Ab initio study of structural, electronic and dielectric ...

Physica E 46 (2012) 259–269

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Ab initio study of structural, electronic and dielectric properties of free standing ultrathin nanowires of noble metals Arun Kumar n, Ashok Kumar, P.K. Ahluwalia Department of Physics, Himachal Pradesh University, Shimla 171005, Himachal Pradesh, India

H I G H L I G H T S c

c

c

c

c

The binding energy of Pt nanowires was largest whereas Ag nanowire having smallest. Ballistic conductance increases for ladder and zigzag topology of Cu, Ag and Au. Ballistic conductance remains same for all the topologies of Pt wire. Dielectric properties of nanowires change significantly with the topology. Reflectance edge for the studied topologies of nanowires is found in infrared region.

G R A P H I C A L

A B S T R A C T

We present electronic and dielectric response of Cu, Ag, Au and Pt nanowires in four topologies namely linear, dimer, ladder and zigzag. Illustration 1: electronic band structure and corresponding total and partial DOS for (a) linear, (b) dimer, (c) ladder and (d) zigzag topology of Pt nanowires. The number of bands crossing the fermi energy is 3 in each topology. The Fermi energy has been set at 0 eV. The possible interband transitions responsible for the structure peaks in E2 of Pt wires have also been shown.

a r t i c l e i n f o

abstract

Article history: Received 15 May 2012 Received in revised form 9 August 2012 Accepted 18 September 2012 Available online 11 October 2012

Structural, electronic and dielectric properties of free standing ultrathin nanowires of noble metals (Cu, Ag, Au and Pt) in linear, dimer, ladder and zigzag topologies have been studied by using ab initio density functional theory. Among the studied topologies of all the noble metals, ladder topology has been found most stable while the dimer topology was least stable. The ballistic conductance of all the studied wires except Pt wires, has been found to be topology dependent. The dielectric properties of the studied nanowires have been found to be significantly different from their bulk counterparts. A prominent peak structure in imaginary part of dielectric function ðE2 Þ, which reveals interband transitions in electronic band structure, has been found between 0.5 and 2.0 eV for linear, dimer topologies of Cu and Au wires along with all the topologies of Pt wires. The reflectance edge of different topologies of all the nanowires except ladder topology of Pt, has been found in infrared region, therefore, shows perfect reflectivity in the infrared region and makes them non-absorbing transparent conductors to the visible region. The ultrathin transparent conductors may find many useful applications in the optoelectronic devices. & 2012 Elsevier B.V. All rights reserved.

1. Introduction It is an established fact that by reducing at least one of the dimensions of the materials to the nanometer scale leads to

n

Corresponding author. Tel.: þ91 9418110563. E-mail address: [email protected] (A. Kumar).

1386-9477/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physe.2012.09.032

quantum confinement [1–13]. The confinement of a material in two dimensions results into a nanowire, which is essentially a one-dimensional (1D) structure. A nanowire may be defined as a structure with a diameter/width on the nanometer scale with a high aspect ratio i.e. ratio of the length to the width (diameter) is of the order of 10 or more. Such quantum confined nanowires have a wide range of applications in electronic systems, for example as interconnects in the fabrication of integrated circuits

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A. Kumar et al. / Physica E 46 (2012) 259–269

