Strain-engineered direct-indirect band gap transition and its mechanism in two-dimensional phosphorene

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.

[1]  A. Radenović,et al.  Single-layer MoS2 transistors. , 2011, Nature nanotechnology.

[2]  Ab-initio Study of Size and Strain Effects on the Electronic Properties of Si Nanowires , 2009, 1010.1556.

[3]  P. Kim,et al.  Experimental observation of the quantum Hall effect and Berry's phase in graphene , 2005, Nature.

[4]  Eugenie Samuel Reich,et al.  Phosphorene excites materials scientists , 2014, Nature.

[5]  Wolfgang Nolting,et al.  Quantum Theory of Magnetism , 2009 .

[6]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[7]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[8]  Xinglong Wu,et al.  Optical transition in discrete levels of Si quantum dots , 2004 .

[9]  Few-layer black phosphorus: emerging 2D semiconductor with high anisotropic carrier mobility and linear dichroism , 2014 .

[10]  S. Rundqvist,et al.  Refinement of the crystal structure of black phosphorus , 1965 .

[11]  A. Thean,et al.  Strain Effect in Large Silicon Nanocrystal Quantum Dots , 2001, Physical Models for Quantum Dots.

[12]  Wei Ji,et al.  High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus , 2014, Nature communications.

[13]  Xihong Peng,et al.  Strain-modulated electronic properties of Ge nanowires: A first-principles study , 2009, 1010.1553.

[14]  Engineering the work function of armchair graphene nanoribbons using strain and functional species: a first principles study. , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[15]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[16]  Xihong Peng,et al.  Origination of the direct-indirect band gap transition in strained wurtzite and zinc-blende GaAs nanowires: A first principles study , 2013 .

[17]  S. Franchi,et al.  The effect of strain on tuning of light emission energy of InAs/InGaAs quantum-dot nanostructures , 2003 .

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  Li Yang,et al.  Strain-Engineering Anisotropic Electrical Conductance of Phosphorene , 2014 .

[20]  A S Rodin,et al.  Strain-induced gap modification in black phosphorus. , 2014, Physical review letters.

[21]  A. Morita,et al.  Electronic structure of black phosphorus: Tight binding approach , 1981 .

[22]  L. Seravalli,et al.  Defect passivation in strain engineered InAs/(InGa)As quantum dots , 2005 .

[23]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[24]  R. Soklaski,et al.  Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus , 2014 .

[25]  J. Kysar,et al.  Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene , 2008, Science.

[26]  Likai Li,et al.  Black phosphorus field-effect transistors. , 2014, Nature nanotechnology.

[27]  Electronic properties of strained Si/Ge core-shell nanowires , 2010, 1010.1555.

[28]  R. Superfine,et al.  Bending and buckling of carbon nanotubes under large strain , 1997, Nature.

[29]  A. Geim,et al.  Two-dimensional gas of massless Dirac fermions in graphene , 2005, Nature.

[30]  Andrew G. Glen,et al.  APPL , 2001 .

[31]  Xihong Peng,et al.  Strain modulated band gap of edge passivated armchair graphene nanoribbons , 2011, 1102.0314.

[32]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[33]  Ki-Ha Hong,et al.  Influence of epitaxial strain on the terrace and inter-layer diffusions in metal epitaxy , 2006 .

[34]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[35]  Xianfan Xu,et al.  Phosphorene: an unexplored 2D semiconductor with a high hole mobility. , 2014, ACS nano.

[36]  F. Xia,et al.  Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. , 2014, Nature communications.

[37]  Xihong Peng,et al.  Band structure of Si/Ge core–shell nanowires along the [110] direction modulated by external uniaxial strain , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[38]  Strain effects on work functions of pristine and potassium-decorated carbon nanotubes. , 2009, The Journal of chemical physics.

[39]  S. Nayak,et al.  Strain-engineered photoluminescence of silicon nanoclusters , 2006 .

[40]  Peidong Yang,et al.  Semiconductor nanowires for energy conversion , 2010, 2010 3rd International Nanoelectronics Conference (INEC).

[41]  Andres Castellanos-Gomez,et al.  Mechanical properties of freely suspended semiconducting graphene-like layers based on MoS2 , 2012, Nanoscale Research Letters.

[42]  David Roundy,et al.  Ideal strength of bcc molybdenum and niobium , 2002 .

[43]  T. Wang,et al.  Improvement of electron transport in a ZnSe nanowire by in situ strain , 2011 .

[44]  O. Hansen,et al.  Strained silicon as a new electro-optic material , 2006, Nature.

[45]  P. Ajayan,et al.  Effect of strain on the band gap and effective mass of zigzag single-wall carbon nanotubes: First-principles density-functional calculations , 2008 .

[46]  Kwang S. Kim,et al.  Large-scale pattern growth of graphene films for stretchable transparent electrodes , 2009, Nature.