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# Mechanical and Electrical Anisotropy of Few-Layer Black Phosphorus

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## Abstract

We combined Reflection Difference Microscopy, electron transport measurements and Atomic Force Microscopy to characterize the mechanical and electrical anisotropy of few-layer black phosphorus. We were able to identify the lattice orientations of the two dimensional material and construct suspended structures aligned with specific crystal axes. The approach allowed us to probe the anisotropic mechanical and electrical properties along each lattice axis in separate measurements. We measured the Young's modules of few layer black phosphorous to be 58.6 ± 11.7 and 27.2 ± 4.1 GPa in zigzag and armchair directions. The breaking stress scaled almost linearly with the Young's modulus, and were measured to be 4.79±1.43 and 2.31±0.71 GPa in the two directions. We have also observed highly anisotropic transport behavior in black phosphorous and derived the conductance anisotropy to be 63.7%. The test results agreed well with theoretical predictions. Our work provided very valuable experimental data and suggested an effective characterization means for future studies on black phosphorous and anisotropic two dimensional nanomaterials in general.

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... Among the all techniques to explore the mechanical properties of 2D materials, the AFM-based nanoindentation is the most popular one due to its relatively simple setup (Lee et al. 2008;Falin et al. 2017;Bertolazzi et al. 2011;Castellanos-Gomez et al. 2012a, b;Cooper et al. 2013;Liu et al. 2014;Song et al. 2010;Tao et al. 2015;Wang et al. 2016a, b;Zhang et al. 2016a, b, c). During the nanoindentation tests, the AFM tip can record the indentation load ( P ) and displacement ( ) as shown in Fig. 2a, b. ...
... (2) also becomes (Cui et al. 2020); b P − curves recoded during AFM-based nanoindentations (Lee et al. 2008); c Experiments setup of AFM-based nanoindentations clamping over trenches; d P − curves recoded during AFM-based nanoindentations revealing anisotropic mechanical of BP (Tao et al. 2015); e Scheme of adhesion between 2D materials and sidewall of the substrate (Bunch et al. 2008); f Strain distribution of graphene under AFM tip simulated by Density Functional Theory (DFT) (Wei and Kysar 2012) negligible. Thus the Prelationship in this membrane limit can be rewritten as where 0 = T∕( ta) is the pre-stress. ...
... similar setups have been conducted to study the mechanical properties of other 2D materials including CVD-grown few-layer (Song et al. 2010) and mechanically exfoliated monolayer h-BN (Falin et al. 2017), TMDs (Bertolazzi et al. 2011;Castellanos-Gomez et al. 2012a, b;Cooper et al. 2013;Liu et al. 2014;Zhang et al. 2016a, b, c;Castellanos Gomez et al. 2012) and BP (Tao et al. 2015;Wang et al. 2016a, b;Xiong and Cao 2017). For example, the defects induced degradation in the mechanical performance of h-BN was revealed by comparing Young's modulus of CVD-grown (223 N/m) and mechanically-exfoliated single-crystal h-BN (289 ± 24 N/m) (Falin et al. 2017;Song et al. 2010), and the interface difference between multilayer h-BN and graphene was also uncovered via this mechanical testing method, indicating higher sliding energies in h-BN compared to graphene (Falin et al. 2017). ...
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The past 2 decades have witnessed the explosion of research on two-dimensional (2D) materials, where notable efforts have been made in the synthesis and design of a wide spectrum of applications. To understand their mechanical properties and responses triggered by deformation, the prerequisites for reliable applications under realistic service conditions, novel experimental methods have to be developed due to the limitations of traditional bulk mechanical testing for atomically-thin structures. Besides, the nearly-ideal 2D crystalline structures of many 2D materials endow them the great capability of deformation, showing promising potentials in “strain engineering” and “interface engineering” applications. This review summaries several representative approaches in experimental nanomechanics and corresponding progresses in the characterization of structural and mechanical properties of 2D materials, with the aim to provide insights into the instrumental design for nanomechanical tests. In addition, examples of strain-tuned material behaviors and changes in their performance are also discussed to demonstrate the significance of the nanomechanical approach for functional device design and applications.
... CAFM can be used to measure the electrical properties of 2D materials. Inserted figures are reproduced with permission (Huang et al., 2011;Ye et al., 2012;Tao et al., 2015). ...
... With the clamped beam model, the elastic properties of thin clay tactoids were studied by Kunz et al. (2009). Recently, Tao et al. (2015) conducted the contact probing experiment of a clamped black phosphorous beam. What is more, Yang et al. (2017b) studied the brittle fracture of 2D MoSe 2 , whose average fracture strength was 4.8 ± 2.9 Gpa. ...
... Bertolazzi et al. (2011) studied stretching and breaking of ultrathin MoS 2 . In addition, Hatter (Lin et al., 2013;Tao et al., 2015). (B) Sketch of pressure-loaded blister test. ...
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Due to the unique properties, two-dimensional materials and van der Waals heterostructures play an important part in microelectronics, condensed matter physics, stretchable electronics and quantum sciences. But probing properties of two-dimensional materials and van der Waals heterostructures is hard as a result of their nanoscale structures, which hinders their development and applications. Therefore, the progress of contact probing measurement in recent years including mechanical properties, interfacial properties, tribological properties, as well as electrical properties are summarized in this paper. It is found that useful properties such as Young’s modulus, adhesive energy, friction coefficient and so on can be well estimated from contact probing methods. We believe that the contact probing methods will be more advanced to promote the blooming applications of two-dimensional materials and van der Waals heterostructures.
... Therefore, in order to test the mechanical properties of nanofilms more efficiently and conveniently, many new methods have been proposed. Common experiments to test the mechanical properties of nanofilms are mainly divided into three types: the free standing indentation test [1,12,13], the bulge test [14][15][16] and the film/substrate indentation test [17][18][19]. With the help of the free standing indentation test, many nanofilms' mechanical properties have been measured such as GO nanofilms, black phosphorus nanofilms, MoS 2 nanofilms and so on [12,13,20]. ...
... Common experiments to test the mechanical properties of nanofilms are mainly divided into three types: the free standing indentation test [1,12,13], the bulge test [14][15][16] and the film/substrate indentation test [17][18][19]. With the help of the free standing indentation test, many nanofilms' mechanical properties have been measured such as GO nanofilms, black phosphorus nanofilms, MoS 2 nanofilms and so on [12,13,20]. However, the accuracy of the free standing indentation test is strongly influenced by the van der waals force between the indenter and the nanofilms and the boundary adhesion [1,21], which will produce significant errors. ...
Article
The hard film/soft substrate systems are widely found in production and life. In order to better understand the indentation response of those systems, a closed-form indentation model is established based on the theory of plates and the assumption of Hertz contact stress distribution. Inspired by the model, a new method of measuring the mechanical properties of nanofilms by indentation on hard film/soft substrate system is proposed. Then, with the help of finite element method (FEM), the effectiveness of the model and the method is systematically verified. The results show that compared with the Xu-Pharr model which established by the perturbation method, our model can better describe the compliance of the hard film/soft substrate system in a lager range of modulus ratio of the film to the substrate. In order to obtain the modulus of the nanofilms more accurately by our method, the optimum indentation depth for testing is 0.5 times the film thickness to 1 times the film thickness, and it is best to use a softer substrate to make the modulus ratio of the film to the substrate greater than 103. In addition, the radius of the AFM tip is preferably more than 1 times the film thickness and less than 4 times the film thickness, and a smooth surface of the sample is most preferred. Compared with free standing indentation test or bulge test, our research provides a more convenient and cheaper method for measuring the nanofilms’ modulus in laboratory.
... 28 Whereas the mechanical properties of in-plane isotropic 2D materials have been extensively studied, 7,30-32 the mechanical properties (elastic moduli, adhesion, etc.) of in-plane anisotropic 2D materials are less understood. 33,34 Large discrepancies are commonly reported for Young's moduli measured by different methods such as AFM (atomic force microscopy) indentation, nanomechanical resonators and buckling metrology. 25,33,35 For example, the reported Young's moduli of bP nanosheets along the ZZ direction vary from 58.6 ± 11.7 GPa obtained by AFM indentation 33 to 116.1 ± 1.9 GPa obtained by nanomechanical resonators. ...
... 33,34 Large discrepancies are commonly reported for Young's moduli measured by different methods such as AFM (atomic force microscopy) indentation, nanomechanical resonators and buckling metrology. 25,33,35 For example, the reported Young's moduli of bP nanosheets along the ZZ direction vary from 58.6 ± 11.7 GPa obtained by AFM indentation 33 to 116.1 ± 1.9 GPa obtained by nanomechanical resonators. 36 Another thing that should be noted is that AFM indentation on circular drumheads is not able to resolve the dependence of the Young's modulus on direction. ...
Article
The mechanical properties and interfacial behaviour of two-dimensional (2D) materials are crucial for their use in a number of technological applications. In this paper, two buckling modes, wrinkling and buckling delamination, were used to characterize the mechanics of As2S3 nanosheets. The plane-strain moduli of As2S3 nanosheets along the armchair (AC) and zigzag (ZZ) directions were determined via periodic wrinkles to be 16.7 ± 0.5 GPa and 51.5 ± 1.9 GPa, respectively. This is one of the largest reported anisotropies of in-plane mechanical properties among 2D materials. Using the delaminated buckles, the adhesion energy of few-layer As2S3 nanosheets on silicon and polymer (polymethyl methacrylate and polydimethylsiloxane) substrates was determined to be 0.110 ± 0.006 and 0.022 ± 0.002 J m-2, respectively. A buckling mode map for As2S3 nanosheets on different substrates is presented.