[14–16], resonators [17–20], nanomagnets [21–23] and spintronic systems [24,25]. Ultrathin nanowires show typical quantum conductance and low thermal conductivity [3] offering new possibilities for their applications. These are important building blocks for nanoscale electronic and optoelectronic devices [2]. Their small size and their high electrical conductivity make nanowires very attractive for applications in nanoelectronics [26]. Sensing is another area in which the application of nanowires is expected to have a great impact. Nanowire sensors have been reported that can detect the presence of many gases like O2, NO2 and NH3 [27] at very low concentrations. Nanowires also have been used for the detection of ultraviolet light [28] as well as highly sensitive biological and chemical species [29]. These sensors often function on the basis of changes in the electrical or physical properties of the nanowires when they come in contact of targeted chemical/biological species. The sensing capabilities of nanowires can be controlled by selective doping that raise their affinities to certain substances. Noble metal nanowires, which is the subject matter of this paper, have been drawing a great deal of attention due to their significantly different structural, electronic, magnetic, optical and transport properties compared to their bulk manifestation [1,4]. As mentioned earlier increased surface to volume ratio and increased density of states (DOS) makes them different from their corresponding bulk materials. The finite monoatomic chains of noble metals can be produced by mechanical break junction experiments [30–34] with conductance nearly 1Go ðGo ¼ 2e2 =hÞ for Cu, Ag and Au and 1:5Go to 2:5Go for Pt chains. Noble metal nanowires, particularly, can be used to create materials that exhibit negative index of refraction in the near-infrared region [35,36]. The nanowires of noble metals have been used as barcode tags for optical read out [37] and they can also be used as detectors to detect different biological molecules at the same time [38]. Silver nanowire network has been found a transparent conductor in recent experimental investigation which can find applications in many optoelectronic devices including LEDs, electronic displays and solar cells [39,40]. Although, many experimental and theoretical studies have been performed to investigate the structural and functional properties of the nanowires [2,3,5–9,11,30–33,42–46], but there is still a lack of the systematic study of the structural, electronic and optical properties of the different topologies of the noble metal nanowires. However, the structural and electronic properties of linear topology of all the noble metals [5–7] and zigzag topology of Cu, Ag and Au [5,6,8] have been studied theoretically, while to the best of our knowledge, theoretical study of the dielectric properties of ultrathin noble metal nanowires remain the untouched part in the literature. Moreover, noble metals are regarded as the best plasmonic materials and their thin wire structures may opens new possibilities for GHz devices [47,48] due to extremely low frequency plasmons. Furthermore, it is interesting to see the effect of quantum confinement on the dielectric properties while going from bulk(3D) to the nanowires(1D) of these metals. In this paper we present a systematic study of structural, electronic and dielectric properties of freely suspended infinite ultrathin noble metal (Cu, Ag, Au and Pt) nanowires with different topologies using SIESTA [49,50] code. Different topologies selected for study were linear, dimer, ladder and zigzag as shown in Fig. 1. Although, as mentioned above that electronic structure of linear and zigzag topology of considered noble metals nanowires was also studied by other authors, but the repetition in the present paper have been carried out to understand the interband transitions corresponding to the structure peaks in the dielectric function. Beside, studying the electronic and dielectric properties of nanowires in different topologies, our calculated structural properties of the nanowires and their bulk properties (lattice parameters,

Fig. 1. Structures of different topologies of ultrathin nanowires, (A) linear, (B) dimer, (C) ladder and (D) zigzag.

Table 1 The cutoff radii used for pseudopotential generation of different noble metals. Cutoff radii shown in brackets are in bohr for each l-channel. Metals

Cu

Ag

Au

Pt

l¼0 l ¼1 l ¼2 l ¼3

4s1 (2.48) 4p0 (2.48) 3d10 (1.64) 4f0 (2.48)

5s1 (2.59) 5p0 (2.59) 4d10 (1.73) 4f0 (2.59)

6s1 (2.70) 6p0 (2.70) 5d10 (1.83) 5f0 (2.70)

6s1 (2.63) 6p0 (2.63) 5d9 (1.79) 5f0 (2.63)

electronic properties and dielectric properties) offers an opportunity to compare the results with available experimental as well as other calculated values in the literature.

2. Computational details We have used Troullier Martin, norm-conserving, relativistic pseudopotentials [51,52] with valence atomic configuration and pseudization radii given in Table 1 for different l-channels. The exchange and correlation energies were treated within the generalized gradient approximation (GGA) according to the PBEsol [53] parametrization. Throughout the geometry optimization, numerical atomic orbitals with double zeta polarization (DZP) basis sets with confinement energy of 20 meV for Cu, Ag and Pt, and 50 meV for Au were used. For brillouin zone integration a 15 15 15 Monkhrost pack mesh for bulk and 1 1 15 Monkhrost pack [54] mesh for nanowires of different topologies have been used. The convergence tolerance for the energy was chosen as 10 6 eV between two consecutive self-consistent field (SCF) steps. Minimization of the energy was carried out using the standard conjugate-gradients (CG) technique. Structures were ˚ relaxed until the forces on each atom were less than 0.01 eV/A. The mesh cut-off energy used to calculate the Hartree, exchange and correlation contribution to the total energy and Hamiltonian was chosen to be 300 Ry. The nanowires were modeled by taking two atoms per unit cell with transverse dimensions of 30 A˚ to ensure no interaction between neighboring wires so that system represents free standing ultrathin nanowires. The stable structures (i.e. minimum energy configuration) for all topologies were obtained by simultaneously relaxing both lattice constant and atomic positions in unit cell. The dielectric properties calculations were performed by using first-order time-dependent perturbation theory [55–57] to find the dipolar transition matrix elements between occupied and unoccupied single-electron eigenstates as implemented in SIESTA, in which the exchange and correlation effects are taken care of by plugging, the self-consistent ground state DFT energies and eigenfunctions into the dipolar transition matrix elements. Thus


