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parameters for our calculations have been obtained from a first - principle approach , as we detail in the following .    as an initial step , first - principle density functional theory ( dft ) calculations were undertaken for a single substitutional boron impurity in two - dimensional ( 2d ) graphene and in gnrs ,  @xcite by means of the siesta code ,  @xcite within the local density approximation and using a double-@xmath4 basis set . following the methodology in refs . @xcite , the onsite energies of the @xmath5 orbitals for the ( bulk ) 2d case were extracted . their variation with the distance from the boron atom is shown in fig . [ fig2 ] ( inset ) . the boron atom acts as an electron acceptor : the resulting impurity potential is repulsive for electrons and the screening length is found to be of the order of a few angstroms ( the screening length  @xcite is defined as the distance from the charged impurity at which the surrounding mobile charges , rearranging under the electrostatic action of the impurity , reduce its potential by a factor equal to euler s number @xmath6 ) . the transport properties of `` quasi - metallic '' and semiconducting armchair gnrs ( following ref . @xcite , we refer to an armchair gnr with @xmath7 dimers contained in its unit cell as an `` n - agnr '' ) with a single boron impurity at different sites across the ribbon width are then computed , using the full _ ab initio _ hamiltonian , in the landauer - bttiker framework . @xcite boron impurities actually induce a strong hole backscattering , with much weaker effect on the electron side . a similar result was already obtained in boron - doped carbon nanotubes ,  @xcite and attributed to strong backscattering at the resonance energies of the quasibound states localized around the boron impurity . due to the lack of the rotational symmetry present in carbon nanotubes , in gnrs the energy of the conductance dip on the hole side depends on the position of the impurity with respect to the ribbon edge ( as illustrated in fig . [ fig2 ] and fig . [ fig3 ] ) .    in ref . @xcite it has been shown that these _ ab initio _ results can be fairly well reproduced with a simpler tight - binding model with a single orbital per carbon and boron atom . for each atom , the onsite energy is taken as the impurity potential extracted from the _ ab initio _ calculation . the onsite energy of the boron atom is the only parameter that has to be adjusted in order to achieve the best match between tight - binding and _ ab initio _ transmission profiles . the success of such a simple tight - binding model in describing boron impurities originates from the preservation of the @xmath8 hybridization of graphene in the presence of substitutional boron .    by using this tight - binding model , transport studies in large armchair gnrs with a random distribution of boron atoms , with concentrations between @xmath9% and @xmath10% , have been performed in ref . the addition of the transmission dips induced by all impurities leads to a _ mobility gap _ in the valence band , _ i.e. _ an energy interval where conductance is nearly suppressed by scattering , while transport in the conduction band is preserved ( the opposite behavior would be found in the case of nitrogen doping ) . this occurs for semiconducting as well as for `` quasi - metallic '' gnrs , independently of ribbon width , as long as the potential can be assumed to be constant along the channel . the mobility gap increases with boron concentration and ribbon length . @xcite suggested a possible exploitation of this phenomenon to obtain field - effect transistors ( fet ) with wide gnrs ( @xmath11 nm ) , within the reach of conventional lithography . the absence of a significant bandgap in these ribbons could be compensated for by the mobility gap . however , the above mentioned study has been performed for ribbons without any gate - induced charge in the channel , since the impurity potential considered was the one extracted directly from an _ ab initio _ calculation without taking into account the effects of screening when a gate is applied .     and @xmath12 directions , to make the drawing clearer ) . ]    in order to simulate the behavior of a realistic transistor structure , we need to perform a self - consistent calculation to include the effects of an applied gate voltage and of a non - zero drain - source bias on the charge density . this can be done , at a reasonable level of computational complexity , with a tight - binding model set up with parameters properly extracted from the _ ab initio _ results . however , differently from ref . @xcite , the impurity potential obtained from _ ab initio _ approaches can not be directly used in a self - consistent simulation , since it would be overscreened , as a result of the poisson / schrdinger iterations . the approach chosen here is to mimic dft self - consistency with the tight - binding model and a proper distribution of fixed charges ; then the final impurity potential arises from the tight - binding poisson / schrdinger self - consistency . in particular , as we will detail in the methods section , the _ ab initio _ results can be reproduced considering a fixed charge @xmath13 ( where @xmath6 is the elementary charge ) in correspondence of each carbon atom , and using the following tight - binding representation : null onsite energies are considered in correspondence of all atoms , while , following ref . @xcite , the hopping parameter is equal to @xmath14 ev for all the pairs of nearest neighbor atoms , with the exception of the edge dimers , for which a value of @xmath15 is used instead .    