... [42,44,46] These drawbacks hinder the wide applications of self-healing materials in high-performance electrical and optoelectrical devices. [41] On the other hand, 2D layered materials, such as graphene, black phosphorus (BP) and molybdenum disulfide (MoS 2 ), have drawn tremendous research interests because of their excellent electrical, [2,47,48] optoelectrical, [2,47] and mechanical properties, [49,50] which are also appealing for developing flexible and wearable devices. [21,28,42,49,[50][51][52][53] Flexible photodetectors based on 2D materials and their van der Waals heterostructure have been extensively studied, [2,12,28,33] which show outstanding photo gain, [2,28] excellent mechanical properties, [28,32] broad spectral response, [28,[56][57][58] and so on. ...
... [41] On the other hand, 2D layered materials, such as graphene, black phosphorus (BP) and molybdenum disulfide (MoS 2 ), have drawn tremendous research interests because of their excellent electrical, [2,47,48] optoelectrical, [2,47] and mechanical properties, [49,50] which are also appealing for developing flexible and wearable devices. [21,28,42,49,[50][51][52][53] Flexible photodetectors based on 2D materials and their van der Waals heterostructure have been extensively studied, [2,12,28,33] which show outstanding photo gain, [2,28] excellent mechanical properties, [28,32] broad spectral response, [28,[56][57][58] and so on. Moreover, several excellent research works have been reported achieving premium photo-electrical conversion rate and high response speed by Adv. ...
Article
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Flexible photodetectors are fundamental elements to develop flexible/wearable systems, which can be widely used for in situ health and environmental monitoring, human–machine interacting, flexible displaying, etc. However, the degraded performance or even malfunction under severe mechanical deformation and/or damage remains a key challenge for current flexible photodetectors. In this article, a flexible photodetector is developed with strong self‐healing capability and stable performance under large deformation. This photodetector is made of the 2D material self‐healing film by mixing 2D materials homogenously with the self‐healing polymer of imidazolium‐based norbornene polymerized with ionic liquids and counterions. The 2D material self‐healing films show enhanced light absorption, and thus, decent photoresponse as compared to the pure self‐healing film. The achieved photoresponse remains stable and even increases under small tensile strain within 150%, while decreases slightly under large tensile strain up to 1000%. Moreover, the photodetector not only can be fully recovered from repeated mechanical cuttings, but also presents excellent long‐term stability in ambient condition for 500 days without showing any obvious degraded performance. Furthermore, a large‐area 2D material self‐healing photodetection array is designed with adjustable pixel size, which successfully recognizes the patterns of “T”, “J”, and “U”. Here, a 2D material‐enhanced flexible and self‐healable photodetector is demonstrated with a decent and stable photoresponse to a broad light spectrum under large and severe mechanical deformation and damage, based on which a large‐area photodetection array is further fabricated for pattern recognition.
... As noted above, earlier data [20,24,25,27,[29][30][31][32][33] suggest (see for example Fig. 3) that the layered structure of b-P single crystals is exhibited in the high anisotropy of carrier transport and largely affects the pattern of the Hall constant R h (Т,В) as well as ρ(Т,В) and µ(Т,В) as functions of temperature and magnetic field for electric current flow along three different axes (а, b and с) of the crystals. Earlier studies showed [2,20,[23][24][25][26][29][30][31][32][33][34][35][36][37] that the electrical conductivity and mobility are always the highest in the ac plane of the single crystals, and on the whole they decrease in the sequence σ c > σ а > σ b [2,23,24,33]. ...
... The first data on the magnetoresistive effect in b-P crystals were reported in the earliest works on the topic [23,24] in which the authors first noted the existence of two contributions to the relative magnetoresistance MR = [ρ(В) -ρ(0)]/ρ(0)] • 100%, i.e., positive magnetoresistance (PMR) at high temperatures (Т > 77 K) and negative one (NMR) at lower temperatures (T < 4 K). Scarce studies after 2014 [20,[32][33][34][35][36][37][38][39][40] reported contradictory results on the behavior of the electrical resistivity of black phosphorus single crystals in magnetic fields. The most detailed study of MR reported so far [35] was carried out for the following experimental conditions: current flow is along the c axis and the B vector is perpendicular to the ac plane of the single crystal. ...
Article
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Black phosphorus (b-P) single crystals having the n-type electrical conductivity produced in a high pressure set-up (~1 GPa) with six diamond anvils at 800 °C for 12 h have been studied. The electrical conductivity σ( Т , В ) and the Hall constant R h ( Т , В ) have been analyzed within one-band and two-band models as functions of temperature in the 2 < Т < 300 K range and magnetic field in the 0 < В < 8 T range. Fitting of the experimental σ( Т , В ) and R h ( Т , В ) curves suggests the following key properties of the crystals: (1) intrinsic conductivity type, (2) approximately equal electron and hole concentrations and mobilities, (3) anisotropic behavior of electron and hole conductivities, concentrations and mobilities and (4) combination of negative and positive contributions to magnetoresistance (magnetoresistive effect, MR). In a zero magnetic field the anisotropy coefficient α = [σ а ( Т ) – σ с (Т)]/σ с ( Т ) below 50–70 K is positive whereas above 220 K its sign changes to negative due to a specific combination of the temperature dependences of carrier concentration and mobility. It has been shown that the negative sign of relative MR (negative magnetoresistive effect) dominates at T < 25 K and B < 6 T and is presumably caused by the effects of strong localization resulting from structural disorder. The positive MR sign (positive magnetoresistive effect) is associated with the Lorentz mechanism of carrier movement and exhibits itself above 25 K in 6–8 T magnetic fields.
... For 2D materials, the critical strain and ideal tensile stress are crucial mechanical parameters which characterize the elastic limit of thin films and the nature of their chemical bonds [36,37]. The elastic limit and related mechanical properties of well-known 2D materials have been widely concerned, such as graphene [29,[38][39][40], monolayer MoS 2 [34,[41][42][43], borophene [44,45], black phosphorene [46,47], h-BN [48][49][50], silicene [51], and Ti 3 C 2 O 2 [52]. ...
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Recently, two-dimensional monolayer MoSi2N4 with hexagonal structure was successfully synthesized in experiment (Hong et al 2020 Science 369, 670). The fabricated monolayer MoSi2N4 is predicted to have excellent mechanical properties. Motived by the experiment, we perform first-principles calculations to investigate the mechanical properties of monolayer MoSi2N4, including its ideal tensile strengths, critical strains, and failure mechanisms. Our results demonstrate that monolayer MoSi2N4 can withstand stresses up to 51.6 and 49.2 GPa along zigzag and armchair directions, respectively. The corresponding critical strains are 26.5% and 17.5%, respectively. For biaxial strain, the ideal tensile strength is 50.6 GPa with a critical strain of 19.5%. Compared with monolayer MoS2, monolayer MoSi2N4 possesses much higher elastic moduli and ideal tensile strengths for both uniaxial and biaxial strains. Interestingly, the critical strain and failure mechanism of zigzag direction in MoSi2N4 are almost the same as those of armchair direction in MoS2, while the critical strain and failure mechanism of armchair direction for MoSi2N4 are similar to the ones of zigzag direction for MoS2. Our work reveals the remarkable mechanical characteristics of monolayer MoSi2N4.
... To further confirm the in-plane optical anisotropy of penta-PdPSe, ADRDM measurements were implemented to study its reflectance anisotropy along different crystalline orientations. ADRDM is a nondestructive and in situ technique used to directly measure the difference in the normalized reflectance (Δr) between two arbitrary orthogonal directions in the surface plane (x and y) when the sample is illuminated by polarized light, [40,41] which was expressed as [42] 2 2 r r r r r r N ...
Article
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Due to their low-symmetry lattice characteristics and intrinsic in-plane anisotropy, 2D pentagonal materials, a new class of 2D materials composed entirely of pentagonal atomic rings, are attracting increasing research attention. However, the existence of these 2D materials has not been proven experimentally until the recent discovery of PdSe2. Herein, penta-PdPSe, a new 2D pentagonal material with a novel low-symmetry puckered pentagonal structure, is introduced to the 2D family. Interestingly, a peculiar polyanion of [SePPSe]⁴⁻ is discovered in this material, which is the biggest polyanion in 2D materials yet discovered. Strong intrinsic in-plane anisotropic behavior endows penta-PdPSe with highly anisotropic optical, electronic, and optoelectronic properties. Impressively, few-layer penta-PdPSe-based phototransistor not only achieves excellent electronic performances, a moderate electron mobility of 21.37 cm² V⁻¹ s⁻¹ and a high on/off ratio of up to 10⁸, but it also has a high photoresponsivity of ≈5.07 × 10³ A W⁻¹ at 635 nm, which is ascribed to the photogating effect. More importantly, penta-PdPSe also exhibits a large anisotropic conductance (σmax/σmax = 3.85) and responsivity (Rmax/Rmin = 6.17 at 808 nm), superior to most 2D anisotropic materials. These findings make penta-PdPSe an ideal material for the design of next-generation anisotropic devices.
