In-layer Strain Research Articles

An Analytical Model of Spontaneous Whisker Growth on Strain Accumulation From Contiguous Film Network

Whiskering has been a reemerging problem affecting the reliability of lead-free electronics. Although the in-layer strain has long been considered one of the major driving forces for whisker growth, the quantitative understanding of the relationship between stress and Sn whiskering is still limited. To fill this technological gap, we develop an analytical model to express the contribution of strain accumulation to the formation of whiskers. The model predicts the average whisker length by calculating the volume of Sn material reallocated by strain in a single whisker site. We apply this model to analyze strain generation (via thermal expansion mismatch, applied forces, and dynamic recrystallization (DRX) process) and strain relaxation processes (creep-law plasticity and material diffusion). The simulated average whisker length is in good agreement with multiple previous experimental data, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> reaches 0.80 after reliable calibration. The sensitivity and uncertainty are conducted to evaluate the reliability of the model in response to variations in external input, including deposition thickness and whisker density. The amount of DRX strain is estimated based on the model results. The application and limitations of the model are theoretically analyzed and discussed.

Strain-tunable electronic and optical properties of novel anisotropic green phosphorene: a first-principles study

The effect of in-layer strain on the optical and electrical properties of monolayer green phosphorene, a new anisotropic two-dimensional (2D) material, has been systematically studied. The studied strain includes in-layer uniaxial strain and biaxial strain. Green phosphorene can be viewed as a combination of black and blue phosphorene segments in regular order. We adopt the HSE06 method to correct the calculated results. The results reveal that, firstly, strain-free monolayer green phosphorene is a stable direct band gap 2D semiconductor with the anisotropic optical property. The transmittance of infrared and visible light along the zigzag direction is better than that along the armchair direction. However, the transmittance of the UV-light along the armchair direction is better than that along the zigzag direction. Secondly, the optical properties, such as the absorption coefficient and reflectivity, along armchair and zigzag direction respond very differently to the various applied strains. As for the electronic properties, the band gap exhibits different changing trends by applying either in-layer biaxial strain or uniaxial strain in different directions. Besides, the near-band-edge electronic orbitals exhibit different bond nature in different directions. These results suggest that green phosphorene shows strong anisotropy in electronic and optical properties. By calculating and comparing the energies of near-band-edge states after applying different strains on green phosphorene, the reason for the anisotropy of the new 2D material is analyzed. This study implies that the electronic and optical properties of green phosphorene, a stable direct band gap anisotropic semiconductor, could be efficiently tuned by in-layer biaxial or uniaxial strain. Therefore, green phosphorene can be used in linear polarizers and other anisotropic photoelectric devices.

Enhanced photocatalytic activity of single-layered Hittorf’s violet phosphorene by isoelectronic doping and mechanical strain: A first-principles research

A systematic theoretically study is performed for violet phosphorus monolayer nanosheet with the objective of improving its photocatalytic activity in water splitting under visible light by isoelectronic elements (N, As, Sb, and Bi) doping and strain engineering. The results show that compared with N-, As-, and Sb-doping, the introduced Bi impurity can effectively enhance visible light absorption efficiency. By applying an in-layer strain for Bi-doping violet phosphorene, the modulation of band edges further narrows the band gap. In particular, for compressive strain, the absorption extends into the overall visible region, greatly increasing the visible light absorption efficiency, which could be attributed to the significant reduced band gap and highly dispersive electronic states around the topmost valence band. Moreover, the band alignments for Bi-doped violet phosphorus monolayer are well positioned for the feasibility of both photo-oxidation and photo-reduction of water within the range of 0 to −3% biaxial strains and 0 to −7% uniaxial strains. Hence, compressive strained Bi-doped violet phosphorus monolayer can be a promising metal-free photocatalyst for water splitting owing to its improved visible light activity as well as the high carrier mobility.

Four allotropes of semiconducting layered arsenic that switch into a topological insulator via an electric field: Computational study

We propose four different thermodynamically stable structural phases of arsenic monolayers based on ab-initio density functional theory calculations all of which undergo a topological phase transition on application of a perpendicular electric field. All the four arsenic monolayer allotropes have a wide band gap, varying from 1.21 eV to 3.0 eV (based on GW calculations), and in general they undergo a metal-insulator quantum phase transition on application of uniaxial in-layer strain. Additionally an increasing transverse electric field induces band-inversion at the {\Gamma} point in all four monolayer allotropes, leading to a nontrivial topological phase (insulating for three and metallic for one allotrope), characterized by the switching of the Z2 index, from 0 (before band inversion) to 1 (after band inversion). The topological phase tuned by the transverse electric field, should support spin-separated gapless edge states which should manifest in quantum spin Hall effect.

