We present an analytic study, based on the tight-binding approximation, of strain effects on the electronic bandgap in single-layer black phosphorus. We obtain an expression for the variation of the bandgap induced by a general strain type that includes both tension in and out of the plane and shear, and use this to determine the most efficient strain direction for different strain types, along which the strongest bandgap manipulation can be achieved. We find that the strain direction that enables the maximum manipulation of the bandgap is not necessarily in the armchair or zigzag direction. Instead, to achieve the strongest bandgap modulation, the direction of the applied mechanical strain is dependent on the type of applied strain.
Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus, the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for opto-electronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit. Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-…
Modern electronics rely on devices whose functionality can be adjusted by the end-user with an external 'knob'. A new tuning knob to modify the band gap of black phosphorus has been experimentally demonstrated.
We study the carrier relaxation dynamics in thin black phosphorus (bP) using time-resolved differential transmission measurements. The inter-band and intra-band transitions, relaxation, and carrier recombination lifetimes are revealed by tuning the mid-infrared probe wavelength above and below the bandgap of black phosphorus. When the probe energy exceeds the bandgap, Pauli blocked inter-band transitions are observed. The differential transmission signal changes sign from positive to negative when the probe energy is below the bandgap, due to the absence of inter-band transitions and enhanceme…
An investigation of the mechanical, electronic, and optical properties of the recently reported material K4 phosphorus was made in this work. The K4 phosphorus has been proved to be mechanically and dynamically stable up to 7 GPa under hydrostatic pressure. We compared the elastic anisotropy, average acoustic velocity and Debye temperature of K4 phosphorus at 0 and 7 GPa. The ideal tensile at large strains of K4 phosphorus was also examined, with the results showing that it would cleave under the tensile strength of 8.5 GPa with the strain of 0.3. In addition, the effect of tensile strain and …
We study theoretically the structural and electronic response of layered bulk black phosphorus to in-layer strain. Ab initio density functional theory (DFT) calculations reveal that the strain energy and interlayer spacing display a strong anisotropy with respect to the uniaxial strain direction. To correctly describe the dependence of the fundamental band gap on strain, we used the computationally more involved GW quasiparticle approach that is free of parameters and superior to DFT studies, which are known to underestimate gap energies. We find that the band gap depends sensitively on the in…
We propose here a two-dimensional material based on a single layer of violet or Hittorf's phosphorus. Using first-principles density functional theory, we find it to be energetically very stable, comparable to other previously proposed single-layered phosphorus structures. It requires only a small energetic cost of approximately $0.04~\text{eV/atom}$ to be created from its bulk structure, Hittorf's phosphorus, or a binding energy of $0.3-0.4~\text{J/m}^2$ per layer, suggesting the possibility of exfoliation in experiments. We find single-layered Hittorf's phosphorus to be a wide band gap semic…
Synthesis of thin-film black phosphorus on a flexible substrate
我们报告了一种可扩展的方法来合成一个大面积（高达4毫米）的薄黑磷（BP）薄膜上的柔性基板。我们首先在柔性聚酯基底上沉积一层赤磷（RP）薄膜，然后在室温下在高压多砧室中将其转化为BP。拉曼光谱和透射电子显微镜测量证实了形成的纳米晶体BP薄膜的厚度约为40 nm。光学表征表明，在转换BP的带隙约为0.28 eV，在剥离的薄膜中测得的带隙类似。薄膜BP晶体管表现出约0.5 cm 2/Vs的场效应迁移率，这可能会进一步提高在高温下的转换过程的优化。我们的工作为将来大规模、高质量的薄膜黑磷的示范开辟了道路。