... Another promising 2D nanomaterials that has recently received tremendous attention is the black phosphorus for its thicknessdependent bandgap, high charge-carrier mobility, in-plane anisotropic structure, and biodegradable properties (Tao et al., 2015). As a new star of the 2D materials family, black phosphorus exhibited huge potential in aiding peripheral nerve regrowth. ...
Article
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Peripheral nerve tissues possess the ability to regenerate within artificial nerve scaffolds, however, despite the advance of biomaterials that support nerve regeneration, the functional nerve recovery remains unsatisfactory. Importantly, the incorporation of two-dimensional nanomaterials has shown to significantly improve the therapeutic effect of conventional nerve scaffolds. In this review, we examine whether two-dimensional nanomaterials facilitate angiogenesis and thereby promote peripheral nerve regeneration. First, we summarize the major events occurring after peripheral nerve injury. Second, we discuss that the application of two-dimensional nanomaterials for peripheral nerve regeneration strategies by facilitating the formation of new vessels. Then, we analyze the mechanism that the newly-formed capillaries directionally and metabolically support neuronal regeneration. Finally, we prospect that the two-dimensional nanomaterials should be a potential solution to long range peripheral nerve defect. To further enhance the therapeutic effects of two-dimensional nanomaterial, strategies which help remedy the energy deficiency after peripheral nerve injury could be a viable solution.
... 2D layered materials with in-plane anisotropy have attracted tremendous research interests due to their highly anisotropic band structures, rich in-plane atomic arrangements and huge potentials in polarized optoelectronic applications. [1][2][3][4][5][6][7][8][9] Compared with typical isotropic graphene, MoS 2 , and MXenes, [10][11][12] emerging anisotropic 2D materials such as black phosphorus, [13][14][15][16][17] ReS 2 , [18][19][20] GeAs 2 , [21] and PdSe 2 [22] show distinctive behavior in optical absorbance, electrical transports, and photodetection. On account of the unique anisotropic properties, such materials are designed as crystal orientation- Figure 1b shows rectangle network lattice. ...
Article
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Exploring in-plane anisotropic 2D materials is of great significance to the fundamental studies and further development of polarizationsensitive optoelectronics. Herein, chiral niobium oxide diiodide (NbOI2) is introduced into the intriguing anisotropic 2D family with the experimental demonstration of anisotropic optical and electrical properties. 2D NbOI2 crystals exhibit highly anisotropic dispersed band structures around the Fermi surface and strong in-plane anisotropy of phonon vibrations owing to the different bonding modes of Nb atoms along the b- and c-axes. Consequently, the anisotropic factors of optical absorbance and photoresponsivity in 2D NbOI2 crystals reach up to 1.75 and 1.7, respectively. These anisotropic properties make 2D NbOI2 an interesting platform for novel polarization-sensitive optoelectronic applications.
... This can be obtained by etching processes. 77 While this requires more complicated fabrication steps, the obtained device is particularly useful to study anisotropic materials where the Young's modulus is directiondependent, such as in the case of BP. For a rectangular suspended stripe, Eq. (2) becomes 77 ...
Article
The variegated family of two-dimensional (2D) crystals has developed rapidly since the isolation of its forerunner: Graphene. Their plane-confined nature is typically associated with exceptional and peculiar electronic, optical, magnetic, and mechanical properties, heightening the interest of fundamental science and showing promise for applications. Methods for tuning their properties on demand have been pursued, among which the application of mechanical stresses, allowed by the incredible mechanical robustness and flexibility of these atomically thin materials. Great experimental and theoretical efforts have been focused on the development of straining protocols and on the evaluation of their impact on the peculiar properties of 2D crystals, revealing a novel, alluring physics. The relevance held by strain for 2D materials is introduced in Sec. I. Sections II and III present the multiplicity of methods developed to induce strain, highlighting the peculiarities, effectiveness, and drawbacks of each technique. Strain has largely widened the 2D material phase space in a quasi-seamless manner, leading to new and rich scenarios, which are discussed in Secs. IV–VI of this work. The effects of strain on the electronic, optical, vibrational, and mechanical properties of 2D crystals are discussed, as well as the possibility to exploit strain gradients for single-photon emission, non-linear optics, or valley/spintronics. Quantitative surveys of the relevant parameters governing these phenomena are provided. This review seeks to provide a comprehensive state-of-the-art overview of the straining methods and strain-induced effects, and to shed light on possible future paths. The aims and developments, the tools and strategies, and the achievements and challenges of this research field are widely presented and discussed.
... In the optical response, the absorption coefficient and the refractive index are strongly dependent on the crystal direction of BP [13,14]. Anisotropies in the electrical transport and thermal conductivity of BP have also been demonstrated [1,[15][16][17]. Additionally, the anisotropic electron-phonon interaction in BP leads to strongly polarization-dependent Raman scattering behaviors [18][19][20][21][22][23][24][25], where sensitive changes by layer thickness were explained by the interference effect of either the incident or the scattered light [18]. ...
Article
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Black phosphorus (BP) has attracted great attention due to its layer-tuned direct bandgap, in-plane anisotropic properties, and novel optoelectronic applications. In this work, the anisotropic characteristics of BP crystal in terms of the Raman tensor and birefringence are studied by investigating polarization dependence in both the generation and detection of Ag mode coherent phonons. While the generated coherent phonons exhibit the typical linear dichroism of BP crystal, the detection process is found here to be influenced by anisotropic multiple thin film interference, showing wavelength and sample thickness sensitive behaviors. We additionally find that the Ag1 and Ag2 optical phonons decay into lower frequency acoustic phonons through the temperature-dependent anharmonic process.
... The anisotropic Young's modulus has been predicted for black phosphorene (BP) 29 and also deduced from experiment measurements of BP nanoflakes with thickness of 14.8 nm. 30 Young's modulus has also been deduced from BP nanoflakes with thicknesses of 14.3−34 nm. 31 The monolayer mechanical analysis model 26 was first used to fit the force curve to calculate the 2D Young's modulus (E 2D ) of monolayer graphene. Later, both a monolayer mechanical analysis model and an improved multilayer mechanical analysis model 26 were adopted to calculate Young's modulus of 2D materials with different thicknesses. ...
... Reduced in-plane symmetry in 2D materials can induce interesting anisotropic properties, furthering applications of 2D materials. Previously, a few low-symmetry 2D materials with puckered or disordered structure such as black phosphorus (BP), rhenium disulfide (ReS 2 ), tin selenide (SnSe), and silicon arsenide (SiAs) have exhibited highly in-plane anisotropy of electrical, mechanical, and optical properties [9][10][11][12][13]. In particular, anisotropy of 2D BP and ReS 2 has been exploited to fabricate the integrated digital inverter [14], logic circuit [15], synaptic device [16], and a linear dichroic photodetector [17]. ...
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In-plane anisotropy of two-dimensional materials remains one of the most attracting properties. By employing first-principles calculations, we systematically explore the electronic, carrier transport, and optical properties of monolayer and bilayer titanium trisulfide (TiS3). They are predicted to be direct semiconductors with eligible bandgap of about 1.4 eV. The two systems have high charge carrier mobility and exhibit highly in-plane anisotropy. The carrier mobility can achieve a large value of 10⁴ cm² V⁻¹ s⁻¹ for electron and 10³ cm² V⁻¹ s⁻¹ for hole. In addition, significant anisotropies in their optical absorptions are revealed over a broad spectral range from near-infrared to near-ultraviolet light. First bright exciton state can possess a large binding energy larger than 500 meV, and light absorption coefficients are as large as 10⁵ cm⁻¹ in the two systems. These results in monolayer and bilayer are potentially useful for designing their optoelectronic devices. Graphical abstract Highly-anisotropic properties of two-dimensional titanium trisulfide (TiS3).
... GPa) along the armchair (zigzag) direction in BP, and the sustained strain can be as high as 0.48 (0.11) along armchair (zigzag) direction owing to the puckered configuration 158 . Tao et al. 169 measured the Young's modulus of few-layer BP averagely to be 27.2 GPa and 58.6 GPa in armchair and zigzag directions, respectively. ...
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In recent years, the integration of graphene and related two-dimensional (2D) materials in optical fibers have stimulated significant advances in all-fiber photonics and optoelectronics. The conventional passive silica fiber devices with 2D materials are empowered for enhancing light-matter interactions and are applied for manipulating light beams in respect of their polarization, phase, intensity and frequency, and even realizing the active photo-electric conversion and electro-optic modulation, which paves a new route to the integrated multifunctional all-fiber optoelectronic system. This article reviews the fast-progress field of hybrid 2D-materials-optical-fiber for the opto-electro-mechanical devices. The challenges and opportunities in this field for future development are discussed.
... That the relation between electronic anisotropy and structure is unusual is also shown by the observation that the long axis of exfoliated CrSBr multilayers (which are platelets having one of their sides much longer than the other) corresponds to the crystallographic a-direction, that is, to the direction with low electrical conductivity. This is indeed rather unique, as it is commonly the case that materials exhibiting strongly anisotropic electronic transport are needles whose long axis points in the high conductivity direction (see, for examples, conductors such as ReS 2 , NbSe 3 , TiS 3 , ZrTe 5 , black phosphorus, or high-mobility organic semiconductors such as rubrene [31][32][33][34][35][36][37][38][39] ). ...
