Boron Nitride Monolayer- A Strain-Tunable Nanosensor

Boron Nitride Monolayer: A Strain-Tunable NanosensorM. Neek-Amal,*,, J. Beheshtian,, A. Sadeghi, K. H. Michel, and F. M. Peeters

Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 AntwerpenBelgium, and Department of Physics, Shahid Rajaee Teacher Training University, Lavizan, Tehran 16785-136, Iran

ABSTRACT: The inuence of triaxial in-plane strain on the electronic properties of ahexagonal boron-nitride sheet is investigated using density functional theory. Dierentfrom graphene, the triaxial strain localizes the molecular orbitals of the boron-nitrideake in its center depending on the direction of the applied strain. The proposed tech-nique for localizing the molecular orbitals that are close to the Fermi level in the centerof boron nitride akes can be used to actualize engineered nanosensors, for instance, toselectively detect gas molecules. We show that the central part of the strained akeadsorbs polar molecules more strongly as compared with an unstrained sheet.

I. INTRODUCTION

Strain engineering can be used to control the electronic prop-erties of nanomaterials. This is of interest for fundamentalphysics but is also relevant for potential device applications innanoelectronics. Because the electronic and mechanical proper-ties of an atomic monolayer are strongly inuenced by strain theyhave attracted considerable attention over the last decades.1,2

Unlike graphene, an h-BN sheet is a wide gap insulator, as isbulk h-BN, and is a promising material for opto-electronictechnologies,35 tunnel devices, and eld-eect transistors.6

Using a combination of mechanical exfoliation and reactive ionetching, monolayer and multilayer suspended h-BN sheets canbe prepared.7 The band gap of boron nitride nanoribbons canbe altered by edge passivation with dierent types of atoms.810

A combination of an odd number of h-BN layers is a non-centrosymmetric ionic crystal that is piezoelectric due to D3hsymmetry.11,12 The corrugations on the h-BN sheet result in astrong polarization in the plane of the sheet, which dependsnonanalytically on the wave vector of the corrugations.13 h-BNsheet has a nonlinear elastic deformation up to an ultimatestrength, followed by a strain softening to failure.14,15 More-over, the band gap of boron nitride nanotubes can be reducedby a transverse electric eld due to a mixing of states within thehighest occupied molecular orbital and the lowest unoccupiedmolecular orbital.1619 The reduction in the band gap due touniaxial strain results in tunneling magnetoresistance ratio,which increases linearly with applied strain.20 Here we proposean alternative approach for electron hole localization based on atunable parameter, that is, inhomogeneous strain.Development of nanosensors of (dierent) gases is to a great

extent related to the response to both the morphology andthe surface states of the material. Single-wall carbon nanotubes(SWNTs) can act as a chemical sensor for sensing gaseousmolecules such as NO2 or NH3, where the electrical resistanceof a semiconducting SWNT is found to dramatically increase or

decrease.2124 Here we study the eect of strain on the ad-sorption mechanism and propose a new and tunable way tocontrol the adsorption of a gas.Using density functional theory (DFT) calculations, we show

a spatial separation of the highest occupied and lowest un-occupied molecular orbitals (i.e., HOMO and LUMO) inresponse to a triaxial in-plane strain. The result is in agreementwith the predictions from piezoelectricity theory. Consequently,the binding energy of an external polar molecule over the strainedsample is considerably enhanced. Depending on the appliedtriaxial strain on the zigzag edges with boron (nitrogen), termi-nation the HOMO (LUMO) is conned in the central portionof the ake. This study opens a new avenue in the eld of strainengineering of a monolayer of h-BN in terms of tunable spatiallocalization of the frontier orbitals. (It controls and enhanceschemical reaction.) In recent experiments the edge structure ofgraphitic nanostructures was successfully controlled25 and well-dened (e.g., hexagonal shape); graphene akes with zigzagedges were observed.26 Consequently, the proposed experimentalset up is realistic; therefore, we expect that the calculated eectswill be measurable on micrometer size samples employing experi-mental realized controlled edge chirality.2527 A simple exper-imental setup for creating triaxial strain was proposed in ref 2.The paper is organized as follows. In Section II, we present

our theoretical approach for triaxial strain and correspond-ing piezoelectricity. In Section III, we present the moleculardynamics (MD) simulation and density functional calculationmethods. Then, in Section IV, we give and discuss our results.We conclude the paper in Section V.

