Recently fabricated two-dimensional phosphorene crystal structures have demonstrated great potential in applications of electronics. In this paper, strain effect on the electronic band structure of phosphorene was studied using first-principles methods including density functional theory (DFT) and hybrid functionals. It was found that phosphorene can withstand a tensile stress and strain up to 10 N/m and 30%, respectively. The band gap of phosphorene experiences a direct-indirect-direct transition when axial strain is applied. A moderate −2% compression in the zigzag direction can trigger this gap transition. With sufficient expansion (+11.3%) or compression (−10.2% strains), the gap can be tuned from indirect to direct again. Five strain zones with distinct electronic band structure were identified, and the critical strains for the zone boundaries were determined. Although the DFT method is known to underestimate band gap of semiconductors, it was proven to correctly predict the strain effect on the electronic properties with validation from a hybrid functional method in this work. The origin of the gap transition was revealed, and a general mechanism was developed to explain energy shifts with strain according to the bond nature of near-band-edge electronic orbitals. Effective masses of carriers in the armchair direction are an order of magnitude smaller than that of the zigzag axis, indicating that the armchair direction is favored for carrier transport. In addition, the effective masses can be dramatically tuned by strain, in which its sharp jump/drop occurs at the zone boundaries of the direct-indirect gap transition.

We used density-functional theory based first-principles simulations to study the effects of uniaxial strain and quantum confinement on the electronic properties of germanium nanowires along the [110] direction, such as the energy gap and the effective masses of the electron and hole. The diameters of the nanowires being studied are up to $50\text{Å}$. As shown in our calculations, the Ge [110] nanowires possess a direct band gap, in contrast to the nature of an indirect band gap in bulk. We discovered that the band gap and the effective masses of charge carries can be modulated by applying uniaxial strain to the nanowires. These strain modulations are size dependent. For a smaller wire $\left(\sim 12\text{Å}\right)$, the band gap is almost a linear function of strain; compressive strain increases the gap while tensile strain reduces the gap. For a larger wire $\left(20\text{Å}–50\text{Å}\right)$, the variation in the band gap with respect to strain shows nearly parabolic behavior: compressive strain beyond $-1\%$ also reduces the gap. In addition, our studies showed that strain affects effective masses of the electron and hole very differently. The effective mass of the hole increases with a tensile strain while the effective mass of the electron increases with a compressive strain. Our results suggested both strain and size can be used to tune the band structures of nanowires, which may help in design of future nanoelectronic devices. We also discussed our results by applying the tight-binding model.

First principles density functional theory calculations were performed to study the effects of strain, edge passivation, and surface functional species on the structural and electronic properties of armchair graphene nanoribbons (AGNRs), with a particular focus on the work function. The work function was found to increase with uniaxial tensile strain and decrease with compression. The variation of the work function under strain is primarily due to the shift of the Fermi energy with strain. In addition, the relationship between the work function variation and the core level shift with strain is discussed. Distinct trends of the core level shift under tensile and compressive strain were discovered. For AGNRs with the edge carbon atoms passivated by oxygen, the work function is higher than for nanoribbons with the edge passivated by hydrogen under a moderate strain. The difference between the work functions in these two edge passivations is enlarged (reduced) under a sufficient tensile (compressive) strain. This has been correlated to a direct-indirect bandgap transition for tensile strains of about 4% and to a structural transformation for large compressive strains at about - 12%. Furthermore, the effect of the surface species decoration, such as H, F, or OH with different covering density, was investigated. It was found that the work function varies with the type and coverage of surface functional species. Decoration with F and OH increases the work function while H decreases it. The surface functional species were decorated on either one side or both sides of AGNRs. The difference in the work functions between one-sided and two-sided decorations was found to be relatively small, which may suggest an introduced surface dipole plays a minor role.

Recent work [Appl. Phys. Lett. 100, 193108 (2012)] has demonstrated that uniaxial strain applied to wurtzite (WZ) GaAs nanowires leads to an interesting direct-indirect band gap transition. Here, we explored the potential of strain engineering on electronic structures of one-dimensional WZ and zinc-blende (ZB) GaAs nanowires along the [0001] and [111] directions, respectively. The studied strain includes uniaxial strain, radial strain, and strain along zigzag and armchair directions in the cross section of the nanowires and shear strains. It was found that the WZ and ZB GaAs nanowires with a diameter of $\sim${}2 nm have an indirect band gap, whereas, bulk GaAs has a direct gap. The near-gap states (valence-band maximum/conduction-band minimum) are dominated by $s$ or $p$ orbitals of Ga or As atoms. The energies of these states respond very differently to the applied strains. For example, the energy increases with a positive uniaxial expansion while decreasing with a negative uniaxial compression for a state dominated by bonding s orbitals. However, for a state dominated by antibonding s orbitals, an opposite trend of its energy response to strain is observed. Furthermore, the energy response to strain of bonding p orbitals was found to be different from that of bonding s orbitals. Due to the different responses of the near-gap state energies with respect to strain, the direct-indirect band gap transition was produced. It was further found that whether a strain can trigger the direct-indirect band gap transition in the GaAs nanowires depends strongly on the type of applied strain. It requires less strain energy to convert the indirect gap to be direct in both the WZ and the ZB nanowires through applying a radial strain in the cross section, compared with applying a strain in the zigzag direction.

Tetrahex carbon is a recently predicted two-dimensional (2D) carbon allotrope that is composed of tetragonal and hexagonal rings. Unlike flat graphene, this new 2D carbon structure is buckled and possesses a direct band gap of approximately 2.6 eV and a high carrier mobility of approximately ${10}^4\mathrm{c}{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})$ with anisotropic features. In this work, we employ first-principles density-functional theory calculations to explore the mechanical properties of tetrahex C under uniaxial tensile strain. We find that tetrahex C demonstrates ultrahigh ideal strength, outperforming both graphene and pentagraphene. It shows superior ductility and sustains uniaxial tensile strain up to 20% (16%) until phonon instability occurs and the corresponding maximal strength is 38.3 N/m (37.8 N/m) in the zigzag (armchair) direction. It shows an intrinsically negative Poisson ratio. This exotic in-plane Poisson ratio takes place when the axial strain reaches a threshold value of 7% (5%) in the zigzag (armchair) direction. We also find that tetrahex C maintains a direct band gap of 2.64 eV at the center of the Brillouin zone. This direct-gap feature remains intact upon strain application, with no direct-indirect gap transition. The ultrahigh ideal strength, the negative Poisson ratio, and the integrity of the direct gap under strain in tetrahex C suggest that it may have potential applications in nanomechanics and nanoelectronics.