Tuning electronic transport properties of zigzag graphene nanoribbons with silicon doping and phosphorus passivation

Density-functional theory in combination with the non-equilibrium Green’s function formalism is used to study the effect of silicon doping and phosphorus passivation on the electronic transport properties of zigzag graphene nanoribbons (ZGNRs). We study the edge structures passivated by H atoms and by P atoms. In this work, Si atoms are used to substitute C atoms located at the edge of the samples. We consider ZGNRs terminated by H and P atoms with four zigzag carbon chains (4-ZGNRs) in case of six various configurations. Our calculated results determine that the Si doping improves significantly the current of samples by the number of dopants. Moreover, there is dramatical difference in the transmission spectrum of P-passivated ZGNRs and H-passivated ZGNRs i.e. P passivation not only destroys an enhanced transmission at the Fermi level, which is typical for graphene nanoribbons, but also increases considerably the intensity of transmission spectrum with ballistic transport properties. Furthermore, the numerical results illustrate that pristine H-terminated samples have a broadening band gap in transmission spectra when the bias voltage increases. The relationship between the outcomes indicates that such silicon doping and phosphorus passivation are effective and providing a promising way to modulate the properties of ZGNRs for nanoelectronic device applications.Density-functional theory in combination with the non-equilibrium Green’s function formalism is used to study the effect of silicon doping and phosphorus passivation on the electronic transport properties of zigzag graphene nanoribbons (ZGNRs). We study the edge structures passivated by H atoms and by P atoms. In this work, Si atoms are used to substitute C atoms located at the edge of the samples. We consider ZGNRs terminated by H and P atoms with four zigzag carbon chains (4-ZGNRs) in case of six various configurations. Our calculated results determine that the Si doping improves significantly the current of samples by the number of dopants. Moreover, there is dramatical difference in the transmission spectrum of P-passivated ZGNRs and H-passivated ZGNRs i.e. P passivation not only destroys an enhanced transmission at the Fermi level, which is typical for graphene nanoribbons, but also increases considerably the intensity of transmission spectrum with ballistic transport properties. Furthermore, the num...


I. INTRODUCTION
Recently, two dimensional (2D) materials have attracted considerable attention because it has exhibited potential applications in optoelectronics devices. 1,2After the isolation of graphene by Novoselov and coworkers, 3 the novel synthetic routes for graphene have emerged.Many experimental developments, together with the fascinating physicochemical properties of graphene have stimulated extensive experimental and theoretical studies. 4,5Furthermore, graphene, a 2-D sheet of carbon atoms arranged in a honeycomb lattice, has been studied as a potential candidate for future electronic applications. 6,7However, graphene is a gapless material.To induce an electronic band gap, the graphene sheets are patterned into ribbons, which are so called graphene nanoribbons (GNRs). 8][11] It has been recently demonstrated that all these variables can be fully engineered.Chemical doping is a powerful method to modify the electronic properties of carbon-based nanomaterials, and hence, it could be used to customize the electronic and quantum transport properties of GNRs. 12,13ano-sized graphene nanoribbons are cut out of graphene sheets with two basic shapes for the edges: armchair and zigzag, which have distinct electronic transport properties. 146][17] These elements provide plenty of opportunities for tuning and greatly enlarging the applications of GNRs.Recent studies show the possibility of controlling the transport properties and their conductance.Several studies focus on hydrogen termination at the edges since they are probably the most stable configurations of this simple planar structure.Nonetheless, the edge passivation by H is not comprehensive enough to cover the realistic edge chemistry.More edge chemistry effects (O, F, H 2 , CO 2 . ..) are considered for more realistic modeling of GNRs. 18,19However, those studies mainly focus on the electronic band structures of the edge chemistry ZGNRs.The transport property with Si substitutional doping and P passivation have not been investigated in details yet, although these structures can exist stably. 20n this report, we investigate the transport property of ZGNRs with edge-chemistry modified by H and P atoms, using the first-principles based on density functional theory (DFT).Especially, it has been demonstrated that Si-doping is an efficient approach to tune the electronic properties and the electronic transport property of the ZGNRs.
The paper is organized as follows.In Section II, the models and computational methods are discussed, and the formulas related to the transport property are derived.Section III demonstrates the results and discussion concerning the effect of passivation atom, the effect of dopant atom and the effect of bias voltage on the electronic transport property.Finally, Section IV presents the conclusions.