Received: March 1, 2013Revised: June 2, 2013Published: June 3, 2013

Article

pubs.acs.org/JPCC

2013 American Chemical Society 13261 dx.doi.org/10.1021/jp402122c | J. Phys. Chem. C 2013, 117, 1326113267

II. THEORETICAL MODELFigure 1a shows a hexagonal h-BN ake with zigzag edgespassivated by hydrogen. The distortion of a hexagonal boron-nitride ake subjected to triaxial strain along three equivalentcrystallographic directions is shown schematically in Figure 1b. Theoriginal shape is shown by the dotted-red circles, and the deformedshape is shown by the blue-solid curves. In polar coordinates (r,),the applied triaxial strain results in a displacement vector2 u =(ur,u) = Cr

2(sin(3), cos(3)), where C is a constant determiningthe strength of the applied strain and has dimension of inverselength. Notice that the r2 dependence in u ensures that the appliedtriaxial strain can also be realized on an innite or macroscopicsheet. In the following, we will rst present a simple analyticaltheory that agrees qualitatively with our numerical DFT results.Linear elasticity theory for an isotropic material leads to the

stressstrain relation, that is, jk = jku + 2 jk, where and are the Lame parameters that determine the stiness ofthe material. If we substitute u in the latter equation, the com-ponents of the stress tensor in polar coordinates are written as

=

r Cr( , ) 4

sin(3 )

cos(3 )

cos(3 )

sin(3 )

Here it is more convenient to use the components of the stresstensor in Cartesian coordinates where the y axis is taken alongthe arm-chair direction and the x axis is taken along the zigzagdirection. The edges under strain can have B (called BN system)or N (called NB system) atoms (e.g., in Figure 1a, the strain isapplied on B atom edges; that is the BN system is stretchedalong the red arrows). Note that the three strained edges (or freeedges) have only one type of atoms. We consider here the caseof strained B edges, that is, the BN ake of Figure 1.Using the product (x,y) = 9(r,) T9 , where 9 is the

rotation matrix about the z axis. The stress tensor in Cartesiancoordinates can be rewritten as

=

x y C

y xx y( , ) 4

An elastic in-plane deformation of the h-BN ake lowers itslattice symmetry, redistributes the valence charges in terms ofshifting and bonds, and produces a nonzero polarization.Using linear piezoelectricity theory, the induced polarizationdue to the applied strain can be written as Pi = di,jkjk, where d isthe third-rank piezoelectricity tensor that has, in general (in twodimensions), eight elements where the indices (i,j,k) can bex and y. The 3m symmetry of the h-BN sheet results in onlyone independent element for the piezoelectricity tensor, d0 =dy,yy. The tensor is invariant under a rotation angle of 2/3about the z axis, which yields the following symmetry relations:dy,yy = dy,xx = dx,yx = dx,xy. Substituting (x,y) in eq 1 resultsin the local induced dipoles:

= = P d mCx P d mCy8 , 8x y0 0 (1)Note that the local dipoles are directed radially inward, that

is, P = 8d0Crer with magnitude 8d0C per unit of radial dis-tance. For a disk with diameter D = 2R and using C = /D, thetotal induced dipole moment is found to be zero by integratingover the disk from 0 to

= = +P d R P d R2 sin( ), 2 cos( )xT yT0 0 (2)where = 2; that is, Px

T (2) = PyT(2) = 0. Notice that Pi

T

() = PiT (). The local P results in a surface charge density

(p = P) and a boundary charge density (p = Per), hencethe corresponding electrostatic potential (ESP) P(x ) that is pro-portional to ((p ds)/(|x x |)) + ((p dl)/(|x x |)) can bewritten in terms of Bessel functions of the second kind and resultsin a radially decreasing potential. For a disk with radius R, therst integral is taken over the disk surface, and the second istaken over its perimeter. In Figure 2, we show P(x ) in xyplane at height z = 2 104R above a circular ake with radiusR. These results are in qualitative agreement with the ESP)obtained from our DFT results shown in Figure 4a,d. Noticethat for uniaxial strain, for example, u = (x,0), and shear strain,for example, u = (y,x), the used formalism gives P = (Px,0) =( d0,0) and P = (0,Py) = (0,2 d0), respectively, which are inagreement with the DFT results of ref 12. It is important to

