1. 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

2.  OUTLINES
Introduction
Calculation Details
Superlattice Models
Numerical Results
Summary

3.  Introduction—Background
Gaphene Monolayer
Single-atom-thick crystallites (graphene) has
been extracted from bulk graphite in 2004. —
Novoselov, et. al., Science 306 (2004).
Boron Nitride Monolayer
Free standing single layer BN has been
fabricated in 2009. —Jin et al., PRL 102, 195505
(2009) .
Superlattice Models
Armchair 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
Graphene
Stripe
Graphene
Stripe
Graphene
Stripe

4.  Introduction—Motivation
Strain Effect
We 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) Boundary
Armchair C-BN Boundary
Zigzag C-BN Boundary
Research Goal
Investigate the feasibility of tailoring the electronic property of C-BN monolayer superlattice by applying mechanical
strain and considering large deformation Poisson effect.

5.  Calculation Details
 Methodology — 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

6.  Superlattice Models
How to Build the C-BN Superlattice Models?
Graphene lattice
constant is smaller
than BN lattice
constant
Stretch Graphene
Or
Compress Boron Nitride
Or
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

7. 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.

8.  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
Parallel
Perpendicular

9. Strain
Direction
Band Gap Curve for One Width 3-D View of Band Gap
 Numerical Result—Strained Armchair C-BN Superlattices
Parallel
Perpendicular

10.  Numerical Result—Strained Armchair C-BN Superlattices
Strain
Direction 3-D View of Band Gap Contour Lateral View (Strain Axis)
Parallel
Perpendicular

11.  Numerical Results—Zigzag C-BN Superlattice
Band structure of zigzag C-BN superlattice.
Spin-Polarized Calculation

12.  Numerical Results— Strained Zigzag C-BN Superlattice
Strained zCBNSL10
Strain (Perpendicular)
Strained zCBNSL20

13.  Numerical Results—Strained Zigzag C-BN Superlattice
Spin-Polarized Energy Gap

14.  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 .

15.  Acknowledgement
NSF 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)