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Effect of structure on electronic properties of the iron-carbon nanotube interface
Chemical Physics Letters 615 (2014) 11–15
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Effect of structure on electronic properties of the iron-carbon nanotube interface Sarah L.T. Jones a , Gabriel Greene-Diniz a , Michael Haverty b , Sadasivan Shankar b , James C. Greer a,∗ a b
Tyndall National Institute, Dyke Parade, Cork, Ireland Intel Corporation, 2200 Mission College Blvd., Santa Clara, CA 95054-1549, USA
a r t i c l e
i n f o
Article history: Received 1 August 2014 In final form 23 September 2014 Available online 2 October 2014
a b s t r a c t The effect of structure and doping on the properties of the iron–CNT interface is studied using ab initio electronic structure methods. We consider two interface structures, one with a metal bump onto which the CNT is docked and one without. The CNT band gap and the position of the Fermi energy are insensitive to the interface structure, however transmission is affected by structural change, with larger transmission occurring for the interface with the dock. Additionally, we study a boron doped CNT in contact with iron and find that the CNT becomes metallic and an Ohmic contact is formed. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Due to their unique electronic properties, carbon nanotubes (CNTs) and related materials have been a focus of intensive research for future micro- and nanoelectronic devices [1]. CNTs exhibit metallic or semiconducting behaviour, which is dependent on their precise structure (chirality). Metallic CNTs are being considered as a replacement for metal interconnects, which fail at small diameters due to current induced electromigration [2,3]. Meanwhile, semi-conducting CNTs are being considered as channel materials in CNT based field effect transistors (FETs) [4–6]. In addition, prototype diodes [7,8] and chemical sensors [9,10] have been fabricated from CNTs. These promising applications require that the CNT is contacted with metal, therefore understanding the nature of the metal-CNT contact is of paramount importance. CNTs can be contacted to metal in two different configurations – side and end contact. In the side contact configuration, the metal is in contact with the CNT sidewall. Such a configuration is typically realised experimentally by depositing metal on the CNT (e.g. Ref. [7]). Conversely, the end contact configuration contacts the metal to one end of the CNT (i.e. the CNT terminates at the metal contact) [11], this configuration is challenging to produce in experiment and resultingly experimental study of metal-CNT contacts has focused on the side contacted configuration. The behaviour of the metal-CNT contact has been found to be Ohmic or Schottky,
∗ Corresponding author. E-mail address: [email protected] (J.C. Greer). http://dx.doi.org/10.1016/j.cplett.2014.09.056 0009-2614/© 2014 Elsevier B.V. All rights reserved.
depending on the metal used as the contact [12]. This dissimilar behaviour has been attributed to differences in metal work function (m ) [13]. Consideration of m has had some success as a simple predictor of contact behaviour but it cannot account for the more complex aspects of the contact such as the interface structure. Early tight binding molecular dynamics studies indicated the importance of understanding the detailed CNT-interface geometry by showing the position on the CNT where Ni C bonds formed dramatically impacted the CNT properties [14,15]. More recently Bai and co-workers have studied a range of different Al-CNT contacts and found the electronic transmission to vary with the contact structure [16]. A comprehensive understanding of the metal-CNT interface is essential to enable the reliable and controllable production CNT nanoelectronic devices, but even if this contact is fully understood, the relationship between CNT chirality and electronic properties causes difficulties. Although preferential growth of certain chiralities have been achieved [17–20], it is currently not possible to control the chirality and hence electronic properties of pristine CNTs during CVD growth precisely. For applications which require metallic CNTs only, doping is a potential solution to the issues resulting from poor chirality control. In particular, substitutional doping by nitrogen or boron results in metallic CNTs, irrespective of chirality [21,22], however some degradation in electronic behaviour after doping has been predicted in the case of intrinsically metallic CNTs [23,24]. In this study we consider end contacts between the semiconducting (10,0)-CNT and two different iron electrode structures. Previous studies have considered the CNT embedded in the metal
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S.L.T. Jones et al. / Chemical Physics Letters 615 (2014) 11–15