261

Table 2 A comparison of structural properties of freely suspended ultrathin noble metal nanowires of different topologies with the corresponding bulk. Here a, b and c are the nanowire parameters, b represents the bond length and ao represents the lattice constant. Other available theoretical and experimental values are also given for comparison in brackets.

Bulk

Linear

Dimer

Ladder

Zigzag

Cu

Ag

Au

Pt

˚ ao (A) ˚ b (A)

3.64 (3.61)a

4.12 (4.09)a

4.13 (4.08)a

3.96 (3.92)a

2.57 (2.56)a

2.91 (2.89)a

2.92 (2.88)a

2.80 (2.77)a

Eb (eV/atom)

4.21 (3.49)a

3.28 (2.95)a

4.12 (3.81)a

6.59 (5.84)a

b

5.3 (5.26)

c

5.2 (5.32)

d

4.8 (4.84)d

˚ a (A) ˚ b (A)

4.6 (4.6) 2.3

2.65

2.6

2.4

Eb (eV/atom)

1.901

1.511

1.98 (2.3)d

3.37 (4.0)d

˚ a (A)

4.5

5.2

5.3

4.8

˚ b (A) ˚ c (A)

2.266

2.632

2.760

2.232

2.234

2.568

2.540

2.568

Eb (eV/atom)

1.888

1.503

1.941

3.365

˚ b (A) ˚ c (A)

2.4

2.7

2.6

2.5

2.234

2.568

2.54

2.568

Eb (eV/atom)

2.509

1.869

2.528

4.243 2.7

b

˚ a (A) ˚ b (A)

2.5 (2.37)

3.0

2.9

2.410 (2.33)b

2.39 (2.68)c

2.36 (2.32)e

2.30

Eb (eV/atom)

2.473

1.817

2.370

4.007

a

Ref. [59]. Frozen core full potential projector augmented wave (PAW) method using GGA [6]. c LDA results [5]. d FP-LMTO using GGA [7]. e Ref. [8]. b

Energy (eV)

5 a’2 0 a2

a’4 a’ 3

a’1 a1

a 4 a3

-10

Total 3d 4s

Total 3d 4s

-5

Γ

2 4 6 x0 N(E) (states/eV/atom)

Γ


Energy (eV)

5 a’6

0

a’7 a7

a6 a5

-5 -10

a’5

Γ

a’8 a8

Total 3d 4s


Γ

x0

Total 3d 4s 2

4

6

N(E) (states/eV/atom)

5

Energy (eV)

a’ b’ 0

b a

-5

-10

Total 3d 4s

W

L

Γ

X W0

2

4

6

N(E) (states/eV/atom) Fig. 2. Electronic band structure and corresponding total and partial DOS for (a) linear (b) dimer (c) ladder and (d) zigzag topology of Cu ultrathin nanowires and corresponding (e) bulk Cu. The Fermi energy has been set at 0 eV. The possible interband transitions responsible for the structure peaks in E2 of Cu wires and bulk have also been shown.

262


the imaginary part of the dielectric function E2 obtained was further used to calculate real part E1 of dielectric function and reflectance spectra with the help of Kramers–Kronig transformations [58]. The electron energy loss spectra (EELS) has been calculated from real and imaginary parts of dielectric functions as 1 e2 ðoÞ Im ¼ 2 ð1Þ eðoÞ e1 ðoÞ þ e22 ðoÞ

