Controlling Electronic Structure and Transport Properties of Zigzag

Aug 18, 2015 - In this work, we report a detailed study of the electronic structure and transport properties of mono- and difluorinated edges of zigza...
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Controlling Electronic Structure and Transport Properties of Zigzag Graphene Nanoribbons by Edge Functionalization with Fluorine Sumanta Bhandary,† Gabriele Penazzi,‡ Jonas Fransson,† Thomas Frauenheim,‡ Olle Eriksson,† and Biplab Sanyal*,† †

Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden BCCMS, Universitat Bremen, Am Fallturm 1, 28359 Bremen, Germany

J. Phys. Chem. C 2015.119:21227-21233. Downloaded from pubs.acs.org by EASTERN KENTUCKY UNIV on 10/19/18. For personal use only.

‡

ABSTRACT: In this work, we report a detailed study of the electronic structure and transport properties of mono- and difluorinated edges of zigzag graphene nanoribbons (ZGNR) using density functional theory (DFT). The calculated formation energies at 0 K indicate that the stability of the nanoribbons increases with the increase in the concentration of difluorinated edge C atoms along with an interesting variation of the energy gaps between 0.0 to 0.66 eV depending on the concentration. This gives a possibility of tuning the band gaps by controlling the concentration of F for terminating the edges of the nanoribbons. The DFT results have been reproduced by density functional tight binding method. Using the nonequilibrium Green functional method, we have calculated the transmission coefficients of several mono- and difluorinated ZGNR as a function of unit cell size and degree of homogeneous disorder caused by the random placement of mono and difluorinated C atoms at the edges.

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ne of the important issues in graphene1−3 research is to modify the electronic properties to open a band gap suitable for transistor applications. Chemical functionalization of bulk graphene by H and F has been regarded as a suitable route to achieve this effect.4−9 The other prominent route is to consider nanoribbons with various types of edge functionalization by light elements (H, F, Cl, O etc.)10,11 or organic molecules.12 It has also been demonstrated that 3d transition metals can be used as functionalizing agents to yield interesting magnetic properties.13,14 For practical applications, one needs to consider the stability conditions of the functionalized nanoribbons under the influence of varying degrees of chemical pressure and temperature. The thermodynamic conditions for the stability of hydrogen terminated ZGNRs have been demonstrated by theoretical calculations.13,15,16 Recently, a considerable attention has been drawn toward functionalization of bulk graphene by F atoms, which may lead to interesting magnetic characteristics.17 Induced paramagnetism with the formation of local moments has been reported as a function of F concentration. The effect of F on graphene nanoflakes has been studied also.18 However, the study of fluorinated graphene in the form of bulk and nanostructures is comparatively less that that of hydrogenation and calls for detailed investigation. From an application point of view, the basic understanding of electronic transport through graphene nanostructures terminated by various agents is an important topic of research. It is useful to characterize the transport properties in the presence of impurities at the edge and bulk of graphene, possibilities of spin transport for magnetic functional agents etc. Here, we have chosen graphene nanoribbons functionalized by different © 2015 American Chemical Society

concentrations of F atoms to study the effect on electronic and transport properties by means of first-principles calculations. We have studied the stability of these nanostructures as a function of F concentration at the nanoribbon edges. Also, we have identified suitable conditions to open up band gaps in the system. Formation energies have been studied under the influence of chemical pressure of F. Finally, we have presented detailed studies of electronic structure and transport properties in these edge-functionalized nanostructures. We have studied the energetics of short-ranged ordering of F atoms at the edges. The effect of disorder on the transport properties is thoroughly studied too.