Figure 1. (a) Hexagonal ake of BN passivated by H atoms (white balls). (b) Schematic representation of the distorted hexagonal boron nitride akeby the applied triaxial strain. The red curves represent the original shape and the blue curves indicate the distorted ake. The ake is stretched alongthe three crystallographic directions that are represented by the three red vectors. The NB system is obtained by interchanging B and N atoms orequivalently by rotating (a) and the central hexagon in (b) by an angle /3; see Figure 3df.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp402122c | J. Phys. Chem. C 2013, 117, 132611326713262

note that the above model is size-independent and is alsovalid for an innitely large h-BN ake. Applying strain on theN-edges (NB-system) is equivalent to the transformation + /3 in u, which yields uNB = Cr2(sin (3), cos(3)).Rewriting the above theory for the latter displacement vectorresults in P = 8d0Crer, which has the opposite direction of thedipole moment of BN. This is in agreement with our DFTresults shown in Figure 4df for NB. (We will discuss our DFTresults later.) We conclude that for an innite hexagonal akewith zigzag edges we have the opposite localization scheme forHOMO and LUMO depending on whether strain is applied onthe N edges or the B edges.

III. COMPUTATIONAL DETAILSFirst, to study the stress distribution28 on a large scale h-BNake, we performed classical MD simulation at T = 300 K for asystem with 2400 atoms. We used a modied Terso potential(which is dened in the LAMMPS package29,30) using theparameters proposed by Sevik et al.31,32 for an h-BN sheet.Figure 3 shows four snapshots of our MD simulation for a h-BN

ake with three of the zigzag edges subject to triaxial strain, asshown by the arrows. Notice that the corners are always underhigher stress (red color), while the central atoms are subject toa reduced stress (blue color). (This results in a high pseudo-magnetic eld at the corners in the case of graphene.2)To study the electronic behavior of the akes in response to

triaxial strain, we employ DFT as implemented in the Gaussian(G09) package.33 The electronic wave function is expandedusing the 6-31G* Gaussian type basis set, and the exchange-correlation is treated using the hybrid functional B3LYP. The

self-consistency loop iterates until the change in the totalenergy is

stress become polarized locally with dierent orientation whilethe total dipole moment is zero, (iii) the polarization and theESP distribution in the system correlate, and (iv) all edges(both BN and NB) are passivated by hydrogens and because ofthe dierence of electronegativity of H, B, and N the results willbe dierent for unsaturated ake edges.Localized States and Electrostatic Potential. The ESP

and highest occupied and lowest unoccupied molecular orbitalsobtained from the DFT calculations for a hexagonal shapedh-BN ake consisting of 252 atoms (d0 = 1.35 nm) are shownin Figure 4 for ve dierent values of = /d0. When the akeis stretched at the B edges (i.e., BN system, Figure 4ac), boththe region with higher ESP and the LUMO are localized in thecentral part. When strain is applied on the N edges (i.e., NBsystem, Figure 4df), the region with lower ESP and theHOMO both is localized again in the center. In the unstrained( = 0) akes the LUMO is localized on the N edges, while theHOMO is not concentrated on the B edges, which is dierentfrom the case of rectangular ribbons.16,34 For a rectangularribbon the N atoms absorb electrons from H and thereforethe HOMO is localized on the N atoms, while in the B edgesthe H atoms gain electronic charge from those B atoms and theB atoms lose their electrons; consequently, the LUMO is onthe B atoms. In the hexagonal unstrained akes, the N atomsabsorb electrons and the HOMO is also on the N atoms, butthe LUMO is only on the B atoms in the midpoint of the Bedge, while the B atoms situated at the corners of the B edge donot contribute in the LUMO. The reason is that the corner Batoms recover their lost electrons from their N neighbors at thesame corner. In Figure 5a, the Mulliken charge change whenapplying 10% strain is shown for a BN ake with 432 atoms. Itis seen that the B atoms transfer electrons to N atoms, whichmake the system highly polarized. The charge distribution revealsthe corresponding triaxial applied stress shown in Figure 1b.The larger , the more localized the HOMO (LUMO) in the

