Mono Vacancies Research Articles

Optoelectronic properties of a van der Waals heterostructure Black-Phosphorene/MoS[formula omitted] considering P-Atoms vacancy defects

We studied how the presence point defects could modify Black-Phosphorene/MoS2 van der Waals heterostructures’ optoelectronic properties. Specifically, we looked into the effects of various vacancy defects created by removing phosphorus atoms from Black-Phosphorene/MoS2 van der Waals heterostructures. We identified seven types of vacancies based on their formation energy and then analyzed their electronic and optical properties using density functional theory (DFT). Our findings revealed that double vacancies are the most likely structural defect and that mono vacancies and tetra vacancies result in a local spin magnetic moment of approximately 1.0 μB. These results emphasize the importance of considering spin polarization in these systems. We also observed that the band gap in the heterostructure is reduced compared to pristine phosphorene, indicating that the interaction with MoS2 plays a significant role in modulating the electronic and optical properties of the defective Black-Phosphorene/MoS2 van der Waals heterostructures.

Exploring spin photovoltaics in defective armchair phosphorene nanoribbons

This study explores the spin photovoltaic potential within armchair phosphorene nanoribbons (APNRs) that feature a periodic distribution of monovacancies (MVs) under the influence of light radiation. We investigate spin-semiconducting behavior induced by MV defects by utilizing both the mean-field Hubbard approximation and the self-consistent non-equilibrium Green's function model. This behavior is characterized by localized and anisotropic band structures around the Fermi energy, particularly within the antiferromagnetic phase. The existence of spin-splitting band gaps in defective APNRs not only enables the crafting of spin-optoelectronic nanodevices but also allows for the manipulation of electronic structure behavior with applied electric fields in both the vertical and transverse directions. Notably, the implementation of electric fields, offering tunability in electronic structure, results in varied spin photovoltaic responses encompassing a broad spectrum of photon energies from visible to ultraviolet. This research reveals promising avenues for advancing the field of spin-optoelectronic devices by MVs in APNRs.

A striking exploration of defect engineering in HfS2, HfSe2, and janus HfSSe through ab initio analysis for HER catalysis application

The present study emphasizes the enhancement in catalytic activity due to the formation of vacancies using dispersion corrected density functional theory. We observed that without vacancy formation, in general the edge site is an active site for hydrogen adsorption, while the lowest Gibbs free energy (ΔGH) is found to be for Janus HfSSe at the S-edge site. Furthermore, interestingly, due to the hindrance of the edge site, it facilitates only the Volmer-Heyrovsky reaction rather than the Volmer-Tafel. Among the mono vacancies, the Hafnium mono vacancy shows the lowest adsorption energy.We observed a competition between the evolution of H2S and H2 gas in the case of HfS2-VHf, whereas in the case of defected Janus and HfSe2, due to the presence of Se layers, we observed no competitiveness with H2S or H2Se gas with hydrogen gas. These defected materials exhibit lower reactional Gibbs free energy than a pristine monolayer due to its metallic nature. We observed that Hafnium vacancy enhances the HER activity, and pave the way for dominating Volmer-Heyrovsky reaction.

Insights into Molten Salts Induced Structural Defects in Graphitic Carbon Nitrides for Piezo‐Photocatalysis with Multiple H2O2 Production Channels

AbstractElucidating the impact of heteroatoms in graphitic carbon nitrides (g‐C3N4) is of utmost importance to rationalize materials. Hence, in this study, oxygen‐doped g‐C3N4 containing trace amounts of halogen in the structures for piezo‐photosynthesis of hydrogen peroxides (H2O2) is fabricated. The findings reveal that oxygen atoms may be inserted into g‐C3N4 in‐plane structures, while halogen atoms tend to become intercalated between g‐C3N4 layers. Furthermore, the presence of ammonium molten salts (NH4X) during the synthesis alters the concentration of mono and cluster vacancies of carbon and nitrogen in the materials, certifying by positron annihilation spectroscopy (PAS). These defective contributions will be meaningfully accelerate catalytic performance by providing trapping states. Additionally, the decomposition of generated H2O2 can produce highly oxidative hydroxyl radicals, inducing degradations on the catalyst's structures and unexpectedly decreasing catalytic outcomes. From the mechanistic view, different reduction and oxidation channels will be play a pivotal role in generating H2O2. Moreover, the influence of ultrasound and light is also carefully investigated in the work to gain more insights into how the catalysts are triggered to improve catalytic performance. Thus, this study highlights the importance of carefully characterizing structures of g‐C3N4 to precisely understand the catalytic properties, benefiting catalytic design and development.