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RESULTS Stability and Band Gaps. We have shown that H- and 2Hterminated zigzag GNRs show interesting magnetic behavior at the edges.16 It was found that 2H-terminated GNRs are unlikely to be formed in comparison to 1H-terminated edges at room temperature and ambient pressure. Fluorine seems to be a potential candidate in this context to saturate dangling bonds of graphene nanoribbons. Similar to the hydrogenated edge, there are several possibilities of edge modification for fluorinated ribbons. This very consideration is aimed to explore the effect of gradual increase in F-density at the edges on ribbons’ structural and electronic properties. Let us start with Z1, i.e., 100% edge coverage with 1F/edge-C and consider it as the reference Received: July 6, 2015 Revised: August 17, 2015 Published: August 18, 2015 21227

DOI: 10.1021/acs.jpcc.5b06469 J. Phys. Chem. C 2015, 119, 21227−21233

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where the chemical potential of the F molecule μF2 is expressed in terms of enthalpy H and entropy S. We refer to the data of Chase et al.23 for the enthalpies and entropies at different temperatures. ρF is the edge F density and the reference pressure, P0, is taken to be 1 bar. We observe that the calculated Gibbs free energies at 300 K follow the same trend as the formation energies calculated at T = 0 K. At 300 K, we have considered a pressure range (P) to control the chemical potential of F molecule. It is observed in Figure 2 that the Gibbs free energies for all structures cross the

structure with zero 2F termination. Z2111 has 25% of 2F termination and Z211, Z21, Z221, and Z2 have 33%, 50%, 66%, and 100% of 2F termination, respectively. From the alternate functionalization point of view, this indeed turns out be an excellent way as increased F-density helps mutually in structural stability unlike its hydrogenated counterpart. In our calculations, the nanoribbons considered are eight rows wide. From the metal−insulator transition point of view, unlike H-terminated counterpart, the width dependence is rather less interesting. For example, Z2 is metallic for different widths of six rows, eight rows and 15 rows, while the H-terminated Z2 structure had a metal insulator transition at a width of eight rows.16 Being lowered in width to six rows, Z221 comes on the verge of opening up a band gap. Thus, transition points may have a width dependence, which can broaden or shrink the region a bit depending on the width. But the variation of edge fluorination has a much profound effect in defining this phase separation and is the primary subject of our paper. We have performed T = 0 K calculation to determine the formation energy of the above-mentioned structures with the following formula: ⎡ E(F2) ⎤ E(1) ⎥ f = E(n F) − ⎢E(bare) + n ⎣ 2 ⎦

(1)

where n is the total number of F atoms attached to the edge. E(nF), E(bare), and E(F2) represent the total energies of ZGNR with nF atoms at the edges, ZGNR without F termination and F2 molecule in the gas phase, respectively. The formation energies presented in Figure 1 show the spontaneous formation of all

Figure 2. Calculated Gibbs formation energies at 300 K as a function of chemical potentials of F2 molecules for different types of edge fluorinations.

zero energy line quite far left from zero chemical potential which is an indication of spontaneous formation in a large range of chemical potential of F. At zero chemical potential, Z1 is the least stable one whereas Z2 has the highest stability. For positive chemical potentials, the ordering of stability for different structures remains the same. This, essentially, establishes the robustness of increasing stability due to increased fluorine density at the edge. However, below a certain negative chemical potential, the order changes and one observes the maximum stability for Z1. This complex behavior indicates the possibility to tune the structures by controlling F concentration. The stability of the fluorinated GNRs can be well explained from the point of view of the strongest single bond nature of C−F bond. C−F bond consists of partial ionic character along with covalent character, which makes the bond dissociation energy (BDE) quite high (≈ 105 kcal/mol) and much larger than C−H bond having BDE ≈ 98.8 kcal/mol. High BDE is originated from the difference in the electronegativity of C and F (2.5 and 4.0) respectively. This results not only in the ionic character of the bond but also localization of charge on F atom. For Z2, localized charges on two F atoms start to repel each other which might help in increasing F−C−F bond angle to ≈105° which is much smaller (≈102°) for hydrogenated GNRs. F2 molecule itself has a BDE of 37.5 ± 2.3 kcal/mol, which means that in a F environment, GNR edges with dangling bonds can break F2 and get passivated spontaneously. This is reflected in both the formation energy and the Gibbs free energy calculations. Fluorination at the edge with different densities not only changes the stability profile but also affects considerably the electronic and the structural properties. Z1 in one end has a perfectly planar structure with 100% sp2 bonds whereas Z2 on the other end has sp3 bonds at the edges with F−C−F angle ≈105°. A mixture of Z1 and Z2 type edge affect each other and that reflects in the electronic properties as well. A metallic

Figure 1. Calculated formation energies and band gaps for different concentrations of edge difluorinations. In the inset, the edge structure of a Z211 nanoribbon is shown, where the black and orange balls represent C and F atoms, respectively.

