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Stabilization of monoatomic gold wires by carbon impurities
Solid State Communications 130 (2004) 755–757 www.elsevier.com/locate/ssc
Stabilization of monoatomic gold wires by carbon impurities N.V. Skorodumova*, S.I. Simak Condensed Matter Theory Group, Department of Physics, Box 530, Uppsala University, 75432 Uppsala, Sweden Received 10 March 2004; accepted 25 March 2004 by H. Eschrig
Abstract The influence of atomic and molecular carbon on the structural and electronic properties of a monoatomic gold wire has been studied by means of projector augmented-wave method (PAW) within density functional theory (DFT). Our calculations show that carbon is able to enhance the stability of linear gold chains with large interatomic separations. The Au –Au spacing at ˚ for the wires incorporating atomic (Au– C) and molecular carbon (Au– C2), breakage can be as long as , 4.5 and 6 A respectively. The calculated band structure for nonmagnetic Au– C reveals the presence of one conduction channel for linear chains, but two channels for zigzag-like ones. A close similarity of this behaviour, to that known for a pure gold wire might indicate little influence of carbon on the conduction properties of gold nanowires. q 2004 Elsevier Ltd. All rights reserved. PACS: 68.65.La; 71.15.Nc; 71.20. 2 b Keywords: A. Carbon; A. Gold; A. Nanowires; D. Electronic structure
The detailed understanding of the mechanical and electronic properties of nanosized junctions is crucial for many domains of modern nanotechnology. Metal nanowires, in particular those of gold, have recently attracted great attention due to their unusual properties and relative simplicity of fabrication. Gold nanowires exhibit electronic conductivity in the ballistic regime with a quantized conductance ðN2e2 =hÞ; approaching its theoretical onedimensional limit ð2e2 =hÞ; when the wire becomes monoatomic. Most common techniques used in these experiments are the mechanically controllable break-junction (MCB) technique, and the scanning tunneling microscopy (STM), when the tip is first driven into the gold sample, and then retracted forming a nanowire [1 – 4]. Another approach is based on the transmission electron microscopy (TEM), which uses a focused electron beam with current density , 100 A/cm2 to fabricate gold nanowires. The structural reorganization of the nanowire is further studied using the electron beam with current density either reduced to , 30 A/ cm2 [3,5], or kept the same as in the preparation process [6]. One of the most puzzling properties of monoatomic gold * Corresponding author. Tel.: þ46-18-471-5856; fax: þ 46-18511784. E-mail address: [email protected] (N.V. Skorodumova). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2004.03.049
chains is their amazing structural stability at large interatomic separations [1]. Numerous experimental observations show that Au– Au distances in such wires range ˚ [3 – 8]. Takai et al. [6] have reported from 2.9 to 3.6 – 4.0 A on the bulk-like spacing in gold monoatomic wires which have been imaged using the electron beam with the current density of 100 A/cm2. Using a similar technique, but lower current density (, 30 A/cm2) during the observation, Ohnishi et al. [3] obtained long-living wires with equally ˚ ), whereas other groups large Au– Au distances (3.6– 4.0 A [5,7,8] reported on different distances occurring within the same gold monowire. Trying to explain these unusual structural properties of gold monoatomic wires, a number of theoretical studies have been undertaken [9 –15]. Their results have shown that a monoatomic wire of pure gold must break at the Au – Au ˚ , that agrees well with the distances of about 2.9 A experimental findings by Takai et al. [6], but does not clarify the origin of larger distances observed in other experiments. At the same time, these distances are impressively well reproduced in calculations assuming a contamination of nanowires with light elements, undetectable in standard experiments [8,11,16]. Generally, there could be many sources of contamination of nanowires, and even in ultra-high vacuum experiments some contamination
756
N.V. Skorodumova, S.I. Simak / Solid State Communications 130 (2004) 755–757
Fig. 1. (Color on line) Energy curves for the infinite monoatomic wires of gold containing carbon atom (a) and carbon dimer (b). The shown energies are given per gold–carbon pair (a) and per gold– carbon dimer (b) versus the average Au–Au distances. These are calculated as ðd1 þ … þ dn Þ=n; with dn being the actual distances between gold atoms in linear chains or the z-projected distances for zigzag-like chains, where n is the number of gold atoms per unit cell. The chain configurations stable in the indicated intervals are also shown.