Regulation of the electronic structure and ferromagnetism by implanting topological defects in a bismuth monolayer

Bismuth (Bi) monolayers have attracted much attention due to their intriguing physical and chemical applications, which are strongly related to the existence of topological defects. However, the intrinsic correlation between the defect types and particular electronic structures of Bi monolayers still needs to be understood. Herein, we intentionally implanted various typical topological defects into Bi monolayers to reveal the differences in the electronic structure, in which the monovacancies (MVs) can lead to a transformation from a semiconductor to a metal. More interestingly, a particular defect configuration can give rise to a spin polarization and room-temperature ferromagnetism, demonstrating the spintronic applications. This work reveals that the physical property differences of Bi monolayers are strongly dependent on their defect types.

Strain tunable quantum emission from atomic defects in hexagonal boron nitride for telecom-bands

This study presents extending the tunability of 2D hBN Quantum emitters towards telecom (C-band − 1530 to 1560 nm) and UV-C (solar blind − 100 to 280 nm) optical bands using external strain inducements, for long- and short-range quantum communication (Quantum key distribution (QKD)) applications, respectively. Quantum emitters are the basic building blocks of this QKD (quantum communication or information) technologies, which need to emit single photons over room temperature and capable of tuning the emission wavelength to the above necessary range. Recent literature revealed that quantum emitters in 2D hBN only has the ability to withstand at elevated temperatures and aggressive annealing treatments, but density functional theory (DFT) predictions stated that hBN can only emit the single photons from around 290 to 900 nm (UV to near-IR regions) range. So, there is a need to engineer and further tune the emission wavelength of hBN quantum emitters to the above said bands (necessary for efficient QKD implementation). One of the solutions to tune the emission wavelength is by inducing external strain. In this work, we examine the tunability of quantum emission in hBN with point defects by inducing three different normal strains using DFT computations. We obtained the tunability range up to 255 nm and 1589.5 nm, for the point defects viz boron mono vacancies (VB) and boron mono vacancies with oxygen atoms (VBO2) respectively, which can enhance the successful implementation of the efficient QKD. We also examine the tunability of the other defects viz. nitrogen mono vacancies, nitrogen mono vacancy with self-interstitials, nitrogen mono vacancy with carbon interstitials, carbon dimers and boron dangling bonds, which revealed the tunable quantum emission in the visible, other UV and IR spectrum ranges and such customized quantum emission can enhance the birth of other quantum photonic devices.

Long-term behavior of vacancy defects in Pu-Ga alloy: Effects of temperature and Ga concentration

Vacancy and its clusters are among the most important defects induced by self-irradiation in plutonium-gallium (Pu-Ga) alloys. For decades-long stockpiles, the generation and evolution of vacancy defects could cause void swelling and helium bubble formation, resulting in the ageing of the Pu-Ga alloys. Therefore, to shed light on the ageing mechanisms caused by vacancies in Pu-Ga alloys, the long-term behaviour of vacancy defects in Pu-Ga alloys is simulated employing an AKMC model parameterized by molecular statics calculations. By tracking the number of vacancy defects, the size distribution of vacancy clusters, and the largest vacancy clusters over time, we found that temperature and Ga concentration significantly influence the evolution of vacancy defects in Pu-Ga alloys. Temperature changes could affect the clustering behaviour of mono vacancies, and critical temperatures initializing the nucleation of vacancy clusters are observed. On the other hand, adding Ga contents in Pu-Ga alloys could increase the migration energy of and attractive interaction among vacancies, leading to increased vacancy cluster numbers at high temperatures.