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We investigate electronic transport through exfoliated multilayers of CrSBr, a 2D semiconductor that is attracting attention because of its magnetic properties. We find an extremely pronounced anisotropy that manifests itself in qualitative and quantitative differences of all quantities measured along the in‐plane a and b crystallographic directions. In particular, we observe a qualitatively different dependence of the conductivities σa and σb on temperature and gate voltage, accompanied by orders of magnitude differences in their values (σb/σa ≈ 3 · 102 − 105 at low temperature and large negative gate voltage). We also find a different behavior of the longitudinal magnetoresistance in the two directions, and the complete absence of the Hall effect in transverse resistance measurements. These observations appear not to be compatible with a description in terms of conventional band transport of a 2D doped semiconductor. The observed phenomenology –together with unambiguous signatures of a 1D van Hove singularity that we detect in energy resolved photocurrent measurements– indicate that electronic transport through CrSBr multilayers is better interpreted by considering the system as formed by weakly and incoherently coupled 1D wires, than by conventional 2D band transport. We conclude that CrSBr is the first 2D semiconductor to show distinctly quasi 1D electronic transport properties. Figure S1 This article is protected by copyright. All rights reserved
... For example, the mechanical properties of graphene oxide, hexagonal boron nitride, phosphorene are extensively studied. [13][14][15] Recent studies experimentally revealed that the elastic properties of layerstructured transition metal dichalcogenides (TMDs) such as molybdenum disulfide (MoS 2 ) and tungsten disulfide (WS 2 ) are three times lower than that of graphene. 16 Over the last decade, numerous experimental and theoretical research efforts have been expended for discovering 2D materials with superior properties. ...
Article
We use first‐principles based density functional theory (DFT) calculations to investigate the structural, elastic, and electronic properties of various pristine and oxygen (O) functionalized double transition metal (DTM) MXenes with general formulas of M2′M′′C2 and M2′M′′C2O2, where M′ = Mo, Cr and M′′ = Ti, V, Nb, Ta. The dynamic stability of the DTM MXenes are assessed and elastic stiffness constants (Cij) are used to investigate the mechanical stability and properties of the compositions. The calculated elastic properties of the pristine Mo‐based MXenes are found to be superior compared to Cr‐based compounds. Furthermore, the O‐functionalized MXenes exhibit improved in‐plane elastic constants, Young's moduli, and shear moduli compared to their pristine counterpart. We observe that the hybridization of the energy states results in stronger covalent interactions as such increased elastic properties for the M2′M′′C2O2 MXenes. Ashby plot clearly demonstrates superior materials properties of O‐functionalized Mo‐based DTM MXenes compared to other commonly known 2D materials. All the MXenes exhibits metallic character evident from the density of states (DOS) calculations. Additionally, the work functions are studied and the calculated values are higher in the case of O‐functionalized MXenes. Overall, this work will be a guide for future investigations on the mechanical properties of DTM MXenes for their targeted applications in structural nanocomposites. This article is protected by copyright. All rights reserved
... That the relation between electronic anisotropy and structure is unusual is also shown by the observation that the long axis of exfoliated CrSBr multilayers (which are platelets having one of their sides much longer than the other) corresponds to the crystallographic a-direction, i.e., to the direction with low electrical conductivity. This is indeed rather unique, as it is commonly the case that materials exhibiting strongly anisotropic electronic transport are needles whose long axis points in the high conductivity direction TiS 3 , ZrTe 5 , black phosphorus or high-mobility organic semiconductors such as rubrene [31][32][33][34][35][36][37][38][39]). ...
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We investigate electronic transport through exfoliated multilayers of CrSBr, a 2D semiconductor that is attracting attention because of its magnetic properties. We find an extremely pronounced anisotropy that manifests itself in qualitative and quantitative differences of all quantities measured along the in-plane \textit{a} and \textit{b} crystallographic directions. In particular, we observe a qualitatively different dependence of the conductivities $\sigma_a$ and $\sigma_b$ on temperature and gate voltage, accompanied by orders of magnitude differences in their values ($\sigma_b$/$\sigma_a \approx 3\cdot10^2-10^5$ at low temperature and large negative gate voltage). We also find a different behavior of the longitudinal magnetoresistance in the two directions, and the complete absence of the Hall effect in transverse resistance measurements. These observations appear not to be compatible with a description in terms of conventional band transport of a 2D doped semiconductor. The observed phenomenology -- together with unambiguous signatures of a 1D van Hove singularity that we detect in energy resolved photocurrent measurements -- indicate that electronic transport through CrSBr multilayers is better interpreted by considering the system as formed by weakly and incoherently coupled 1D wires, than by conventional 2D band transport. We conclude that CrSBr is the first 2D semiconductor to show distinctly quasi 1D electronic transport properties.
... Owing to the critical role in advanced manufacturing, many researchers have attempted to exploit the opportunity of producing microand nanodevices in the past decades since the discovery of graphene in 2004 [7][8][9][10]. Particularly, the nanodevices based on two-dimensional (2D) materials have attracted great attention owing to their extraordinary properties, thus becoming the focus of research in the field of nanodevice manufacturing [11][12][13][14][15][16]. Considering material structure for nanodevices, the hybrid systems consisting of 2D and organic semiconductor thin films have sparked new research directions [17][18][19][20][21], and the combination of the advantages of both 2D and organic materials [22][23][24] has been widely con-sidered to be promising for developing the novel nanodevices in the future. ...
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The advanced manufacturing of ultra-thin-film devices, especially the nano-semiconductor products, has drawn a significant research interest over the past decades. In this field, monitoring the properties and thickness of the semiconductor layers is of paramount importance, which has significant impact on the device quality. In this study, an in situ monitoring scheme for manufacturing of nanodevices has been proposed, which is able to accurately analyse the optical absorption properties of the semiconductor layers of varying thickness in nanodevices. The in situ reflectance spectral analysis of monolayer, bilayer, and bulk-phase samples confirms the practicability and reliability of the monitoring scheme. The findings reported in this study form the basis for the advanced manufacturing of nano- and sub-nanodevices in the future.
... The mechanical response of Cr/CrN and (Cr/CrN) 2 thin films was reported [104] with Y of 0.22 TPa and 0.26 TPa, respectively. The Y values of thin films of some other common materials have been measured using AFM based nanoindentation experiments; e.g., Mica -0.202 ± 0.022 TPa [105], GaS -0.17 TPa [106], GaSe -0.08 TPa [106], GaTe -0.025 TPa [106], zigzag-BP -0.059 ± 0.012 TPa [107], Bi 2 Se 3 -0.021 ± 0.003 TPa [108], Bi 2 Te 3 -0.019 ...
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The study of the mechanical properties of two-dimensional (2D) materials is one of the most pursued areas of materials research. Nanoindentation, an experimental technique, is commonly used to determine the mechanical strength of materials, ranging from 2D materials to bulk. It can also be simulated using the molecular dynamics method, thereby providing atomic-level insights into the material’s mechanical response. In this paper, we review the results obtained for 2D materials, including atomically thin monolayers to a few nanometer-thick thin films in the scientific literature. We find that an accurate description of chemical bonding is essential in these materials to gain an insight into their in-plane (or out-of-plane) mechanical response, which can be exploited in next-generation nanoscale devices.
... This technique inspired similar characterizations and measurements of various 2D materials. Using this approach, researchers have measured the Young's modulus and strength of h-BN, MoS 2 monolayers, and few-layer phosphorene strips [130][131][132][133][134]. Few-layer phosphorene strips are observed to exhibit anisotropic mechanical properties [135]. Table 1 summarizes the mechanical properties of various 2D materials. ...
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Since the success of monolayer graphene exfoliation, two-dimensional (2D) materials have been extensively studied due to their unique structures and unprecedented properties. Among these fascinating studies, the most predominant focus has been on their atomic structures, defects, and mechanical behaviors and properties, which serve as the basis for the practical applications of 2D materials. In this review, we first highlight the atomic structures of various 2D materials and the structural and energy features of some common defects. We then summarize the recent advances made in experimental, computational, and theoretical studies on the mechanical properties and behaviors of 2D materials. We mainly emphasized the underlying deformation and fracture mechanisms and the influences of various defects on mechanical behaviors and properties, which boost the emergence and development of topological design and defect engineering. We also further introduce the piezoelectric and flexoelectric behaviors of specific 2D materials to address the coupling between mechanical and electronic properties in 2D materials and the interactions between 2D crystals and substrates or between different 2D monolayers in heterostructures. Finally, we provide a perspective and outlook for future studies on the mechanical behaviors and properties of 2D materials.
... Among the post-graphene 2D materials, black phosphorus (BP) is one of the rising stars and has gained much attention recently due to its excellent tribological properties. Similar to other 2D materials, BP also has a layered structure, and its unique wrinklelike anisotropic geometry provides superior optical, electrical, and mechanical properties (Tao et al., 2015). BP nanosheets can be used as additive materials in combination with oil or waterbased lubricants. ...