II. SIMULATION MODELS AND CALCULATION METHODS
We consider six various structures with four zigzag carbon chains.These structures are illustrated in Fig. 1  First-principles calculations based on DFT and the non-equilibrium Green's function (NEGF) formalism implemented in the Atomistix ToolKit (ATK) software package (version 2016.4) 21,22are carried out to study electronic transport properties of the doped ZGNRs in terms of H passivation and P passivation.All considered samples are first optimized using DFT calculations within the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) for the exchangecorrelation energy. 23The Brillouin zone sampling is performed using 1 x 1 x 12 k-point sampling. 24he electrostatic potentials are determined on a real-space grid with a mesh cutoff energy of 150 Ry.The electron wave function is expanded using double-zeta-double-polarized basis set.Van der Waals interactions are accounted for by using Grimme's DFT-D2 empirical dispersion correction 25 to the PBE.Geometry optimization can be done until all atomic forces are smaller than 0.02 eV/Å.Using the optimized structures, we construct device geometries, which consists of three regions: semi-infinite left lead (L), central scattering region (SC), and semi-infinite right lead (R).Each lead consists of 2 unit cells with a length of 4.92 Å and the length of the scattering region in each device is 17.22 Å.The electrodes are modeled as an electron gas with a fixed chemical potential.The transmission is calculated along the z-direction.Quantum transport properties of all considered systems are calculated using NEGF formalism with the Brillouin zone sampled with (1, 1, 100) points.Periodic boundary conditions and vacuum spaces of at least 15 Å are imposed on the plane perpendicular to the z axis of the ZGNR layer.
The transmission function at energy E and bias V b is calculated through the following formula: 26 where G † and G represent the retarded and advanced Green functions of the scattering region, respectively.Γ L /R are the coupling functions from the left and right leads, respectively.The current is calculated by integrating the transmission function over the energy bias window by the Landauer Büttiker formula: 27 where f (E − µ L /R ) are the Fermi distribution functions of the electrons in the leads; are the electrochemical potentials of the left and right leads, where E F is the Fermi energy at zero bias.

III. RESULTS AND DISCUSSION
To obtain stable geometry structures of the doped systems, we optimize the atomic structure of each ZGNR.Numerical results show that after doping, the lattice constants have slight changes, and also local changes of the bond lengths and bond angles can be found.The P-passivated ribbons are reconstructed.[30][31][32]

A. The effect of passivation atom
In order to investigate the passivation effects on transport of ZGNR, in Fig. 2 we present the transmission spectra T(E) and device density of states (DDOS) at zero voltage.In the case of H passivation, T(E) exhibits a sequence of steps of integer transmission and an enhanced transmission at the Fermi level, which are distinctive of zigzag graphene nanoribbons.These features derive from the edge-localized electronic states with energies close to the Fermi energy.The transmission spectrum changes significantly when P atoms are used to passivate the structure instead of H atoms. Now the intensity of T(E) increases significantly in most of energy levels and has a value of 5 (5 times larger than that of H-ZGNR) in the range of -1.33 eV to ∼ -0.98 eV and a value of 3 in the range of -0.77 eV to ∼ 1.05 eV.Exceptionally, the value of T(E) remains unchanged at Fermi energy.Remarkably, the existence of unitized transmission flats around the Fermi level instead of the Fermi peak of ZGNR indicates the ballistic transport. 34The same remarks are for doped-ZGNR, but the values of T(E) at Fermi level are higher when using P termination.Interestingly, the obtained minima in the transmission curves are reflected in DDOS as broad maxima at the same electron energies.
To explore the anisotropic transport properties, in Fig. 3, we further illustrate the currentvoltage (I-V ) curves as a function of bias.There is an obvious fluctuation with four peaks and three valleys along H-ZGNR, which indicates that NDR behavior occurs in H passivation, while the P-ZGNR current increases linearly in the range of [0 V, 1 V] and [1 V, 2 V].Interestingly, the current values of P-ZGNR are dramatically higher in comparison with those of H-ZGNR.In addition, we can see that in doped systems, P atoms offers high current and destroys NDR behavior, exceptionally in the range [1 V, 1.2 V] of 2Si-doped ZGNR.Therefore, we can conclude from numerical results that P termination decreases significantly the anisotropic behaviors of electronic transport.
To further explore the I-V curves of doped systems, we study the transmission spectra as a function of the applied bias voltage and electron energy in Fig. 4. Numerical results show that for pristine H-ZGNR T(E) almost remains unchanged with the increasing bias voltage.Nevertheless, to be precise there exist higher coefficients at the border of bias window that leads to the current fluctuation under the applied bias.Meanwhile, in pristine P-ZGNR case the width of transmission flat around the Fermi level remains narrow when the bias increases until 2.0 V, whereas the intensity remains nearly unchanged.For Si-H-ZGNR, there arise two flag-shaped transmission regions below and above the Fermi level.There are obviously transmission coefficients contributing to the linear growth of current when the bias voltage rises to around 0.4 V.For Si-P-ZGNR, the intensity of T(E) is nearly constant until 1.0 V, which reflects the linear growth of current in Fig. 3. Additionally, the transmission values extremely larger than that of H termination case in the whole range of voltage, resulting current values being larger along H-terminated zigzag direction.For 2Si-H-ZGNR, transmission values vary below 0.6 V but they almost remain constant in 2Si-P-ZGNR.However, the intensity of 2Si-doped ZGNR with P passivation is significantly higher than that of H passivation situation.

