Electronic structure of graphene functionalized with boron and nitrogen

0.75 MB·English

by  Magdalena Woinska

Electronic structure of graphene functionalized with boron and nitrogen
Magdalena Woi´nska
Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, PL-02-093 Warszawa,
Poland
Karolina Z. Milowskaa) and Jacek A. Majewski
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Hoz˙a 69, PL-00-681 Warszawa,
Poland
(Dated: 18 January 2013)
Wepresentatheoreticalstudyofthestructuralandelectronicpropertiesofgraphenemonolayerfunctionalized
3
1 with boron and nitrogen atoms substituting carbon atoms. Our study is based on the ab initio calculations
0 in the framework of the density functional theory. We calculate the binding energies of the functionalized
2 systems, changes in the morphology caused by functionalization, and further the band gap energy as a
n function ofthe concentrationof dopants. Moreover,we address the problemof possible clustering of dopants
a at a given concentration. We define the clustering parameter to quantify the dependence of the properties
J of the functionalized systems on the distribution of B/N atoms. We show that clustering of B/N atoms in

7 graphene is energetically unfavorable in comparison to the homogenous distribution of dopants. For most of
1 the structures, we observe a nonzero energy gap that is only slightly dependent on the concentration of the

substituent atoms.
]
i Keywords: functionalized graphene, boron and nitrogen, density functional theory, energy band gap
c
s
-
l
r I. INTRODUCTION II. CALCULATION DETAILS
t
m
. Graphene,atwo-dimensionalmonolayerformedoutof Our studies of functionalized graphene layer are
at sp2 hybridizated carbon atoms ordered in the hexago- based on ab initio calculations within the framework of
m nal lattice, is a material with unique properties. Due the spin polarized denstity functional theory (DFT)8,9.
- to the hexagonal symmetry, its valence and conduction Generalized Gradient Approximation of the exchange-
d bandswithlineardispersioncrossatthesocalledKpoint correlationfunctionalinPerdew-Burke-Ernzerhof(PBE)
n
anddeterminesemimetalliccharacterofgrapheneandits parametrization has been applied10. Calculations with
o
extremely high electron mobility.1 This, in connection periodic boundary conditions have been performed us-
c
[ with excellent mechanical properties, renders graphene ing Siesta package11,12. Valence electronshavebeen rep-