is possible. One can expect a presence of some light elements either in the chamber or already dissolved in the sample. Interestingly, similar results on Au – Au spacing in monoatomic wires have been reported by groups using different experimental techniques, vacuum and temperature conditions. An enhanced reactivity of gold nanostructures is well known, and provides another argument supporting the proposed theory of contamination. Moreover, gold nanowires were shown to be one of the most reactive gold structures [12]. Among the considered contaminants are atomic H, C, O [8,11,12] as well as molecules, such as CO and C2 [8,12]. As it follows from the calculations [8,11,16], the presence of light atoms in the wire structure has a clearly stabilizing effect, essentially increasing the cohesion and equilibrium interatomic spacing in the wire. A possible concentration of light impurities in such structures is a matter of discussion. The interatomic spacings at breakage obtained in the ˚ ) [11] are calculations for an ordered Au – H wire (3.8 A ˚ ). very close to the ones observed experimentally (3.6– 4.0 A At the same time, Novaes et al. [8] have suggested that, most experimental data can be explained assuming a presence of one impurity atom in the structure of a gold wire. However, this model fails to predict the existence of more than one
large Au– Au link in the wire [16], that clearly contradicts experimental data [3,4,8]. Here we present the results of our ab initio investigation of the structural and electronic properties of ordered nonmagnetic Au – C and Au– C2 wires done by the projector augmented-wave (PAW) method [17,18], based on the density functional theory (DFT) within the generalized gradient approximation (GGA) [19]. The cut-off of 500 eV was used for both Au – C and Au– C2. The one-dimensional chains were modeled by three dimensional periodic tetragonal supercells, with the chains situated along the z˚ of axis and separated in the x – y dimensions by 14 A vacuum. Hellmann – Feynmann forces were systematically calculated, and the positions of nuclei were relaxed accordingly. The integration over the Brillouin zone was performed on the 1 £ 1 £ 24 k-point mesh, which allowed the accuracy in the description of the total energy to be about 1 meV per atom. In Fig. 1 we show the total energy curves for free standing nonmagnetic Au –C (Fig. 1(a)) and Au – C2 wires (Fig. 1(b)). The equilibrium configurations are linear chains ˚ (Au– C) and 5.2 A ˚ with the Au – Au distances of about 3.8 A (Au– C2). These values agree well with the results of ˚ (Au– C) and previous calculations by Legoas et al.: 3.6 A ˚ (Au– C2) [8]. For the Au – C wire, a zigzag arrange5.0 A ment of atoms is most stable at the Au – Au distances smaller ˚ (Fig. 1(a)). At compression Au– C2 still than ,3.8 A exhibits a linear arrangement of gold atoms, whereas the incorporated C2 dimers turn off the chain axis (Fig. 1(b)). At stretching the wires dimerize and eventually break when the ˚ (Au– C) and 6.0 A ˚ (Au– Au– Au distances exceed 4.5 A C2). Thus, our results suggest that gold wires incorporating carbon can be stable up to much larger interatomic separations, than those observed in experiment. We note that previous attempts to explain the experimentally observed Au – Au distances, based on the calculations of the Au– C chains [8] have used a wrong assumption, that the monoatomic wire is in its optimized and, therefore, equilibrium configuration. Indeed for this ˚ configuration, the Au – Au distance in the wire is about 3.8 A (Fig. 1(a)) in good agreement with experiment. In experiment, however, a tensile stress is permanently applied to the monoatomic wire, and one can expect it to be in a stretched rather than equilibrium state. Most gold – gold separations observed in experiments, are in the range of ˚ , that is much smaller than the distances in the 2.8– 3.7 A Au– C, Au– C2 wires at breakage (Fig. 1). It has also been suggested that, the observed Au –Au separations in gold wires might be explained not by ordered impurities, but by a single light atom present in the wire [16]. However, as it follows from the results by Novaes et al. [16], the observations of neighbouring Au –Au links with the length ˚ [5,8], are difficult to explain by an influence exceeding 3.0 A of a single impurity, therefore, requiring an assumption of some impurity ordering. Experimental reports on the conductance of monoatomic
N.V. Skorodumova, S.I. Simak / Solid State Communications 130 (2004) 755–757
757
range of experimentally observed interatomic distances in monoatomic gold wires.