contact [16], we take a different approach and instead contact the CNT to a raised ‘bump’ on the metal surface. We specifically choose iron as the metal contact because it is commonly used as a CNT growth catalyst and such a configuration has previously been assessed experimentally for the frequently used growth catalyst Ni [11]. Additionally, we consider the B-doped (10,0)-CNT interface, again in end contact with iron metal. 2. Computational methods Density functional theory (DFT) and the non-equilibrium Green function (NEGF) [25] method as implemented by the software package OpenMX are used to calculate the transport characteristics of the Fe–CNT interface. All calculations use the PBE [26] formulation of the generalised gradient approximation (GGA) exchange and correlation functional, along with norm conserving pseudopotentials [27]. We model the Fe–CNT interface by bonding directly a (10,0) CNT (pristine and boron doped (B-doped)) to an Fe slab. The Fe slabs consists of 7×7 (1 1 1) Fe, with an additional raised Fe ‘dock’, used to sample varying contact configurations. In addition we consider two model systems: an iron nanowire and a small diameter CNT contacted to an iron nanowire. Full structural optimisations are carried out for all interfaces and the Fe and CNT leads, with the exception of Fe back plane, which is frozen for all interfaces until all forces are less than 5 × 10−4 Hartree/Bohr. The OpenMX code employs a linear combination of pseudoatomic orbitals method [28,29], the numeric pseudoatomic orbitals (PAOs) chosen for geometry optimisations are as given in Table 1. An energy cut-off of 150 Ry is used for numerical integration and supercells were chosen such that there was a minimum vacuum of 1 nm in all non-periodic directions. The NEGF method is used the generate the transport characteristics of the Fe–CNT junctions and enables study of the non-periodic interface with periodic, semi-infinite electrodes (leads). The basis sets used are described in Table 1. A 128 × 128 × 128 grid is used for the numerical integration. The calculations are considered converged when the norm of the residual density matrix was below at least 1 × 10−4 and ideally below 1 × 10−6 , although this stricter convergence criterium has negligible impact on the electronic properties. First the Hamiltonians of the periodic left L and right R leads are calculated in a standard DFT calculation. In the NEGF calculation, only the extended scattering region C, which contains the non-periodic interface as well as one of each lead unit, is calculated explicitly the effect of the semi-infinite leads on C is included through self-energy terms in the Green function. Thus while the junction itself is finite, the system as a whole is infinite in the transport direction. Figure 1(a) gives a schematic representation of the NEGF system. A detailed description of the NEGF implementation used in this work can be found in Ref. [25]. The results of NEGF calculations are used by the TranMain code to generate transmission spectra. Additionally, we use the linear response method, the accuracy of which we have previously assessed for similar Al-CNT systems [30], to generate IV characteristics for the Fe-B-doped CNT interface. Table 1 Basis sets used for geometry optimisations and NEGF calculations. The first part of the basis set notation, i.e. preceding the angular momentum designation (s, p) is the cut-off radius of the PAO in Bohr, the second part indicates the number of orbitals used for the valence electrons. For example, B 4.5-s2p2 implies a cut-off of 4.5 Bohr and a total of 8 basis functions (2 s functions and 6 p functions). Element
Geometry
NEGF
H B C Fe
4.0-s2 4.5-s2p2 4.5-s2p2 6.0-s2p2d2
– 4.5-s2p2 4.5-s2p1 6.0-s2p2d1
Figure 1. (a) Schematic of the structure used in NEGF calculations. L0 and R0 have structure identical to the left and right lead repeat units, respectively. The region L0 +C0 +R0 is the extended scattering region and is computed explicitly in NEGF calculations. L1 and R1 are the first units of the semi-infinite left and right leads, respectively. In this work C consists of the Fe–CNT interface while Li is an Fe Slab and Ri is a CNT unit cell. (b) (5,0)-FeNW structure. (c) B-doped (10,0)-Fe structure. (d) Interface 1 structure. (e) Interface 2 structure. Fe is purple, C is grey and B is pink. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Results and discussion It is essential that the effect of spin polarisation, particularly in the vicinity of the Fermi level, on calculations involving iron are understood before drawing conclusions from closed shell calculations. Open-shell calculations greatly increase the cost of calculations, both in terms of memory requirements and computational time. Two model systems consisting of a 6 A˚ diameter iron nanowire (FeNW – see the Supplementary Information) and the interface between a (5,0)-CNT and Fe are considered to study the importance of spin polarisation on the calculation of electron transport. The Fe–(5,0)-CNT interface (Fig. 1(b) provides a realistic model of the Fe–(10,0)-CNT interface we wish to study while still being computationally tractable for both closed and open shell calculations. The pristine (5,0)-CNT exhibits a vanishingly small band gap. This result is not unexpected as CNT electronic properties contrary
S.L.T. Jones et al. / Chemical Physics Letters 615 (2014) 11–15
Figure 2. (a) Total DOS for the (5,0)-FeNW system for polarised (open shell) and unpolarised (closed shell) NEGF calculations. (b) DOS for the repeat unit of the CNT furthest from the interface for the polarised and unpolarised case.