We explore the impact of strain on charge carrier mobility of monolayer $α$, $β$, $γ$ and $δ$-P, the four well known atomically thin allotropes of phosphorus, using density functional theory. Owing to the highly anisotropic band dispersion, the charge carrier mobility of the pristine allotropes is significantly higher (more than 5 times in some cases) in one of the principal directions (zigzag or armchair) as compared to the other. Uniaxial strain (upto 6% compressive/tensile) leads to bandgap alteration in each of the allotropes, especially a direct to indirect bandgap semiconductor transitio…
The identification of the crystalline axis of anisotropic black phosphorus (BP) is key for the study of its physical properties and for its optical and electronic applications. Herein, we show that by applying an in-plane uniaxial strain and measuring the changes of Raman shifts, the crystalline axis of BP can be reliably determined. The strain effects on Raman shifts are angle-dependent, which can be expressed as a combination of Raman responses under zigzag and armchair strains. Different from previous polarized optical spectroscopic means, the proposed method does not rely on the laser pola…
Interlayer interactions in 2D materials, also known as van der Waals (vdWs) interactions, play a critical role in the physical properties of layered materials. It is fascinating to manipulate the vdWs interaction, and hence to "redefine" the material properties. Here, we demonstrate that in-plane biaxial strain can effectively tune the vdWs interaction of few-layer black phosphorus with thickness of 2-10 layers, using infrared spectroscopy. Surprisingly, our results reveal that in-plane tensile strain efficiently weakens the interlayer coupling, even though the sample shrinks in the vertical d…
The low formation energy of atomic vacancies in black phosphorus allows it to serve as an ideal prototypical system for exploring the dynamics of interlayer interstitial-vacancy (I-V) pairs (i.e. Frenkel defects) which account for Wigner energy release. Based on a few-layer model of black phosphorus, we conduct discrete geometry analysis and investigate the structural dynamics of intimate interlayer Frenkel pairs from first-principles calculations. We reveal a highly metastable I-V pair state driven by anisotropic dipole-like strain fields which can build strong connections between neighbourin…
The effects of size, strain, and vacancies on thermal properties of armchair black phosphorus nanotubes are investigated based on qualitative analysis from molecular dynamics simulations. It is found that the thermal conductivity has a remarkable size effect because of the restricted paths for phonon transport, strongly depending on the diameter and length of nanotube. Owing to the intensified low-frequency phonons, axial tensile strain can facilitate thermal transport. On the contrary, compressive strain weakens thermal transport due to the enhanced phonon scattering around the buckling of na…
In this work, we present a computational study on the possibility of strain engineering in monolayer Black Phosphorus (black P) and Blue Phosphorus (blue P) based MOSFETs. The material properties like band structure, carrier effective masses, carrier densities at band extrema are evaluated using Generalized Gradient Approximation (GGA) in Density Functional Theory (DFT).Thereafter self-consistent Non-Equilibrium Greens Function (NEGF) simulations are carried out to study the device performance metrics (such as output characteristics, ON currents, transconductance etc.) of such strained black P…
Photoinduced topological phase transitions (TPTs) in black phosphorous (BP) under compressive strain were investigated by combining Floquet theory and first-principles calculations. Intriguing photo-dressed electronic states including Floquet-Dirac semimetals and Floquet topological insulators have been identified, which can be feasibly engineered by changing the direction, intensity and frequency of incident laser. Remarkably, tunable TPT from type-I to type-II Floquet-Dirac fermions can be realized by irradiating circularly polarized laser (CPL), with an origin rooted in optical Stark effect…