‘‘b’’ and ‘‘c’’ for different topologies of nanowires are marked in Fig. 2. The bond lengths in different topologies of the nanowires are found to be smaller than the corresponding bulk counterpart. This decrease in the bond lengths is due to the reduction in the coordination number as one moves from 3D to 1D. The effect of dimensionality on bond length due to the change in the coordination number has also been reported in the literature [8,12,13,42]. Our calculated structural parameters are in good agreement with available results in literature [5–7,59]. To find the stability of the wires, we have also calculated the binding energy per atom ðEb Þ, which is the difference of the wire energy per atom of the unit cell and the energy of isolated atom [60]. It is found that Eb is smaller for nanowires as compared to corresponding bulk values. On comparing the binding energy of topologically different nanowires, we found that ladder topology has maximum stability with largest Eb and dimerized topology has least stability due to least Eb for all the noble metals. The order of stability is: ladder 4 zigzag4 linear 4 dimer. Furthermore, the binding energy of Pt nanowire is found to be largest and of the Ag nanowires as smallest. Therefore, the order of stability is found to be: Pt 4Au 4 Cu 4Ag for all the topologies except zigzag topology. The order of the stability in zigzag topology is Pt 4Cu 4Au 4 Ag, which is the same as in corresponding bulk state.

To study the dielectric properties of nanowires, electric vector was taken along the wire axis. An optical mesh of 45 45 45 for bulk and 3 3 45 for nanowires of different topologies has been used for dielectric calculations. A Gaussian broadening of 0.2 eV was used for the optical spectra of both bulk and nanowires. Relaxation time ðtÞ for dielectric calculations were chosen respectively as 0.001 Ha, 0.0005 Ha, 0.003 Ha and 0.001 Ha for Cu, Ag, Au and Pt for both bulk as well as different topologies of respective nanowires. Corresponding to these values of relaxation time, our results are in good agreement with the experimental results of real and imaginary part of dielectric function for bulk.

3. Results and discussions 3.1. Structural properties of freely suspended ultrathin nanowires The structural parameters (a, b and c) corresponding to the relaxed structures of different topologies of noble metal ultrathin nanowires and their comparison with structural parameters (ao and b) of corresponding bulk are given in Table 2. The parameters ‘‘a’’,

3.2. Electronic properties of freely suspended ultrathin nanowires The electronic band structures have been calculated along the

G-X direction of the brillouin zone. Figs. 2–5 represent the electronic

5 Energy (eV)

b’2

b’4

b’1

0 b1

b3

b2 -5

-10

b’3

b4

Total 4d 5s

x

Γ

0

Total 4d 5s

2 4 6 N(E) (states/eV/atom)

x

Γ

0

2 4 N(E) (states/eV/atom)

6

5 Energy (eV)

b’6

b’5

-5 -10

b6

b’7

b’8

0

b8

Total 4d 5s

b5

x

Γ

0

b7

x

Γ


Total 4d 5s 0

2 4 N(E) (states/eV/atom)

6

Energy (eV)

5 c’ 0 c

-5 -10

W

L

Γ

X

Total 4d 5s W0


Fig. 3. Electronic band structure and corresponding total and partial DOS for (a) linear (b) dimer (c) ladder and (d) zigzag topology of Ag ultrathin nanowires and corresponding (e) bulk Ag. The Fermi energy has been set at 0 eV. The possible interband transitions responsible for the structure peaks in E2 of Ag wires and bulk have also been shown.


5 Energy (eV)

c’2

c’4

c’1

0 c2

c4

c1

-5

-10

263

c’3 c3

Total 5d 6s Γ

X 0

Total 5d 6s Γ


X 0


Energy (eV)

5 c’7 0

c’5

c6

c7

-5 -10

c’6

c’8

c5

c8 Total 5d 6s

Γ

X 0

Total 5d 6s

2 4 6 Γ N(E) (states/eV/atom)

X 0


Energy (eV)

5 f’

0

f Total 5d 6s

-5 -10

W L

Γ

X W 0


Fig. 4. Electronic band structure and corresponding total and partial DOS for (a) linear (b) dimer (c) ladder and (d) zigzag topology of Au ultrathin nanowires and corresponding (e) bulk Au. The Fermi energy has been set at 0 eV. The possible interband transitions responsible for the structure peaks in E2 of Au wires and bulk have also been shown.