to the simple zone-folding picture which predicts that the (5,0)CNT should be a semi-conductor have previously been reported for narrow diameter CNTs [31,32]. The total DOS of the Fe–CNT interface is dominated by iron and as a result closely resembles the DOS of the FeNW (compare Fig. 2(a) with Fig. S3). Spin polarisation of the CNT atoms is negligible even at the interface, although up and down spin DOS do differ slightly at the Fermi level for carbon atoms bonded to iron. Far from the interface up and down spin DOS are quite similar and the open and closed shell DOS agree closely (Fig. 2(b)). Transmission close to the Fermi level (from −0.3 eV to 0.3 eV) is relatively low for both the open and closed shell cases (Fig. 3(a) and (b)) and is similar in both cases. In addition the transmission results are dominated by the CNT. Figure 4 shows the IV curves obtained using the linear response method for the closed and open shell calculations. There is reasonable agreement between the closed and open shell currents, with the closed shell current being larger for both forward and reverse bias. These results suggest that the transmission around the Fermi energy is strongly affected by the CNT DOS, which is lower than the Fe DOS at this energy. Therefore, provided the CNT DOS is lower than the Fe DOS, closed shell calculations should provide a reasonable approximation to the open shell case near the Fermi energy. Structures for the Fe–CNT interfaces are given in Figure 1. Following the above discussion, all calculations of the Fe–(10,0)-CNT interfaces do not consider spin polarisation. Two interface geometries are consider for the junction between Fe and an undoped CNT. Interface 1 (Fig. 1(d)) has a ‘bump’ of Fe on the Fe surface and models the presence of catalytic Fe at the CNT growth edge. Such catalyst-CNT structures have been observed by in situ TEM of CNT growth [33]. Interface 2 (Fig. 1(e)) presents a flat surface which the CNT bonds to and represents an idealised system in which a
13
Figure 3. Transmission of the (5,0)-FeNW system. (a) Transmission per spin channel for closed and open shell calculations of the (5,0)-FeNW system. (b) Total transmission for both open and closed shell calculations.
Figure 4. Comparison of the IV curves obtained for the closed and open shell (5,0)FeNW.
CNT is placed directly onto a perfect FeNW. The two structures could be considered as the limiting cases, with the real situation somewhere between. In spite of the differing structures of interface 1 and 2, the average length of the Fe C bonds is similar being 1.960 A˚ for interface 1 and 1.924 A˚ for interface 2. The range of Fe C bonds lengths is larger for interface 2 than for interface 1, thus the interface structure is less uniform in the case of interface 2. The structure of the B-doped CNT/Fe interface (Fig. 1(b)) is based on interface 1 (i.e. it retains the ‘bump’ at the interface). The dopant concentration is 1.7 at. % which is on the lower end of the doping levels seen in experiment. The dopant atoms are as uniformly dispersed as possible within the constraints of periodicity. Given the structural similarities it is unsurprising that the bonding at the
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the transmission of the B-doped interface is lower than that of interface 1 through most of the region close to the Fermi energy with the exception of region of zero transmission for interface 1 which results from the CNT band gap. This difference in transmission is caused by the presence of B in the CNT, which acts as a defect in the ideal CNT structure. This reduced transmission on incorporation of a substitutional dopant is consistent with literature reports of poorer electronic properties of substitutionally doped CNTs [23,24]. The precise position of the dopant atoms in the CNT will influence the exact transmission obtained, however we believe that the CNT with uniformly dispersed dopants used in this work provides a reasonable average picture for this dopant concentration. The voltage region found to give reasonable accuracy using the linear response method is in the range of zero transmission for interface 1 and 2 and so the linear response IV is considered for the B-doped CNT/Fe interface only, shown in Figure 5(b). A linear IV curve is obtained which is suggestive of Ohmic contact formation at this interface. We have previously found similar behaviour for interfaces between Al and B- and N-doped CNTs [30]. Thus, it may indeed be possible to reliably produce Ohmic contacts with CNTs through doping, although further research for doped armchair and chiral CNTs is necessary to establish this point explicitly for a wider range of CNT chiralities. 4. Summary
Figure 5. (a) Transmission of the (10,0)-FeNW systems. The Fermi energy is 0 eV. (b) Linear response IV curve for B doped-CNT Fe interface around the Fermi energy, corresponding to a resistance of R ≈ 6 k.
