J. Phys. Chem. C 2007, 111, 12175-12180
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Computational Design of a Rectifying Diode Made by Interconnecting Carbon Nanotubes with Peptide Linkages Mohammad Khazaei,*,† Sang Uck Lee,† Fabio Pichierri,‡ and Yoshiyuki Kawazoe† Institute for Materials Research, Tohoku UniVersity, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan, and COE Laboratory, Tohoku UniVersity, IMRAM 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan ReceiVed: December 28, 2006; In Final Form: May 29, 2007
With the use of first-principles total energy calculations, the optimized geometrical structures of seven different junctions constructed from different carbon nanotube units (metallic and semiconducting) and different covalent linkages (peptide bonds, -CONH-C6H4-CONH-, and >CON-C6H4-CONCONC6H4-CON< linkers, respectively. The former can be synthesized if one follows the chemical reaction shown in Scheme 1, parts a and b,8 whereas the latter could be obtained from the
10.1021/jp0689767 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/27/2007
12176 J. Phys. Chem. C, Vol. 111, No. 33, 2007
Khazaei et al. described by ultrasoft Vanderbilt pseudopotentials. We use a plane-wave (PW) basis set for the expansion of the electronic states. The number of plane-wave basis functions is determined by a cutoff energy of 200 eV. All the geometrical optimizations are performed with the Vienna ab initio simulation package (VASP).10 The conjugate gradient method is used to optimize all the models. The convergence criteria adopted here assumes that the maximum force acting on each atom in the relaxed structure is less than 0.06 eV/Å. We checked the reliability of our method by comparing our PW results against the available experimental data in the case of the formamide molecule.11 The results for the calculated bond lengths and angles are in good agreement within the relative errors of less than 1.8%. To study the transport properties of the proposed junctions, we implement some two-probe systems, “electrode-deviceelectrode”, from the optimized junctions. Those systems are obtained first by detaching the terminal CH moieties from the CNT ends of the optimized model junctions and then by connecting the left and right sides of the junctions to appropriate semi-infinite CNT electrodes. To achieve maximum coupling between the junctions and the electrodes, the chiralities of the latter are the same as those of the former (see Table 1). To simulate the electron transport of the proposed junctions, a set of calculations is carried out using the nonequilibrium Green’s function combined with DFT at the finite biases. The DFT calculations are based on the GGA and the exchange-correlation functional of Perdew-Burke-Ernzerhof.12 The core electrons are represented by improved Troullier-Martins pseudopotentials,13 whereas the valence electrons are described by a numerical atomic orbital basis set of single-ξ type. All the transport calculations are performed using Atomistix ToolKit (ATK) software package (version 2.0.4).14,15 The above software package has the ability to model the transport properties of nanoscale devices that consist of an atomic-scale device coupled to hetero bulk systems, or electrodes. Our model junctions J1J4, J6, and J7 can be considered as typical examples of such two-probe systems consisting of an atomic-scale device region flanked by two electrodes. More details on the method employed here can be found in refs 14 and 15. 3. Results and Discussion
Figure 1. DFT-optimized geometries of seven different molecular junctions for interconnecting carbon nanotubes.
TABLE 1: Constitution Details of Different Junctions Shown in Figure 1 molecular junction
block unit 1
linker
block unit 2
J1 J2 J3 J4 J5 J6 J7
(10,0) (5,5) (5,5) (5,5) (5,5) (10,0) (10,0)
-CONH-CONH-CONH-CONH-CONH-CONH-C6H4-CONH>CON-C6H4-CON
CON-C6H4-CONCON-C6H4-CONCONC6H4-CON< linkages. There exist strong steric repulsions among the C-H bonds of the benzene rings that belong to the >CON-C6H4-CON< linkages which provokes the distortion of the benzene rings at the middle of the J7 model junction, as seen in Figure 1. Finally, it is interesting to notice that the C-C bonds of the benzene rings of the -CONH-C6H4-CONHlinkages are slightly shorter (∼1.40 Å) than the corresponding C-C bonds in the >CON-C6H4-CON< linkages (∼1.42 Å). 3.2. Electron Transport Properties. To investigate the electron transport properties of the proposed nanotube junctions, owing to the expensive nature of transport calculations, we limit ourselves to study the electron transport properties of model junctions J1, J2, and J3. In J1, J2, and J3, two CNT units with the same or different chiralities (i.e., metallic or semiconducting) are attached together through five peptide linkages (see Figure 1). As explained in the Computational Details and Models section, to consider the electron transport properties of the above model junctions, the terminal CH moieties are detached from the CNT units of each model. Then, the left and right sides of the junctions are connected to two semi-infinite CNT electrodes. Their I-V characteristics are obtained by generating currents through the junctions at positive and negative applied voltages. For estimating the current, it is necessary to calculate the electron transmission probability of electrons19 from one electrode to the other through the junctions exactly. Hence, we calculate the induced potentials and, consequently, the transmission matrixes of the electrons at each bias voltage separately so as to estimate the currents in the most correct way. Figure 3a-c shows the calculated I-V characteristics of J1, J2, and J3, respectively. By comparing the I-V curves, it is
Carbon Nanotubes Rectifying Diode
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Figure 3. I-V characteristics and total transmissions curves of model junctions J1 (a and d), J2 (b and e), and J3 (c and f).