References
Fig. 2. The band structure of the gold–carbon monoatomic wires ˚ (Fig. 1(a)), with the Au–Au distances of 3.2, 3.8 and 4.3 A calculated on a dense k-point mesh (30 k-points in the GZ direction along the wire). The energy is given with respect to the Fermi level.
gold wires show the existence of a single conduction channel in such systems. This is also confirmed by the electronic structure calculations of pure gold chains [9,10]. To evaluate the influence of carbon contamination on the conduction properties of gold wires the band structure for the Au– C chains with different Au – Au spacing has been calculated (Fig. 2). Our results reveal the existence of one conduction channel for the linear wires, and two channels for the wire adopted a zigzag-like shape at compression (Fig. 2). This behaviour is very similar to the one observed for pure gold wires indicating little effect of carbon on their conduction characteristics. In summary, our results have shown that monoatomic gold wires incorporating carbon exhibit similar structural transformations and conduction properties to those obtained for pure gold chains. We find, however, that at stretching, such wires can be stable up to very large Au – Au separations ˚ (Au– C), 6 A ˚ (Au– C2)) that essentially exceeds the (4.5 A
[1] N. Agraı¨t, A.L. Yeyati, J.M. van Ruitenbeek, Phys. Rep. 377 (2003) 81. [2] Y. Kondo, K. Takayanagi, Science 289 (2000) 606. [3] H. Ohnishi, Y. Kondo, K. Takayanagi, Nature 395 (1998) 780. [4] A.I. Yanson, G.R. Bollinger, H.E. van den Brom, N. Agraı¨t, J.M. van Ruitenbeek, Nature 395 (1998) 783. [5] V. Rodrigues, D. Ugarte, Phys. Rev. B 63 (2001) 073405. [6] Y. Takai, T. Kawasaki, Y. Kimura, T. Ikuta, R. Shimizu, Phys. Rev. Lett. 87 (2001) 106105–106111. [7] T. Kizuka, S. Umehara, S. Fujisawa, Jpn. J. Appl. Phys. 40 (2001) L71. [8] S.B. Legoas, et al., Phys. Rev. Lett. 88 (2002) 0761051. [9] N.V. Skorodumova, S.I. Simak, Comp. Mater. Sci. 17 (2000) 178. [10] L. De Maria, M. Springborg, Chem. Phys. Lett. 323 (2000) 293. [11] N.V. Skorodumova, S.I. Simak, Phys. Rev. B 67 (2003) 121404. [12] S.R. Bahn, et al., Phys. Rev. B 66 (2002) 081405(R). [13] U. Landman, W.D. Luedtke, B.E. Salisbury, R.L. Whetten, Phys. Rev. Lett. 77 (1996) 1362. [14] D. Sa´nchez-Portal, et al., Phys. Rev. Lett. 83 (1999) 3884. [15] G. Rubio-Bollinger, S.R. Bahn, N. Agraı¨t, K.W. Jacobsen, S. Vieira, Phys. Rev. Lett. 87 (2001) 026101–026101. [16] F.D. Novaes, A.J.R. da Silva, E.Z. da Silva, A. Fazzio, Phys. Rev. Lett. 90 (2003) 036101. [17] G. Kresse, J. J. Furthmu¨ller, Comp. Mater. Sci. 6 (1996) 15. G. Kresse, J. Furthmu¨ller, Phys. Rev. B 54 (1996) 11169. G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758. [18] P.E. Blo¨chl, Phys. Rev. B 50 (1994) 17953. [19] J.P. Perdew, et al., Phys. Rev. B 46 (1992) 6671.