B. The effect of dopant atom
Fig. 5 and Fig. 6 depict (a) the transmission spectra and (b) DDOS at zero voltage in the case of H termination and P termination, respectively.Solid-cyan curves show the reference results for pristine ZGNR.The H-ZGNR has a good symmetry and a great transmittance near the Fermi surface.As the Si atoms substitute the edge carbons atoms, they introduce impurities. 35The scattering of electrons and impurity atoms are enhanced in the systems.The scattering of impurities rises as the number of Si dopants increases so the transmittance of electrons near the Fermi surface becomes small.T(E) becomes smaller at the Fermi level and it drops sharply with increasing (decreasing) electron energy away from the Fermi energy.Obviously, the zero transmission coefficient at the Fermi level indicates that scattering is greater in 2Si-H-ZGNR than in Si-H-ZGNR.Interestingly, there is a strong relationship between T(E) and DDOS.H-ZGNR has a high density of electronic states at the Fermi level, which exhibits metallic behavior.Nevertheless, the Fermi peak decreases considerably due to the number of Si atoms and several new peaks appear after doping Si.These obtained peaks far away from the Fermi level are reflected as minima in the same electron energies in T(E).Similar remarks are acquired for P termination samples.The flat band of P-ZGNR around Fermi level disappears and the transmission coefficients reduce considerably after substituting Si atoms because of the impurities of dopant.More Si atoms appear more lower intensity of T(E) is revealed.Thus, doping two Si atoms results in a larger impact on the electronic transport properties in ZGNRs than doping one Si atom.
In order to see the contribution of the dopant atoms to the density of states (DOS) of the system, Fig. 7 describes the projected density of states (PDOS) of ZGNR.In the case of the edge Si-doping (Fig. 7(a)), the largest contribution of dopant atom is obtained at the Fermi level.This is also reflected in the device density of states (see the inset in Fig. 5(b)).The contribution of Si atom becomes less pronounced away from the Fermi energy.In contrast, the dominant contribution of Si atom appears outside Fermi level in 2Si-H-ZGNR.Next, we consider the instance of P passivation.The influence of Si atoms is found in the valence band.Obviously, the maxima in PDOS corresponds to the reduced electronic transmission and orbital p of Si atom is the main factor affecting to DDOS of all samples.
We next turn to study the current-voltage (I-V ) curves as a function of bias (see Fig. 3).In situation of H passivated structures, Si doping decreases NDR in H-ZGNR by the number of  dopants.However, Si provides giant current values at each voltage.It is clear that the highest current of 2Si-H-ZGNR is nearly eleven times higher than that of H-ZGNR and almost four times higher than that of Si-H-ZGNR.For P passivated situations, it is contrary to H passivation.NDR appears in 2Si-H-ZGNR due to the presence of Si atoms.Additionally, the reduction of current at each voltage comes from doping Si atoms.