structures considered. At the same time, the observed lowering of the formation energy with increasing F density at the edges indicates higher stability with the maximum at all 2F edge functionalization. In addition to the T = 0 K calculations, thermodynamic stability is calculated by determining Gibbs free energies including the effect of finite temperature and pressure. Gibbs free energy is defined as follows: G F ̅ = E(1) f −

1 ρμ 2 F F2

⎛P⎞ μ F = Hen0 (T ) − Hen0 (0) − TS °(T ) + kBT ln⎜ 0 ⎟ 2 ⎝P ⎠

(2) 21228

DOI: 10.1021/acs.jpcc.5b06469 J. Phys. Chem. C 2015, 119, 21227−21233

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The Journal of Physical Chemistry C magnet Z1 becomes nonmagnetic once a certain percentage of Z2-edge is mixed. All the mixed edge structures that we have considered are nonmagnetic but depending on the percentage of Z2 edge, these show a metallic or a semiconducting behavior. Z2111, which has only 25% of 2F termination introduces a small band gap of 0.182 eV. Increasing 2F termination density to 33% in Z211, we observe a larger band gap of 0.66 eV. Interestingly, that was the highest band gap we observed among our considered structures. A 50% mixture of each types gives a band gap of 0.151 eV. Next two structures with 66% and 100% 2F termination are metallic and nonmagnetic. In Figure 3, we show the calculated band structures for four selected structures (Z2111, Z211, Z21, and Z221). It is observed

Figure 4. Bader charge analysis. Local charges at C sites are shown for four different structures. Also, the type of fluorination, i.e., F or 2F at respective edge C atoms, is indicated.

In particular, to propose the tuning of electronic properties by heterogeneous edge functionalization, it is necessary to carefully evaluate the aspects related to disorder induced by the deviations from the desired concentration and distribution of functional groups, which can affect the electronic properties of the material. In the next section, we will show how the chemical disorder between mono- and difluorinated edge C atoms affects the transport properties for the Z211 configuration showing the maximum value of the DFT gap. We expect that the other configurations will also have similar qualitative effects regarding the transport properties.

Figure 3. Electronic band structures calculated with DFT for four different structures. Fermi levels (defined as the center of the band gaps) are set to be zero.

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TRANSPORT PROPERTIES: EFFECTS OF DISORDER In order to describe the effects of disorder on the transport properties, the calculations of larger structures with different realizations of edge functionalization may be needed, which can make the computational expense of fully ab initio methods rapidly prohibitive. To overcome this problem and achieve a fast analysis of the effects induced by disorder in the proposed functionalization, we have employed the DFTB approach. The features of the electronic band structures are correctly reproduced for all the geometries, an example of band structure is given in Figure 5 for Z211 structure, which can be compared to the DFT band structure presented in Figure 3. It is noteworthy to mention that, due to the minimal basis set, mild quantitative discrepancies between DFTB and DFT may be expected. In some cases, the band gaps calculated by DFTB come

that Z2111 and Z21 have the gaps at X point of the Brillouin zone, whereas Z211 yields the gap at the Γ point. While these are direct band gaps, a very small indirect band gap is observed for the Z221 structure. Bader Analysis. Now we discuss the charge distribution due to edge fluorination. An important factor is the ionic nature in chemical bonding, which helps in the localization of charges on atoms. This is not prominent in hydrogenated ribbons, where the ionic character of C−H bond is less significant. A considerable difference in the electronegativities of C and F results in a reorganization of electronic charges mostly at the edge of the ribbon, whereas the bulk part is not much affected. It should be noted that hydrogenated Z211 has a semiconducting nature with a little edge charge distribution. But the other hydrogenated structures are metallic with a flat charge-profile. So, charge distribution in this context can play a key role in controlling or introducing a band gap.We have performed Bader charge analysis to determine charge on an individual atom and the results are shown in Figure 4. A F atom, being highly electronegative, pulls 0.8e charge from each edge C atom bonded to it and introduces a +δ charge on the C atom connected to it. This +δ charge is distributed to the neighboring C atoms in order to minimize charge localization. But the way of distribution is different for different edge combinations and is associated with structural deformation as well. So far, we have discussed the electronic properties due to different admixtures of mono- and difluorinated edges of graphene nanoribbons. However, from an application point of view, it is of utmost importance to study the transport properties.