Modelling the primary damage in Fe and W: influence of the short-range interactions on the cascade properties: Part 2 – multivariate multiple linear regression analysis of displacement cascades

Neutrons and high energy ions create displacement cascades in materials, which have been simulated using Molecular Dynamics, for many decades now. The breakthrough of this work is to explore in a large statistics of more than 7000 cascades the relation between early cascade morphology and the final primary damage using a multivariate multiple regression analysis. For two energies in Fe and W, the total number of defects, the number of SIA and vacancy clusters and their full size distributions have been characterized using a multivariate multiple linear regression analysis based on 7 descriptors of the primary damage and 3 morphology descriptors. We find that the combination of the volume and the sphericity is significant. This analysis highlights several cascade properties, among them, that the large and spherical cascades create less defects and in particular, less mono defects than small and fragmented ones. 13 interatomic potentials differing either by their equilibrium part or the way they were hardened have been included in this study and the multivariate analysis shows that the choice of potential has a limited influence on the total number of defects but a large one on the number of mono vacancies. On average, soft potentials create cascades of larger volume, smaller sphericity and producing more defects than hard potentials. Finally, the formation of vacancy clusters is different in Fe than in W. In Fe, the fraction of vacancies in clusters is larger than that of SIAs and larger vacancy clusters are created than SIA clusters. In W, it is the opposite. The reasons are the differences of stopping power and threshold displacement energies, which result in different spatial distributions of open volumes that form during the expansion stage of the cascade.

Engineering defect clusters in distorted NaMgF3 perovskite and their important roles in tuning the emission characteristics of Eu3+ dopant ion.

An attempt has been made to explore various new defect clusters in distorted NaMgF3 perovskite and their important role in tuning optical properties. We have tried to tailor the defect clusters and to understand the impact on the luminescence of the lanthanide, for example the Eu3+ ion. Defect engineering has been carried out by doping aliovalent dopant ions to create a charge imbalance in the matrix, which in turn led to the creation of various mono-, di- and new cluster vacancies. Such vacancies have been characterized by Electron Para-magnetic Resonance (EPR), Positron Annihilation Lifetime Spectroscopy (PALS) and Photoluminescence (PL) studies. The PALS data of both undoped and Eu3+ doped compounds confirmed that in addition to Mg mono vacancies, cluster vacancies with different configurations comprising Mg, Na and F atom vacancies also exist in the matrix. The PL study revealed that depending on the surrounding defect structure, three different types of Eu3+ components can be created. The position of the Eu3+ ion with respect to these cluster vacancies determines the respective emission profiles and the decay kinetics. It has been found that when Li+ ions are co-doped with Eu3+, there is a sudden change in the decay kinetics and the emission profiles. The PALS study revealed that Li+ co-doping modified the configuration of the vacancy clusters, which in turn changes the emission characteristics. The EPR study confirmed the presence of different types of F-centers (F, F2, etc.) which are responsible for the host emission. Overall, this new study will be very helpful for a detailed understanding of the defect structures, in particular the cluster vacancies in distorted NaMgF3 perovskite, which have a direct or indirect impact on many physical properties.

A density functional theory study of electric, magnetic and optical properties of perfect and defected Germanium Carbide (GeC) sheet

In this paper, we use spin-polarized density functional theory (DFT) to study the electric, magnetic and optical properties of perfect and defected Germanium Carbide (GeC) sheets. We consider both mono vacancies (1C and 1Ge) and divacancies (1Ge-1C, 2C, and 2Ge). The optimized structure, formation energy, band structure, gap energy, projected density of states, the imaginary part of the dielectric tensor, electron density and the total magnetic moment are computed. Our results show that the formation energy of 1C is lower than the formation energy of 1Ge, meaning that 1C is a preferable defect. Also, 2Ge defect has the lowest formation energy in divacancies. According to band structure, perfect, 1C, 1Ge-1C, 2C and 2Ge are semiconductors while 1Ge is half-metal. The imaginary part of the dielectric tensors for perfect, 1Ge,1Ge-1C, 2C, and 2Ge show a peak near their gap energy thus transition between the valence band maximum (VBM) and conduction band minimum (CBM) is an allowed transition while for 1C is a forbidden transition. To study the magnetic properties, we plot the electron density for up spin (n↑), down spin (n↓) and n↑-n↓. We find that perfect, 1Ge-1C, 2C and 2Ge are non-magnetic (NM) while 1C and 1Ge are ferromagnetic (FM).