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Superlubricity is a terminology often used to describe a sliding regime in which the adhesion leading to friction or resistance to sliding literally vanishes. For improved energy security, environmental sustainability, and a decarbonized economy, achieving superlubric sliding surfaces in moving mechanical systems sounds very exciting, since friction adversely impacts the efficiency, durability, and environmental compatibility of many moving mechanical systems used in industrial sectors. Accordingly, scientists and engineers have been exploring new ways to achieve macroscale superlubricity through the use of advanced materials, coatings, and lubricants for many years. As a result of such concerted efforts, recent developments indicate that with the use of the right kinds of solids, liquids, and gases on or in the vicinity of sliding contact interfaces, one can indeed achieve friction coefficients well below 0.01. The friction coefficient below this threshold is commonly termed the superlubric sliding regime. Hopefully, these developments will foster further research in the field of superlubricity and will ultimately give rise to the industrial scale realization of nearly-frictionless mechanical systems consuming far less energy and causing much-reduced greenhouse gas emissions. This will ultimately have a substantial positive impact on the realization of economically and environmentally viable industrial practices supporting a decarbonized energy future. In this paper, we will provide an overview of recent progress in superlubricity research involving solid, liquid, and gaseous media and discuss the prospects for achieving superlubricity in engineering applications leading to greater efficiency, durability, environmental quality, and hence global sustainability.
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Designing devices with excellent spin-polarized properties has been a challenge in physics and materials science. In this work, we report a theoretical investigation of the spin injection and spin-polarized transport properties of monolayer and bilayer phosphorene devices with Co electrodes. Based on the analysis of transmission coefficients, spin-polarized current, magnetoresistance (MR) (or tunnel MR) ratio and spin injection efficiency (SIE), both devices show superior spin-polarized transport properties. As phosphorene in the device is changed from monolayer to bilayer, the charge carrier type can be tuned from n-type to p-type. For the monolayer phosphorene device, the tunnel MR ratio reaches about 210% and the SIE is about 80.7% at zero bias. Notably, the SIE and tunnel MR ratio maintain almost constant values against bias voltage and gate voltage, which makes it suitable for magnetic sensors. As for the bilayer phosphorene device, it not only exhibits a considerable tunnel MR ratio, but also shows significantly enhanced conductance, beneficial to the sensitivity of spintronic devices. Further analysis shows that the improvement of conductance is attributed to the low barrier height between the bilayer phosphorene channel and Co electrodes. According to our results, the studied phosphorene devices with Co electrodes demonstrate superior spin injection and transport properties. We believe that these theoretical findings will be a strong asset for future experimental works in spintronics.
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Birefringence and dichroism are very important properties in optical anisotropy. Understanding the intrinsic birefringence and dichroism of a material can provide great help to utilize its optical anisotropy. But the direct experimental investigation of birefringence in nanoscale materials is rarely reported. As typical anisotropic transition metals trichalcogenides (TMTCs) materials with quasi-1D structure, TiS3 and ZrS3 have attracted extensive attention due to their special crystal structure and optical anisotropy characteristics. Here, the optical anisotropy properties such as birefringence and dichroism of two kinds of quasi-1D TMTCs, TiS3 and ZrS3 , are theoretically and experimentally studied. In experimental results, the anisotropic refraction and anisotropic reflection of TiS3 and ZrS3 are studied by polarization-resolved optical microscopy and azimuth-dependent reflectance difference microscopy, respectively. In addition, the birefringence and dichroism of ZrS3 nanoribbon in experiment are directly measured by spectrometric ellipsometry measurements, and a reasonable result is obtained. This work provides the basic optical anisotropy information of TiS3 and ZrS3 . It lays a foundation for the further study of the optical anisotropy of these two materials and provides a feasible method for the study of birefringence and dichroism of other nanomaterials in the future.
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Recently, two-dimensional monolayer MoSi2N4 with hexagonal structure was successfully synthesized in experiment (Hong et al 2020 Science 369, 670). The fabricated monolayer MoSi2N4 is predicted to have excellent mechanical properties. Motived by the experiment, we perform first-principles calculations to investigate the mechanical properties of monolayer MoSi2N4, including its ideal tensile strengths, critical strains, and failure mechanisms. Our results demonstrate that monolayer MoSi2N4 can withstand stresses up to 51.6 and 49.2 GPa along zigzag and armchair directions, respectively. The corresponding critical strains are 26.5% and 17.5%, respectively. For biaxial strain, the ideal tensile strength is 50.6 GPa with a critical strain of 19.5%. Compared with monolayer MoS2, monolayer MoSi2N4 possesses much higher elastic moduli and ideal tensile strengths for both uniaxial and biaxial strains. Interestingly, the critical strain and failure mechanism of zigzag direction in MoSi2N4 are almost the same as those of armchair direction in MoS2, while the critical strain and failure mechanism of armchair direction for MoSi2N4 are similar to the ones of zigzag direction for MoS2. Our work reveals the remarkable mechanical characteristics of monolayer MoSi2N4.
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Composites (or complex materials) are formed from two or many constituent materials with novel physical or chemical characteristics when integrated. The individual components can be combined to create a unique composite material through mechanical transfer, physical stacking, exfoliation, derivative chemical mixtures, mixtures of solid solutions, or complex synthesis processes. The development of new composites based on emerging 2D nanomaterials has allowed for outstanding achievements with novel applications that were previously unknown. These new composite materials show massive potential in emerging applications due to their exceptional properties, such as being strong, light, cheap, and highly photodegradable, and their ability to be used for water splitting and energy storage compared to traditional materials. The blend of existing polymers and 2D materials with their nanocomposites has proven to be immediate solutions to energy and food scarcity in the world. Although much literature has been reported in the said context, we tried to provide an understanding about the relationship of their mechanisms and scope for future application in a comprehensive way. In this review, we briefly summarize the basic characteristics, novel physical and chemical behaviors, and new applications in the industry of the emerging 2D-material-based composites.
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Black phosphorous (BP), in the recent decade, has attracted the attention of researchers as a potential sensing material due to its exceptional physical and chemical properties. This review provides a concise report on the recent trends in gas sensing applications of two-dimensional black phosphorous (2D BP). The review begins with the important properties of BP and its synthesis using both top-down and bottom-up methods. Further, an overview of the significant achievements in the gas sensing of BP for reducing and oxidizing gases is presented with a focus on both theoretical and practical findings. Most of the studies on the gas sensing capabilities of BP are simulation-based due to the unstable nature of black phosphorous. Therefore, the review represents both the theoretical and fabrication aspects of the BP-based gas sensors. As the pristine BP suffers from some intrinsic lacks such as environmental instability and poor solubility, some tuning of the property is required to obtain a stable sensing device. Therefore, the last part of the review highlights some of the methods accepted for tuning the BP properties for a stable gas sensing device.
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Hexagonal boron nitride (h‐BN) is one of the most important 2D materials which attracts tremendous attention for the demonstrated great potential applications in optical and electronic devices. However, whether there are significant differences in the electrical properties of h‐BN with different layers and its mechanism is not revealed clearly. Based on the atomic force microscopy (AFM) technology, the electrical properties of monolayer h‐BN and bilayer h‐BN are investigated. It is found that bilayer h‐BN shows quite different electrical characteristics from monolayer h‐BN. It is proposed that the difference of work functions between monolayer h‐BN and bilayer h‐BN contributes to the different electrical characteristics. Meanwhile, the interlayer coupling resistance due to coupling between the layers of h‐BN also plays a vital role in electron transport. Besides, the effect of load force on electrical characteristics of h‐BN with different layers is also investigated. This work provides a new insight to understand the effect of the different layers on electrical properties of h‐BN. It is hoped that this valuable experimental data can offer meaningful suggestions for future studies and applications on h‐BN and other 2D nanomaterials in general. The electrical properties of monolayer hexagonal boron nitride (h‐BN) and bilayer h‐BN are investigated by atomic force microscopy (AFM) technology. The bilayer h‐BN showed quite diﬀerent electrical characteristics from monolayer h‐BN. The mechanism that made this difference is investigated. Besides, the eﬀect of load force on electrical characteristics of h‐BN with diﬀerent layers is also studied.
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A systematic study of the adsorption of several harmful gases (CO2, NO, SO2, NH3 y H2S) onto black phosphorene and three diﬀerent black phosphorene oxides is carried out through density functional theory calculations. In general, it is shown that black phosphorene oxides are more suitable adsorbents than pure black phosphorene. Smaller values of adsorption energy correspond to CO2 molecules, whilst those exhibiting larger ones are NH3, H2S, NO y SO2. It is found that SO2 shows the greater diﬀerence in electronic charge transfer as well as the longer time of recovery among all species, being an electron acceptor molecule. Besides, it is revealed that physisorption induces changes of diﬀerent order in the electronic, magnetic and optical responses of phosphorene systems involved. Greater changes in the electronic structure are produced in the case of NO adsorption. In that case, semiconductor nature and magnetization features of black phosphorene band structure become signiﬁcantly modiﬁed. Moreover, a notorious eﬀect of an externally applied electric ﬁeld on the molecule adsorption onto black phosphorene oxides has been detected. In accordance, adsorption energy changes with the applied electric ﬁeld direction, in such a way that the higher value is favored through an upwards-directed orientation of NO y SO2 adsorbates. Results presented could help to enhancing the understanding of black phosphorene oxides as possible candidates for applications in gas sensing.