band structure along with corresponding total as well as partial DOS of freely suspended ultrathin nanowires in different topologies (linear, dimer, ladder and zigzag) of Cu, Ag, Au and Pt respectively with their corresponding bulk band structure. The Fermi energy ðEF Þ has been set at 0 eV. On analyzing the electronic band structure and corresponding DOS at the Fermi energy ðNðEF ÞÞ, we find that the dimer topology of Ag wire and linear topology of the Ag as well as Cu wire are nearly semi-metallic in nature due to negligible number of bands and DOS at Fermi energy. Among all the topologies of studied noble metals, zigzag topology of Pt is found to have

largest DOS at Fermi level, which results in its most metallic nature. The partial DOS of all the studied topologies of noble metals shows that the maximum contribution comes mainly from ‘d’ orbitals, however, significant contribution from ‘s’ orbitals have also been found for linear and dimer topologies of all the noble metals. DOS of the nanowires are found to be sharp as compared to their bulk counterpart, which shows a typical behavior of one-dimensional systems. Furthermore, the quantum ballistic conductance of a wire under ideal situation can be determined by the number of bands

264


Energy (eV)

5 d’1

0

d’2

d1

d2

-10

Total 5d 6s

Total 5d 6s

-5

Γ

x0

x0

Γ



Energy (eV)

5 d’4

d’5

d’3

d’6

d3

d6

0 d4

d5

-5

-10

Total 5d 6s

Γ

x0

Total 5d 6s

2 4 6 Γ N(E) (states/eV/atom)

x0


5 Energy (eV)

d’

e’

0 d -5

-10

Total 5d 6s

e

0


Fig. 5. Electronic band structure and corresponding total and partial DOS for (a) linear (b) dimer (c) ladder and (d) zigzag topology of Pt ultrathin nanowires and corresponding (e) bulk Pt. The Fermi energy has been set at 0 eV. The possible interband transitions responsible for the structure peaks in E2 of Pt wires and bulk have also been shown.

crossing the Fermi energy (EF) [11]. For each band crossing the EF, the ballistic conductance is Go which results into nGo for n number of bands crossing the EF. Therefore, on counting the number of bands crossing the EF in the electronic band structure of the different topologies of all the studied nanowires, it is found that for all the topologies of Pt, the number of bands crossing EF are three, which corresponds a conductance of 3Go , which is consistent with 2:5Go for finite Pt monoatomic wire in break junction experiments by Smit et al. [30]. The conductance of linear and dimer topologies of Cu, Ag and Au is 1Go as number of bands crossing the EF is only one, which is consistent with the ballistic conductance 1Go of break junction experiments for linear monoatomic chains of Cu [30], Ag [33] and Au [31,32]. The ladder and zigzag topology of Cu, Ag and Au have two

bands crossing the EF resulting in conductance as 2Go . Hence ballistic conductance increases for ladder and zigzag topology of Cu, Ag and Au, while it remains same for all the topologies of Pt wire. The results are consistent with the fact that the conductance of the nanowires is dependent on wire structure [41,46].

3.3. Dielectric properties of freely suspended nanowires The dielectric functions (E1 and E2 ), EELS and reflectance spectra for free standing ultrathin nanowires of Cu, Ag, Au and Pt with different topologies (linear, dimer, ladder and zigzag) along with corresponding bulk have been shown in Figs. 6–9,


Bulk

Linear

4

Dimer

265

Ladder

Zigzag

2

0

ε1

0

-4 -2 -8

0

5

10

15

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

16

ε2

1 8

0

0

5

10

15

0 30

2

Im(-1/ε)

20 1

0

10

0

20

40

1

0 1

R(ω)

1 0.5 0.5

0

0

0

0.5 0 2 4

20

ω(eV)

40

0

ω(eV)

ω(eV)

ω(eV)

2

4

ω(eV)

Fig. 6. Real part of the dielectric function ðE1 Þ, imaginary part of the dielectric function ðE2 Þ, EELS spectra and reflectance spectra for different topologies (linear, dimer, ladder and zigzag) of Cu ultrathin nanowires and corresponding bulk. The available experimental results of bulk (in dark green colour) have also been ploted for comparison. Reflectance in low energy range (see inset) is also shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

