Eur. Phys. J. B 76, 421–425 (2010) DOI: 10.1140/epjb/e2010-00181-7
THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Electronic transport for a crossed graphene nanoribbon junction with and without doping B.H. Zhou1 , W.H. Liao1 , B.L. Zhou1 , K.-Q. Chen2 , and G.H. Zhou1,3,a 1 2 3
Department of Physics and Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), Hunan Normal University, Changsha 410081, P.R. China Department of Applied Physics, Hunan University, Changsha 410082, P.R. China International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110015, P.R. China Received 8 March 2010 / Received in final form 25 May 2010 c EDP Sciences, Societ` Published online 17 June 2010 – a Italiana di Fisica, Springer-Verlag 2010 Abstract. The electronic transport property for a crossed junction of graphene nanoribbons with and without impurity doping is investigated numerically by a fully self-consistent non-equilibrium Green’s function method combined with density functional theory. It is demonstrated that the transport property of the junction depends sensitively on both the dopant positions and the geometry of junction. Specifically, the I-V characteristics of the junction with either nitrogen- or boron-doped stems always show metallic behavior. However, the current strongly depends on the doping atomic species and sites, but slightly depends on the geometry of junction under small bias voltage. The findings here may be important in the design of graphene-based electronic devices for realizing on/off states.
Graphene has been attracting considerable attention these years since the successful fabrication experiment by Novoselov et al. [1] Various graphene-based nanodevices and nanocircuits have been extensively studied, and many peculiar quantum transport phenomena have been observed [2–6]. The graphene nanoribbons (GNRs) with finite width are important components of graphene nanostructures. Comparing with other quasi-one-dimensional quantum wire systems, the electrical properties of GNRs are much more sensitive to the geometry and edge structures. For instance, the zigzag-edge GNRs (ZGNRs) are always metallic regardless of their widths due to the two edge states degenerated at the Fermi level [7]. However, the armchair-edge GNRs (AGNRs) are either semiconducting or metallic depending on their widths, and the energy gaps exhibit three distinct family behavior [8]. Moreover, for the lithium (Li) adsorption on GNRs, the interaction of Li with ZGNRs is much stronger than with armchairs [9]. Recently, the GNR junctions with various shapes, such as Z-shaped [10,11], L-shaped [12], and T-shaped [13,14] based on the above two kinds of GNRs, have been investigated since the experimental realization of GNRs [6]. The rectifying behavior [10] can be achieved by applying an external gate voltage in the heterjunction region of a Z-shaped junction consisting of two AGNR leads and a ZGNR bridge. Chen et al. [12] have investigated the dependence of electron transmission on the included angle of a L-shaped GNR, and they found that it is nearly reflectionless to electrons for a L-shaped GNR junction a
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with large included angle but highly reflected in the case of small included angle. Moreover, the I-V curves for a T-shaped GNR junction with impurity doping have been numerically calculated [14], and it is shown that the current through the junction strongly depends on the stem height of the junction but slightly depends on the doping atomic species. Most recently, a crossed junction fabricated from epitaxial graphene grown on SiC(0001) has been realized, and the observation of negative bend resistance has been found [15]. Wang et al. [16] have revealed that a pure transverse spin current can be generated without spin-orbital interaction and without external magnetic field for a cross-shaped device. However, the dependence of transport property on the geometry, size and impurity doping for crossed GNR junctions has not been studied and it would be an interesting problem for the application of GNRs. In this paper we study the transport property for a crossed junction of GNRs with and without nitrogen (N) or boron (B) doping. Both N (n-type) and B (ptype) atoms are typical substitutional dopants in carbon (C) materials, and their binding with C is covalent and quite strong. The incorporation of N or B atoms into carbon materials will influence the electronic structures and transport properties of the C host system by introducing extra carriers and new scatters. Therefore, it is of importance to study the effect of N or B doping in the performance for a graphene-based device design. In the present work we show that the transport property of the crossed GNR junction depends sensitively on the geometry and selective doping in different atomic sites. Peculiarly, the current through the junction strongly depends on the
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top stem RR
L shoulder bottom stem (a)
(b)
Fig. 1. (Color online) Schematic view of the crossed GNR junctions with contacted by left (L) and right (R) electrodes. (a) A symmetry junction, (b) a asymmetry junction. The gray balls represent H atoms, and red and blue balls represent impurity N(B) atoms with doping stems and shoulder, respectively.