B-doped interface is very similar to interface 1, with an average ˚ For the interfaces studied Mulliken popubond length of 1.972 A. lation analysis shows that charge is transferred from Fe to the CNT. A larger charge transfer takes place for interface 1 (∼2.1 e) than interface 2 (∼1.4 e), which could be attributed to the differences in the interface structures. Two of the carbon atoms at the interface between the B-doped CNT and Fe also bond to boron, which complicates the charge transfer at this interface, however total charge transfer to the CNT (∼2.2 e) is very similar to interface 1, as would expected given the structural similarities. The size of the CNT gap and the position of the Fermi energy appear to be relatively insensitive to the exact structure of the interface. This can be seen in the zero-bias transmissions of interface 1 and interface 2 shown in Figure 5, where the gaps in transmission associated with the isolated CNT gap coincide. Below the Fermi energy, the transmission of interface 1 and interface 2 is similar, with that of interface 2 becoming larger than interface 1 below −1.5 eV. Above the Fermi energy transmission for interface 1 is at the majority of points greater than interface 2. In particular, near the Fermi energy in the range 0.35–1.0 eV we see significantly larger transmission for interface 1. This difference in transmission is presumed to be related to the differences in structure and charge transfer at the interfaces. From this result, it is to be anticipated that structural changes (including local chemistry) may lead to substantial alteration of the IV characteristics of Fe–CNT devices. Similar to our previous report on the Al-B-doped CNT system [30], the B-doped (10,0)-CNT is metallic, with gap of the undoped CNT pushed above the Fermi energy. The shifted band gap also becomes smaller than in the undoped CNT. This is reflected in the transmission of the B-doped CNT seen in Figure 5(a). The are no significant differences in the interfacial structure or charge transfer between the interface 1 and the B-doped interface. In spite of this,
We have found spin polarisation not to be critical for transmission or linear response IV close the the Fermi level for the Fe–CNT junction. The exact structure of the Fe–CNT end contact is found to affect neither the position of the Fermi energy nor the extent of the region of zero transmission for the interfaces that were studied under 0 K conditions. However, changes in the structure of the interface are found to impact on the transmission of the Fe–CNT interface. On doping with boron, the (10,0)-CNT is found to become metallic but overall transmission is reduced relative to the undoped CNT. We obtain a linear IV curve for the interface between the boron doped CNT and iron nanowire which demonstrates the formation of an Ohmic contact and at the Fermi level we find a resistance of 6 k. Acknowledgments S.L.T.J. was funded under an Irish Research Council EMBARK Postgraduate Scholarship. This work was also supported by Science Foundation Ireland under a Principal Investigator Grant No. 06/IN.1I857. The Tyndall team also acknowledges research funding by Intel Corporation. We acknowledge the Irish Centre for High End Computing (ICHEC) for access to computational resources. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett. 2014.09.056. References [1] [2] [3] [4] [5] [6]
R.H. Baughman, A.A. Zakhidov, W.A. de Heer, Science 297 (2002) 787. P. Avouris, Z.H. Chen, V. Perebeinos, Nat. Nanotechnol. 2 (2007) 605. G.F. Close, S. Yasuda, B. Paul, S. Fujita, H.S.P. Wong, Nano Letters 8 (2008) 706. S.J. Tans, A.R.M. Verschueren, C. Dekker, Nature 393 (1998) 49. A. Javey, et al., Nat. Mater. 1 (2002) 241. R.T. Weitz, U. Zschieschang, F. Effenberger, H. Klauk, M. Burghard, K. Kern, Nano Lett. 7 (2007) 22. [7] H.M. Manohara, E.W. Wong, E. Schlecht, B.D. Hunt, P.H. Siegel, Nano Lett. 5 (2005) 1469. [8] C. Lu, L. An, F. Qiang, J. Liu, H. Zhang, J. Murdock, Appl. Phys. Lett. 88 (2006) 133501.
S.L.T. Jones et al. / Chemical Physics Letters 615 (2014) 11–15 [9] J. Kong, N.R. Franklin, C. Zhou, M.G. Chapline, S. Peng, K. Cho, H. Dai, Science 287 (2000) 622. [10] A. Modi, N. Koratkar, E. Lass, B. Wei, P.M. Ajayan, Nature 424 (2003) 171. [11] C. Santini, A. Volodin, C. Van Haesendonck, S. De Gendt, G. Groeseneken, P.M. Vereecken, Carbon 49 (2011) 4004. [12] W.G. Zhu, E. Kaxiras, Nano Lett. 6 (2006) 1415. [13] F. Leonard, J. Tersoff, Phys. Rev. Lett. 84 (2000) 4693. [14] A.N. Andriotis, M. Menon, G.E. Froudakis, Appl. Phys. Lett. 76 (2000) 3890. [15] A.N. Andriotis, M. Menon, G.E. Froudakis, Chem. Phys. Lett. 320 (2000) 425. [16] P. Bai, E. Li, K.T. Lam, O. Kurniawan, W.S. Koh, Nanotechnology 19 (2008) 115203. [17] G. Lolli, L.A. Zhang, L. Balzano, N. Sakulchaicharoen, Y.Q. Tan, D.E. Resasco, J. Phys. Chem. B 110 (2006) 2108. [18] X.L. Li, X.M. Tu, S. Zaric, K. Welsher, W.S. Seo, W. Zhao, H.J. Dai, J. Am. Chem. Soc. 129 (2007) 15770. [19] H. Wang, et al., J. Am. Chem. Soc. 132 (2010) 16747.
