Activating impurity effect in edge nitrogen-doped chevron graphene nanoribbons

Doping has been regarded as one of the most important band structure engineering methods for graphene and its derivatives. Here, we theoretically investigate the chevron-type graphene nanoribbon (CGNR) which is doped by nitrogen in its edges (N-CGNR). The impurity effect can be activated by hydrogen efficiently. When each N atom is adsorbed by a H atom, the σ bond of N induced by self-hybridization is replaced by the N-H sp2 bond, leaving two pz electrons perpendicular to the CGNR plane. Only one pz electron can be bonded with the nearest C atom. Therefore, the residual pz electron is delocalized from the N atom and induces the n-type impurity effect. We have calculated the binding energies of N-H bonds and found they are stable and can be manipulated independently without impacting the other bonds. A molecular dynamic (MD) simulation under high temperature further verifies that the N-H bonds in some specific positions can even be stable at 2000 K. Finally, the activated impurity effect is exhibited in the transport properties of CGNR based devices, indicating its wide application prospects.


Introduction
The bottom-up graphene nanoribbon (GNR) synthesis approach using molecular precursors has stimulated the studies of GNRs, because of the precisely controlled edges [1][2][3][4][5][6][7][8]. Besides the fabrications of GNRs with different widths and chiralities (from zigzag to armchair), a unique structure named chevron-type GNR (CGNR) is also reported frequently and predicted to have good thermoelectric and optical properties [9][10][11][12][13]. As a common band structure modulation strategy [14], doping is also investigated intensely in CGNRs, although the mechanisms in low-dimensions may be more complicated than bulk materials. The CGNRs can be doped by nitrogen (N-CGNRs) in their edges via N-substituted hydrocarbon precursors. Bronner et al have discovered that the Fermi levels of CGNRs can be moved up by several hundred meV along the increasing of N densities, which indicates a light doping phenomenon [15]. Later, Vo et al have synthesized the N-CGNRs in a solution environment [10,11]. The up-shifting of Fermi levels has also been observed by Zhang et al [16] Based on the shifting, Cai et al have synthesized heterojunction structures using the N-substituted precursors at partial regions of the CGNRs [9]. In these studies, despite the heavy doping reality, the heavy doping phenomenon is still not observed. There are still some visible distances between the Fermi levels and the conduction band minimum (CBM), no matter the impurity densities. In other words, the N impurity effect is not so ideal in the edges of CGNRs and this may hinder the applications of the N-CGNRs.
To explore the restricting factor behind and find out if the impurity effect can be activated in N-CGNRs, we have investigated the N-CGNRs in detail using first-principle method. We have discovered that the impurity effect is mainly restrained by the self-hybridization of the N atomic orbitals. When a N atom is only bonded with two nearest C atoms, the self-hybridization is occurred and only one p z electron is left, which makes the N atom behave like other C atoms. The impurity effect is restrained consequently. However, when a H atom is adsorbed to the N atom, the self-hybridization can be eliminated, resulting in two p z electrons in the N atom. Therefore, Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the impurity effect is activated by the adsorbed H atom. Besides, this phenomenon can also be observed in the edges of armchair GNRs (aGNRs). The edge N-H bonds of N-CGNRs are stable and can be manipulated independently, indicating the flexibility of impurity effect control. They can endure high temperatures, especially in some specific positions of the CGNRs. The excellent impurity activation ability of H atoms offers a better method to control doping in CGNRs.

Simulation method
The calculations are performed using first-principle theory imbedded in the QUNTUM ESPRESSO code [17]. The Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) functional is employed and the pseudopotential is ultrasoft [18,19]. We have also verified the GGA with the Van der Waals forces correction and the result differences are negligible. In the structure optimizations, the criteria of total energies and forces are 1.4×10 −3 eV and 2.6×10 −2 eV/Å [20,21]. The k-point samplings in self-consistent and non-self-consistent steps are 1×1×10 and 1×1×50, respectively [22]. The kinetic energy cutoff and estimated energy error in self-consistent calculations are 544 and 1.4×10 −11 eV [23].
To obtain the quantum transport properties of CGNRs with varies impurity effects, the maximally localized Wannier function (MLWF) method is adopted to transform the electron Bloch wave functions into a tight binding (TB) form [24]. Different from the empirical TB hopping parameters, the transformations are unitary which can retain the overall impurity effect into the carrier transports. Using an open source code Wannier90 [25], we have realized the transformations on many materials, such as silicon, GNR, and phosphorene [18,22,23]. After the transformations, the quantum transport properties of CGNR based devices are obtained utilizing the non-equilibrium Green's function (NEGF) method which is incorporated into the open source code NanoTCAD ViDES.
The Car-Parrinello method is adopted in the molecular dynamic (MD) simulation. The exchangecorrelation functional and kinetic energy cutoff are the same as the first-principle calculations. Only the Gamma point is considered. The convergence thresholds on total energies and forces are 1.4×10 −5 eV and 2.6×10 −3 eV/Å [26,27], respectively. At the ground state calculation step, both the steepest descent (sd) and damped dynamics algorithms are used for 1.2×10 −3 and 3.4×10 −1 ps, respectively. Then, the temperature of 2000 K is induced, and both the electron and ion dynamics are set to verlet. The ionic kinetic energies are controlled by the Nose-Hoover thermostat [28].