respectively. The experimentally measured dielectric function for bulk are also plotted with our calculated data of bulk for comparison. The calculated dielectric function for bulk agrees well with the measured dielectric function by Johnson et al. [61] and Yu et al. [62]. The position of the structure peaks associated with E2 and corresponding interband transitions in electronic band structures of all the ultrathin nanowires of various topologies of noble metals and corresponding bulk are listed in Table 3. The interband transitions corresponding to the structure peaks in E2 of the different topologies of Cu, Ag, Au and Pt and corresponding bulk are also shown in the electronic band structures in Figs. 6–9, respectively. It is found that linear, dimer and zigzag topology of Pt along with zigzag topology of Au have only one structure peak for each in E2 , while all other topologies of wires have two or more structure peaks, revealing interband transitions in the corresponding electronic band structure. A sharp resonance in E2 below 0.5 eV for all the topologically different wires is due to intraband transitions, which remains beyond the scope of the present paper. A prominent structure peak between 0.5–2.0 eV has been found for linear and dimer topologies of Cu, Au and Pt along with ladder and zigzag topology

of Pt, while the structure peaks above 2 eV are found to be feeble in intensity for all other remaining topologies of ultrathin nanowires. It can be seen in Table 3 that different topologies of same wire have distinctly different positions of structure peaks in E2 . The interband transitions in the topologically different nanowires are also found distinctly different as compared to their bulk counterpart, which is expected due to effect of quantum confinement. EELS shows a single sharp resonance peak for all the topologies of studied wires except linear, dimer topologies of both Au and Pt wires, and zigzag topology of Pt wire, for which two EEL peaks are found. The real part of the dielectric function ðE1 Þ have zero value at the EELS peak positions as can be seen from Figs. 6–9, therefore, these peaks correspond to collective excitation of electrons (plasmons) at these energies. The plasmon frequencies (in eV) for different topologies of studied wires and corresponding bulk are also listed in Table 3. The plasmons frequencies are found to change as one goes from linear topology to zigzag topology. The plasmon frequencies (o2p ¼ Ne2 =E0 meff , where N, E0 , e and meff are number density of electrons, permittivity of the free space, charge on the electrons and effective mass of the

266


Bulk

Linear

Dimer

Ladder

Zigzag

2

4 0

ε1

0

-4 -2 -8 0

5

10

15

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

0

2

4

6

0

2

4

6

0

2

4

6

0

2

0

2

4

6

0

2

4

6

0

2

4

6

1

ε2

16 0.5 8

0

0

5

10

15

0 40

Im(-1/ε)

2 20 1

0

0

20

40

0

4

6

1

1 1

R(ω)

0.5 0.5

0.5 0 0 2 4 6 0

0

20

ω(eV)

40

0

4

6

ω(eV)

ω(eV)

ω(eV)

ω(eV)

Fig. 7. Real part of the dielectric function ðE1 Þ, Imaginary part of the dielectric function ðE2 Þ, EELS spectra and reflectance spectra for different topologies (linear, dimer, ladder and zigzag) of Ag ultrathin nanowires and corresponding bulk. The available experimental results of bulk (in dark green colour) have also been ploted for comparison. Reflectance in low energy range (see inset) is also shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

electrons respectively) for all the nanowires are found smaller than their bulk counterparts. This is due to the fact that in case of wires the average concentration of electrons decreases which results in considerable enhancement in the effective mass of electrons [65] and hence results in lower value of op for nanowires. The reflectance spectra for all the studied topologies of ultrathin nanowires along with corresponding bulk have also been shown in Figs. 6–9. The reflectance spectra for all the studied topologies of wires show sharp dip corresponding to the point at which E1 cuts the zero axis and EELS shows resonance peak. Therefore, the strong minima in the reflectance spectra corresponds to the collective excitation of electrons and sudden change in the reflectance spectra corresponds to the reflectance edge. The reflectance edge for all the studied topologies of wires is found infrared region (0–1.6531 eV) except for ladder topology of Pt, for which reflectance edge has been found at 1.7 eV i.e near visible region. The reflectance edges of the nanowires of different

topologies have been found to be shifted towards infrared region as compared to their bulk counterpart. The reflectance edge for bulk noble metals lies in the visible region (1.6531–3.2627 eV) which results into the perfect reflectivity of noble metals in visible region. Percentage decrease in position of reflectance edge of different topologies ultrathin nanowires w.r.t. bulk is shown in Table 4. It is found that zigzag topology of Pt shows largest decrease in the reflectance edge i.e. 90 %, while smallest decrease (34%) has been found for zigzag topology of Cu ultrathin nanowires. Furthermore, all the topologies of Pt ultrathin nanowires shows largest decrease in reflectance edge among all the studied topologies of noble metals.The reflectance of different topologies of Cu, Ag and Au increases as linear odimer oladder ozigzag, while for Pt the increase is zigzag odimer o linearo ladder. It is concluded that all the topologies of ultrathin nanowires except ladder topology of Pt show reflectivity in the IR region and becomes non-absorbing transparent conductor in the visible region. Despite nearly similar structure of linear and dimer