Stabilization of monoatomic gold wires by carbon impurities N.V. Skorodumova*, S.I. Simak Condensed Matter Theory Group, Department of Physics, Box 530, Uppsala University, 75432 Uppsala, Sweden Received 10 March 2004; accepted 25 March 2004 by H. Eschrig
Abstract The influence of atomic and molecular carbon on the structural and electronic properties of a monoatomic gold wire has been studied by means of projector augmented-wave method (PAW) within density functional theory (DFT). Our calculations show that carbon is able to enhance the stability of linear gold chains with large interatomic separations. The Au –Au spacing at ˚ for the wires incorporating atomic (Au– C) and molecular carbon (Au– C2), breakage can be as long as , 4.5 and 6 A respectively. The calculated band structure for nonmagnetic Au– C reveals the presence of one conduction channel for linear chains, but two channels for zigzag-like ones. A close similarity of this behaviour, to that known for a pure gold wire might indicate little influence of carbon on the conduction properties of gold nanowires. q 2004 Elsevier Ltd. All rights reserved. PACS: 68.65.La; 71.15.Nc; 71.20. 2 b Keywords: A. Carbon; A. Gold; A. Nanowires; D. Electronic structure
The detailed understanding of the mechanical and electronic properties of nanosized junctions is crucial for many domains of modern nanotechnology. Metal nanowires, in particular those of gold, have recently attracted great attention due to their unusual properties and relative simplicity of fabrication. Gold nanowires exhibit electronic conductivity in the ballistic regime with a quantized conductance ðN2e2 =hÞ; approaching its theoretical onedimensional limit ð2e2 =hÞ; when the wire becomes monoatomic. Most common techniques used in these experiments are the mechanically controllable break-junction (MCB) technique, and the scanning tunneling microscopy (STM), when the tip is first driven into the gold sample, and then retracted forming a nanowire [1 – 4]. Another approach is based on the transmission electron microscopy (TEM), which uses a focused electron beam with current density , 100 A/cm2 to fabricate gold nanowires. The structural reorganization of the nanowire is further studied using the electron beam with current density either reduced to , 30 A/ cm2 [3,5], or kept the same as in the preparation process [6]. One of the most puzzling properties of monoatomic gold * Corresponding author. Tel.: þ46-18-471-5856; fax: þ 46-18511784. E-mail address: [email protected] (N.V. Skorodumova). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2004.03.049
chains is their amazing structural stability at large interatomic separations [1]. Numerous experimental observations show that Au– Au distances in such wires range ˚ [3 – 8]. Takai et al. [6] have reported from 2.9 to 3.6 – 4.0 A on the bulk-like spacing in gold monoatomic wires which have been imaged using the electron beam with the current density of 100 A/cm2. Using a similar technique, but lower current density (, 30 A/cm2) during the observation, Ohnishi et al. [3] obtained long-living wires with equally ˚ ), whereas other groups large Au– Au distances (3.6– 4.0 A [5,7,8] reported on different distances occurring within the same gold monowire. Trying to explain these unusual structural properties of gold monoatomic wires, a number of theoretical studies have been undertaken [9 –15]. Their results have shown that a monoatomic wire of pure gold must break at the Au – Au ˚ , that agrees well with the distances of about 2.9 A experimental findings by Takai et al. [6], but does not clarify the origin of larger distances observed in other experiments. At the same time, these distances are impressively well reproduced in calculations assuming a contamination of nanowires with light elements, undetectable in standard experiments [8,11,16]. Generally, there could be many sources of contamination of nanowires, and even in ultra-high vacuum experiments some contamination
756
N.V. Skorodumova, S.I. Simak / Solid State Communications 130 (2004) 755–757
Fig. 1. (Color on line) Energy curves for the infinite monoatomic wires of gold containing carbon atom (a) and carbon dimer (b). The shown energies are given per gold–carbon pair (a) and per gold– carbon dimer (b) versus the average Au–Au distances. These are calculated as ðd1 þ … þ dn Þ=n; with dn being the actual distances between gold atoms in linear chains or the z-projected distances for zigzag-like chains, where n is the number of gold atoms per unit cell. The chain configurations stable in the indicated intervals are also shown.