Strain-controlled fundamental gap and structure of bulk black phosphorus

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 is superior to DFT studies, which are known to underestimate gap energies. We find that the band gap depends sensitively on the in-layer strain and even vanishes at compressive strain values exceeding $\ensuremath{\approx}2$%, thus suggesting a possible application of black P in strain-controlled infrared devices.

Two-Dimensional Phosphorus Carbide: Competition between sp(2) and sp(3) Bonding.

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 sp(2) bonding found in graphitic C and sp(3) 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, semimetallic with an anisotropic Dirac cone, or direct-gap semiconductors with their gap tunable by in-layer strain.

Designing Isoelectronic Counterparts to Layered Group V Semiconductors.

In analogy to III-V compounds, which have significantly broadened the scope of group IV semiconductors, we propose a class of IV-VI compounds as isoelectronic counterparts to layered group V semiconductors. Using ab initio density functional theory, we study yet unrealized structural phases of silicon monosulfide (SiS). We find the black-phosphorus-like α-SiS to be almost equally stable as the blue-phosphorus-like β-SiS. Both α-SiS and β-SiS monolayers display a significant, indirect band gap that depends sensitively on the in-layer strain. Unlike 2D semiconductors of group V elements with the corresponding nonplanar structure, different SiS allotropes show a strong polarization either within or normal to the layers. We find that SiS may form both lateral and vertical heterostructures with phosphorene at a very small energy penalty, offering an unprecedented tunability in structural and electronic properties of SiS-P compounds.

Strain-induced metal-semiconductor transition in monolayers and bilayers of gray arsenic: A computational study

We study the equilibrium geometry and electronic structure of thin films of layered gray arsenic using ab initio density functional theory. In contrast to bulk gray As that is semimetallic, thin films display a significant band gap that depends sensitively on the number of layers, in-layer strain, layer stacking, and interlayer spacing. We find that metallic character can be introduced by increasing the number of layers beyond two or by subjecting semiconducting monolayers and bilayers to moderate tensile strain. The strain-induced metal-semiconductor transition is triggered by changes in the band ordering near the top of the valence band that causes an abrupt change from $\ensuremath{\sigma}$ to $\ensuremath{\pi}$ character of the frontier states.

Continuously tunable electronic structure of transition metal dichalcogenides superlattices.

Two dimensional transition metal dichalcogenides have very exciting properties for optoelectronic applications. In this work we theoretically investigate and predict that superlattices comprised of MoS2 and WSe2 multilayers possess continuously tunable electronic structure with direct bandgaps. The tunability is controlled by the thickness ratio of MoS2 versus WSe2 of the superlattice. When this ratio goes from 1:2 to 5:1, the dominant K-K direct bandgap is continuously tuned from 0.14 eV to 0.5 eV. The gap stays direct against −0.6% to 2% in-layer strain and up to −4.3% normal-layer compressive strain. The valance and conduction bands are spatially separated. These robust properties suggest that MoS2 and WSe2 multilayer superlattice should be a promising material for infrared optoelectronics.

Phase coexistence and metal-insulator transition in few-layer phosphorene: a computational study.

Based on ab initio density functional calculations, we propose γ-P and δ-P as two additional stable structural phases of layered phosphorus besides the layered α-P (black) and β-P (blue) phosphorus allotropes. Monolayers of some of these allotropes have a wide band gap, whereas others, including γ-P, show a metal-insulator transition caused by in-layer strain or changing the number of layers. An unforeseen benefit is the possibility to connect different structural phases at no energy cost. This becomes particularly valuable in assembling heterostructures with well-defined metallic and semiconducting regions in one contiguous layer.

Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility

We introduce the 2D counterpart of layered black phosphorus, which we call phosphorene, as an unexplored p-type semiconducting material. Same as graphene and MoS2, single-layer phosphorene is flexible and can be mechanically exfoliated. We find phosphorene to be stable and, unlike graphene, to have an inherent, direct, and appreciable band gap. Our ab initio calculations indicate that the band gap is direct, depends on the number of layers and the in-layer strain, and is significantly larger than the bulk value of 0.31-0.36 eV. The observed photoluminescence peak of single-layer phosphorene in the visible optical range confirms that the band gap is larger than that of the bulk system. Our transport studies indicate a hole mobility that reflects the structural anisotropy of phosphorene and complements n-type MoS2. At room temperature, our few-layer phosphorene field-effect transistors with 1.0 μm channel length display a high on-current of 194 mA/mm, a high hole field-effect mobility of 286 cm(2)/V·s, and an on/off ratio of up to 10(4). We demonstrate the possibility of phosphorene integration by constructing a 2D CMOS inverter consisting of phosphorene PMOS and MoS2 NMOS transistors.