The field of topological mechanics has recently emerged due to the interest in robustly transporting various types of energy in a flaw and defect-insensitive fashion. While there have been a significant number of studies based on discovering and proposing topological materials and structures, very few have focused on tuning the resulting topological bandgaps, which is critical because the bandgap frequency is fixed once the structure has been fabricated. Here, we perform both lattice dynamical calculations and molecular dynamical simulations to investigate strain effects on the phononic topolo…
Recently, black phosphorus (BP) has joined the two dimensional material family as a promising candidate for photonic applications, due to its moderate bandgap, high carrier mobility, and compatibility with a diverse range of substrates. Photodetectors are probably the most explored BP photonic devices, however, their unique potential compared with other layered materials in the mid-infrared wavelength range has not been revealed. Here, we demonstrate BP mid infrared detectors at 3.39 um with high internal gain, resulting in an external responsivity of 82 A/W. Noise measurements show that such …
Negative Poisson's ratio (NPR) materials have attracted tremendous interest due to their unusual physical properties and potential applications. Certain two-dimensional (2D) monolayer materials have also been found to exhibit NPR and the corresponding deformation mechanism varies. In this study, we found, based on first-principles calculations, that the Poisson's ratio (PR) sign of monolayer Blue Phosphorus Oxide (BPO) can be tuned by strain: the PR is positive under uniaxial strain <= -1% but becomes negative under > 0. The deformation mechanism for BPO under strain depends on the mutual comp…
Contrary to empirical observations, lowest-order $k\cdot\hat{p}$ theory predicts that monolayer black phosphorus ("phosphorene") is completely immune to zigzag-polarized optical excitation at the bandgap energy. Using symmetry arguments, we derive a $2\times2$ Hamiltonian under the $k\cdot\hat{p}$ formalism including higher-order corrections, which is used to show that the experimentally-measured band-gap transition with zigzag polarization is dominated by the third order $k\cdot\hat{p}$ perturbation in the interband optical matrix element, whereas the effects of spin-orbit interaction are neg…
The allotropes of a new layered material, phosphorus carbide (PC), have been predicted recently and a few of these predicted structures have already been successfully fabricated. Herein, by using first-principles calculations we investigated the effects of rippling a PC monolayer, one of the most stable modifications of layered PC, under large compressive strains. Similar to phosphorene, layered PC was found to have the extraordinary ability to bend and form ripples with large curvatures under a sufficiently large strain applied along its armchair direction. The band gap size, workfunction, an…
Functionalization of atomically thin nanomaterials enables the tailoring of their chemical, optical, and electronic properties. Exfoliated black phosphorus, a layered two-dimensional semiconductor exhibiting favorable charge carrier mobility, tunable bandgap, and highly anisotropic properties, is chemically reactive and degrades rapidly in ambient conditions. In contrast, here we show that covalent aryl diazonium functionalization suppresses the chemical degradation of exfoliated black phosphorus even following weeks of ambient exposure. This chemical modification scheme spontaneously forms ph…
The encapsulation of two-dimensional layered materials such as black phosphorus is of paramount importance for their stability in air. However, the encapsulation poses several questions, namely, how it affects, via the weak van der Waals forces, the properties of the black phosphorus and whether these properties can be tuned on demand. Prompted by these questions, we have investigated the impact of hexagonal boron nitride encapsulation on the structural and vibrational properties of few layer black phosphorus, using a first-principles method in the framework of density functional theory. We de…
Phosphorene oxides: bandgap engineering of phosphorene by oxidation
我们发现，磷烯的氧化可以导致形成一个新的家庭的平面（2D）和管状（1D）的氧化物和亚氧化物，其中大部分是绝缘的。这赋予黑磷可以用作阻挡材料和保护层的天然氧化物。此外，磷烯氧化物的带隙取决于氧浓度，这表明受控氧化可以用作设计带隙的手段。对于氧饱和的组成P $_2$ O $_5$，平面相和管状相都具有约8.5eV的大的带隙能量，并且在近紫外区是透明的。预计这两种形式的磷烯氧化物具有与o $^\prime$ -P $_2$ O $_5$相同的生成焓，所述O是五氧化二磷的先前已知形式中最稳定的。