Oxygen vacancies mediated cooperative magnetism in ZnO nanocrystals: A d0 ferromagnetic case study

This article reports on the oxygen vacancies and defects induced cooperative magnetism of 28nm (as prepared) and 74nm (annealed) sized nanocrystals of ZnO synthesized through sol- gel auto-combustion route. UV–Vis–NIR optical absorption and photoluminescence (PL) spectroscopic measurements showed marginal red shifting in the band gap energy and characteristic blue shift in the UV absorption peak position with the size reduction of ZnO nanocrystallites. PL analysis revealed that 28nm sized ZnO nanocrystals have higher number of oxygen vacancies and lower interstitial defects in comparison to 74nm (annealed) nanocrystals of ZnO. Both the sample display oxygen vacancy and defect mediated ferromagnetic behaviour at 300K but 28nm ZnO nanocrystals are better ferromagnetic in comparison to annealed ZnO nanocrystals. The annealed ZnO nanocrystals also showed considerable diamagnetic character. High field (±7 Tesla) magnetization measurements down to 5K and PL analysis establish presence, inter-conversion of oxygen vacancies and valence fluctuations in neutral, mono and divalent oxygen vacancies. The monovalent oxygen and zinc vacancies play important role in the mediation of d0 type cooperative magnetism in the ZnO nanocrystals.

OH molecule-involved formation of point defects in monolayer graphene

Point defects in freestanding graphene monolayers such as monovacancies (MVs) and divacancies have been investigated at atomic scale with aberration-corrected transmission electron microscopy and theoretical calculations. In general, these defects can be formed simply by the absence of individual carbon atoms and carbon bond reconstructions in the graphene lattice under electron and ion irradiation. However, in this study, we found that oxygen and hydrogen atoms can be involved in the formation of these point defects caused by the simultaneous detachment of oxygen–carbon atoms. Here we report the effect of the oxygen and hydrogen atoms on the graphene surface forming the point defects under electron beam irradiation, and their role of stabilizing other MVs when composed of 13–5 ring pairs. In addition, theoretical analysis using density functional theory calculations demonstrates that the participating atoms can form the point defects in the intermediate states and stabilize 13–5 ring pairs under electron beam irradiation.

Investigation of the mono vacancy effects on the structural, electronic and magnetic properties of graphene hexagonal-boron nitride in-plane hybrid embracing diamond shaped graphene island

The preparation of an atomically thin sheet of graphene/h-BN (GBN) hybrid with lack of defects is almost unachievable as in three dimensional crystals. Here, we first discussed the stability and electronic properties of GBN hybrid nanosheet which is formed by implanting a diamond shaped graphene (G) island into the hexagonal boron nitride (h-BN) layout. We further investigated the effects of mono vacancy on the electronic and magnetic properties of defective GBN nanosheet. The band gap of pristine hybrid decreases with growing G island as expected and the island induces flat (dispersionless) energy bands near the Fermi energy of the h-BN nanosheet. We searched for the energetics of 7 distinct C, B and N mono vacancies created at various places such as h-BN region, G region and interface of the optimized pristine hybrid. The G-BN interface is found as the energetically most favourable place for vacancy formation. Depending on the size of the graphene island, the C vacancy is the most favourable defect type in our DFT calculations. The N vacancy is energetically preferred over the B vacancy due to its lower formation energy with the exception of biggest G island. Although pristine hybrids are non-magnetic semiconductors, the GBN hybrid can become magnetic with a reasonable amount of magnetic moment depending on the type of vacancy and vacancy site. The vacancy defected hybrids also show the properties of semiconductor except for the hybrid involving the smallest size island with the B vacancy in the h-BN layout (VBL). Defected hybrids involving the smallest G island have the highest amount of band gaps due to high ratio of carbon atoms at the interface to the island interior. Accordingly, the band gap tends to decrease with expanding G island. However, the band gap of VBL defected structures broadens with increasing size of island interestingly. Moreover, this defected hybrid introduces the greatest amount of magnetic moment (3 μB) as the island expands. The C vacancies in the G island and around the N atom introduce a magnetic moment of 2 μB as the G island expands as well. The magnetic moment of the N vacancy defected hybrid is 1 μB irrespective of island size. The vacancy defect leads local in-plane/out-of-plane distortions rather than structural reconstructions in our calculations. In general, no correlation was observed between the island size and the magnetic moment of a defective hybrid.