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Using first-principles density functional theory (DFT) calculations, we demonstrate that the heterointerface of black phosphorus and graphene (BP/Gr) should be a promising lubricant, especially under high pressure conditions. The ultralow interfacial frictional sliding motion is enabled by graphene oxide (GO) functional groups, such as epoxy and hydroxyl groups. These functional groups significantly modulate the interfacial charge distribution to facilitate interfacial slip. The epoxy functional group enables a reduction in not only the bilayer adhesion but also the shear strength along the armchair direction by approximately 40% compared with that without functionalization. The potential energy surface (PES) calculation shows the possibility of an ultralow friction sliding process in BP/Gr and BP/GO due to the presence of almost frictionless paths. In addition, high-accuracy PES calculations predict an almost frictionless sliding path even under pressure. Interestingly, our calculation shows that the corrugation energy and shear strength of BP/Gr decrease under 10 GPa. We elucidated that the origin of the improved frictional properties under high pressure stems from the unique heterostructure of BP/Gr. These results consistently suggest that BP/Gr is promising lubricants for high-pressure applications, which can be further improved using a design principle of exploring optimal interfaces and functional groups.
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Metal-halide perovskites (MHPs) possess enormous potential in optoelectronic and semiconductor devices. In these applications, MHPs are often subjected to mechanical stress, resulting in distorted lattice, severe degradation, and catastrophic failure in MHPs and their interfaces. Understanding these mechanics-coupled stability issues is crucial to the durability and, thus, commercial viability of MHP-based devices. Here, we review the impact of mechanical stress on the integrity and robustness of MHP devices to provide insights into mitigating the mechanics-coupled stability issues. We start with an overview of the structure-elastic-property relationship of MHPs, after which we discuss the current understanding of the cohesive and adhesive failures within MHPs and at MHP interfaces forced by mechanical stress, respectively. We further review the chemical stability issues of MHPs and interfaces induced by the mechanical strain. Finally, we summarize the existing strategies to mitigate the mechanics-coupled stability issues and conclude with an outlook of future research directions.
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2D crystals can serve as templates for the realization of new van der Waals (vdW) heterostructures via controlled assembly of low-dimensional functional components. Among available 2D crystals, black phosphorus (BP) is unique due to its puckered atomic surface topography, which may lead to strong epitaxial phenomena through guided vdW assembly. Here, it is demonstrated that a BP template can induce highly oriented assembly of C60 molecular crystals. Transmission electron microscopy and theoretical analysis of the C60/BP vdW heterostructure clearly confirm that the BP template results in oriented C60 assembly with higher-order commensurism. Lateral and vertical devices with C60/BP junctions are fabricated via a lithography-free clean process, which allows one to investigate the ideal electrical properties of pristine C60/BP junctions. Effective tuning of the C60/BP junction barrier from 0.2 to 0.5 eV and maximum on-current density higher than 104 mA cm−2 are achieved with graphite/C60/BP vertical vdW transistors. Due to the formation of high-quality C60 film and the semitransparent graphite top-electrode, the vertical transistors show high photoresponsivities up to ≈100 A W−1 as well as a fast response time under visible light illumination.
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Two-dimensional (2D) materials offer novel platforms to meet the increasing demands of next-generation miniaturized electronics. Among them, the recently emerged 2D Bi2O2Se with unique non-van der Waals interlayer interaction, high mobility, sizeable bandgap, and capability to fabricate homologous heterojunction, is of particular interest. In this Review, we introduce recent progress in preparation, transfer, mechanical and electrical properties, and electronic applications of 2D Bi2O2Se. First, we summarize methodologies to synthesize and massively produce 2D Bi2O2Se, as well as recent advances in transferring them from growth substrate to arbitrary substrates. Then, we review current understandings on the intrinsic mechanical properties of Bi2O2Se at 2D thickness limit, and its in-plane and out-of-plane electrical properties. Electronic devices including field-effect transistors, memristors, and sensors based on 2D Bi2O2Se for neuromorphic computing, memory, logic and integrated circuits are discussed. Finally, challenges and prospects for the development of 2D Bi2O2Se are proposed.
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Anisotropic mechanics of van der Waals (vdWs) materials offers opportunity to peel off individual atomic layers, initiating a two‐dimensional (2D) revolution in fields of materials science, physics and chemistry. The elasticity, bending and fracture strength of most of their 2D derivatives are also orientation‐dependent, which not only determines the reliability of devices based on 2D materials but also offering a vast playground for atomic manufacturing with tunable functions. Therefore, a comprehensive understanding of the anisotropic mechanical properties of 2D materials is imminent. In this review, the anisotropic mechanical properties of 2D materials are summarized in attempt to capture the current progress in this field, as well as the route towards their applications. Following a brief discussion of the anisotropic lattice structures of 2D materials, we discuss unique experimental methodologies that have been developed to characterize their anisotropic mechanics. Then, our review pivots on recent processes in anisotropic elastic, fracture, friction and bending properties of 2D materials. We further highlight unique applications of these anisotropic properties, such as mechanical fabrication of atomic precision, as well as anisotropic strain‐induced piezoelectric and band modulation. Finally, besides emphasizing the need for breakthrough in anisotropic mechanics, we suggest prospects for the developments of this field. This article is protected by copyright. All rights reserved.
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In this article, I want to show some properties of black phosphorus (BP) and some of its applications. In particular, in Sec. 1, I give an introduction to the topic and some historical notes, in Sec. 2, the two-dimensional crystal structure of the BP is explained, in Sec. 3, the optical and electronic properties of the BP are shown, in Sec. 4, the biomedical applications of the BP are listed and finally in Sec. 5, there are conclusions.
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The Amontons-Coulomb law shows that friction is proportional to load, which limits application of materials. Lubricants can, black phosphorus (BP), effectively inhibit the rapid increase of friction under high-load. However, there are fewer researches focusing on the friction mechanism of BP under load. Based on first-principles, bilayer BP as friction interface is approved. The increasing average shear strength is positively correlated and almost negligible for σZ < 20.1 and σZ ≥ 20.1 GPa, respectively, implying high-load friction insensitivity of BP. Comparing to Gr and MoS2, high-load friction insensitivity of BP is remarkable, although its friction performance under zero load is inferior relatively. High-load friction insensitivity of BP is closely related to its negative Poisson’s ratio that is observed first-time in friction calculation. This will reduce potential dissipation and friction of BP during high-load sliding, due to interlayer-intralayer electronic reconstruction. The conclusions are of great significance for the design of lubrication and microscale mechanism analysis in engineering application.
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2D materials, such as graphene, hexagonal boron nitride (hBN), and transition‐metal dichalcogenides (TMDs), are intrinsically flexible, can withstand very large strains (>10% lattice deformations), and their optoelectronic properties display a clear and distinctive response to an applied stress. As such, they are uniquely positioned both for the investigation of the effects of mechanical deformations on solid‐state systems and for the exploitation of these effects in innovative devices. For example, 2D materials can be easily employed to transduce nanometric mechanical deformations into, e.g., clearly detectable electrical signals, thus enabling the fabrication of high‐performance sensors; just as easily, however, external stresses can be used as a “knob” to dynamically control the properties of 2D materials, thereby leading to the realization of strain‐tuneable, fully reconfigurable devices. Here, the main methods are reviewed to induce and characterize, at the nm level, mechanical deformations in 2D materials. After presenting the latest results concerning the mechanical, elastic, and adhesive properties of these unique systems, one of their most promising applications is briefly discussed: the realization of nano‐electromechanical systems based on vibrating 2D membranes, potentially capable of operating at high frequencies (>100 MHz) and over a large dynamic range. Atomically thin 2D materials exhibit outstanding mechanical robustness as compared to 3D crystals. This feature and the exceptional tunability of the optical and electronic properties of 2D crystals under strain has boosted the emerging fields of flextronics and straintronics. Knowledge of the adhesion and elasticity properties is thus pivotal to the manufacturing and integration of 2D crystal‐based devices.
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The growing demand for energy in wearable sensors and portable electronics necessitates the development of self‐contained, sustainable, and mobile power sources capable of harvesting environmental energies. Researchers have made significant strides in implementing photovoltaics, thermoelectrics, piezoelectrics, and triboelectrics in 2D materials. This has resulted in significant advancements in wearable energy harvesting systems based on 2D materials. This review discusses the relationship between synthesis procedures, material structures/properties, and device performance in the context of 2D materials‐based wearable energy harvesting technologies. Finally, challenges and future research opportunities are identified and discussed based on current progress. Overview of 2D materials with unique structure, properties and prepared by various techniques in energy harvesting and application for human‐related applications.
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Violet phosphorene, a recently determined semiconducting two-dimensional elemental structure, is a promising electronic and optoelectronic material. The nano-tribological properties of violet phosphorene nanoflakes are essential for their micro device applications. A friction anisotropy has been demonstrated for the violet phosphorene nanoflakes by lateral force microscope due to the sub-nanorod components of violet phosphorus. The friction forces of the violet phosphorene nanoflakes have been demonstrated to be valley along sub-nano rod direction and peak across the sub-nanorod direction with a period of 180°, resulting in a fast identification of the surface structure direction of violet phosphorene. The friction of violet phosphorene nanoflakes has also been shown to increase with increasing scanning pressure. However, it is not sensitive to scanning speed or layers. The friction of the violet phosphorene nanoflakes have also been demonstrated to increase when exposure to air for hours. The friction and adhesion features of violet phosphorene nanoflakes provide valuable foundation for violet phosphorene based devices.