anidealcandidateforapplicationsinflexibleelectronics. resented with double zeta basis sets of orbitals local-
1
However,the ability of generating controllable band gap ized onatoms; with polarizationfunctions also included.
v
is a prerequisite for effective applications of graphene in The influence of core electrons has been covered within
6
5 transistor based electronic devices. Therefore, an effec- pseudopotential formalism. Norm-conserving Troullier-
9 tive functionalization that would open the zero energy Martins nonlocal pseudopotentials13 used in this study
3 band gap in pristine graphene without significant de- have been cast into the Kleinman-Bylander14 separable
1. terioration of the remaining advantageous properties is form. The energy cut-off determining the density of the
0 searchedfor, and practicallyany thinkable wayof reach- utilized real space grid has been set to 800 Ry.The Bril-
3 ing this goal is currently investigated. louinzonehasbeensampledinthe5x5x1Mokhorst-Park
1 Thereexistthreegeneralmethodsofopeningtheband scheme. Forthebandstructureanddensityofstatescal-
v: gapofgraphene: applicationofexternalelectricfield,us- culations k-sampling changed to 15x15x1 scheme. Cal-
i ageofgraphenenanoribbons,andfunctionalization. One culations were performed within the supercell geome-
X
ofthepracticalrealizationsofthethirdtechniqueconsid- try with graphene layers separated by a distance large
ar eredinthisworkisdopingthegraphenelayerwithboron enough to eliminate any interactions. Structural opti-
andnitrogen2–6. Theseelements,standingnearbycarbon mization has been conducted using the conjugate gra-
intheperiodictable,shouldactaselectronacceptors(B) dient algorithm to achieve residual forces acting on the
anddonors(N),allowingforfabricationofcontemporary atoms lower than 0.001 eV/˚A.
devices in the manner of the CMOS silicon technology7. Wehaveperformedcalculationsfor5x5supercellscon-
Here, we report new results of our theoretical studies of taining 25graphene’sprimitive unit cells (i.e., consisting
electronic properties of graphene doped with boron and of 50 atoms). Such supercell has been chosenin orderto
nitrogen atoms. examinewide rangeofdopantconcentrationsandavari-
etyofpossibledistributionsofthesubstituentatoms,and
alsotoavoidbandgapreductioncausedbycertainsuper-
cell symmetries15. In the described graphene supercell,
one to ten B/N atoms have been introduced (leading to
a)Electronicmail: [email protected] thecorrespondingconcentrationof2-20%). Inthecaseof
2
twosubstituentatomsinasupercellallthe11symmetri- III. RESULTS AND DISCUSSION
callynonequivalentconfigurationsoftheatomshavebeen
examined. In the remaining cases 12 different randomly
We start the presentation of results by considering
chosenconfigurationshavebeentakeninto account. Op-
structural properties of functionalized graphene mono-
timized geometries and band structures, as well as re-
layers. The geometries of optimized structures for two
lated properties - energy band gaps, binding energies, boron (c=0.97) and nitrogen (c=0.99) atoms in 5x5
and shifts of the Fermi level with respect to the top of
graphenesupercell,thecortespondingelectrondensity,as
the valence bandand bottomof the conduction bandfor
well as bond lengths and angles between the substituent
B and N dopants, respectively, have been also obtained
atom and carbon atoms are presented in Fig. 1(a) and
for all the considered concentrations and symmetrically
(b).
nonequivalent configurations of substituent atoms. All
Boron atoms in comparison to nitrogen atoms have a
the values, for each concentrations, have been averaged
greaterinfluence onthe geometryofthe dopedgraphene
over the investigated configurations and compared with
layer, mostly due to the fact that the covalent radius of
relevant results for B/N substitution.
boronislargerthanthatofacarbonatom,whereasnitro-
The binding energy per atom, which has been calcu-
genhasthecovalentradiussimilartocarbon. Itturnsout
lated according to the formula:
that the graphene monolayer functionalized with boron
atomsisnolongerflatbecauseBatomsstickoutfromthe
50
1 surface. SimilarobservationwaspointedoutinRefs.2,3,6.
E = E − E , (1)
b/n 50 tot atom,α Analyzing isolines in Fig.1(a)and (b), one cansee re-
!
α=1
X gions of electron density depletion around the positions
is used as the measure of the stability of the systems of boron atoms, as well as an increase of electron den-
studied. E is total energy of functionalized graphene sity in the vicinity of nitrogenatoms. Substituent atoms
tot
and E is the total energy of the free atom of type influence only the electron density around those carbon
atom,α
α (i.e., C, N, or B). atoms with which they are linked by a chemical bond.
To quantify the effect of B/N atoms distribution over Electronic density around the second and further neigh-
the graphene lattice on the calculated properties of the bors remains unchanged.
dopedsystems,aspecialparametermeasuringthelevelof To measure stability of the considered structures, we
clustering (further called clustering parameter) of atoms have plotted, in Fig. 1(c), the dependence of the bind-
has been introduced. This parameter is, in general, lin- ing energy per atom on concentration of B/N atoms.
early proportionalto the sum of n-1 shortest nonequiva- Bothtypesofstructuresdonotsegregateafterthegeom-
lentdistancesbetweenB/Natoms(wherenisthenumber etryoptimizationandbindingenergiesaremorenegative,
ofB/Natomsinasupercell)anditisnormalizedtoreach for B-functionalized graphene than for N-functionalized
the value of -1 for maximal and 1 for minimal clustering one. Therefore the boron doped structures are more
