this work, we systematically investigated the lattice thermal properties of black and blue phosphorene by using first-principles calculations based on the quasiharmonic approximation approach. Similar to the optoelectronic and electronic properties, we predict that black phosphorene has highly anisotropic thermal properties, in contrast to the blue phase. The linear thermal expansion coefficients along the zigzag and armchair direction differ up to 20% in black phosphorene. The armchair direction of black phosphorene is more expandable as compared to the zigzag direction and the biaxial expansion of blue phosphorene under finite temperature. Our comparative analysis reveals that the inclusion of finite-temperature effects makes the blue phase thermodynamically more stable over the black phase above 135 K.

Tiling phosphorene.

We present a scheme to categorize the structure of different layered phosphorene allotropes by mapping their nonplanar atomic structure onto a two-color 2D triangular tiling pattern. In the buckled structure of a phosphorene monolayer, we assign atoms in "top" positions to dark tiles and atoms in "bottom" positions to light tiles. Optimum sp3 bonding is maintained throughout the structure when each triangular tile is surrounded by the same number N of like-colored tiles, with 0≤N≤2. Our ab initio density functional calculations indicate that both the relative stability and electronic properties depend primarily on the structural index N. The proposed mapping approach may also be applied to phosphorene structures with nonhexagonal rings and 2D quasicrystals with no translational symmetry, which we predict to be nearly as stable as the hexagonal network.