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Epoxy resins are thermosetting polymers with an extensive set of applications such as anticorrosive coatings, adhesives, matrices for fibre reinforced composites and elements of electronic systems for automotive, aerospace and construction industries. Τhe use of epoxy resins in many high-performance applications is often restricted by their brittle and flammable nature, the relatively low fracture toughness and poor thermal and electrical properties. Various two-dimensional (2D) materials, such as graphene (Gr), hexagonal boron nitride (h-BN), transition metal dichalcogenides and MXenes, provide vast opportunities to endow multifunctional properties and reinforce epoxy resins for advanced applications. In this review, the current literature status of epoxy nanocomposites reinforced with 2D materials has been thoroughly examined. The structures and intrinsic properties of epoxy resins and two-dimensional materials have been briefly summarized. Recent advances in the strategies of incorporating 2D materials into epoxy matrices have also been presented. Most importantly, the mechanical, tribological, thermal, electrical, flame retardant and anticorrosive properties of epoxy nanocomposites reinforced with 2D materials have been reviewed in detail. Finally, the current status of the field along with future perspectives have been discussed with regards to the effectiveness of various 2D nanofillers towards reinforcement.
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Highly anisotropic black phosphorus (BP) has recently attracted significant interest for electronic and optoelectronic devices. To date, in‐plane anisotropic properties of BP field effect transistors (FETs) have been reported only with top contact. However, the 2D top contact geometry is unable to measure the in‐plane electrical conductance precisely, due to the presence of the out‐of‐plane conductance, resulting in underestimation of anisotropy. Here, 1D edge contact method is employed to measure the in‐plane conductance precisely along the armchair and zigzag directions of BP without the contribution of out‐of‐plane conductance. The conductance and mobility anisotropies for BP FETs are measured with edge contact at 300 K to be ≈5.5 and ≈7.5, respectively. The results further show that the mobility of BP FETs with edge contact weakly depends on temperature, indicating that the edge roughness scattering limits the mobility. In contrast, the mobility of BP FETs with top contact strongly depends on temperature, showing that the impurity scattering and phonon scattering limit the mobility at below and above 150 K, respectively. Finally, a scattering phase diagram is demonstrated to understand the role of different scattering mechanisms on the modulation of mobility anisotropy in BP FETs with edge and top contacts. This work demonstrates very high electrical conductance anisotropies between armchair (AC) and zigzag (ZZ) directions in a 2D black phosphorus (BP) crystal by using edge‐contacted BP field effect transistors (FETs), in contrast to top‐contacted BP FETs, which cannot attain true high in‐plane conductance due to the presence of out‐of‐plane conductance.
Article
Murnaghan’s polynomial based nonlinear elastic constitutive model has been previously applied to 2D materials of hexagonal symmetry. We present a general approach for determining the nonlinear elastic constants of 2D materials of arbitrary symmetries and any constitutive polynomial order. The methodology, which is based on ray sampling of the strain energy density in strain space, is independent of the energy calculation method. The ray based methodology is verified by evaluating the elastic constants of graphene which is a hexagonally symmetric 2D material previously considered in the literature. The methodology is then applied to determine the elastic constants of black phosphorus, an orthorhombic 2D material whose comprehensive nonlinear elastic behavior has not been previously considered in the literature. The energy calculations are carried out using plane-wave density functional theory. Detailed convergence analyses are performed to assess the accuracy of the nonlinear elastic constants. The linearized mechanical properties of black phosphorus are obtained from the elastic constants for comparison with the results published in the literature.
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More than a century ago, A.A. Griffith published the seminal paper establishing the foundational framework for fracture mechanics. The elegant theory creatively introduced the concepts of elastic energy and surface energy to the science of fracture, and solved the problem of brittle fracture of glass materials. Many subsequent milestone studies in fracture mechanics were motivated by the real problems encountered in different materials. The emergence of two-dimensional (2D) materials provides an exciting opportunity to examine fracture processes at the 2D limit. An important question to be addressed is whether the classic Griffith theory is still applicable to 2D materials. Therefore, recent progress in both experimental and theoretical studies of fracture of 2D materials will be briefly reviewed, with new developments and discoveries in relevant techniques and theories highlighted. Given the early stage of exploring fracture behaviors in 2D materials, more emphasis will be placed on challenges and opportunities for this budding field.Graphical abstract
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Epoxy resins are thermosetting polymers with an extensive set of applications such as anticorrosive coatings, adhesives, matrices for fibre reinforced composites and elements of electronic systems for automotive, aerospace and construction industries.
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We experimentally determine the elastic properties of 2D HfS2 and HfSe2 - two emerging nano-materials whose moderate energy bandgap and dielectric oxidized layer make them highly attractive for functional electronic and optoelectronic systems. We found that the average Young's moduli of HfS2 and HfSe2 nano-drumheads are relatively low (45.3 ± 3.7 GPa for a 12.2 nm thick HfS2 and 39.3 ± 8.9 GPa for a 13.4 nm thick HfSe2) and depend on the thickness of the nano-drumhead (increasing with thickness for HfS2 and decreasing for HfSe2). Moreover, both materials demonstrate outstanding stretchability (fracture strength and maximal strain of 5.7 ± 0.4 GPa and 12.2-14.3%, respectively, for HfS2; fracture strength and maximal strain of 4.5 ± 1.4 GPa and 14.0-20.9%, respectively, for HfSe2), which far exceeds the stretchability of other 2D materials and of polymers that are commonly used in flexible electronic applications. Finally, we describe the controlled oxidation of HfSe2 using a relatively simple laser treatment, which increased the Young's moduli of the thin oxidized layers to 182.6 ± 54.3 GPa. The extraordinary elastic properties of HfS2 and HfSe2, together with their excellent electrical and optoelectrical properties, make these 2D materials highly attractive for use in strain engineering and in various stretchable electronic and optoelectronic applications, such as wearable devices.
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The temperature-dependent stress-strain relations of monolayer black phosphorus (BP) under biaxial and uniaxial tension as well as shear deformation are investigated using molecular dynamics (MD) simulations. The predicted strength and moduli are in good agreement with the available results from the first-principle method. In particular, the amplitude to wavelength ratio of wrinkles under shear deformation using MD simulations also agrees well with that from the existing theory. This study provides physical insights into the origins of the temperature-dependent mechanical properties of the monolayer BP.
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The ability to detect light over a broad spectral range is central to practical optoelectronic applications and has been successfully demonstrated with photodetectors of two-dimensional layered crystals such as graphene and MoS2. However, polarization sensitivity within such a photodetector remains elusive. Here, we demonstrate a broadband photodetector using a layered black phosphorus transistor that is polarization-sensitive over a bandwidth from ∼400 nm to 3,750 nm. The polarization sensitivity is due to the strong intrinsic linear dichroism, which arises from the in-plane optical anisotropy of this material. In this transistor geometry, a perpendicular built-in electric field induced by gating can spatially separate the photogenerated electrons and holes in the channel, effectively reducing their recombination rate and thus enhancing the performance for linear dichroism photodetection. The use of anisotropic layered black phosphorus in polarization-sensitive photodetection might provide new functionalities in novel optical and optoelectronic device applications.
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Phosphorus is one of the most abundant elements preserved in earth, and it comprises a fraction of 0.1% of the earth crust. In general, phosphorus has several allotropes, and the two most commonly seen allotropes, i.e. white and red phosphorus, are widely used in explosives and safety matches. In addition, black phosphorus, though rarely mentioned, is a layered semiconductor and has great potential in optical and electronic applications. Remarkably, this layered material can be reduced to one single atomic layer in the vertical direction owing to the van der Waals structure, and is known as phosphorene, in which the physical properties can be tremendously different from its bulk counterpart. In this review article, we trace back to the research history on black phosphorus of over 100 years from the synthesis to material properties, and extend the topic from black phosphorus to phosphorene. The physical and transport properties are highlighted for further applications in electronic and optoelectronics devices.
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Ultrathin black phosphorus, or phosphorene, is a two-dimensional material that allows both high carrier mobility and large on/off ratios. Similar to other atomic crystals, like graphene or layered transition metal dichalcogenides, the transport behavior of few-layer black phosphorus is expected to be affected by the underlying substrate. The properties of black phosphorus have so far been studied on the widely utilized SiO2 substrate. Here, we characterize few-layer black phosphorus field effect transistors on hexagonal boron nitride—an atomically smooth and charge trap-free substrate. We measure the temperature dependence of the field effect mobility for both holes and electrons and explain the observed behavior in terms of charged impurity limited transport. We find that in-situ vacuum annealing at 400 K removes the p-doping of few-layer black phosphorus on both boron nitride and SiO2 substrates and reduces the hysteresis at room temperature.