is possible. One can expect a presence of some light elements either in the chamber or already dissolved in the sample. Interestingly, similar results on Au – Au spacing in monoatomic wires have been reported by groups using different experimental techniques, vacuum and temperature conditions. An enhanced reactivity of gold nanostructures is well known, and provides another argument supporting the proposed theory of contamination. Moreover, gold nanowires were shown to be one of the most reactive gold structures [12]. Among the considered contaminants are atomic H, C, O [8,11,12] as well as molecules, such as CO and C2 [8,12]. As it follows from the calculations [8,11,16], the presence of light atoms in the wire structure has a clearly stabilizing effect, essentially increasing the cohesion and equilibrium interatomic spacing in the wire. A possible concentration of light impurities in such structures is a matter of discussion. The interatomic spacings at breakage obtained in the ˚ ) [11] are calculations for an ordered Au – H wire (3.8 A ˚ ). very close to the ones observed experimentally (3.6– 4.0 A At the same time, Novaes et al. [8] have suggested that, most experimental data can be explained assuming a presence of one impurity atom in the structure of a gold wire. However, this model fails to predict the existence of more than one
large Au– Au link in the wire [16], that clearly contradicts experimental data [3,4,8]. Here we present the results of our ab initio investigation of the structural and electronic properties of ordered nonmagnetic Au – C and Au– C2 wires done by the projector augmented-wave (PAW) method [17,18], based on the density functional theory (DFT) within the generalized gradient approximation (GGA) [19]. The cut-off of 500 eV was used for both Au – C and Au– C2. The one-dimensional chains were modeled by three dimensional periodic tetragonal supercells, with the chains situated along the z˚ of axis and separated in the x – y dimensions by 14 A vacuum. Hellmann – Feynmann forces were systematically calculated, and the positions of nuclei were relaxed accordingly. The integration over the Brillouin zone was performed on the 1 £ 1 £ 24 k-point mesh, which allowed the accuracy in the description of the total energy to be about 1 meV per atom. In Fig. 1 we show the total energy curves for free standing nonmagnetic Au –C (Fig. 1(a)) and Au – C2 wires (Fig. 1(b)). The equilibrium configurations are linear chains ˚ (Au– C) and 5.2 A ˚ with the Au – Au distances of about 3.8 A (Au– C2). These values agree well with the results of ˚ (Au– C) and previous calculations by Legoas et al.: 3.6 A ˚ (Au– C2) [8]. For the Au – C wire, a zigzag arrange5.0 A ment of atoms is most stable at the Au – Au distances smaller ˚ (Fig. 1(a)). At compression Au– C2 still than ,3.8 A exhibits a linear arrangement of gold atoms, whereas the incorporated C2 dimers turn off the chain axis (Fig. 1(b)). At stretching the wires dimerize and eventually break when the ˚ (Au– C) and 6.0 A ˚ (Au– Au– Au distances exceed 4.5 A C2). Thus, our results suggest that gold wires incorporating carbon can be stable up to much larger interatomic separations, than those observed in experiment. We note that previous attempts to explain the experimentally observed Au – Au distances, based on the calculations of the Au– C chains [8] have used a wrong assumption, that the monoatomic wire is in its optimized and, therefore, equilibrium configuration. Indeed for this ˚ configuration, the Au – Au distance in the wire is about 3.8 A (Fig. 1(a)) in good agreement with experiment. In experiment, however, a tensile stress is permanently applied to the monoatomic wire, and one can expect it to be in a stretched rather than equilibrium state. Most gold – gold separations observed in experiments, are in the range of ˚ , that is much smaller than the distances in the 2.8– 3.7 A Au– C, Au– C2 wires at breakage (Fig. 1). It has also been suggested that, the observed Au –Au separations in gold wires might be explained not by ordered impurities, but by a single light atom present in the wire [16]. However, as it follows from the results by Novaes et al. [16], the observations of neighbouring Au –Au links with the length ˚ [5,8], are difficult to explain by an influence exceeding 3.0 A of a single impurity, therefore, requiring an assumption of some impurity ordering. Experimental reports on the conductance of monoatomic
N.V. Skorodumova, S.I. Simak / Solid State Communications 130 (2004) 755–757
757
range of experimentally observed interatomic distances in monoatomic gold wires.
