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.

Two dimensional few-layer black phosphorus crystal structures have recently fabricated and demonstrated great potential in applications of electronics. In this work, we employed first principles density functional theory calculations to study the edge effects and quantum confinement on the electronic properties of the phosphorene nanoribbons (PNR). Different edge functionalization groups, such as H, F, Cl, OH, O, S, and Se in addition to a pristine case, were studied for a series width of the ribbon up to 3.5 nm. It was found that the armchair-PNRs

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.

Electronic structures of wurtzite GaAs nanowires in the [0001] direction were studied using first-principles calculations. It was found that the band gap of GaAs nanowires experience a direct-to-indirect transition when the diameter of the nanowires is smaller than ~28 Å. For those thin GaAs nanowires with an indirect band gap, it was found that the gap can be tuned to be direct if a moderate external uniaxial strain is applied. Both tensile and compressive strain can trigger the indirect-to-direct gap transition. The critical strains for the gap-transition are determined by the energy crossover of two states in conduction bands. etc. In particular, GaAs has been considered as a promising channel material for the high speed NMOS beyond Si based technology. GaAs has two different crystal structures zinc blende (ZB) and wurtzite (WZ) phases. In bulk GaAs, ZB phase is energetically more favorable than WZ. In nanoscale, however, WZ phase was observed more often experimentally. Theoretical work,8 including abinitio calculations, has shown that at small size WZ structure is energetically more favorable, [8][9][10] and the interface energy may also facilitate the growth of WZ structure. 11Recent experiments have shown it is possible to grow GaAs nanowires in ZB, 12 WZ, 13 and mixed crystal phases. 14 While bulk GaAs (both ZB and WZ) has a direct band gap, GaAs nanowires may demonstrate an indirect gap when the diameter of nanowire is sufficiently small. 15,16 This band gap transition could fundamentally alter the electronic properties of nanowires. In addition to size, strain has become a routine factor to engineer band gaps of semiconductors in the field of microelectronics. Researchers have theoretically demonstrated the modulated band gap by external strains in a variety of systems such as pure Si 17 and Ge 18and Si/Ge Core-shell nanowires. 19It would be very interesting to investigate strain effects on the band structure of WZ GaAs nanowires and examine if the direct-indirect band gap transition can be engineered for applications.The ab-initio density functional theory (DFT) 20 calculations were carried out using VASP code 21,22 . The DFT local density approximation and the projector-augmented wave potentials 23,24 were used along with plane wave basis sets. The kinetic energy cutoff for the plane wave basis set was chosen to be 300.0 eV. The energy convergence criteria for electronic and ionic iterations are 10 -4 eV and 0.03 eV/Å, respectively. The GaAs nanowires were generated along the [0001] direction (i.e. z-axis) from bulk WZ GaAs with different diameters in the wire cross section (see Figure 1). The dangling bonds on the wire surface are saturated by hydrogen atoms.

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 ∼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.