Rectifying performance in zigzag graphene nanoribbon heterojunctions with different edge hydrogenations

b_{School of Computer Science and Technology, University of South China, Hengyang 421001, China}

a r t i c l e

i n f o

a b s t r a c t

Article history:

Received 21 December 2012 Received in revised form 16 April 2013 Accepted 2 May 2013

Available online 10 May 2013 Communicated by R. Wu

Keywords:

Electronic transport property

Zigzag graphene nanoribbon heterojunction Edge hydrogenation

Rectifying effect

Using nonequilibrium Green’s functions in combination with the density functional theory, we investigated the electronic transport behaviors of zigzag graphene nanoribbon (ZGNR) heterojunctions with different edge hydrogenations. The results show that electronic transport properties of ZGNR heterojunctions can be modulated by hydrogenations, and prominent rectification effects can be observed. We propose that the edge dihydrogenation leads to a blocking of electronic transfer, as well as the changes of the distribution of the frontier orbital at negative/positive bias might be responsible for the rectification effects. These results may be helpful for designing practical devices based on graphene nanoribbons.

Crown Copyright©2013 Published by Elsevier B.V.

1. Introduction

Since the experimental synthesis of stable single graphene layer at room temperature was achieved, graphene has been the sub-ject of numerous experimental and theoretical investigations due to the high electron mobility and the potential for scaling elec-tronics devices to true nanosizes[1–7]. In particular, much effort is focused on obtaining graphene nanoribbons (GNR) with tailored properties that could be key elements in future electronics appli-cations [8–13]. Two basic nanoribbons are mostly studied, which are the edge of GNR pointing along the C–C bond referred to as the armchair GNR, and the edge perpendicular to the C–C bond referred to as the zigzag GNR. It is well known that the C atoms of GNR are sp2 bonded. Hence, an edge atom would have dan-gling bonds, which would be saturated by atoms or molecular species[14–16]. Recently, much research have been done concern-ing the modification of edges because it can be used to control the electronic properties of GNRs for different purposes. Biplab Sanyal et al. [17] studied the effects of passivation of zigzag graphene nanoribbons (ZGNRs) by one hydrogen atom (monohydrogenation, 1H), and found that each edge C atom bonded with two hydrogen atoms (dihydrogenation, 2H) opens up a gap and destroys

mag-*

Corresponding author.

E-mail addresses:[email protected](M.-Q. Long),[email protected](H. Xu).

netism for small width (less than 8 rows) of the nanoribbon. And thesp3 _{bonded edge atoms with 2H atoms at the edge can be} sta-bilized over 1H atom terminated edge at high temperatures and pressures. Zeng et al.[18] investigated electron transport proper-ties of a heterostructure which consists of hydrogen-terminated ZGNR and oxygen-terminated ZGNR and found the heterostructure shows a large charge transmission gap near the Fermi energy, and rectification behaviors were observed. Chen et al.[19] reported a perfect spin filtering effect and a rectifying behavior with a ratio larger than 105, based on the monohydrogenated and dihydro-genated ZGNR heterojunctions at finite bias voltages. Very recently, Zheng and his coworkers [20] found a ZGNR heterojunction with different edge hydrogenations can be switched between a conduct-ing state and an insulatconduct-ing state by tunconduct-ing the external magnetic fields. Despite of great progresses which have been made, it re-mains some way from being a practical device at present, and further understandings of the structure–property relationship are needed. In this Letter, we present a theoretical description of trans-port properties of three kinds of heterojunctions that are based on ZGNRs, and all of them are believed to be capable of making in the experiment[17,21]. The geometry structure of three calculated models have been shown inFig. 1, there are bare ZGNR/monohy-drogenated ZGNR junction (M1), dihyZGNR/monohy-drogenated ZGNR/bare ZGNR junction (M2), and dihydrogenated ZGNR/monohydrogenated ZGNR (M3), respectively. The electronic transport properties have been studied by the first-principles calculation, and find that dihydro-genated ZGNR has a low conductance compared with the bare and monohydrogenated ZGNRs and the prominent rectification effects can be observed clearly.

0375-9601©2013 Published by Elsevier B.V.

http://dx.doi.org/10.1016/j.physleta.2013.05.004

Open access under CC BY license.

1906 C. Cao et al. / Physics Letters A 377 (2013) 1905–1910

Fig. 1.(Color online.) The geometry structure of three calculated models: (a) M1, (b) M2 and (c) M3. The shadowed areas indicate the electrodes. The region between the shadowed areas is the central scattering regions. The bold lines indicate the interface of heterojunctions.