Using the density functional theory of electronic structure, we compute the anisotropic dielectric response of bulk black phosphorus subject to strain. Employing the obtained permittivity tensor, we solve Maxwell's equations and study the electromagnetic response of a layered structure comprising a film of black phosphorus stacked on a metallic substrate. Our results reveal that a small compressive or tensile strain, $\sim 4\%$, exerted either perpendicular or in the plane to the black phosphorus growth direction, efficiently controls the epsilon-near-zero response, and allows a perfect absorp…
Nominally-pure black phosphorus (BP) is commonly found to be a p-type semiconductor, suggesting the ubiquitious presence of impurity species or intrinsic, charged defects. Moreover, scanning tunnelling microscopy (STM) images of black phosphorus reveal the presence of long-ranged double-lobed defect features superimposed onto the surface atomic lattice. We show that both the p-type doping of BP and the defect features observed in STM images can be attributed to substitutional tin impurities. We show that black phosphorus samples produced through two common synthesis pathways contain tin impuri…
The newly synthesized ultrathin carbon nanothreads have drawn great attention from the carbon community. Here, based on first-principles calculations, we investigate the electronic properties of carbon nanothreads under the influence of two important factors: the Stone-Wales (SW) type defect and the lattice strain. The SW defect is intrinsic to the polymer-I structure of the nanothreads and is a building block for the general hybrid structures. We find that the bandgap of the nanothreads can be tuned by the concentration of SW defects in a wide range of $3.92 \sim 4.82$ eV, interpolating betwe…
Graphene, as a passivation layer, can be used to protect the black phosphorus from the chemical reaction with surrounding oxygen and water. However, black phosphorus and graphene heterostructures have low efficiency of heat dissipation due to its intrinsic high thermal resistance at the interfaces. The accumulated energy from Joule heat has to be removed efficiently to avoid the malfunction of the devices. Therefore, it is of significance to investigate the interfacial thermal dissipation properties and manipulate the properties by interfacial engineering on demand. In this work, the interfaci…
Black phosphorous (BP) is a layered semiconductor with high carrier mobility, anisotropic optical response and wide bandgap tunability. In view of its application in optoelectronic devices, understanding transient photo-induced effects is crucial. Here, we investigate by time- and angle-resolved photoemission spectroscopy BP in its pristine state and in the presence of Stark splitting, chemically induced by Cs ad-sorption. We show that photo-injected carriers trigger bandgap renormalization and a concurrent valence band attening caused by Pauli blocking. In the biased sample, photoexcitation l…
Controlling the bandgap through local-strain engineering is an exciting avenue for tailoring optoelectronic materials. Two-dimensional crystals are particularly suited for this purpose because they can withstand unprecedented non-homogeneous deformations before rupture: one can literally bend them and fold them up almost like a piece of paper. Here, we study multi-layer black phosphorus sheets subjected to periodic stress to modulate their optoelectronic properties. We find a remarkable shift of the optical absorption band-edge of up to ~0.7 eV between the regions under tensile and compressive…
We propose previously unknown allotropes of phosphorus carbide (PC) in the stable shape of an atomically thin layer. Different stable geometries, which result from the competition between sp2 bonding found in graphitic C and sp3 bonding found in black P, may be mapped onto 2D tiling patterns that simplify categorizing of the structures. Depending on the category, we identify 2D-PC structures that can be metallic, semi-metallic with an anisotropic Dirac cone, or direct-gap semiconductors with their gap tunable by in-layer strain.