Figure 5. Electronic band structure for the Z211 structure calculated with DFTB. 21229

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for electronic applications: a metal−insulator heterojunction and a disordered semiconducting ribbon. A metal−insulator junction can be realized by selectively adding or removing 1F and 2F termination in a specific region of the ribbon, as both the homogeneous mono- and difluorinated ribbons exhibit a metallic behavior. In Figures 6 and 7, the

out to be closer to experimental values. While DFT-LDA is known to underestimate band gaps, the compressed DFTB basis often leads to an overestimation of the band gap with respect to DFT reference, leading to a fortunate although not systematic error compensation.30 In Table 1, we show the comparison Table 1. Comparison of Electronic Band Gaps (eV) Calculated by DFTB and Plane Wave PAW within DFT Z21 Z221 Z211 Z2111

DFTB

PW-DFT

0.38 0.17 0.68 0.30

0.48 0.07 0.68 0.22

between the band gaps calculated by DFTB and DFT methods. For all the 2F concentrations, we observe a fair agreement between these two methods. Specifically, the values agree very well for the percentage of 33% (Z211), which we have considered for the analysis of transport properties later on. We have shown that controlling the concentration of 2F groups at the edge of the ZGNR, it is possible to induce a metal to insulator transition and to control the value of the energy gap. Such a band gap modulation can be very intriguing, as it can potentially be used to realize electronic devices.26 Edge functionalization is known to affect the electronic properties of armchair nanoribbon (AGNR) as well, however with a very different band gap tuning mechanism. AGNRs can have an intrinsic gap depending on their width, according to well encoded aromaticity rules. Fluorination, in particular, does not modify the aromaticity patterns of AGNRs and the band gap is predicted to be close to hydrogen-terminated AGNRs.40 On the other hand, the band gap modulation of ZGNRs proposed in this work does not require a width modulation as the electronic properties around the Fermi level are determined by edge state modulation rather than aromaticity. As a consequence, a ZGNR based metal−insulator junction could be engineered by locally modifying the chemical composition of a single ribbon. However, the technological feasibility of such techniques is limited by the possibility of controlling the concentration and the spatial distribution of doping and/or functionalization. In fact, it is wellknown that the presence of disorder is of particular importance in one-dimensional systems, as it implies localization of all the electronic states by means of backscattering28,29 and can lead to an apparent widening of the band gap.31 In armchair graphene nanoribbons with random substitution of H with F, the electronic states have been calculated to be localized over a length of hundreds of nanometers by means of the varying potential at the ribbon edge,25 thus allowing for robust ballistic transport. However, the functionalization scheme proposed in this paper is fundamentally different as edge termination by F or 2F groups implies a different coordination of the edge carbons and the effect of disorder on the electronic structure can be expected to be more pronounced. The localization length can be evaluated with different techniques, including transfer matrix,37 recursive Green’s functions24 or real space Kubo method.36 However, these approaches are usually applied when the Hamiltonian can be conveniently partitioned or when a minimal tight binding calculation allows direct calculation of long structures. The evaluation of the localization lengths goes beyond the scope of the present paper, here we present an analysis of backscattering for some specific realizations of interest

Figure 6. Electronic transmission spectra through an insulating region composed by repetition of Z211 unit cells. The contacts are modeled by ideal double fluorinated semi-infinite ribbons (Z2). The black curve represents the transmission of an ideal homogeneous Z2 ribbon, for reference.

