Strain Effect on the Electronic Properties of Single Layer and Bilayer Graphene

Wong, Jen-Hsien; Wu, Bi-Ru; Lin, Ming–Fa

doi:10.1021/jp300840k

Cited by 131 publications

(80 citation statements)

References 36 publications

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“…Calculated band-gaps for similarly strained graphene can range from 0.2-0.5 eV depending on the model. 15,17,21 Comparing this strain energy with a finite size band-gap expected for a 1.4 nm graphene ribbon, E g ∼ 1eV-nm/1.4nm = 0.8 eV, 5,18 shows that both effects lead to band gaps similar to the experimental value. Because the energy scales are similar, Peierl's like distortion are potentially important.…”

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confidence: 61%

A wide-bandgap metal–semiconductor–metal nanostructure made entirely from graphene

et al. 2012

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A blueprint for producing scalable digital graphene electronics has remained elusive. Current methods to produce semiconducting-metallic graphene networks all suffer from either stringent lithographic demands that prevent reproducibility, process-induced disorder in the graphene, or scalability issues. Using angle resolved photoemission, we have discovered a unique one-dimensional metallic-semiconducting-metallic junction made entirely from graphene, and produced without chemical functionalization or finite size patterning. The junction is produced by taking advantage of the inherent, atomically ordered, substrate-graphene interaction when it is grown on SiC, in this case when graphene is forced to grow over patterned SiC steps. This scalable bottomup approach allows us to produce a semiconducting graphene strip whose width is precisely defined within a few graphene lattice constants, a level of precision entirely outside modern lithographic limits. The architecture demonstrated in this work is so robust that variations in the average electronic band structure of thousands of these patterned ribbons have little variation over length scales tens of microns long. The semiconducting graphene has a topologically defined few nanometer wide region with an energy gap greater than 0.5 eV in an otherwise continuous metallic graphene sheet. This work demonstrates how the graphene-substrate interaction can be used as a powerful tool to scalably modify graphene's electronic structure and opens a new direction in graphene electronics research.Patterning a flat graphene sheet to alter its electronic structure was envisaged to be the foundation of graphene electronics. 1 The early focus was to open a finite-size gap in lithographically patterned nanoribbons, a necessary step for digital electronics. 1-5 While early transport measurements supported this possibility, 6 it soon became apparent that these "transport gaps" originated from a series of mismatched-level quantum dots caused by the inability of current lithographically to produce sufficiently narrow, well ordered, and crystallography define graphene edges. 7-10 A working solution to the graphene "gap problem" has yet to be formulated, let alone demonstrated. We show that in fact such a solution exists, not by patterning graphene, but instead by controlling the graphene-substrate geometry.We have been able to construct a unique, reproducible, and scalable semiconducting graphene ribbon with a gap larger than 0.5 eV. Using pre-patterned SiC trenches to force graphene to bend between a high symmetry (0001) face to a low symmetry (112n) facet, we produce a narrow curved graphene bend with localized strain. This "topologically-defined" ribbon is a wide-gap graphene semiconductor strip a few lattice constants wide that extends hundreds of microns long. The strip is connected seamlessly to metallic graphene sheets on both of its sides. One metallic sheet is n-doped and the other pdoped. From this simple morphology, we have not only produced a gap suitable for room temperature...

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confidence: 61%

A wide-bandgap metal–semiconductor–metal nanostructure made entirely from graphene

et al. 2012

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“…(9) shows that the force between dislocations is zero (i.e., E total is independent of d D ). This is a direct result of the assumption that the dislocation core is of zero width.…”

Section: −10mentioning

confidence: 99%

“…Bandgap modulation induced by application of an electric field in bilayer graphene has been experimentally confirmed 2 . The bandgap of layered materials, such as bilayer graphene [3][4][5] , hexagonal boron nitride, MoS 2 as well as phosphorene can also be varied by changes in bilayer stacking [3][4][5][6][7][8] and elastic strain [8][9][10] . While the relatively weak vdW-like interactions between graphene layers (compared to the strong interlayer covalent bonds) are sufficient to adhere two layers, the energy difference and barriers between different (sliding) translational states are sufficiently small that several distinct bilayer states can be realized.…”

Section: Introductionmentioning

confidence: 99%

Structure and energetics of interlayer dislocations in bilayer graphene

2016

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We present a general hybrid model based upon the continuum generalized Peierls-Nabarro model (with density functional theory parametrization) to describe interlayer dislocations in bilayer systems. In this model, the bilayer system is divided into two linear elastic 2D sheets, the strains in each sheet can be relaxed by both elastic in-plane deformation and out-of-plane buckling; this deformation is described via classical linear elastic thin plate theory. The interlayer bonding between these two sheets is described by a 3-dimensional Generalized Stacking-Fault Energy (GSFE) determined from first principle calculations and based upon the relative displacement between the sheets. The structure and energetics of various interlayer dislocations in bilayer graphene was determined by minimizing the elastic and bonding energy with respect to all displacements. The dislocations break into partials and pronounced buckling is observed at the partial dislocation locations to relax the strain induced by their edge components. The partial dislocation core width is reduced by buckling. An analytical model is also developed based upon the results obtained in numerical simulation. We develop an analytical model for the bilayer structure and energy and show that these predictions are in excellent agreement with the numerical results.

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“…Due to the hexagonal symmetry with a rotational angle of 60 • , a non-doped graphene is a zero-gap semiconductor with a vanishing density of state at the Fermi level. The essential electronic properties can be drastically changed by the layer number [35][36][37], stacking configuration [37][38][39][40][41][42], magnetic field [43,44], electric field [45][46][47], dopping [48,49], mechanical strain [50][51][52], and temperature variation [53,54]. Few-and multi-layer graphenes have been successfully produced by experimental methods such as exfoliation of highly orientated pyrolytic graphite [55][56][57][58], metalorganic chemical vapour deposition (MOCVD) [61][62][63][64][65][66], chemical and electrochemical reduction of graphene oxide [67][68][69], and arc discharge [70,71].…”

Section: Introductionmentioning

confidence: 99%

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

Lin

et al. 2015

Carbon

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We developed the generalized tight-binding model to study the magneto-electronic properties of AAB-stacked trilayer graphene. Three groups of Landau levels (LLs) are characterized by the dominating subenvelope function on distinct sublattices. Each LL group could be further divided into two sub-groups in which the wavefunctions are, respectively, localized at 2/6 (5/6) and 4/6 (1/6) of the total length of the enlarged unit cell. The unoccupied conduction and the occupied valence LLs in each subgroup behave similarly. For the first group, there exist certain important differences between the two sub-groups, including the LL energy spacings, quantum numbers, spatial distributions of the LL wavefunctions, and the field-dependent energy spectra.The LL crossings and anticrossings occur frequently in each sub-group during the variation of field strengths, which thus leads to the very complex energy spectra and the seriously distorted wavefunctions. Also, the density of states (DOS) exhibits rich symmetric peak structures. The predicted results could be directly examined by experimental measurements. The magnetic quantization is quite different among the AAB-, AAA-, ABA-, and ABC-stacked configurations.

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Strain Effect on the Electronic Properties of Single Layer and Bilayer Graphene

Cited by 131 publications

References 36 publications

A wide-bandgap metal–semiconductor–metal nanostructure made entirely from graphene

A wide-bandgap metal–semiconductor–metal nanostructure made entirely from graphene

Structure and energetics of interlayer dislocations in bilayer graphene

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

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