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F. Yang, et al., Nature 510 (2014) 522. K. Liu, Ph. Avouris, R. Martel, Phys. Rev. B 63 (2001) 161404. J.A. Talla, Physica B 407 (2012) 966. C.-C. Kaun, B. Larade, H. Mehrez, J. Taylor, H. Guo, Phys. Rev. B 65 (2002) 205416. S. Latil, S. Roche, D. Mayou, J.-C. Charlier, Phys. Rev. Lett. 92 (2004) 256805. T. Ozaki, K. Nishio, H. Kino, Phys. Rev. B 81 (2010) 035116. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. I. Morrison, D.M. Bylander, L. Kleinman, Phys. Rev. B 47 (1993) 6728. T. Ozaki, Phys. Rev. B 67 (2003) 155108. T. Ozaki, H. Kino, Phys. Rev. B 69 (2004) 195113. S.L.T. Jones, J.C. Greer, J. Appl. Phys. 114 (2013) 153709. I. Cabria, J.W. Mintmire, C.T. White, Phys. Rev. B 67 (2003) 121406. V. Barone, G.E. Scuseria, J. Chem. Phys. 121 (2004) 10376. H. Yoshida, S. Takeda, T. Uchiyama, H. Kohno, Y. Homma, Nano Lett. 8 (2008) 2082.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Effect of structure on electronic properties of the iron-carbon nanotube interface Sarah L.T. Jones a , Gabriel Greene-Diniz a , Michael Haverty b , Sadasivan Shankar b , James C. Greer a,∗ a b
Tyndall National Institute, Dyke Parade, Cork, Ireland Intel Corporation, 2200 Mission College Blvd., Santa Clara, CA 95054-1549, USA
a r t i c l e
i n f o
Article history: Received 1 August 2014 In final form 23 September 2014 Available online 2 October 2014
a b s t r a c t The effect of structure and doping on the properties of the iron–CNT interface is studied using ab initio electronic structure methods. We consider two interface structures, one with a metal bump onto which the CNT is docked and one without. The CNT band gap and the position of the Fermi energy are insensitive to the interface structure, however transmission is affected by structural change, with larger transmission occurring for the interface with the dock. Additionally, we study a boron doped CNT in contact with iron and find that the CNT becomes metallic and an Ohmic contact is formed. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Due to their unique electronic properties, carbon nanotubes (CNTs) and related materials have been a focus of intensive research for future micro- and nanoelectronic devices [1]. CNTs exhibit metallic or semiconducting behaviour, which is dependent on their precise structure (chirality). Metallic CNTs are being considered as a replacement for metal interconnects, which fail at small diameters due to current induced electromigration [2,3]. Meanwhile, semi-conducting CNTs are being considered as channel materials in CNT based field effect transistors (FETs) [4–6]. In addition, prototype diodes [7,8] and chemical sensors [9,10] have been fabricated from CNTs. These promising applications require that the CNT is contacted with metal, therefore understanding the nature of the metal-CNT contact is of paramount importance. CNTs can be contacted to metal in two different configurations – side and end contact. In the side contact configuration, the metal is in contact with the CNT sidewall. Such a configuration is typically realised experimentally by depositing metal on the CNT (e.g. Ref. [7]). Conversely, the end contact configuration contacts the metal to one end of the CNT (i.e. the CNT terminates at the metal contact) [11], this configuration is challenging to produce in experiment and resultingly experimental study of metal-CNT contacts has focused on the side contacted configuration. The behaviour of the metal-CNT contact has been found to be Ohmic or Schottky,
∗ Corresponding author. E-mail address: [email protected] (J.C. Greer). http://dx.doi.org/10.1016/j.cplett.2014.09.056 0009-2614/© 2014 Elsevier B.V. All rights reserved.