Results and discussions
Eight atom positions in a supercell of the CGNR are likely to be substituted by N atoms [9,11], which can be seen in the dark blue atoms of figure 1(a). For convenience, the N-CGNRs with and without H adsorption on N atoms are named HN-CGNR and bare N-CGNR (bN-CGNR), respectively. The CGNR without impurity is also shown in figure 1(c). The supercell sizes are shown by the black rectangles outsides. Vacuum layers with thicknesses of more than 10 Å are added in the x and y directions to avoid image interactions. After crystal optimizations, the band structures of the three CGNRs are shown below. The Fermi levels are moved to the zeroenergy point. The bandgap of CGNR in figure 1(f) is 1.59 eV which is very similar with some other works [1,10]. The Fermi level in HN-CGNR locates inside the conduction bands, implying the n-type impurity effect. The bandgap is also reduced to 0.52 eV because of the additional impurity bands. In comparisons, the variation of Fermi level in the bN-CGNR is limited and its bandgap is 1.51 eV which is also comparable with the CGNR's. The bandgap invariance and Fermi level shift are very similar with the results obtained previously [29]. Thus, the bandgap engineering ability of the bN-CGNR is lower than the HN-CGNR.
Besides, the CGNR supercells with only four substituted N atoms are also calculated in figure S1 is available online at stacks.iop.org/JPCO/2/045028/mmedia of the supplementary material. When the density of N atoms is reduced by 50%, similar phenomenon can also be observed. We have further examined the edge-Nsubstituted aGNR (N-aGNR) in figure S2 of the supplementary material and found that this phenomenon seems to be ubiquitous in GNR edges. The interesting band structure variations indicate the strong impurity effect activation ability of the H atoms.
The activation of impurity effect can be explained by the bonding manners of the electrons around the N atoms. As seen in the projected density of states (PDOS) plot in figure 2(a), the impurity levels are contributed by both the C and N atoms. They are originally generated by the p z orbitals of N atoms, which is shown in the inserted real space distribution plot. After the generations, they widely spread to C atoms nearby. For each N impurity, it can be inferred that three σ bonds are formed by N-C and N-H sp 2 hybridizations, leaving two p z electrons. Only one p z electron can be bonded together with the nearest C to form π bond. Therefore, the residual p z electron is delocalized from the corresponding N atom and generates the impurity level. In contrast, the PDOS plots of bN-CGNR are shown in figure 2(b). It is interesting that a PDOS peak inside the valence bands are mainly contributed by the p x and p y electrons of the N atoms. From the real space distributions in the inserted plots, two in-plane electrons of each N atom are self-hybridized and form a σ bond. Together with the other two N-C σ bonds, only one p z electron is left outside. This p z electron is then hybridized with another one comes from the nearest C atom and forms a π bond. Therefore, no residual electron is found, and the band structure is  The feasibility of the impurity effect activation is not exclusively guaranteed by the great ability of H atoms, since the N-H bonds also should be stable enough. First, we have defined and calculated the mean thermodynamic gain as E gain =(E bN-CGNR +nE H -E HN-CGNR ) / n, where the E bN-CGNR , E HN-CGNR , and E H are the energies of the bN-CGNR, HN-CGNR, and an isolated H ion, and the n denotes the number of H in the HN-CGNR. The E gain is calculated as 3.13 eV, a positive value indicating the feasibility of the adsorption reaction. Furthermore, we have calculated two typical N-H bond energies and compared with two C-H's. Since the adsorption process is reversible and the original state of the adsorption is not easy to be determined, we start form the H adsorbed state in which the energy of the whole system is relaxed to the lowest value. As seen in figure 3, two C-H (figures 3(a) and (b)) and N-H (figure 3(c) and (d)) bonds are calculated. The original system is the supercell of the HN-CGNR after crystal optimization. Then the H atoms are moved opposite to the bond directions gradually, denoted by the red arrows in the plots. The total energy variations of these four processes are concluded in figure 3(e). The energy and the atom displacement of the original system are set to zero. It is clear that the N-H bonds are stable and the energy of 1.5 eV is needed at least to break them. The N-H binding energies close to the middle of the ribbon are even higher (about 2.2 eV). Along the increasing N-H bond lengths, the energies increase rapidly until the displacements