to validate this approach , a self - consistent poisson / schrdinger calculation ( described in the methods section ) is performed for an isolated graphene layer with a single impurity , as in the _ ab initio _ calculation . as shown in fig . [ fig2 ] ( inset ) , the obtained self - consistent potential around the impurity is very close to the _ ab initio _ result . also the _ ab initio _ transmission spectra are accurately reproduced for all positions of the impurity , keeping the boron onsite energy equal to zero and with no further parameter adjustment . transmission spectra comparisons are shown in fig . [ fig2 ] .     and @xmath16 , where @xmath17   is the hexagonal lattice constant . the bold lines represent the results with our self - consistent tight - binding model . the thin dotted line represents the _ ab initio _ results . inset : comparison between the results for the impurity potential in 2d graphene obtained with self - consistent tight - binding and _ ab initio _ approaches . ]    before performing full negf calculations , the effect of a gate with a nonzero applied voltage was analyzed on short ribbons with a single impurity . the ribbon is surrounded by a double gate with a dielectric thickness of 1 nm , as shown in fig .  [ fig1 ] . the source - drain voltage and the fermi level are set to @xmath18 . the charge and potential on the ribbon adjust self - consistently as a function of the gate potential @xmath19 . first , the calculation was performed at @xmath20 with vacuum chosen as gate dielectric . the obtained potential is very close to the result discussed above for the neutral isolated ribbon . this gate configuration does not induce any significant additional screening . a more realistic model is obtained by considering a silicon dioxide dielectric between the gate plates and the ribbon , with relative dielectric permittivity @xmath21 . however , thin vacuum layers are kept just below and above the ribbon , with a thickness of @xmath22 nm , of the order of the calculated graphene / sio@xmath23 distance . @xcite the impurity potentials and the corresponding transmission spectra are shown in fig . [ fig3 ] , for @xmath20 and @xmath24 v. screening is enhanced at a negative gate voltage , due to the accumulation of holes in the ribbon . this has a strong effect on transmission : the conductance dip is less pronounced and is shifted in energy , which could compromise the presence of a clear mobility gap in a transistor configuration . it was verified that the effect of the gates is much larger than that of the thin air layers , in terms of the global electrostatics , and , in particular , of the screening . this is the reason why in the runs for the evaluation of the transistor characteristics we will not introduce the air layers , that would make convergence of the poisson - schrdinger iterations much slower .     from the edge . the calculation was performed with silicon dioxide as gate dielectric and a thin vacuum layer surrounding the graphene sheet . inset : influence of the gate voltage on the impurity potential . ]    to assess the performance of complete boron - doped graphene transistors biased in a typical operating point , we have used the open - source code nanotcad vides . @xcite in this code , the 3d poisson equation is solved self - consistently with the schrdinger equation ( with open - boundary conditions ) , within the non - equilibrium green s function ( negf ) formalism . @xcite schottky contacts have been modeled at the gnr ends with the phenomenological approach described in ref . @xcite , including self - energies that mimic metallic contacts . the considered device structure is reported in the inset of fig . the device is a double - gate fet and the channel is a 32-agnr ( 3.81  nm wide ) embedded in sio@xmath23 dielectric . this is consistent with typical nanofabrication techniques , in which the dielectric is deposited after the creation of the drain and source contacts . top and bottom field oxides are 1  nm thick , and the channel length is equal to 20  nm . in fig . [ fig4 ] , we show the transfer characteristics of the gnr - fet for a drain - source voltage @xmath25 = 0.1  v , for different boron doping concentrations ( defined as the ratio of the number of boron atoms to the total number of atoms in the channel ) . dopant atoms are randomly placed along the channel . results in fig . [ fig4 ] refer to a single distribution of dopants .    ) , for a given random distribution of the dopant atoms . the transfer characteristic for the undoped device is also reported . ] as expected , transfer characteristics for the undoped device are symmetric with respect to @xmath26  v. as soon as some boron doping is considered , the p - branch of the @xmath27-@xmath28 curve is suppressed , as previously observed also in carbon nanotubes . @xcite the p - branch suppression increases as the doping concentration is increased . from these results , it appears that with the considered boron doping concentrations , while still not obtaining a sufficient @xmath29 ratio for logic applications  @xcite with the considered 32-agnr ( which , however , having a `` quasi - metallic '' behavior in the absence of doping , represents , in this regard , a worst - case scenario ) , a clear onset of unipolarity occurs . increasing boron doping , while further reducing the current in the p - branch ( due to holes ) , also leads to a degradation of the device performance above threshold .    in fig . [ fig5](a)-(b ) , we show the transfer characteristics for 23 different distributions of doping atoms along the channel , for the same doping concentrations as in fig . the thick solid lines correspond to the average transfer characteristics computed over the considered statistics of the doping distribution . as can be seen , different doping distributions lead to a large dispersion of the transfer characteristics , which could be reduced if several nanoribbon devices were operated in parallel ( as can be necessary in some cases in order to increase the on current ) . nevertheless , we remark that the electron - hole asymmetry is clearly developing with chemical doping , and , based on the results of ref . @xcite , it can be strengthened by increasing the gate length up to few hundreds of nanometers ( especially for the case with @xmath30 ) . indeed , longer channel lengths could result in cumulated contributions of multiple scattering effects and localization , which will even more inhomogeneously impact on transport characteristics ( as shown in equilibrium situations  @xcite ) . due to computational limitations , we are not reaching such channel lengths here . computational hurdles , in terms of difficulties in achieving self - consistence , also limit the doping level that can currently be simulated with our method to about 0.6% . thus , at present we can not handle the extremely high doping concentrations , of the order of 10% , that have been reached in a recent experiment  @xcite reporting unexpectedly large gap opening effects . in conclusion , by coupling a dft - based tight - binding parameterization ( validated _ via _ a multi - scale approach based on _ ab initio _ techniques ) with self - consistent negf quantum - mechanical transport simulations , we have found the onset of an electron / hole transport asymmetry and mobility gaps in boron - doped graphene nanoribbon transistors , confirming that chemical doping could serve as a way to shape the current - voltage characteristics of such devices . this is just a first step , because the achieved @xmath29 ratio , although for a worst - case condition , is still far too small for practical applications . there is however ample room for improvement and several different approaches could be used to selectively incorporate chemical entities into graphene , thus engineering separate chemically modified areas from a single graphene layer . a doping strategy could therefore be elaborated to implement pn junctions , logic gates and complex architectures directly patterned on the same underlying graphene layer . conventional state - of - the - art patterning methods , such as e - beam lithography , could be exploited to design superimposed material architectures ( with either metallic or other semiconducting materials ) onto the selectively doped and functionalized graphene - based substrates . although our transistor simulations have been performed for graphene nanoribbons with a width below 5  nm ( due to the otherwise prohibitive computational cost ) , we wish to point out that the scaling analysis detailed in refs . @xcite suggests that our main finding ( electron - hole transport asymmetry ) should be confirmed for ribbon widths above 10  nm , that is within the reach of conventional fabrication lithography techniques . finally , longer ribbon lengths and low temperature are also factors which are capable of widening the mobility gaps . the simulation approach is based on the observation that the dft results can be recovered performing a self - consistent poisson / schrdinger calculation , within the negf formalism , on the system , which is described using a tight - binding model and a proper distribution of fixed charges .    