References
Fig. 2. The band structure of the gold–carbon monoatomic wires ˚ (Fig. 1(a)), with the Au–Au distances of 3.2, 3.8 and 4.3 A calculated on a dense k-point mesh (30 k-points in the GZ direction along the wire). The energy is given with respect to the Fermi level.
gold wires show the existence of a single conduction channel in such systems. This is also confirmed by the electronic structure calculations of pure gold chains [9,10]. To evaluate the influence of carbon contamination on the conduction properties of gold wires the band structure for the Au– C chains with different Au – Au spacing has been calculated (Fig. 2). Our results reveal the existence of one conduction channel for the linear wires, and two channels for the wire adopted a zigzag-like shape at compression (Fig. 2). This behaviour is very similar to the one observed for pure gold wires indicating little effect of carbon on their conduction characteristics. In summary, our results have shown that monoatomic gold wires incorporating carbon exhibit similar structural transformations and conduction properties to those obtained for pure gold chains. We find, however, that at stretching, such wires can be stable up to very large Au – Au separations ˚ (Au– C), 6 A ˚ (Au– C2)) that essentially exceeds the (4.5 A
[1] N. Agraı¨t, A.L. Yeyati, J.M. van Ruitenbeek, Phys. Rep. 377 (2003) 81. [2] Y. Kondo, K. Takayanagi, Science 289 (2000) 606. [3] H. Ohnishi, Y. Kondo, K. Takayanagi, Nature 395 (1998) 780. [4] A.I. Yanson, G.R. Bollinger, H.E. van den Brom, N. Agraı¨t, J.M. van Ruitenbeek, Nature 395 (1998) 783. [5] V. Rodrigues, D. Ugarte, Phys. Rev. B 63 (2001) 073405. [6] Y. Takai, T. Kawasaki, Y. Kimura, T. Ikuta, R. Shimizu, Phys. Rev. Lett. 87 (2001) 106105–106111. [7] T. Kizuka, S. Umehara, S. Fujisawa, Jpn. J. Appl. Phys. 40 (2001) L71. [8] S.B. Legoas, et al., Phys. Rev. Lett. 88 (2002) 0761051. [9] N.V. Skorodumova, S.I. Simak, Comp. Mater. Sci. 17 (2000) 178. [10] L. De Maria, M. Springborg, Chem. Phys. Lett. 323 (2000) 293. [11] N.V. Skorodumova, S.I. Simak, Phys. Rev. B 67 (2003) 121404. [12] S.R. Bahn, et al., Phys. Rev. B 66 (2002) 081405(R). [13] U. Landman, W.D. Luedtke, B.E. Salisbury, R.L. Whetten, Phys. Rev. Lett. 77 (1996) 1362. [14] D. Sa´nchez-Portal, et al., Phys. Rev. Lett. 83 (1999) 3884. [15] G. Rubio-Bollinger, S.R. Bahn, N. Agraı¨t, K.W. Jacobsen, S. Vieira, Phys. Rev. Lett. 87 (2001) 026101–026101. [16] F.D. Novaes, A.J.R. da Silva, E.Z. da Silva, A. Fazzio, Phys. Rev. Lett. 90 (2003) 036101. [17] G. Kresse, J. J. Furthmu¨ller, Comp. Mater. Sci. 6 (1996) 15. G. Kresse, J. Furthmu¨ller, Phys. Rev. B 54 (1996) 11169. G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758. [18] P.E. Blo¨chl, Phys. Rev. B 50 (1994) 17953. [19] J.P. Perdew, et al., Phys. Rev. B 46 (1992) 6671.