Thin layers of black phosphorus present an ideal combination of a 2D material with a tunable direct bandgap and high carrier mobility. However the material suffers from degradation in ambient conditions due to an oxidation reaction which involves water, oxygen and light. We have measured the spatial profile of the conductivity on flakes of black phosphorus as a function of time using scanning microwave impedance microscopy. A microwave excitation (3 GHz) allows to image a conducting sample even when covered with a dielectric layer. We observe that on bare black phosphorus, the conductivity cha…
Applying elastic deformation can tune a material physical properties locally and reversibly. Spatially modulated lattice deformation can create a bandgap gradient, favouring photo-generated charge separation and collection in optoelectronic devices. These advantages are hindered by the maximum elastic strain that a material can withstand before breaking. Nanomaterials derived by exfoliating transition metal dichalcogenides TMDs are an ideal playground for elastic deformation, as they can sustain large elastic strains, up to a few percent. However, exfoliable TMDs with highly strain-tunable pro…
The objective of this work is to study the effects of charge redistribution, applied layer-normal electric fields, applied strain, and layer engineering on the band alignment of Black Phosphorus (BP)/Molybdenum disulphide (MoS2) heterostructure through Density Functional Theory (DFT) simulations. Black phosphorus works as a p-type material with high mobility, mechanical flexibility, and sensitivity to number of layers. Combining it with the more electronegative material, MoS2 results in strong carrier confinement and a Type II heterostructure. Charge redistribution among the layers shifts the …
Lattice distortion due to octahedral rotation and distortion are high focussed, and it produces profound effect on a material's properties, such as its bandgap, magnetism and optical properties etc. Rutile-type \b{eta}-MnO2 is a wide used non-Perovskite magnetic material with octahedrons. We systematically studied its stability, electronic structures, magnetic structures, and optical properties within 0-100 GPa with density-functional theory (DFT). We find that the competition between bondlength and bonding angle leads its bandgap enlarging or shrinking within in the Pnnm phase with increasing…
Black phosphorus has attracted interest as a material for use in optoelectronic devices due to many favorable properties such as a high carrier mobility, field-effect, and a direct bandgap that can range from 0.3 eV in its bulk crystalline form to 2 eV for a single atomic layer. The low bandgap energy for bulk black phosphorus allows for direct transition photoabsorption that enables detection of light out to mid-infrared frequencies. In this work we characterize the room temperature optical response of a black phosphorus photoconductive detector at wavelengths ranging from 1.56 $μ$m to 3.75 $…
High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus
二维晶体是纳米电子学的新兴材料。该领域的发展需要候选系统具有高载流子迁移率和与石墨烯相反的足够大的电子带隙。在这里，我们提出了一个详细的理论研究的原子和电子结构的少层黑磷（BP），以预测其电学和光学性质。该系统具有直接带隙，可调从1.51 eV的单层到0.59 eV的5层样品。我们预测的迁移率是空穴占主导地位，相当高，高度各向异性。该单层具有极高的空穴迁移率（约10000 cm $^{2}$ V $^{-1}$ s $^{-1}$）和反转各向异性的异常弹性性质。光吸收光谱表明垂直面内方向之间的线性二向色性，这允许光学测定的晶体取向和光学激活的各向异性传输特性。这些结果使少层BP成为未来电子学的一个有前途的候选者。
Strain engineering in single-layer semiconducting transition metal dichalcogenides aims to tune their bandgap energy and to modify their optoelectronic properties by the application of external strain. In this paper we study transition metal dichalcogenides monolayers deposited on polymeric substrates under the application of biaxial strain, both tensile and compressive. We can control the amount of biaxial strain applied by letting the substrate thermally expand or compress by changing the substrate temperature. After modelling the substrate-dependent strain transfer process with a finite ele…
The bowing of the energy of the three lowest band-to-band transitions in $β$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ alloys was resolved using a combined density functional theory (DFT) and generalized spectroscopic ellipsometry (GSE) approach. The DFT calculations of the electronic band structure of both, $β$-Ga$_2$O$_3$ and $θ$-Al$_2$O$_3$, allow extracting of the linear portion of the energy shift in the alloys, and provide a method for quantifying the role of coherent strain present in the $β$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ thin films on (010) $β$-Ga$_2$O$_3$ substrates. The energies of band-to-band …
The tunability of the bandgap, absorption and emission energies, photoluminescence (PL) quantum yield, exciton transport, and energy transfer in transition metal dichalcogenide (TMD) monolayers provides a new class of functions for a wide range of ultrathin photonic devices. Recent strain-engineering approaches have enabled us to tune some of these properties, yet dynamic control at the nanoscale with real-time and -space characterizations remains a challenge. Here, we demonstrate a dynamic nano-mechanical strain-engineering of naturally-formed wrinkles in a WSe2 monolayer, with real-time inve…