2. Computational method and details

As show inFig. 1(a)–(c), the model configuration for a molecu-lar junction is connected to two semi-infinite zigzag

(

7

,

0

)

GNRs of the same width, i.e., 7 carbon dimer lines, which is called 7-ZGNR in some previous references [22,23]. The edge carbon atoms are bare or terminated by 1H or 2H of both scattering re-gion and electrodes. Fig. 1(a) shows the model structure of M1 heterojunction, in which the edge carbon atoms of the left half are not hydrogen-terminated while the ones of the right half are terminated by 1H. Fig. 1(b) shows the model structure of M2 heterojunction and the left half is terminated by 2H while the right half is not hydrogen-terminated. Fig. 1(c) shows the model structure of M3 heterojunction, in which the left half is terminated by 2H while the right half by 1H. Transport calcu-lations are based on density functional theory (DFT) combined with nonequilibrium Green’s function (NEGF) with ATK [24–26] package. The current is obtained from the Landauer–Büttiker for-mula,

Fig. 2.(Color online.) Transmission spectraT(E,Vb)at zero bias. (a) M1, (b) M2 and

(c) M3. I

=

e h +∞

−∞ T

(

E

,

Vb

)

fL

(

E

−

μ

L

)

−

fR

(

E

−

μ

R

)

dE (1)

where fL/R

(

E

,

Vb

)

is the Fermi–Dirac distribution function for

the left(L)/right(R) electrode, and the difference in the electro-chemical potentials is given by eVb with the applied bias

volt-ageVb, i

.

e

.

μ

L

(

Vb

)

=

μ

L

(

o

)

−

eVb

/

2 and

μ

R

(

Vb

)

=

μ

R

(

o

)

+

eVb

/

2.

And the positive/negative bias refers to the electrochemical po-tential of left electrode is higher/lower that of the right elec-trode. The transmission coefficient T

(

E

,

Vb

)

can be performed

as, T

(

E

,

Vb

)

=

Tr

Γ

L

(

E

,

Vb

)

GR

(

E

)Γ

R

(

E

,

Vb

)

GA

(

E

)

(2) where GR(A) _{is the retarded (advanced) Green’s function of the}

scattering region,

Γ

L(R)is the contact broadening functions

associ-ated with the left (right) electrode.

In our calculations, the vacuum layers between ZGNRs in neigh-boring along the xand y directions (defined inFig. 1) are 10 Å. The Perdew–Zunger exchange and correlation function within the local density approximation is used. A cutoff energy of 150 Ry and a Monkhorst–Pack k-mesh of 1

×

1

×

100 are chosen which yielded a good balance between computational time and accuracy of the results, and single-

ζ

plus polarized basis set is adopted for electron wave function which has been proved to be capable of well describing the

π

-conjugated bond system and the transport calculation including transmission and current–voltage character-istics [27]. Geometry optimization is performed until the force is less than 0

.

01 eV

/

Å. The NEGF-DFT self-consistency is controlled by a numerical tolerance of 5

×

10−5eV. The electron temperature is set to 300 K in the transport calculations.

3. Results and discussions

Using Green’s first-principle nonequilibrium function method, shown in Fig. 2(a)–(c), we present the transmission coefficient T

(

E

,

Vb

)

at zero bias for M1, M2 and M3, respectively. From the

figures, we find the M1 system shows a good conductivity within the energy range

[−

2

,

2

]

eV. But a transmission gap (TG) about 0.32 and 0.28 eV appears around the Fermi level (FL) for M2 and M3 systems respectively, which indicates semiconductor transport behaviors. The low conductance of M2 and M3 systems is related to the sp3 hybridization of the edge C atoms terminated by 2H, which are accompanied by the distortion in the ZGNR plane, re-sulting in the energy gap in the electronic structure [17]. It also

Fig. 3.(Color online.) (a)–(d) Band structure for 2H-ZGNR (left panels), transmission curve(middle panels), and band structure for the H-ZGNR (right panels) at zero bias. (e), (f) Isosurface plots ofΓ-point wave functions ofπ andπ∗ subbands for 2H-7ZGNR and H-7ZGNR. (g), (h) Isosurface plots ofΓ-point wave functions ofπ andπ∗ subbands for 2H-8ZGNR and H-8ZGNR.

can be observed clearly that the conductance curves of the last two systems are asymmetric with respect to the Fermi level, which is the origin of large rectifying behaviors.