Figure 7. Electronic transmission spectra through an insulating region composed by repetition of Z211 unit cells. The contacts are modeled by ideal mono fluorinated semi-infinite ribbons (Z1). The black curve represents the transmission of an ideal homogeneous Z1 ribbon, for reference.

transmission of the junction is shown. The transmission rate is evaluated by means of open boundary Green’s function scheme as implemented in the DFTB+NEGF code.22,32 Figures 6 and 7 refer respectively to homogeneous Z2 and Z1 injecting electrodes. The scattering region includes an increasing number of adjacent Z211 unit cells, perfectly ordered. The opening of a transmission gap with the increasing number of Z211 unit cells, i.e., the width of the insulating region, can be clearly distinguished for both structures. Qualitative and quantitative differences in the backscattering are due to the different electronic properties of the nanoribbons chosen as metallic leads. The Z1 ribbon exhibits a band structure similar to a pristine zigzag ribbon, with metallic edge states and particle-hole symmetry in proximity of the Fermi 21230

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energy per F atom for an ensemble of configuration with different amounts of disorder: the energy has a minimum corresponding to the ideal Z211 ribbon and it increases for increasing disorder. Vibrational entropy should be taken into account to correctly describe the free energy at room temperature, however this implies the calculation of vibrational spectra for all the configurations.33 We did not take into account explicitly this effect for all the structures, but we instead studied a subset of configurations to find that the correction due to the vibrational contribution is small even at room temperature and does not change significantly the results shown in Figure 8. We can therefore expect that given a concentration of fluorine corresponding to the Z211 structure the distribution of 2F and 1F terminations will not be random, but will tend to maintain a certain degree of order. On the basis of these results, we evaluate the amount of backscattering due to the presence of 2F and 1F displacement in a Z211 ribbon by varying the amount of short-range order. Applying the same procedure used for the metal−insulator junctions, the transmission spectra of configurations with different values of η connected with semi infinite Z211 ribbons have been calculated. The result is shown in Figure 9 for five

level. As a consequence of the latter, the transmission gap in Figure 7 opens up symmetrically around the Fermi level, while it appears wider than the electronic band gap calculated in the periodic Z211 structure due to a strong suppression of edge states. In fact, a consistent behavior can be observed in a ZGNR with a similar heterogeneous hydrogen passivation: a H1−H2 heterostructure exhibits large transmission gaps despite a small or vanishing electronic band gap.16 This is in agreement with the results recently reported by other authors39 by means of DFT calculations. The Z2 ribbon is also metallic, but it exhibits a qualitatively different band structure, lacking metallic edges and particle-hole symmetry. This results in qualitatively different transmission curves (in Figure 6) with a pronounced asymmetry around the Fermi level. As previously mentioned, any kind of disorder which breaks the translational symmetry of the system introduces backscattering and asymptotic localization of electronic states. In the proposed chemically functionalized ribbons, disorder is introduced whenever the concentration of F and 2F termination can not be exactly controlled globally or locally. This is potentially an issue in any edge-functionalization scheme; in this particular case, the semiconducting ribbons will be more critical as a short-range ordering could occur even when globally the 2F percentage can be controlled with absolute precision. This will happen if the ideal alternation of 1F and 2F functionalization groups is lost, thus breaking translational symmetry. Such a source of displacement disorder is technologically relevant as being intrinsically related to the functionalization strategy. We estimate the tendency to displacement disorder in the semiconducting ribbon with largest band gap, i.e., the Z211, by total energy analysis. An ordering parameter η which measures the amount of short-range order is defined in the following way: considering any group of three adjacent edge atoms in the system, η is the probability that the concentration of 2F terminations is exactly 1 /3. This parameter is similar to the conditionally probability commonly applied to partially ordered alloys analysis.34 For the ideal periodic Z211 system η = 1, while η → 0 when 2F and 1F termination are completely clustered in separated segments of the system. By calculating the total energies of longer periodic ribbons (15 monolayers) it can be shown that Z211 ribbons are likely to preserve short-range order. Figure 8 shows the total

Figure 9. Transmission coefficient for five Z211 ribbons with three different values of η. The black curve refers to the ideal Z211 ribbon, for reference. The scattering region has a length of 3.7 nm. The energy zero is placed at the mid gap.

single representative configurations. For intermediate ordering (η ≤ 0.60), a large backscattering all over the first and second valence and conduction band is always observed, and the transmission is largely suppressed. For the smallest amount of disorder considered, corresponding to η = 0.87, transmission is recovered even though a significant backscattering is still evident. A rough estimate of the corresponding elastic mean free path, only valid in the limit where phase interference effects can be neglected,24 is given by le ∼ L/(1 − T), where L is the length of the scattering region and T the transmission probability. In the systems with η = 0.87, this corresponds to a mean free path in the order of 10−20 nm in first conduction band and 5−10 nm in first valence band. Although these quantities come from a rough estimate, they are in the same order of magnitude as the elastic mean free path due to short-range edge order in pristine ribbons.38 For an intermediate amount of disorder (η = 0.73) such an estimate is not meaningful: broad scattering peaks, signature of quasi bound states, arise leading to qualitative, and quantitative differences between different disordered configurations. Nevertheless, backscattering systematically increases by