depending on the metal used as the contact [12]. This dissimilar behaviour has been attributed to differences in metal work function (m ) [13]. Consideration of m has had some success as a simple predictor of contact behaviour but it cannot account for the more complex aspects of the contact such as the interface structure. Early tight binding molecular dynamics studies indicated the importance of understanding the detailed CNT-interface geometry by showing the position on the CNT where Ni C bonds formed dramatically impacted the CNT properties [14,15]. More recently Bai and co-workers have studied a range of different Al-CNT contacts and found the electronic transmission to vary with the contact structure [16]. A comprehensive understanding of the metal-CNT interface is essential to enable the reliable and controllable production CNT nanoelectronic devices, but even if this contact is fully understood, the relationship between CNT chirality and electronic properties causes difficulties. Although preferential growth of certain chiralities have been achieved [17–20], it is currently not possible to control the chirality and hence electronic properties of pristine CNTs during CVD growth precisely. For applications which require metallic CNTs only, doping is a potential solution to the issues resulting from poor chirality control. In particular, substitutional doping by nitrogen or boron results in metallic CNTs, irrespective of chirality [21,22], however some degradation in electronic behaviour after doping has been predicted in the case of intrinsically metallic CNTs [23,24]. In this study we consider end contacts between the semiconducting (10,0)-CNT and two different iron electrode structures. Previous studies have considered the CNT embedded in the metal
12
S.L.T. Jones et al. / Chemical Physics Letters 615 (2014) 11–15
contact [16], we take a different approach and instead contact the CNT to a raised ‘bump’ on the metal surface. We specifically choose iron as the metal contact because it is commonly used as a CNT growth catalyst and such a configuration has previously been assessed experimentally for the frequently used growth catalyst Ni [11]. Additionally, we consider the B-doped (10,0)-CNT interface, again in end contact with iron metal. 2. Computational methods Density functional theory (DFT) and the non-equilibrium Green function (NEGF) [25] method as implemented by the software package OpenMX are used to calculate the transport characteristics of the Fe–CNT interface. All calculations use the PBE [26] formulation of the generalised gradient approximation (GGA) exchange and correlation functional, along with norm conserving pseudopotentials [27]. We model the Fe–CNT interface by bonding directly a (10,0) CNT (pristine and boron doped (B-doped)) to an Fe slab. The Fe slabs consists of 7×7 (1 1 1) Fe, with an additional raised Fe ‘dock’, used to sample varying contact configurations. In addition we consider two model systems: an iron nanowire and a small diameter CNT contacted to an iron nanowire. Full structural optimisations are carried out for all interfaces and the Fe and CNT leads, with the exception of Fe back plane, which is frozen for all interfaces until all forces are less than 5 × 10−4 Hartree/Bohr. The OpenMX code employs a linear combination of pseudoatomic orbitals method [28,29], the numeric pseudoatomic orbitals (PAOs) chosen for geometry optimisations are as given in Table 1. An energy cut-off of 150 Ry is used for numerical integration and supercells were chosen such that there was a minimum vacuum of 1 nm in all non-periodic directions. The NEGF method is used the generate the transport characteristics of the Fe–CNT junctions and enables study of the non-periodic interface with periodic, semi-infinite electrodes (leads). The basis sets used are described in Table 1. A 128 × 128 × 128 grid is used for the numerical integration. The calculations are considered converged when the norm of the residual density matrix was below at least 1 × 10−4 and ideally below 1 × 10−6 , although this stricter convergence criterium has negligible impact on the electronic properties. First the Hamiltonians of the periodic left L and right R leads are calculated in a standard DFT calculation. In the NEGF calculation, only the extended scattering region C, which contains the non-periodic interface as well as one of each lead unit, is calculated explicitly the effect of the semi-infinite leads on C is included through self-energy terms in the Green function. Thus while the junction itself is finite, the system as a whole is infinite in the transport direction. Figure 1(a) gives a schematic representation of the NEGF system. A detailed description of the NEGF implementation used in this work can be found in Ref. [25]. The results of NEGF calculations are used by the TranMain code to generate transmission spectra. Additionally, we use the linear response method, the accuracy of which we have previously assessed for similar Al-CNT systems [30], to generate IV characteristics for the Fe-B-doped CNT interface. Table 1 Basis sets used for geometry optimisations and NEGF calculations. The first part of the basis set notation, i.e. preceding the angular momentum designation (s, p) is the cut-off radius of the PAO in Bohr, the second part indicates the number of orbitals used for the valence electrons. For example, B 4.5-s2p2 implies a cut-off of 4.5 Bohr and a total of 8 basis functions (2 s functions and 6 p functions). Element