With further considerations in terms of the influences of ZGNR width on the transport behavior, we calculate the transmission spectra and band structures of both left and right electrodes for M3 junctions with 7, 8, 9 and 10 carbon dimmer lines at zero bias, as shown inFig. 3(a)–(d). One can find that the transmission gaps are small for odd carbon dimmer lines, i.e., 2H-7ZGNR/1H-7ZGNR and 2H-9ZGNR/1H-9ZGNR; however, the gaps are much larger for even carbon dimmer lines, i.e., 2H-8ZGNR/1H-8ZGNR and 2H-10ZGNR/1H-10ZGNR, which is consistent with the findings of Chen et al. [19]. To demonstrate the dependency of the trans-mission gap on the geometric symmetry, we also include the isosurface plots of

Γ

-point wave functions of

π

and

π

∗ sub-bands in the right panel ofFig. 3. It is known that for symmetric ZGNRs, the

π

(

π

∗

)

states of 2H-8ZGNR and H-8ZGNR have oppo-site

σ

parity (Fig. 3(g)–(h)), and they cannot couple with each other to contribute to the transmission. The same situation oc-curs in 2H-10ZGNR/1H-10ZGNR junction. But there is no such limitation for the asymmetric ZGNRs due to the indefinite par-ity[28] (Fig. 3(e)–(f)), thus the electron transmission from

π

(

π

∗

)

state of 2H-7GNR to

π

(

π

∗

)

state of H-7ZGNR is possible. More-over, the narrow transmission gap is determined by the band gap of the electrodes on the left which appear near the Fermi level [19] and decreases with the increases of the width [29] (this is also true for symmetric ZGNRs), and thus the transmission coef-ficient can be found in a large part of energy region (Fig. 3(a) and (c)).

Fig. 4shows the currents as a function of the applied bias volt-age for the three junctions given inFig. 1. As shown inFig. 4(a),

the M1 system shows metallic characteristics, the current increases rapidly and almost linearly, and a small deviation is observed only when the bias voltage exceeds 0.7 V. More interestingly, both of the M2 and M3 systems display prominent rectifying behaviors, as shown in Fig. 4(b) and (c). The threshold voltages are 0.3 V and 0.4 V, respectively. In the negative bias, the current is nearly zero, but in the positive bias (more than 0.3 and 0.4 V), a linear I–V curve is shown. These can be realized based on the molecular projected self-consistent Hamiltonian (MPSH) inFig. 4(d) for M3 systems with a bias of

−

0

.

6 and 0.6 V, respectively. It is known that the main contribution to the transport comes from the fron-tier molecular orbitals, i.e., HOMO and LUMO, so only the two key molecular orbitals have been presented. One can see that the HOMO and LUMO are delocalized nearly in the whole junction at 0.6 V, while they are localized deeply in the 2H-ZGNR moiety at

−

0

.

6 V. It should be noted that if the orbital is delocalized across the central scattering region, an electron enters into the central region at the energy of the orbital has a high probability of go-ing through the central scattergo-ing region from the left to the right electrode [13,30], and vice versa. Therefore, the frontier orbitals are opened for electronic transport at the bias of 0.6 V, while they are suppressed at the bias of

−

0

.

6 V. Moreover, it is found that when the applied bias voltage is larger than 0.4 V, the currents are M1

>

M2

>

M3 for the same bias voltage. These characteris-tics of I–V curves indicate that the introduction of edge C atom bonded with 2H atoms decreases the electronic transport proper-ties for ZGNRs.

In order to explain the rectifying effect of the M3, in Fig. 5, we present the transmission spectrum and the band structure of both the left (spin-up) and the right electrodes for M3 at

±

0

.

5 V. When the positive bias is applied, the energy bands are shifted

1908 C. Cao et al. / Physics Letters A 377 (2013) 1905–1910

Fig. 4.(Color online.) (a)–(c) refer to the current–voltage (I–V) characteristic for M1, M2 and M3, respectively. (d) Presents the MPSH of HOMO and LUMO for M3 at 0.6 and

−0.6 V.

Fig. 5.(Color online.) Band structure for the left electrode (left panels), transmission curve (middle panels), and band structure for the nonmagnetic right electrode (right panels) for M3 atVb= ±0.5 V, respectively. The region between the blue solid lines

represent the bias window.

downward and upward for the left and right electrodes, respec-tively. We can see that, when the bias is 0.5 V (in reference of Fig. 5(a)), a new transmission peak entering into the bias win-dow due to the matching region between the

π

∗ subband of the

left electrode and the

π

subband of the right electrode, resulting in the increase of the current. When the negative bias is applied (in reference of Fig. 5(b)), the shift of the energy bands for both electrodes is opposite to the positive case. If the bias is

−

0

.

5 V, the

π

(

π

∗

)

subbands for both electrodes cannot couple with each other to contribute to the transmission due to parity mismatch-ing of the orbitals with respect to the yz mirror, and thus the transmission coefficient is essentially zero. As the transmission co-efficients within the bias window at 0.5 V are significantly larger than that at

−

0

.