C. The effect of bias voltage
It is evident that at zero bias, there is a peak transmission at the Fermi level for H-ZGNR (see Fig. 8) while there is a wide transmission across Fermi energy for P-ZGNR (see Fig. 11).As bias increases from zero to 1.8 V, the energy gap appears and widens in H-ZGNR, which contributes to the transformation from half-metallicity to semiconductor.However, for doped samples the finite transmission is still observed for both values of the applied voltage near the Fermi level (see Fig. 9, Fig. 10, Fig. 12 and Fig. 13).The reason for such finite transmission is the formation of electronic states extended between electrodes.Within low bias, the flat transmission keeps unchanged in bias window and the valley becomes visible at 1.2 V in P-ZGNR, as a result, just after zero bias the current rises sharply.In all structures of P termination, the integration of transmission function in the transport window is always larger than that of H-terminated structures.Consequently, the current of P-terminated samples is always larger than the current in case of H termination.
Experimentally, there are some essential remarks associated with the above outcomes.Firstly, using atomically resolved quantitative STEM-ADF imaging, Lopez-Bezanilla et al. 36 shows that the presence of isolated silicon atoms are unequivocally detected at the edges of graphene nanoribbons.Si atoms are identified terminating armchair graphene edges in pentagonal rings as well as part of reconstructed pentagonal rings in zigzag edges.Charge transport features created upon the incorporation of Si atoms at random position along a graphene sheet exhibit a wide variability depending on both position and hybridization of the impurity atom.Secondly, according to Susi et al., 37  buckled substitutional configuration.Based on Bader analysis of the all-electron density derived from the DFT simulation, the P is found to donate 1.79 electrons, with its three C neighbors receiving 1.68.Therefore, even at temperature of zero kelvin, there is indication of charge transfer to the lattice.

IV. CONCLUSION
In summary, we have investigated the effects of Si substitutional doping and P passivation on the electronic transport properties of ZGNRs.The calculated results reveal that the transmission spectrum changes dramatically when P atoms are used to passivate the structures.This effect originates from the fact that P atoms cause high carrier concentration (P termination atoms still have a few of unpaired electrons) and P-ZGNR exhibits an interesting massless Dirac fermion-like behavior (see supplementary material Fig. S1) so its charge carriers are equivalent to the relativistic quasiparticles with zero rest mass. 38The existence of flat transmission around the Fermi level indicates the ballistic transport characteristic.Furthermore, the current values of P-ZGNR are dramatically higher in comparison with those of H-ZGNR.In all structures of P passivation, the integration of transmission function in the transport window is always larger than that of H-terminated structures.Consequently, P termination decreases significantly the anisotropic behaviors of electronic transport.Additionally, our calculations show that Si causes contrary effects between H-terminated and P-terminated models.The bias voltage has a considerable impact on opening transmission gap of H-passivated structures as well as decreasing ballistic transport of P-passivated models.This study paves a promising way for improving the performance of ZGNR-based electronic devices.

SUPPLEMENTARY MATERIAL
See supplementary material for the complete tuning electronic transport properties of zigzag graphene nanoribbons with silicon doping and phosphorus passivation.

8 ,
FIG. 5. (a) Transmission spectrum T(E) and (b) device density of states DDOS as a function of electron energy at zero bias voltage for H-ZGNR, Si-H-ZGNR, and 2Si-H-ZGNR.

FIG. 6 .
FIG. 6.(a) Transmission spectrum T(E) and (b) device density of states DDOS as a function of electron energy at zero bias voltage for P-ZGNR, Si-P-ZGNR, and 2Si-P-ZGNR.

TABLE I .
Changes in bond length (in unit Å) from each determined atom to its nearest neighbors.
FIG.2.Transmission spectrum T(E) and device density of states DDOS as a function of electron energy at zero bias voltage for (a) H-ZGNR and P-ZGNR, (b) Si-H-ZGNR and Si-P-ZGNR, and (c) 2Si-H-ZGNR and 2Si-P-ZGNR.