Geometry
NEGF
H B C Fe
4.0-s2 4.5-s2p2 4.5-s2p2 6.0-s2p2d2
– 4.5-s2p2 4.5-s2p1 6.0-s2p2d1
Figure 1. (a) Schematic of the structure used in NEGF calculations. L0 and R0 have structure identical to the left and right lead repeat units, respectively. The region L0 +C0 +R0 is the extended scattering region and is computed explicitly in NEGF calculations. L1 and R1 are the first units of the semi-infinite left and right leads, respectively. In this work C consists of the Fe–CNT interface while Li is an Fe Slab and Ri is a CNT unit cell. (b) (5,0)-FeNW structure. (c) B-doped (10,0)-Fe structure. (d) Interface 1 structure. (e) Interface 2 structure. Fe is purple, C is grey and B is pink. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Results and discussion It is essential that the effect of spin polarisation, particularly in the vicinity of the Fermi level, on calculations involving iron are understood before drawing conclusions from closed shell calculations. Open-shell calculations greatly increase the cost of calculations, both in terms of memory requirements and computational time. Two model systems consisting of a 6 A˚ diameter iron nanowire (FeNW – see the Supplementary Information) and the interface between a (5,0)-CNT and Fe are considered to study the importance of spin polarisation on the calculation of electron transport. The Fe–(5,0)-CNT interface (Fig. 1(b) provides a realistic model of the Fe–(10,0)-CNT interface we wish to study while still being computationally tractable for both closed and open shell calculations. The pristine (5,0)-CNT exhibits a vanishingly small band gap. This result is not unexpected as CNT electronic properties contrary
S.L.T. Jones et al. / Chemical Physics Letters 615 (2014) 11–15
Figure 2. (a) Total DOS for the (5,0)-FeNW system for polarised (open shell) and unpolarised (closed shell) NEGF calculations. (b) DOS for the repeat unit of the CNT furthest from the interface for the polarised and unpolarised case.
to the simple zone-folding picture which predicts that the (5,0)CNT should be a semi-conductor have previously been reported for narrow diameter CNTs [31,32]. The total DOS of the Fe–CNT interface is dominated by iron and as a result closely resembles the DOS of the FeNW (compare Fig. 2(a) with Fig. S3). Spin polarisation of the CNT atoms is negligible even at the interface, although up and down spin DOS do differ slightly at the Fermi level for carbon atoms bonded to iron. Far from the interface up and down spin DOS are quite similar and the open and closed shell DOS agree closely (Fig. 2(b)). Transmission close to the Fermi level (from −0.3 eV to 0.3 eV) is relatively low for both the open and closed shell cases (Fig. 3(a) and (b)) and is similar in both cases. In addition the transmission results are dominated by the CNT. Figure 4 shows the IV curves obtained using the linear response method for the closed and open shell calculations. There is reasonable agreement between the closed and open shell currents, with the closed shell current being larger for both forward and reverse bias. These results suggest that the transmission around the Fermi energy is strongly affected by the CNT DOS, which is lower than the Fe DOS at this energy. Therefore, provided the CNT DOS is lower than the Fe DOS, closed shell calculations should provide a reasonable approximation to the open shell case near the Fermi energy. Structures for the Fe–CNT interfaces are given in Figure 1. Following the above discussion, all calculations of the Fe–(10,0)-CNT interfaces do not consider spin polarisation. Two interface geometries are consider for the junction between Fe and an undoped CNT. Interface 1 (Fig. 1(d)) has a ‘bump’ of Fe on the Fe surface and models the presence of catalytic Fe at the CNT growth edge. Such catalyst-CNT structures have been observed by in situ TEM of CNT growth [33]. Interface 2 (Fig. 1(e)) presents a flat surface which the CNT bonds to and represents an idealised system in which a
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Figure 3. Transmission of the (5,0)-FeNW system. (a) Transmission per spin channel for closed and open shell calculations of the (5,0)-FeNW system. (b) Total transmission for both open and closed shell calculations.
Figure 4. Comparison of the IV curves obtained for the closed and open shell (5,0)FeNW.