exceed 0.8 Å, approximately. As the continuous bond length increasing, the energies begin to decrease gradually and the decreases in the two types of N-H bonds are all about 0.2 eV. Considering the backward reaction process, energies of only 0.2 eV are needed to generate bonds between the edge N and H atoms. Therefore, the N-H bond generation is promising. In comparisons, the C-H binding energies are larger, and the H atom displacement processes remain endothermic, which means the C-H bonds can always restore the original length after fluctuations. Besides, the larger binding energies of C-H manifest that the N-H bonds can be flexibly controlled according to varies doping requirements, without disturbing others. From the analyses above, the stabilities of HN-CGNRs are proved from energy.
Besides the bond energy calculations, we have also performed MD simulations on the HN-CGNR to examine the N-H bond strengths. After the ground state, the system is exposed to a high temperature of 2000 K for 1.2 ps. As seen in figure 4(a), the ion temperatures converge to the environment rapidly. The cell temperatures fluctuate around 2000 K which may be induced by electrons. The kinetic and total energies in figures 4(b) and (c) also converge quickly. The C-H (red) and N-H (blue) bond length variations and the ultimate state of the system are displayed in figures 4(d) and (e). Consistent with the bond energy calculations, four N-H bonds close to the middle can endure the high temperature because of their larger binding energies. In contrast, the other four bonds at the ribbon edges are broken. It also suggests that the activation ratios and positions are also controllable in this impurity effect modulation method. For example, if the temperature is appropriate (such as 2000 K), a half activation state can be achieved. All the C-H bonds remain stable during the high temperature because of their persistent endothermic property. Hence, the independence of N-H bond control is also verified.
It is known that doping can significantly affect the transport properties of the GNRs. Here, we have examined the impurity effect activation ability of H atoms by the quantum transport simulations of CGNRs based devices. The TB Hamiltonian are directly come from the first-principle calculations to guarantee the parameterization of the impurity effects. The band structure restorations by Wannier TB parameters are compared together with the first-principle results, as shown in figure S5 of the supplementary material. The restorations are accurate near the valence band maximum (VBM) and the CBM.
As shown in figure 5(a), the quantum transport simulations are implemented in the form of a double gate MOSFET which is commonly used for GNRs [30,31]. The thickness of oxide layer in each side is 1 nm and the channel length is 20 nm [32]. The channel materials are HN-CGNR, bN-CGNR, and CGNR. No extra doping is induced in the source and drain regions and the drain voltage (V d ) is fixed to 0.1 V. To show the doping effect more clearly, we have neglected the work function differences between the gate and channel materials [33,34]. The transmission spectrums shown in figure 5(b) are obtained at zero gate voltage (V g ). The transmissions of the three CGNR devices are consistent with their band structures. The impurity effect is activated in the HN-CGNR MOSFET, while it is restrained in the bN-CGNR MOSFET. This is more obvious in the transfer characteristics shown in figure 5(c). In comparisons with the CGNR MOSFET, currents in the bN-CGNR MOSFET are only shifted along the x axis by about 0.2 V, implying a light doping phenomenon. The ambipolar behavior is also observed, which is a common effect in undoped semiconductor devices. However, the current curve in the HN-CGNR MOSFET is varied totally. When the V g is varied from −0.2 V to 0.8 V, the currents can maintain high values which are comparable with the on-state currents of the other two MOSFETs. The excellent n-type  impurity effect of the HN-CGNR indicate that it is suitable for the source and drain materials in device applications.

Conclusion
In summary, the impurity effect of the edge-N-substituted CGNRs can be activated by the adsorbed H atoms. The H atoms can modulate the number of π electrons in N atoms which is critical for the impurity effect. The N-H bonds are stable and can be manipulated independently. The manipulation can be implemented by high temperatures, in which the impurity effect can be restrained, half activated, and totally activated, according to different doping requirements. The impurity effect activation ability of H atoms is also exhibited in the transport properties of the HN-CGNR, implying its potential applications in electronic devices.