center of the NB (BN) ake. This is due to the appearance oflonger bond lengths (aBN). The longer the BN bond length,the less the 2pz hybridization. In Figure 5b, the distribution ofaBN for a strained BN ake ( = 10%) is shown. (Bonds longerthan 1.6 are not shown for clarity.) This bond length distribu-tion shows the weakening of the covalent bond perpendicularto the stressed edges. One can connect this pattern to thoseshown in Figure 4ac. The longer the bonds perpendicular to

the B (N) edge in a BN (NB) ake, the larger the inward(outward) dipole moment.The gradient in ESP from the edges into the center increases

with increasing . We also performed DFT calculations to studysimilar eects in a graphene ake with the same size, but nosuch localization/polarization eects were found.To ensure that the observed eect is independent of the ake

size, we performed calculations35,36 for a larger ake with 2520atoms (d0 = 4.6 nm) and found similar localized frontierorbitals, as shown in Figure 6. The reason for the specic spatial

localization of the frontier orbitals is the rehybridization ofthe electronic orbitals due to the new position of the atoms.The induced inhomogeneous strain changes the bonds non-uniformly and yields local dipoles that are mainly orientedradially. Note that in general nite akes or nanoribbons of h-BN might be polarized due to their nite size.16 However, herethe nite ake has zero total dipole moment because of thesymmetry of the ake even when it is subject to triaxial stain.Strain Energy and Gap Variation. Figure 7a shows the

variation of the strain energy as a function of the applied strain,which exhibits a quadratic behavior as expected from Hookeslaw. Figure 7b shows the variation of the HOMOLUMOenergy gap with . The density of states (DOS) spectra forstrained ( = 10%) and unstrained BN akes are shown inFigure 5c. By applying the strain, the HOMOLUMO gapdecreases by 2 eV, and new peaks appear above the LUMO.The decreasing of the gap and modication of the DOS prolewith increasing strain is attributed to the spatial localization of

Figure 5. (a) Change in the Mulliken charges induced by applying strain ( = 10%) to the BN ake. Circle radius corresponds to the chargedierence between strained and unstrained BN akes. (b) Bond length, that is, aBN, distribution in a strained BN ake ( = 10%). For clarity, bondslonger than 1.6 are not shown. (c) DOS spectra of strained (10%) and unstrained BN akes.

Figure 6. HOMO of NB (left) and LUMO of BN (right) akes with2520 atoms (d0 = 4.6 nm) subjected to the strain = 0.15. Notice thatfor this lager system we can apply larger strain as compared with thesmaller system shown in Figure 4.



the HOMO and LUMO on regions with dierent ESP. Forexample, applying strain on the BN ake localizes the LUMO atthe center of the ake, where the electrostatic energy of anelectron is lower because of high ESP. Similarly, applying strainon the NB ake increases its HOMO energy level because itlocalizes the HOMO at the center, where ESP is lower in thiscase. For larger strains the energy dierence of the localizedstates at the center and the edges becomes larger, resulting in asmaller energy dierence of the frontier orbitals, that is, smallergap. The dierent dependence of the gap on the strain for BNand NB (see Figure 7b) is a consequence of the distributedHOMO along all of the edges and mostly the corners of thestrained BN system and the fact that the LUMO is localized atthe B edges in the NB system. A similar eect has been seen byapplying an external electric eld to nanoribbons.16 Note thatthe strain-induced change in the conductance of graphene waspreviously investigated,2,37 but at present no similar study isavailable yet for h-BN.Application as a Gas Nanosensor. Two alternative methods

to realize this kind of triaxial stretching of 2D materials1,2 havebeen recently proposed. It was reported experimentally1 thatnanobubbles of graphene grown on a Pt(111) surface sucevery high inhomogeneous triaxial strain, which signicantlychanges the electronic properties of graphene resulting in, forexample, pseudomagnetic elds larger than 300 T. The follow-ing experimental setup might also be possible: Fixing the 2D layer(here h-BN) on a triangular-shaped trench and subsequently

injecting a high-pressure gas into the hole will stretch the 2Dlayer and exert a triaxial inhomogeneous strain on the ake.The controllable localizing of the frontier orbitals in the

central part of the h-BN ake is important for nanosensoringtechnological applications, for example, for ltering gasadsorbates. The key idea is to control the binding energy of amolecule, namely