CNT is placed directly onto a perfect FeNW. The two structures could be considered as the limiting cases, with the real situation somewhere between. In spite of the differing structures of interface 1 and 2, the average length of the Fe C bonds is similar being 1.960 A˚ for interface 1 and 1.924 A˚ for interface 2. The range of Fe C bonds lengths is larger for interface 2 than for interface 1, thus the interface structure is less uniform in the case of interface 2. The structure of the B-doped CNT/Fe interface (Fig. 1(b)) is based on interface 1 (i.e. it retains the ‘bump’ at the interface). The dopant concentration is 1.7 at. % which is on the lower end of the doping levels seen in experiment. The dopant atoms are as uniformly dispersed as possible within the constraints of periodicity. Given the structural similarities it is unsurprising that the bonding at the
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the transmission of the B-doped interface is lower than that of interface 1 through most of the region close to the Fermi energy with the exception of region of zero transmission for interface 1 which results from the CNT band gap. This difference in transmission is caused by the presence of B in the CNT, which acts as a defect in the ideal CNT structure. This reduced transmission on incorporation of a substitutional dopant is consistent with literature reports of poorer electronic properties of substitutionally doped CNTs [23,24]. The precise position of the dopant atoms in the CNT will influence the exact transmission obtained, however we believe that the CNT with uniformly dispersed dopants used in this work provides a reasonable average picture for this dopant concentration. The voltage region found to give reasonable accuracy using the linear response method is in the range of zero transmission for interface 1 and 2 and so the linear response IV is considered for the B-doped CNT/Fe interface only, shown in Figure 5(b). A linear IV curve is obtained which is suggestive of Ohmic contact formation at this interface. We have previously found similar behaviour for interfaces between Al and B- and N-doped CNTs [30]. Thus, it may indeed be possible to reliably produce Ohmic contacts with CNTs through doping, although further research for doped armchair and chiral CNTs is necessary to establish this point explicitly for a wider range of CNT chiralities. 4. Summary
Figure 5. (a) Transmission of the (10,0)-FeNW systems. The Fermi energy is 0 eV. (b) Linear response IV curve for B doped-CNT Fe interface around the Fermi energy, corresponding to a resistance of R ≈ 6 k.
B-doped interface is very similar to interface 1, with an average ˚ For the interfaces studied Mulliken popubond length of 1.972 A. lation analysis shows that charge is transferred from Fe to the CNT. A larger charge transfer takes place for interface 1 (∼2.1 e) than interface 2 (∼1.4 e), which could be attributed to the differences in the interface structures. Two of the carbon atoms at the interface between the B-doped CNT and Fe also bond to boron, which complicates the charge transfer at this interface, however total charge transfer to the CNT (∼2.2 e) is very similar to interface 1, as would expected given the structural similarities. The size of the CNT gap and the position of the Fermi energy appear to be relatively insensitive to the exact structure of the interface. This can be seen in the zero-bias transmissions of interface 1 and interface 2 shown in Figure 5, where the gaps in transmission associated with the isolated CNT gap coincide. Below the Fermi energy, the transmission of interface 1 and interface 2 is similar, with that of interface 2 becoming larger than interface 1 below −1.5 eV. Above the Fermi energy transmission for interface 1 is at the majority of points greater than interface 2. In particular, near the Fermi energy in the range 0.35–1.0 eV we see significantly larger transmission for interface 1. This difference in transmission is presumed to be related to the differences in structure and charge transfer at the interfaces. From this result, it is to be anticipated that structural changes (including local chemistry) may lead to substantial alteration of the IV characteristics of Fe–CNT devices. Similar to our previous report on the Al-B-doped CNT system [30], the B-doped (10,0)-CNT is metallic, with gap of the undoped CNT pushed above the Fermi energy. The shifted band gap also becomes smaller than in the undoped CNT. This is reflected in the transmission of the B-doped CNT seen in Figure 5(a). The are no significant differences in the interfacial structure or charge transfer between the interface 1 and the B-doped interface. In spite of this,
We have found spin polarisation not to be critical for transmission or linear response IV close the the Fermi level for the Fe–CNT junction. The exact structure of the Fe–CNT end contact is found to affect neither the position of the Fermi energy nor the extent of the region of zero transmission for the interfaces that were studied under 0 K conditions. However, changes in the structure of the interface are found to impact on the transmission of the Fe–CNT interface. On doping with boron, the (10,0)-CNT is found to become metallic but overall transmission is reduced relative to the undoped CNT. We obtain a linear IV curve for the interface between the boron doped CNT and iron nanowire which demonstrates the formation of an Ohmic contact and at the Fermi level we find a resistance of 6 k. Acknowledgments S.L.T.J. was funded under an Irish Research Council EMBARK Postgraduate Scholarship. This work was also supported by Science Foundation Ireland under a Principal Investigator Grant No. 06/IN.1I857. The Tyndall team also acknowledges research funding by Intel Corporation. We acknowledge the Irish Centre for High End Computing (ICHEC) for access to computational resources. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett. 2014.09.056. References [1] [2] [3] [4] [5] [6]
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