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Ultra-short cantilevers are a new type of cantilever designed for the next generation of high-speed atomic force microscope (HS-AFM). Ultra-short cantilevers have smaller dimensions and higher resonant frequency than conventional AFM cantilevers. Moreover, their geometry may also be different from the conventional beam-shape or V-shape. These changes increase the difficulty of determining the spring constant for ultra-short cantilevers, and hence limit the accuracy and precision of force measurement based on a HS-AFM. This paper presents an experimental method to calibrate the effective spring constant of ultra-short cantilevers. By using a home-made AFM head, the cantilever is bent against an electromagnetic compensation balance under servo control. Meanwhile the bending force and the cantilever deflection are synchronously measured by the balance and the optical lever in the AFM head, respectively. Then the effective spring constant is simply determined as the ratio of the force to the corresponding deflection. Four ultra-short trapezoid shape cantilevers were calibrated using this method. A quantitative uncertainty analysis showed that the combined relative standard uncertainty of the calibration result is less than 2%, which is better than the uncertainty of any previously reported techniques.
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One hundred years after its first successful synthesis in the bulk form in 1914, black phosphorus (black P) was recently rediscovered from the perspective of a two-dimensional (2D) layered material, attracting tremendous interest from condensed matter physicists, chemists, semiconductor device engineers and material scientists. Similar to graphite and transition metal dichalcogenides (TMDs), black P has a layered structure but with a unique puckered single layer geometry. Because the direct electronic band gap of thin film black P can be varied from 0.3 to around 2 eV, depending on its film thickness, and because of its high carrier mobility and anisotropic in-plane properties, black P is promising for novel applications in nanoelectronics and nanophotonics different from graphene and TMDs. Black P as a nanomaterial has already attracted much attention from researchers within the past year. Here, we offer our opinions on this emerging material with the goal of motivating and inspiring fellow researchers in the 2D materials community and the broad readership of PNAS to discuss and contribute to this exciting new field. We also give our perspectives on future 2D and thin film black P research directions, aiming to assist researchers coming from a variety of disciplines who are desirous of working in this exciting research field.
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We present a liquid crystal variable retarder (LCVR)-based design for reflectance difference (RD) spectrometry, which offers one high quality RD spectrum in the visible range within several seconds. The measurement principle and the instrument development of this design are provided. As the LCVR is a key component, investigations are focused on its wavelength-dependent optical characteristics, the systematic errors induced by its imperfections, and the temperature effect on the measurement results. With careful calibration and data correction, the qualities of corrected RD spectra, defined as standard deviations of the RD signals as a function of wavelength and time, are better than 3 x 10(-4) and 1.3 x 10(-3), respectively. (C) 2013 Published by Elsevier B.V.
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High-mobility two-dimensional (2D) semiconductors are desirable for high-performance mechanically flexible nanoelectronics. In this work, we report the first flexible black phosphorus (BP) field-effect transistors (FETs) with electron and hole mobilities superior to what has been previously achieved with other more studied flexible layered semiconducting transistors such as MoS2 and WSe2 . Encapsulated bottom-gated BP ambipolar FETs on flexible polyimide afforded maximum carrier mobility of about 310cm(2)/V∙s with field-effect current modulation exceeding three orders of magnitude. The device ambipolar functionality and high-mobility were employed to realize essential circuits of electronic systems for flexible technology including ambipolar digital inverter, frequency doubler, and analog amplifiers featuring voltage gain higher than other reported layered semiconductor flexible amplifiers. In addition, we demonstrate the first flexible BP amplitude-modulated (AM) demodulator, an active stage useful for radio receivers, based on a single ambipolar BP transistor, which results in audible signals when connected to a loudspeaker or earphone. Moreover, the BP transistors feature mechanical robustness up to 2% uniaxial tensile strain and up to 5000 bending cycles.
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Unencapsulated, exfoliated black phosphorus (BP) flakes are found to chemically degrade upon exposure to ambient conditions. Atomic force microscopy, electrostatic force microscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, and Fourier transform infrared spectroscopy are employed to characterize the structure and chemistry of the degradation process, suggesting that O2 saturated H2O irreversibly reacts with BP to form oxidized phosphorus species. This interpretation is further supported by the observation that BP degradation occurs more rapidly on hydrophobic octadecyltrichlorosilane self-assembled monolayers and on H-Si(111), versus hydrophilic SiO2. For unencapsulated BP field-effect transistors, the ambient degradation causes large increases in threshold voltage after 6 hours in ambient, followed by a ~103 decrease in FET current on/off ratio and mobility after 48 hours. Atomic layer deposited AlOx overlayers effectively suppress ambient degradation, allowing encapsulated BP FETs to maintain high on/off ratios of ~10^3 and mobilities of ~100 cm2/V-s for over two weeks in ambient. This work shows that the ambient degradation of BP can be managed effectively when the flakes are sufficiently passivated. In turn, our strategy for enhancing BP environmental stability will accelerate efforts to implement BP in electronic and optoelectronic applications.
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The piezoelectric characteristics of nanowires, thin films and bulk crystals have been closely studied for potential applications in sensors, transducers, energy conversion and electronics. With their high crystallinity and ability to withstand enormous strain, two-dimensional materials are of great interest as high-performance piezoelectric materials. Monolayer MoS2 is predicted to be strongly piezoelectric, an effect that disappears in the bulk owing to the opposite orientations of adjacent atomic layers. Here we report the first experimental study of the piezoelectric properties of two-dimensional MoS2 and show that cyclic stretching and releasing of thin MoS2 flakes with an odd number of atomic layers produces oscillating piezoelectric voltage and current outputs, whereas no output is observed for flakes with an even number of layers. A single monolayer flake strained by 0.53% generates a peak output of 15 mV and 20 pA, corresponding to a power density of 2 mW m(-2) and a 5.08% mechanical-to-electrical energy conversion efficiency. In agreement with theoretical predictions, the output increases with decreasing thickness and reverses sign when the strain direction is rotated by 90°. Transport measurements show a strong piezotronic effect in single-layer MoS2, but not in bilayer and bulk MoS2. The coupling between piezoelectricity and semiconducting properties in two-dimensional nanomaterials may enable the development of applications in powering nanodevices, adaptive bioprobes and tunable/stretchable electronics/optoelectronics.
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We report on experimental demonstration of a new type of nanoelectromechanical resonators based on black phosphorus crystals. Facilitated by a highly efficient dry transfer technique, crystalline black phosphorus flakes are harnessed to enable drumhead resonators vibrating at high and very high frequencies (HF and VHF bands, up to ~100MHz). We investigate the resonant vibrational responses from the black phosphorus crystals by devising both electrical and optical excitation schemes, in addition to measuring the undriven thermomechanical motions in these suspended nanostructures. Flakes with thicknesses from ~200nm down to ~20nm clearly exhibit elastic characteristics transitioning from the plate to the membrane regime. Both frequency- and time-domain measurements of the nanomechanical resonances show that very thin black phosphorus crystals hold interesting promises for moveable and vibratory devices, and for semiconductor transducers where high-speed mechanical motions could be coupled to the attractive electronic and optoelectronic properties of black phosphorus.
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The mechanical properties of single-layer black phosphrous under uniaxial deformation are investigated using first-principles calculations. Both Young's modulus and the ultimate strain are found to be highly anisotropic and nonlinear as a result of its quasi-two-dimensional puckered structure. Specifically, the in-plane Young's modulus is 44.0 GPa in the direction perpendicular to the pucker, and 92.7 GPa in the parallel direction. The ultimate strain is 0.48 and 0.20 in the perpendicular and parallel directions, respectively.
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Passivated phosphorene nanoribons, armchair (a-PNR), diagonal (d-PNR) and zigzag (z_PNR), were investigated using Density Functional Theory. Z-PNRs demonstrate the greatest quantum-size effect, tuning the bandgap from 1.4 to 2.6 eV when the width is reduced from 26 to 6 Å. Strain effectively tunes charge carrier transport, leading to a sudden jump of electron effective mass around +8% strain in a-PNRs or hole effective mass around +3% strain in z-PNRs - differentiating the hole-to-electron mass ratio by an order of magnitude in each case. Straining of d-PNRs results in a direct-to-indirect bandgap transition at either -7% or +5% strain, and therein creates degenerate energy valleys, with potential applications for valleytronics and/or photocatalysis.
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Few-layer black phosphorus, a new elemental 2D material recently isolated by mechanical exfoliation, is a high-mobility layered semiconductor with a direct bandgap that is predicted to strongly depend on the number of layers, from 0.35 eV (bulk) to 2.0 eV (single-layer). Therefore, black phosphorus is an appealing candidate for tunable photodetection from the visible to the infrared part of the spectrum. We study the photoresponse of field-effect transistors (FETs) made of few-layer black phosphorus (3 nm to 8 nm thick), as a function of excitation wavelength, power and frequency. In the dark state, the black phosphorus FETs can be tuned both in hole and electron doping regimes allowing for ambipolar operation. We measure mobilities in the order of 100 cm2/V s and current ON/OFF ratio larger than 103. Upon illumination, the black phosphorus transistors show response to excitation wavelengths from the visible up to 940 nm and rise time of about 1 ms, demonstrating broadband and fast detection. The responsivity reaches 4.8 mA/W and it could be drastically enhanced by engineering a detector based on a PN junction. The ambipolar behavior coupled to the fast and broadband photodetection make few-layer black phosphorus a promising 2D material for photodetection across the visible and near-infrared part of the electromagnetic spectrum.