Positron Annihilation Spectroscopy of KCl (Zn) crystals

Four samples of nominally pure KCl crystals and doped with Zn2+ impurities are grown by the Czochralski method and characterized by X-ray diffraction and Proton Induced X-ray Emission techniques. Positron Annihilation Lifetime Spectroscopy (PALS) is performed to obtain information on the cation vacancy type defects and their evolution under doping. The results of the PALS experiment indicate that doping KCl by Zn2+ ions, at first increases the concentration of mono vacancies and in the second stage leads the creation of divacancy sites. Coincidence Doppler Broadening Spectroscopy (CDBS) is carried out to obtain the chemical environment of positron annihilation sites. The results of CDBS show that cation vacancies have a significant role in the annihilation process. An interesting observation is the participation of Zn2+ cations in the positron annihilation process which confirms that positrons are not completely localized on the anion sites. The internal consistency between the results of PALS and CDBS experiments is also clarified.

Vacancy induced robust magnetism in graphene hexagonal-boron nitride in-plane hybrids with hexagonal shaped islands

We present the results of density functional theory (DFT) calculations on the vacancy-defected graphene-hBN (GBN) nanosheet embracing a hexagonal island. Hexagonal shaped h-BN and G islands of varying sizes are respectively patterned in G and h-BN nanosheets for possible uses of GBN hybrid in device applications. Three different types of mono vacancies were formed at various sites of GBN hybrid. Two distinct C mono vacancies, B and N mono vacancy were formed at G/h-BN interface. We additionally formed C mono vacancy in G region, and B and N mono vacancies in h-BN region of the hybrid nanosheet. Possible effects of vacancies and size effects of island on the electronic and magnetic properties of hybrid were examined in great detail. Calculated vacancy formation energies show that N vacancy exhibits lower formation energy than B one. Besides, the interface is the energetically most favorable place, regardless of the type of vacancy. All pristine hybrids with hexagonal islands are non-magnetic semiconductors. However, depending on the type of vacancy and vacancy site, the GBN hybrid can become magnetic with a considerable amount of magnetic moment. Because of the high magnetization energy, the magnetic order is considered to be robust against thermal excitations at finite temperatures. Our results indicated that defective hybrids with G islands have greater potential for magnetic applications. Mono vacancies introduce flat (dispersionless) states near the Fermi level, and these flat energy states lead to localized, integer-valued magnetic moment. In general, no correlation was observed between the island size and the magnetic moment of a defective hybrid. Nevertheless, in the case of C (B) vacancy in G (h-BN) layout, the magnetic moment increases with increasing island size. This result could point to a possible coupling between the defect and hexagonal island.

Defects and oxygen vacancies tailored structural, optical, photoluminescence and magnetic properties of Li doped ZnO nanohexagons

In this study, Zn1-xLixO (x = 0.02, 0.04, 0.06, 0.08 and 0.10) nanohexagons were prepared by sol-gel combustion route and characterized using standard techniques for understanding their crystallography, surface morphology, optical, photoluminescence and magnetic properties. Single phase wurtzite type hexagonal crystal structure of the synthesized Li doped ZnO nanoparticles was identified from the Rietveld profile refinement of the powder XRD patterns and HRTEM & SAED analysis. HRTEM micrographs and XRD peak profile analysis confirmed formation of highly crystalline Li doped ZnO nanohexagons (ZnO:Li NHs) with average crystallite size in the 20–40nm range. Formation of functional Zn(Li)–O bonds in ZnO:Li NHs was confirmed by FTIR. SEM micrographs of the prepared samples showed random shaped, uniform distribution and well dispersed grains of ZnO:Li NHs. All the ZnO:Li NHs absorbs significant light in the UV band and the band gap energy monotonically decreases with increasing Li concentration in ZnO:Li NHs. Photoluminescence spectra exhibited two characteristic emission bands in all the ZnO:Li NHs and the UV emission band showed red shifting with increasing Li concentration, which is ascertained with the optical absorbance spectrums. Visible band spectral analysis of the PL data revealed formation of neutral, mono, and divalent oxygen vacancies along with the other defects like Zn vacancy in the ZnO lattice by Li doping and synthesis mechanism. All the ZnO:Li NHs exhibited weak ferromagnetism at RT. Lattice defects and oxygen vacancies created by Li1+ ions in the host ZnO lattice play significant role in band gap narrowing, photoluminescence in orange-red region and weak ferromagnetic ordering in ZnO:Li NHs.

Structure and properties of intrinsic and extrinsic defects in black phosphorus.