doping atomic species and sites, but slightly depends on the shoulder width and stem height of the junction under small bias voltage. The geometry of the device proposed in this work is a crossed GNR junction as shown in Figure 1. The edge C atoms of the GNRs are saturated by hydrogen (H) atoms. Figure 1a is a symmetry crossed junction, which made of a 10-ZGNR shoulder and 11-AGNR top and bottom stems, and Figure 1b is a asymmetry crossed junction. The geometry considered here is already proved to have a potential impact in thermoelectric applications [17]. We note that the definition of GNRs in this work is accordant with previous convention [18], the ZGNR (or AGNR) is classed by the number of C–C zigzag chains forming the width of the ribbon, and the ZGNRs (AGNRs) with n C– C chains is named as n-ZGNRs (n-AGNRs) with integer n. The electrodes consist of two semi-infinite 10-ZGNRs which are metallic. The edge atomic sites of shoulder or stems are doped either by N or B atoms, which are shown in Figure 1a. It is noted that the most stable sites of N or B doping and their distribution in a single GNR have been tested in the previous work [19,20], which indicted that edge doping and a periodic distribution are the most favorable in energy. The transport property for the system in this work is investigated by an ab initio code package, Atomistix ToolKit 10.0 (ATK) [21,22], which is based on real space, nonequilibrium Green’s function formalism (NEGF) and the density functional theory. The calculation of the complete system can be obtained from two independent calculations of the two electrode regions, and a two probe central scattering region. The transport properties of such devices can be calculated by using the Landauer-B¨ uttiker formalism [23,24] which gives the conductance of the system in terms of the electron transmission coefficient, expressed as 2e2 G= T, (1) h where h is the Planck constant and T is the transmission coefficient from left (L) lead to right (R) lead, which can be expressed as A T = T r(ΓR GR C ΓL GC ),
(2)
Fig. 2. The transmission probability T (E) (solid line) and the corresponding DOS (dashed line) at T = 0 K for the pristine crossed GNR junction with h = 1.28 nm under zero bias (VB = 0), where (a) for a symmetry junction with stem width w = 0.74 nm , (b) for a symmetry junction with w = 1.23 nm and (c) for a asymmetry junction with w = 1.23 nm. A where GR C and GC are the retarded and advanced Green’s functions of the conductor, respectively, and ΓL(R) is the coupling matrices from the conductor to the left (right) lead. Within the NEGF formalism the ΓL(R) become
and
ΓL = i[ΣL − ΣL† ],
(3)
† ΓR = i[ΣR − ΣR ],
(4)
where ΣL and ΣR are the self-energies describing the coupling of the left and right electrode to the semi-infinite electrodes. By using NEGF combined with equation (1), the current through this system can be obtained 1 ∞ I= d[nF ( − μL ) − nF ( − μR )G], (5) e −∞ where μL and μR are the electrochemical potentials of the left and right electrodes, respectively. In our transport calculations, single-ζ basis set is used and a mesh cutoff is set to be 100 Ry to save computational time. The approximation for the exchange correlation function is the spin-unpolarized local density approximation. The C–C and C–H bond lengths are set to 1.42 and 1.1 ˚ A, respectively [25]. The test calculations with single-ζ and single-ζ plus polarization basis sets for a 10-ZGNR are performed, which give almost the same results. Figure 2 shows the calculated zero temperature (T = 0 K) transmission probability T (E) and the corresponding
B.H. Zhou et al.: Electronic transport for a crossed graphene nanoribbon junction with and without doping
density of states (DOS) for the symmetry pristine crossed GNR junctions with different stem widths but the same height (h = 1.28 nm) as a function of electron energy, where the zero energy is set at the Fermi level. Figures 2a and 2b plot the results for the symmetry junctions with w = 0.74 and w = 1.23 nm, respectively. While Figure 2c plots the result for a asymmetry junction with w = 1.23 nm. Firstly, it is interesting that the crossed GNR junctions always show metallic behavior regardless of their widths and symmetrical characteristic because of the sharp peak in DOS around the Fermi energy, which is contributed by the edge states of the ZGNR shoulder of the system [26,27]. The spectra of T (E) and DOS are correlated, especially in the positions of energy value for the peaks. As shown in Figure 2a, a junction with narrower stem shows two very low side peaks in DOS, which is similar to those of a T-shaped junction [14]. But in the case of wider stem, as shown in Figure 2b, the two side peaks in DOS become sharper, and T (E) exhibits more oscillatory behavior and sharp dips. For instance, once a transmission dip emerges at the Fermi energy, then more broad resonant side peaks appear compared with Figure 2a for the case of wider stems. In addition, the resonant tunneling peaks become much more shaper for the asymmetry junction as shown in Figure 2c compared with Figure 2b. These phenomena can be reasonably explained as the quantum interference and quantum size effect [28,29]. Specifically, the existence of the stems can destroy the systematic structure of the system, and the quantum interference inside the nanoribbon intersection of the crossed junction plays a key role in the electronic transport. The resonant tunneling peaks obviously arise from the constructive interference effect. However, the appearance of transmission dips is caused by the destructive interference effect between different paths (channels) introduced by lateral branch of the system [13,30]. For example, a path where the electrons go from left to right without passing through the stem, a path where the electrons enter the stem once, twice, etc, these different paths allow for destructive interference. These destructive interference is also known as antiresonance which has been observed early in other quantum transport systems [31–33]. Next, we turn to the impurity doping effects on the transport property for a symmetry crossed GNR junction with different doping species and positions (atomic sites). In Figure 3, we show the calculated T (E) and the corresponding DOS as a function of the electron energy for the symmetry cross junction at T = 0 K with w = 1.23 nm and h = 1.28 nm (corresponding to Fig. 2b). Figures 3a and 3b correspond respectively to N- and B-doped stems, while Figures 3c and 3d correspond to N- and B-doped shoulder, respectively. Firstly, we can see that different doping atomic sites and species result in obvious different T (E) compared with Figure 2b for a pristine (undoped) crossed GNR junction with the same width w and height h of stems, especially around the vicinity of the Fermi energy. Specifically, sharp peaks in DOS appear near the vicinity of the Fermi energy in Figures 3a and 3b, while the similar behavior happens only far from the Fermi energy
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Fig. 3. The T (E) (solid line) and DOS (dashed line) at T = 0 K for the crossed GNR junction with w = 1.23 nm and h = 1.28 nm under zero bias, where (a) for N- and (b) for B-doped stems, (c) for N- and (d) for B-doped shoulder, respectively.