in a system with geometry of pristine graphene. The stable and the differences in binding energies between
described clustering parameter is given by the following B- and N-doped graphene increase with growing con-
mathematical formula: centration of dopants, from 0.02 eV up to 0.25 eV for
2% and 20% concentration, respectively. Our observa-
2 − − tions are in agreement with previous theoretical work16
c= max min, (2)
− which shows that substitution with boron atoms costs
P mPax mPin
less energy than substitution with nitrogen atoms. Mo-
where is a sum ofPn-1 shoPrtest nonequivalent dis- rover, boron doped monolayer graphene and nitrogen
tances between B or N atoms in the system measured doped monolayer graphene were already sythesized by
after gePometry optimization, and are max- CVD method3,7,17 and are stable enough for studying
max min
imal and minimal value that reaches for a given n their physical and chemical properties.
P P
for ideal hexagonal lattice. We have assumed that both Toaccountfortheinfluenceofthe distributionofB/N
P
substituent atoms, B and N, create bonds among them- atoms in a supercell on stability of the functionalized
selvesoneanotherequalorgreaterthanCatomsinideal graphene,theclusteringparameterchasbeencalculated
hexagonal lattice and change the symmetry. Defined in accordingto the formula givenby Eq. 2 for eachconcen-
this way, the clustering parameter for two dopants in trationofdopants. Exemplaryresultsfor12%concentra-
the supercell (n=2) is the most negative, if B/N atoms tionbothforboronandnitrogen,areshowninFig.2. As
are linked by a chemical bond, and the most positive if one can see, from the (dotted) lines fitted to each case,
they are the furthest apart as possible for a given su- the binding energy barely dependends on the clustering
percell. For example for the case of two N atoms, in level. Fornitrogen,aswellasforboron,theconfiguration
considered 5x5 supercell, in which the the shortest dis- ofdopantsbeingclosertoitsownspeciesislessenergeti-
tanceinminimalclusteringis7.143˚A( )aftergeometry cally preferablethan being surroundedandseparatedby
optimization, the minimal andmaximaldistance in pris- carbon atoms. To have a better insight into this prob-
tine graphene are equal to 1.433 ˚A ( P ) and 7.165 ˚A lem, further calculations including more symmetrically
min
( ), respectively; the clustering parameter c is 0.99. nonequivalent realizations of each concentration should
max P
P
3
FIG.2. Thedependenceof bindingenergyperatom on clus-
tering parameter for 12% concentration of B and N atoms.
ing of the band gap is observed in case of the majority
of configurations, with maximal gap amounting to al-
most 0.5 eV for B- and 0.6 eV for N-doping. The mean
valueofthebandgapslightlyincreaseswiththe growing
number of substituent atoms. This trend is more pro-
nounced for lower concentrations, where the band gaps
range from about 0.1 eV for two atoms per supercell to
nearly 0.25 eV for 7-10 atoms. The average band gap
saturates slightly for higher concentrations. In the case
of six B/N atoms in the supercell, a decrease in an av-
erage energy gap width by over 0.5 eV can be noticed
in comparisonwith five B/N atoms. It canindicate that
averagingover12randomconfigurationsmaynotbesuf-
FIG. 1. The optimized structure and electron density de-
ficient to eliminate the strong influence of some particu-
picted for clustering parameter close to 1for two B/N atoms
larconfigurationsonthe averagevalues of the band gap.
in 5x5 graphene supercell. Depletion of electron density in
The results of our calculations signalize a limited possi-
the vicinity of B atoms (a) and its higher values around the
bilityofbandgapengineeringbymeansofincreasingthe
position of N atoms (b) can be observed. Bond lengths and
angles between B/N and C atoms are also denoted for each concentration of functionalizing species.
case. (c)Thedependenceofthemaximum,minimumandav-
eragedbindingenergyperatom(withstandarddeviations)for
functionalized graphene on theconcentration of B/N atoms.
IV. CONCLUSIONS
In this paper we report the results of ab initio calcu-
be supportive.
lations for graphene functionalized with boron and ni-
? ?
FermilevelshiftwithrespecttoVBT /CBB result- trogen atoms. We investigate structures with one to
ingfromB/Nfunctionalizationandloss/gainofoneelec- ten borons or nitrogens in a graphene supercell for vari-
tron per substituent atom is depicted in Fig. 3. Similar ous symmetrically nonequivalent configurations. All the
observation, but for smaller concentrations was denoted structures are stable with slightly more negative binding
in Refs.4,5,18. energies in the case of B-doping. Doping with B atoms
Within each of the considered concentrations of B/N introduces more changes in the morphology of the func-
atoms, we have performed electronic structure calcula- tionalized structures than doping with N atoms. Both
tions for different configurations of dopants correspond- types of dopants prefer to be homogenously distributed
ing with this concentration. In the next step, we have over the lattice rather than clustered. We conclude that
performed averaging of the calculated band gaps. The the effects of the band gap oppening in the boron and
average band gaps for N-doped graphene together with nitrogen functionalized graphene are qualitatively and
the maximal and minimal values of the band gaps are quantitatively very similar. However, the magnitude of
presented in Fig. 4. For B-doped graphene, the picture thebandgapcouldbestronglydependentonaparticular
is analogous and is therefore not presented here. Open- configurationofdopants. Toclarifythisissue,theroleof
4
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