in detail , we found that , following this procedure , the tuning of a single parameter of the tight - binding model is sufficient to properly reproduce the _ ab initio _ impurity potential and transmission spectra . the method is inspired by what actually occurs in the dft calculation . the total charge of a carbon nucleus and of its core electrons is @xmath31 , while it is @xmath32 for boron . in the isolated atoms , this charge is compensated by @xmath33 valence electrons for carbon and @xmath34 valence electrons for boron . in graphene , @xmath34 electrons per atom ( including , in the case of doped graphene , the boron atoms ) tend to hybridize in a `` @xmath8 '' fashion , while the remaining valence electron on each carbon lies on the `` @xmath35 '' bonding subband formed by the @xmath5 orbitals . also the @xmath5 orbital on the boron atom is not empty , since it tends to attract an electron from the neighboring carbon atoms , and this determines the shape of the impurity potential shown in fig . [ fig2 ] . in the single @xmath5 orbital tight - binding approach , the `` @xmath8 '' valence electrons are included in the global ionic charge of the atoms , which becomes @xmath13 for carbon and @xmath18 for boron . therefore this is the net charge `` localized '' on each atom that we have to sum to the negative charge of the @xmath5 atomic orbitals considered in the simulation . as far as the tight - binding parameters are concerned , the onsite energy for carbon atoms is @xmath18 , while the hopping energy between nearest neighbors is set to @xmath36 ev . the hopping energy of edge dimers is adjusted to @xmath37 in order to reproduce the small bandgap obtained in dft for `` quasi - metallic '' n - agnrs ( @xmath38 , where @xmath39 is an integer ) . @xcite    only the onsite energy of boron may be further adjusted , performing a self - consistent poisson / schrdinger calculation for an isolated graphene ribbon with a single boron atom and comparing the obtained results with those deriving from the _ ab initio _ simulation of the same structure .    for the poisson equation the same boundary conditions are used in the _ ab initio _ and in the tight - binding calculations : neumann boundary conditions ( _ i.e. _ derivative of the potential energy , and thus electric field , constant and , in particular , zero ) in the longitudinal direction , at the ends of the nanoribbon , and periodic in the transverse direction , with a separation of 2  nm between the adjacent edges of nanoribbon replicas ( indeed , with a large enough separation between the replicas this is equivalent to a neumann boundary condition ) . the gate stack has been treated considering a constant permittivity , the one of silicon oxide , between the nanoribbon and each gate , where a dirichlet boundary condition is assumed . at each iteration , the eigenvalues of the hamiltonian are computed and the fermi level is adjusted to obtain charge neutrality . the local charge density is then calculated and the poisson equation is solved . the obtained electrostatic potential is subtracted from the onsite energies and the process is repeated until self - consistency is achieved . for all of the meshes tested in this work , it was possible to fit the _ ab initio _ data simply by adjusting the boron onsite energy . a typical choice was to spread the charge of each atom in a spatial region of half - width @xmath40 , the interatomic distance , and to choose a mesh interval of 0.1  nm , small enough to achieve convergence of the poisson solution . this charge repartition around each atom was defined using a smooth envelope function . in this case , the best fitting was obtained for a value of the boron onsite energy of about zero , thus substantially coincident with that for carbon . b.b . acknowledges financial support from the juan de la cierva program and the fis2008 - 05805 contract of the spanish micinn . acknowledges the fondation nanosciences _ via _ the rtra dispograph project . we acknowledge the use of the software vmd @xcite for graphical design . this work was partly funded by the european union under contract no . 215752 grand ( graphene - based nanoelectronic devices ) , by the french national research agency ( anr ) , in the framework of its 2009 program in nanosciences , nanotechnologies & nanosystems ( p3n2009 ) , through the nanosim - graphene project n@xmath41 anr-09-nano-016 - 01 , and by the italian ministry for the university and research ( miur ) through the granfet project ( n. 2008s2clj9 ) . part of the calculations were performed with the support of the genci ( grand equipment national de calcul intensif ) initiative . iannaccone ,  g. ; 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we report fully quantum simulations of realistic models of boron - doped graphene - based field effect transistors , including atomistic details based on dft calculations . 