in Figure 2b. This indicates that the electronic transport is mainly contributed by the two peaks near the Fermi energy, the existence of the transmission peaks also shows the metal behavior for the crossed junction with N- or Bdoped stems. However, if N or B atoms are doped at the edge sites of shoulder as shown in Figure 3c or Figure 3d, T (E) decreases notably compared with Figure 2b (from 0.2 to 0.05) at the Fermi energy. The above results indicate that the transport property of a crossed GNR junction can be controlled by using selective doping atomic sites and species in the system. To further understand the transport property around the Fermi level for the system, in Figure 4 we demonstrate the calculated I-V characteristics for the systems corresponding to Figure 3. For comparison, the I-V curve of the junction without impurity doping is also shown as black square line in the figure. We can see that the I-V curves for the all doping cases are found to be basically linear and symmetrical with respect to the Fermi level because of the symmetry of the systems. The current is about zero for junction with N(B)-doped shoulder [circle (down-triangle) lines] when the voltage ranges from −0.5 to 0.5 V, but increases notably with N(B)-doped stems (up (transverse)-triangle line). Therefore, one may control the transmission behavior of a crossed GNR junction
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Fig. 4. (Color online) The I-V curves of the crossed GNR junctions corresponding to Figure 3, where the circle (red), uptriangle (blue), down-triangle (green), and transverse-triangle (purple) lines for N-doped shoulder, N-doped stem, B-doped shoulder, and B-doped stem, respectively.
by selective doping positions for realizing switch states in experiment. Finally, we calculate the I-V characteristics for the symmetry pristine crossed junction with different widths and heights, which is shown in Figure 5. Firstly, the current of the system as a function of top stem height for the symmetry cross junction with w = 1.23 nm at T = 0 K has been calculated, the square (dark) and down-triangle (green) lines correspond to the bias voltage VB = 0.5 V and VB = 1.0 V, respectively. One can note that the current presents non-monotonic behavior. For the junction with no top stem h = 0 nm, corresponding to the case of a T-shaped junction, the values of the current is 9.66 μA under bias voltage 0.5 V. This result is in agreement with the previous work [14]. One can also observe that the current basically enhances with the top stem height increase. This phenomenon is differen from that in the T-shaped junction where the current decreases remarkably with the stem height increase. On the other hand, the current as a function of the top stem height with w = 0.74 nm also has been calculated in Figure 5, the up-triangle (red) and transverse-triangle (blue) lines correspond to the bias voltage VB = 0.5 V and VB = 1.0 V, respectively. Similar results have been obtained compared with the above crossed junction of width w = 1.23 nm. Generally, in Figure 5, the current smoothly increases when the width of the crossed junction decreases under the same bias voltage, the result is as expected since the transport properties of the crossed junction will be the same to the ideal zigzag GNRs as the width decreases to zero. However, it is clear that there are several current values which exhibit irregular behavior at positions of certain top stem heights, and the current values become more irregular under bias voltage 1.0 V. The physical reasons for this are that the system becomes unstable with bias voltage increase. Generally speaking, the above results are very suitable for device application because the current has low sensitivity to the widths and top stem heights of the junction under small bias voltages. In conclusion, the transmission probabilities and the I-V characteristics for the crossed GNR junctions with
Fig. 5. (Color online) The current as a function of the height of the top stem for a symmetry pristine junction shown in Figure 1a, where the square (black) and up-triangle (red) lines for width 1.23 nm and 0.74 nm under bias voltage 0.5 V, while the down-triangle (green) and transverse-triangle (blue) lines for width 1.23 nm and 0.74 nm under bias voltage 1.0 V, respectively.
and without impurity doping are investigated by a fully self-consistent non-equilibrium Green’s function method combined with density functional theory. It is found that the transport property of the crossed junction is obviously different from other type of GNR junctions [10–14], and is sensitive to its geometry and impurity doping. Moreover, the I-V characteristics of the crossed junction without doping, or with N or B doping stem are all shown metallic behavior, and the current depends slightly on the width and height of stem. Interestingly, doping in the stems of junction does not change the transmission probability at the Fermi level, either N or B doping in the shoulder of junction yields Schottky-barrier-type devices. Our results may be helpful in designing GNR-based nanoscale electronic devices. This work was supported by National Natural Science Foundation of China (Grant Nos. 10974052, 10574042).
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