The Effect of Strain on Electronic

Structures of Hybridized Graphene-Boron Nitride Monolayer Superlattices

Shiqi Zhang, Sukky Jun, Xiaobao Li, Fanchao Meng

Department of Mechanical Engineering, University of Wyoming

OUTLINES

IntroductionCalculation Details Superlattice ModelsNumerical Results Summary

Introduction—BackgroundGaphene MonolayerSingle-atom-thick crystallites (graphene) has been extracted from bulk graphite in 2004. —Novoselov, et. al., Science 306 (2004).

Boron Nitride MonolayerFree standing single layer BN has been fabricated in 2009. —Jin et al., PRL 102, 195505 (2009) .

Superlattice ModelsArmchair Graphene Superlattice (AGSL(10,14;8,3)) Models — Sevinçli, Topsakal, et. al., PRB 78, (2008) 245402.

Graphene Boron Nitride (C-BN) Superlattice Monolayer

BN Stripe

BN Stripe

BN Stripe

GrapheneStripe

GrapheneStripe

GrapheneStripe

Introduction—MotivationStrain EffectWe find that if the magnitude of strain is less than 26.2%,no gap opens with the Z (along zigzag direction) strain. Graphene with the A (along armchair direction) strain also has no energy gap up to a magnitude of 30%.—S.M. Choi, S.H. Jhi, et al., PRB 81, (2010) 081407R.

Graphene Boron Nitride (C-BN) BoundaryArmchair C-BN Boundary

Zigzag C-BN Boundary

Research GoalInvestigate the feasibility of tailoring the electronic property of C-BN monolayer superlattice by applying mechanical strain and considering large deformation Poisson effect.

Armchair Edge of

BN MonolayerZigzag Edge of

Graphene Monolayer

Calculation DetailsMethodology — First-Principles Calculations• Total-energy calculation based on density-functional theory (SIESTA).• Norm-conserving nonlocal Troullier-Martins pseudopotentials, factorized in the Kleinman-

Bylander (KB) separate form and ultrasoft pseudopotentials.• Local-density approximation (LDA)by using the Ceperley-Alder (CA) exchange-correction

functional as parameterized by Perdew and Zunger.• A basis set of double-zeta plus polarization functions is used for the valence electrons

with the energy shift of 0.01 Ry.• Energy cutoff of 250 Ry is set for real-space integrations.• Atomic positions are relaxed by the conjugate gradient optimization until forces on each

atom are smaller than 0.02 eV/Å.• Using the Monkhorst-Pack scheme, k-point grids are carefully selected as16

Major Procedures• Calculate Lattice Constants for individual graphene and boron nitride monolayer• Build C-BN Superlattice Models (computational supercell)• Large deformation Poisson effect • Band Structure and Energy Gap

Superlattice Models

How to Build the C-BN Superlattice Models?Graphene lattice constant is smallerthan BN lattice constant

Stretch GrapheneOr

Compress Boron NitrideOr

Half Stretch and Half Compress

Model Type Total Energy

Compress BN -4014.89899

Stretch C -4035.37286

Half - Half -4035.37306

Stretch Graphene

Examples of Computational Supercells

ACBNSL20

ACBNSL12

ACBNSL6

ZCBNSL6

ZCBNSL12

ZCBNSL18

Width Width

Bond Length Range

Set a range for graphene bond length, and chose several value in this range by purpose

Set a range for BN bond length, and chose several value in this range by purpose

Build Primitive Unit Cell

Total Energy Calculation

Lattice Constant Graphene lattice constant is 2.463 Å.

Numerical Results—Lattice Constants

Graphene Primitive Unit Cell BN Primitive Unit Cell

BN lattice constant is 2.491 Å.

Numerical Results—Large Deformation Poisson Effect

Large Deformation Poisson Ratio of Hybridized Superlattices

Poisson Ratio

Fix by Certain Strain,

Apply Certain Strain

Fix by Certain Strain,

Change the other direction

Total Energy Calculation

ParallelPerpendicular

Strain Direction Band Gap Curve for One Width 3-D View of Band Gap

Numerical Result—Strained Armchair C-BN Superlattices

Parallel

Perpendicular

Numerical Result—Strained Armchair C-BN Superlattices

Strain Direction 3-D View of Band Gap Contour Lateral View (Strain Axis)

Parallel

Perpendicular

Numerical Results—Zigzag C-BN Superlattice

Band structure of zigzag C-BN superlattice.

Spin-Polarized Calculation

Numerical Results— Strained Zigzag C-BN Superlattice

Strained zCBNSL10

Strain (Perpendicular)

Strained zCBNSL20

Numerical Results—Strained Zigzag C-BN Superlattice

Spin-Polarized Energy Gap

Summary

Armchair C-BN Superlattice• Energy gap value for strained armchair C-BN superlattices

monolayer oscillate with respect to not only width but also strain.• Ranges of 0.2 - 1.5 eV (parallel) and 0.05 – 1.2 eV (perpendicular).

Zigzag C-BN Superlattice • Strain can change not only spin properties of zigzag C-BN

superlattice monolayer, but also its electronic property from metal to half-metallic then to semi-conductor .

AcknowledgementNSF CMMI #0856250

Prof. Cristian V. Ciobanu Division of Engineering Colorado School of Mines

Dr. In-Ho Lee at KRISS

Converging Research Center Program through the Ministry of Education, Science and Technology of Korea (#2011K00622)