The electronic and geometric structures of a range of intrinsic and extrinsic defects in black phosphorus (BP) are calculated using Density Functional Theory (DFT) and a hybrid density functional. The results demonstrate that energy barriers to form intrinsic defects, such as Frenkel pairs and Stone-Wales type defects, exceed 3.0 eV and their equilibrium concentrations are likely to be low. Therefore, growth conditions and sample preparation play a crucial role in defect chemistry of black phosphorus. Mono-vacancies (MV) are shown to introduce a shallow acceptor state in the bandgap of BP, but exhibit fast hopping rates at room temperature. Coalescence of MVs into di-vacancies (DV) is energetically favourable and eliminates the band gap states. Thus MVs are not likely to be the main contributor to p-doping in BP. Extrinsic defects are a plausible alternative, with SnP found to be the most promising candidate. Other defects considered include I, O, Fe, Cu, Zn and Ni in surface adsorbed, intercalated and substitutional geometries, respectively. Furthermore, BP was found to be magnetic for isolated MVs and Fe doping, motivating further research in the area of magnetic functionalisation.

Short-range order clustering in BCC Fe–Mn alloys induced by severe plastic deformation

The effect of severe plastic deformation, namely, high-pressure torsion (HPT) at different temperatures and ball milling (BM) at different time intervals, has been investigated by means of Mössbauer spectroscopy in Fe100–xMnx (x = 4.1, 6.8, 9) alloys. Deformation affects the short-range clustering (SRC) in BCC lattice. Two processes occur: destruction of SRC by moving dislocations and enhancement of the SRC by migration of non-equilibrium defects. Destruction of SRC prevails during HPT at 80–293 K; whereas enhancement of SRC dominates at 473–573 K. BM starts enhancing the SRC formation at as low as 293 K due to local heating at impacts. The efficiency of HPT in terms of enhancing SRC increases with increasing temperature. The authors suppose that at low temperatures, a significant fraction of vacancies are excluded from enhancing SRC because of formation of mobile bi- and tri-vacancies having low efficiency of enhancing SRC as compared to that of mono vacancies. Milling of BCC Fe100–xMnx alloys stabilises the BCC phase with respect to α → γ transition at subsequent isothermal annealing because of a high degree of work hardening and formation of composition inhomogeneity.

Structure stability and magnetism in graphene impurity complexes with embedded V and Nb atoms

The appearance of vacancy defects could produce appropriate magnetic moment in graphene and the sensitivity to absorb atoms/molecules also increases with this. In this direction, a DFT study of embedding V and Nb atom in graphene containing monovacancies (MV) and divacancies (DV) is reported. Complete/almost complete spin polarization is detected for V/Nb embedding. The origin of magnetism has been identified via interaction of 3d-states of embedded atom with C-p states present in the vicinity of embedded site. The band structures have been analyzed to counter the observed semiconducting nature of graphene in minority spin on embedding V/Nb atom. The isosurface analysis also confirms the induced magnetism of present nanosystems. The present results reveal that these nanosystems have the potential for futuristic applications like spintronics and energy resources.

Highly Itinerant Atomic Vacancies in Phosphorene.

Using detailed first-principles calculations, we investigate the hopping rate of vacancies in phosphorene, an emerging elemental 2D material besides graphene. Our work predicts that a direct observation of these monovacancies (MVs), showing a highly mobile and anisotropic motion, is possible only at low temperatures around 70 K or below where the thermal activity is greatly suppressed. At room temperature, the motion of a MV is 16 orders faster than that in graphene, because of the low diffusion barrier of 0.3 eV. Built-in strain associated with the vacancies extends far along the zigzag direction while attenuating rapidly along the armchair direction. We reveal new features of the motion of divacancies (DVs) in phosphorene via multiple dissociation-recombination processes of vacancies owing to a small energy cost of ∼1.05 eV for the splitting of a DV into two MVs. Furthermore, we find that uniaxial tensile strain along the zigzag direction can promote the motion of MVs, while the tensile strain along the armchair direction has the opposite effect. These itinerant features of vacancies, rooted in the unique puckering structure facilitating bond reorganization, enable phosphorene to be a bright new opportunity to broaden the knowledge of the evolution of vacancies, and a proper control of the exceedingly active and anisotropic movement of the vacancies should be critical for applications based on phosphorene.