5 V, the rectification effect is obvious.

In order to further understand the rectification effects, we cal-culate the electron transfer of the four carbon unit cells that are in the right of the interface at different bias voltages for the three systems, as shown inFig. 1. FromFig. 6(a), we find that the trans-ferred charges increase rapidly with the bias increase and the cur-rent also rapidly rises (in reference ofFig. 4(a)). FromFig. 6(b), it is clear that at negative bias voltage, the transferred charges are very small. This is because the frontier orbitals are suppressed for elec-tronic transport, as discussed above, and the electrons can hardly cross the junction. But in the positive bias voltage, with the in-creasing of the bias voltage, the transfer charge increases rapidly and the current also rises rapidly (in reference ofFig. 4(b)). Similar behaviors are expected for the M3 junction (Fig. 6(c)).

To further understand the transport behaviors of the three junc-tions, the transmission spectrum is used as a function of the elec-tron energy and the bias are plotted in Fig. 7. As shown in the region i (negative) and ii (below 0.2 V) of Fig. 7(a), the area of transmission coefficient with a constant value of 2 in the bias window increases linearly as a function of the bias, resulting in a linear I–V curve as mentioned in Fig. 4(a). However, once the bias voltage reaches 0.2 V (region iii), the rate of the increases in the area of transmission in the bias window is slower due to the

Fig. 6.(Color online.) The transferred charge on the four ZGNR-H units in the right of the interface at the bias range of−1.0 to 1.0 V for M1, M2 and M3.

Fig. 7.(Color online.) Calculated transmission spectrum as a function of electron energy Eand bias for (a) M1, (b) M2 and (c) M3. The region between the solid lines is referred to bias window.

presence of regions with smaller transmission coefficient, which results in the increased speed of current slowdown, and the de-viation from the linear I–V curve becomes obvious above 0.7 V. FromFig. 7(b) and (c), we can see that the transmission within the bias window is always zero under a negative bias. Thus the current is always suppressed under the negative bias (region i inFig. 7(b) and (c)). Under a positive bias, the variation of the current with the bias voltage goes through two different stages. With a small bias (less than 0.3/0.4 V), the transmission is zero, resulting in a sup-pressed current (region ii). At a higher bias voltage (

>

0

.

3/0

.

4 V, i.e., region iii), the rate of increases in the transmission area with the bias voltage is linear, leading to a linear I–V curve as shown inFig. 4(b) and (c).

The length effect is always important in nanodevices. So we investigate the length dependence of electronic transport proper-ties in M3 by increasing the number of carbon unit cells in the scattering region. Here we present the transport results when the numbers of carbon unit cells in the scattering region are 10 and 12, which are called M4 and M5, respectively. The current–voltage characteristics shown inFig. 8. We can see that the large rectifying ratio still can be observed irrespective of the length of heterojunc-tions. This is due to the fact that the electronic transport properties for M3 are mainly determined by the parity of the

π

and

π

∗ sub-bands of left and right electrodes. Thees results indicate that the lengths of the two parts in the scattering regions have no affects on the qualitative charge transport in M3.

Fig. 8.(Color online.) Current–voltage (I–V) characteristic for 2H-ZGNR/1H-ZGNR heterojunctions with different lengths of scattering regions. M3, M4 and M5 in-dicate the numbers of carbon unit cells in the central scattering region are 8, 10 and 12, respectively. The insets show the geometry structures of M4 and M5.

1910 C. Cao et al. / Physics Letters A 377 (2013) 1905–1910

4. Conclusion

In summary, using the first-principle quantum transport cal-culations, we have investigated the transport property of M1, M2 and M3 heterojunctions. The results of our calculation show that the transport properties of ZGNR heterojunctions can be modu-lated by the different edge hydrogenations. From the I–V char-acteristics, we find that M1 exhibits good conductivity while the transmission gap and rectification effects can be observed for M2 and M3 junctions. We present the first-principle theoretical anal-ysis for the rectification effects and find the dihydrogenation can lead to the blocking of electron transfer and decreases of the elec-tronic transport properties in comparison to the monohydrogena-tion ZGNR and bare ZGNR, as well as the changes in the distribu-tion of the frontier orbital at negative/positive bias. This mecha-nism of rectification effects could be considered in the designing of the practical electronic devices based on graphene nanorib-bons.

Acknowledgements

This work was supported by the Natural Science Foundation of China (No. 21103232), the Natural Science Foundation of Hunan Province (No. 11JJ3073), and High Performance Computing Center of Central South University.

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