observed that when the chiralities of the CNTs electrodes are different, the corresponding I-V curve is completely asymmetric as shown in Figure 3c. However, when the CNTs possess the same chirality, the I-V curve is quasi-symmetric (see Figure 3, parts a and b). Interestingly from the asymmetric I-V curve of Figure 3c it appears that J3 behaves like a rectifying molecular diode. Molecular diodes are constituted of electron-rich (n-type) and electron-poor (p-type) subunits (similar to p-n junctions) which are effectively insulated from each other by a σ-electron system (i.e., covalent linkages).20-22 Model junction J3 displays a diode-like behavior because it is made of two carbon units (which can potentially act either as electron donor or electron acceptor) insulated from each other by peptide linkages. Due to the tilting of the five peptide planes with respect to the CNT surfaces (∼50°), the C1-N (1.48 Å) and C2-C3 (1.54 Å) bonds become closer to single bonds thus resembling a σ-electron system bridging two CNT units. By carefully looking at the I-V curves of J1 and J2, it is seen that they are not completely symmetric albeit not as asymmetric as that computed for J3. The small asymmetry observed in the I-V curves of J1 and J2 is due to the nonsymmetrical nature of the peptide linkages. Indeed, it is
expected that a small dipole moment be created along the nanotubes’ axes resulting from the vectorial sum of all the peptide bond dipole moments (the dipole moment of one peptide bond is ∼3.5 D23). The direction of the electric field induced by the dipole moment associated from the linkage can be either the same or opposite to the direction of the applied voltages thereby resulting in the small asymmetries observed in the I-V curves of J1 and J2. To explain the differences in I-V curves of the junctions, we now present a brief discussion about the transmission curves of J1, J2, and J3 shown in Figure 3d-f, respectively, computed at zero and (1.5 V. Although we have calculated the transmission curves for all the applied voltages in the I-V curves, we just show the results of transmission at three applied bias voltages in the figures because the trends of curve at the higher bias voltages are similar to the curves at the (1.5 V as exaggerated forms. From the inspection of Figure 3d-f, it is seen that the transmission curves dramatically change with the applied bias voltages by increasing of energy gap, shifting of peaks, and the appearance of new peaks. This result indicates the importance of calculating the potentials, and consequently the transmission coefficients, at each bias voltage separately. From
12180 J. Phys. Chem. C, Vol. 111, No. 33, 2007 the transmission curve of J1, shown in Figure 3d, it is observed that there exists a gap near the Fermi energy, in the range between -1.5 and +1.5 V. In contrast, the transmission curve of J2 is gapless (see Figure 3e) even at zero voltage. Since the current is an integration of the transmission probability of the electrons moving through the junctions,19 zero transmission definitely implies zero current as seen from Figure 3, parts a and d. According to our I-V calculations for perfect zigzag and armchair CNTs (not shown), the observed gap in the transmission curve of J1 (at zero voltage) and the absence of gap in that of J2 arise from the intrinsic physical properties of CNTs. From Figure 3d, it is seen that at applied voltages of (1.5 V as well as at higher applied voltages (not shown) a new peak appears near the Fermi energy thus resulting in the increase of current at (1.5 V as seen from Figure 3a. The height of this peak increases by increasing the applied voltage. From Figure 3e, it is observed that the transmission curves of J2 at low applied voltages, (1.5 V, are very similar (within the bias window for current calculation) to its transmission spectrum at zero bias. Here the very high peak is not observed near the Fermi energy even at the high applied voltages. Furthermore, from Figure 3, parts d and e, it is observed that in J1 and J2 the described trends of transmission curves are similar under both positive and negative voltages resulting in their quasi-symmetric I-V curves. On the other hand, the calculated I-V curve of J3 is not symmetric due to the different transmission curves obtained at the same positive and negative voltages (see Figure 3f). By comparing the transmission curves of J3 with those of J1 and J2, it is clearly seen that the transmission curves of J3 are similar to those of J2 (with metallic electrodes) at positive biases, whereas they are similar to those of J1 (with semiconducting electrodes) at negative voltages lower than -1.5 V (since a peak is created near the Fermi energy). From the above discussion it appears that the I-V curves of our model junctions are very much affected by the chirality of the CNT electrodes employed. It is worth mentioning that theoretical calculations performed by Esfarjani et al.1 show that nanotubes doped with donor atoms on one side and acceptor atoms on the opposite side can function as nanodiodes. Also, in some theoretical studies it has been reported that different linkages as well as different donor/ acceptor atoms are able to drastically change the effectiveness and functionality of the resulting molecular diodes.24-27 Hence, it would be interesting if we dope the carbon units of our designed junctions with different donor and acceptor elements so as to improve their rectification properties. Moreover, there exists the possibility that our model junctions may be highly resistive even though they do function as diode switches. 4. Conclusions The ability of peptide bonds to interconnect different types of CNTs (semiconducting and metallic) with different diameters is demonstrated by designing a series of different CNT junctions. To increase the flexibility of the peptide linkages necessary to join the nanotubes with larger differences in diameters, two longer length linkers, -CONH-C6H4-CONH- and >CONC6H4-CON