= + E E E E( ) /b molecule flake molecule flake (3)via the applied strain. Here Emolecule and Eflake are the energies ofthe pristine molecule and ake, respectively, while Emolecule/flakeis the energy of the molecule over the examined ake. As anexample, we study here the adsorption of an ammonia moleculeas a function of the strain on the h-BN ake. We put the NH3molecule in the central region of the stretched ake and relaxthe system under external triaxial strain. Starting from dierentorientations, we found the minimum energy when the moleculeis adsorbed onto a B atom in the middle, as shown in Figure8a,b. More importantly, as seen in Figure 8c, the binding energystrongly depends on the strain such that by applying a strain of10% the binding energy is almost doubled. One notes that = 0indeed gives the minimal Eb. We performed similar calculationswhen the ake is triaxially compressed and found that thebinding energy also increases.NH3 has one lone pair of electrons on the nitrogen atom,

making it an electron donor. Therefore, the molecule ispositively charged when chemically bonded to the B atom.Figure 9a depicts the electron density mapped on the planecontaining this BN bond when the ake is not stretched. Theimpact of strain on the redistribution of the electronic charge isseen in Figure 9b, and it predicts a stronger covalent bondingbetween the molecule and the ake. Consistently, the totalMulliken charge on NH3 increases monotonically from 0.19 efor the unstrained ake to 0.23 e when = 0.1. In the sametime, the binding energy increases from 0.41 to 0.82 eV, asshown in Figure 8c. Triaxally stretching the ake also quenchesits buckling due to the interaction with the adsorbed moleculesuch that the out-of-plane height of the B atom under theammonia molecule is 0.68 and 0.34 for zero and = 0.1strains, respectively. Finally, the length of the chemical bondbetween the N atom of NH3 and the B atom of the ake also

Figure 8. Top (a) and side (b) view of the adsorbed NH3 on a h-BN hexagonal ake. (c) Variation of the binding energy and Mulliken charge on theNH3 molecule (inset) versus the strain.

Figure 7. (a) Strain energy of the hexagonal -shaped BN and NBakes as a function of the strain parameter, that is, . (b) Variation ofthe energy gap with . Each ake consists of 252 atoms.



decreases monotonically form 1.83 to 1.75 between thementioned strains. Notice that the binding energy of the NH3molecule is almost the same on any B atom in the region aroundthe center of the BN system where the LUMO is extended.The enhancement of the adsorption of NH3 on the BN ake

by strain can be explained in the framework of the so-calledfrontier molecular orbitals theory,38 which implies that there isa higher tendency for adsorption of such a molecule onto thosesites of the ake where the LUMO is localized, that is, thecentral part. However, for the NB ake the central part has nocontribution to the LUMO, and we found that the bindingenergy is more than two times smaller than for the BN ake.

V. CONCLUSIONS

In summary, by using DFT calculations we showed that theoccupied (unoccupied) orbitals of a hexagonal-shaped h-BNake can be localized in the center of the ake by applyingtriaxial strain on the N(B) atoms at the edges of the sample.The h-BN ake is locally polarized, but the net polarization iszero. As an example, we investigated the adsorption of ammoniaand found that its adsorption on the B-edges-stretched BN akeis more likely than that on the N-edges-stretched ake. This is aconsequence of the specic spatial localization of the frontierorbitals. This particular kind of localization of the frontierorbitals might have technological applications for the designof piezoelectric and nanosensor devices.

AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Tel: +3232653661.NotesThe authors declare no competing nancial interest.

ACKNOWLEDGMENTSThis work was supported by the EU-Marie Curie IIF postdocFellowship/299855 (for M.N.-A.), the ESF EuroGRAPHENEproject CONGRAN, the Flemish Science Foundation (FWO-Vl),and the Methusalem Funding of the Flemish government. A.S.would like to thank the Universiteit Antwerpen for its hospitality.

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Boron Nitride Monolayer- A Strain-Tunable Nanosensor