 we show that the self - consistent solution of the three - dimensional ( 3d ) poisson and schrdinger equations with a representation in terms of a tight - binding hamiltonian manages to accurately reproduce the dft results for an isolated boron - doped graphene nanoribbon . using a 3d poisson / schrdinger solver within the non - equilibrium green s functions ( negf ) formalism , 
 self - consistent calculations of the gate - screened scattering potentials induced by the boron impurities have been performed , allowing the theoretical exploration of the tunability of transistor characteristics . 
 the boron - doped graphene transistors are found to approach unipolar behavior as the boron concentration is increased , and by tuning the density of chemical dopants the electron - hole transport asymmetry can be finely adjusted . correspondingly , the onset of a mobility gap in the device is observed . 
 although the computed asymmetries are not sufficient to warrant proper device operation , our results represent an initial step in the direction of improved transfer characteristics and , in particular , the developed simulation strategy is a powerful new tool for modeling doped graphene nanostructures . 
 the discovery of graphene has opened a promising alternative to silicon - based electronics . 
 @xcite reported charge mobilities in undoped graphene layers are actually orders of magnitude larger than those measured in silicon , but the unfortunate zero - gap semiconductor nature of this material severely limits the achievable @xmath0/@xmath1 ratio  @xcite ( ratio infinite for an ideal switch of the current flowing through the device in the conducting state to that flowing in the nonconducting state ) for graphene transistors , making them not yet able to compete with mainstream silicon technologies . 
 @xcite another adverse feature of graphene - based devices is their ambipolar electrical behavior , which precludes the development of a complementary logic architecture . 
 a way to induce an energy gap in graphene is to reduce its lateral dimension . 
 @xcite by using e - beam lithographic techniques and oxygen plasma etching processes , graphene nanoribbons ( gnrs ) down to a width of 10 nanometers can be successfully fabricated . 
 @xcite the resulting energy gap , however , is not sufficient for the achievement of a practically useful @xmath0/@xmath1 ratio in a transistor structure . 
 chemical , in - solution techniques have been developed that allow one to obtain nanoribbons with a smaller width  @xcite but are hard to integrate into a large - scale device production technology . 
 a mixed approach has been followed by wang and dai ,  @xcite who use lithography to define the nanoribbons , whose width is then shrunk by means of gas - phase chemical etching . although quite interesting , this procedure could have some limitation in terms of the achievable device density . 
 furthermore , energy bandgaps are very unstable with regards to edge reconstruction and defects ,  @xcite thus preventing the fabrication of graphene transistors with performances comparable with their silicon counterparts . indeed , almost ideal graphene nanoribbons have been obtained by means of careful chemical synthesis ,  @xcite however such an approach 
 can not be applied to the fabrication of complex circuits on insulating substrates in a straightforward way . 
 strong chemical damage of graphene could in principle be used to tune the current flow , but with the drawback of a significant decay of the conductance that leads to poor performance in terms of current drive . 
 @xcite    some of us have recently proposed a new class of devices based on the chemical doping of graphene by boron or nitrogen . 
 @xcite using first - principles and mesoscopic quantum transport calculations ( within the landauer - bttiker formalism ) some indications of different behaviors for electrons and holes were predicted in ribbons with lateral sizes as large as 10  nm , with mobility gaps in the order of 1  ev . 
 @xcite here the mobility gaps are typically defined by the corresponding energy window for which the conductance is smaller than a typical value of @xmath2 ( @xmath3 ( see ref . 
 @xcite for details ) . 
 recent experimental findings confirmed the possibility to include boron and nitrogen impurities in graphene ,  @xcite therefore suggesting doped graphene transistors as a genuine alternative to ultranarrow gnrs with a more controlled tuning of the conductance features . 
 however , fully self - consistent simulations of doped graphene transistors are mandatory to ascertain the real impact of graphene doping . 
 we explore the effect , at room temperature , of boron doping in graphene - based field effect transistors using the device geometry illustrated in fig . 
 [ fig1 ] . 
 self - consistent negf calculations are performed , allowing for a proper treatment of the screened impurity potential and a more robust assessment of the doping effects on the electron - hole transport asymmetry and on the onset of mobility gaps .