Figure 8. Total energy per F atom in an ensemble of periodic Z211 ribbons as a function of the ordering parameter η. The relaxed structures and the total energies are obtained from DFTB calculations. Each configuration contains 15 zigzag rows and 40 fluorine atoms at the edges. 21231

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The Journal of Physical Chemistry C increasing the short-range disorder and is significantly more pronounced for valence states. This result suggests that edge functionalization disorder can have a significant impact on the transport properties of a semiconductor ribbon, comparable to edge disorder in pristine ribbons.

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ACKNOWLEDGMENTS

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REFERENCES

B.S. acknowledges the Carl Tryggers Stiftelse and VR/SIDA for financial support. O.E. is in addition grateful to the KAW foundation, eSSENCE, and the ERC (Project 247062-ASD) for support. We also acknowledge SNIC-UPPMAX, SNIC-HPC2N, and SNIC-NSC centers under the Swedish National Infrastructure for Computing (SNIC) resources for the allocation of time in high performance supercomputers.

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CONCLUSIONS Our density functional calculations on edge-fluorinated graphene nanoribbons show interesting features in the electronic and transport properties. The stability of the nanoribbons increases if the concentration of 2F functionalization at the edges is increased, which could be analyzed with the help of electronegativity and charge transfer. We also observe the opening of band gaps for a certain regime of concentration of 2F. We calculated the electronic transmission in a metal−insulator junction realized with the functionalization scheme proposed in the paper and showed the opening of transmission gaps. The possible presence of broken lattice translational symmetry in Z211 ribbons due to disorder in mono and double fluorinated edges has been discussed and a total energy analysis was shown to demonstrate that short-range order is favored, for which we eventually evaluated the backscattering. Our study indicates the possibility of controlling the electronic structure and hence, the transport characteristics of graphene nanoribbons by controlled fluorine terminations at the nanoribbon edges, which may lead to suitable applications for 2D electronics.

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METHODS First-principles spin-polarized density functional calculations were performed using a plane-wave projector augmented wave (PAW) method based code, VASP.19,20 The generalized gradient approximation as proposed by Perdew, Burke, and Ernzerhof (PBE) was used for the exchange-correlation functional. We have considered zigzag-edged GNRs, which were infinite along the x axis. To create sufficient vacuum in order to avoid the interactions within adjacent cells, unit cell dimensions along y and z axis were considered as 42 and 20 Å respectively. The electronic wave functions were expanded using plane waves up to a kinetic energy of 400 eV. The electron smearing used was Fermi smearing with a broadening of 0.1 eV. The energy and the Hellman−Feynman force thresholds were kept at 10−5 eV and 10−3 eV/Å respectively. All atomic positions were allowed to relax and the elemental cell was kept at a constant size during the optimization. For all calculation we used 30−80 k-points according to the size of the unit cell. We have also employed density functional based tight binding (DFTB) approach, which offers a trade off between the precision and portability of DFT and the speed of empirical tight binding descriptions.The method itself has been applied, for example, to investigate defects formation in pristine and hydroxylated GNRs35 with accuracy near to ab initio treatment. We employed the pbc parametrization21,27 and tested it against the DFT calculation. Geometrical relaxations are reproduced within an error of 0.01 Å, therefore the parametrization can be safely used to perform relaxation of large supercells with nearly the same accuracy of ab initio calculations.

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Article

AUTHOR INFORMATION

Corresponding Author

*(B.S.) E-mail: [email protected]. Notes

The authors declare no competing financial interest. 21232

DOI: 10.1021/acs.jpcc.5b06469 J. Phys. Chem. C 2015, 119, 21227−21233

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DOI: 10.1021/acs.jpcc.5b06469 J. Phys. Chem. C 2015, 119, 21227−21233