Bulk

Linear

267

Dimer

Ladder

Zigzag

2

4 0

ε1

0 -4 -2

-8 0

5

10

15

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

16

ε2

1 8

0

0

Im(-1/ε)

0

5

10

15

2

6

1

3

0

0 0

20

40 1

1

1

R(ω)

0.5 0.5

0.5

0 0

2

4

6 0

0 0

20

ω(eV)

40

ω(eV)

ω(eV)

ω(eV)

ω(eV)

Fig. 8. Real part of the dielectric function ðE1 Þ, imaginary part of the dielectric function ðE2 Þ, EELS spectra and reflectance spectra for different topologies (linear, dimer, ladder and zigzag) of Au ultrathin nanowires and corresponding bulk. The available experimental results of bulk (in dark green colour) have also been ploted for comparison. Reflectance in low energy range (see inset) is also shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

topologies, their dielectric properties are found to be distinctly different from each other. This strongly suggests that since dielectric properties of nanowires changes with the change in the topology, these optical characteristics can be used as a tool for characterization of the nanowires.

4. Summary and conclusion We have studied the structural, electronic and dielectric properties of free standing noble metal (Cu, Ag, Au and Pt) ultrathin nanowires in different topologies. The binding energy has been found largest for Pt nanowires and smallest for Ag nanowires. Dimer topology of Ag wire and linear topology of the Ag and Cu wires are found nearly semi metallic in nature as compared to metallic nature of all other topologies of studied wires. The partial DOS of all the studied topologies of noble metals have been found to have contribution mainly from ‘‘d’’

orbitals, however, significant contribution from ‘‘s’’ orbitals has been found to come from linear and dimer topologies of all the noble metals. Ballistic conductance increases for ladder and zigzag topology of Cu, Ag and Au as compared to other topologies, while it remains same for all the topologies of Pt wire. The reflectance edge for all the studied topologies of wires is found in infrared and near visible region as compared to the visible region reflectance edge for corresponding bulk. The substantial percentage decrease in the position of reflectance edge w.r.t. bulk has been found largest for Pt ultrathin nanowires among all the studied ultrathin nanowires of noble metals. Dielectric properties of nanowires has been found to change significantly with the topology, therefore, it is suggested that the optical properties can be used as a tool for characterization of the nanowires. Furthermore, our results suggest that due to transparent thin structure of the studied noble metal nanowires, they can find application as an important component in the optoelectronic devices including LEDs and solar cells.

268


Bulk

Linear

4

Dimer

Ladder

Zigzag

2

ε1

0 0 -4 -8

0

5

10

-2

15

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

0

2

4

2

4

0

2

4

0

2

4

ε2

16 2 8

Im(-1/ε)

0

0

5

10

15

0

2

8

1

4

0

0

20

1

40

0 1

1

R(ω)

0.5 0.5

0

0

0

0.5 024 6

20

ω(eV)

40

0

0

2

4

ω(eV)

0

ω(eV)

ω(eV)

ω(eV)

Fig. 9. Real part of the dielectric function ðE1 Þ, imaginary part of the dielectric function ðE2 Þ, EELS spectra and reflectance spectra for different topologies (linear, dimer, ladder and zigzag) of Pt ultrathin nanowires and corresponding bulk. The available experimental results of bulk (in dark green colour) have also been ploted for comparison. Reflectance in low energy range (see inset) is also shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 3 The calculated location of structure peaks in E2 , interband transitions corresponding to the structure peaks in E2 and plasmon frequency (op ) for bulk and corresponding ultrathin noble metal nanowires of different topologies.

Bulk

Au

Pt

3.5, 10.8, 23.0 (3.8, 7.5, 18.0)a

3.03 6.83 0 f -f g-g 0 6.7, 12.1, 23.4 (8.83)b

6.97 9.21 0 d-d e-e0 6.6, 24.4, 31.5 (6.5)c

1.34 3.20 a1 -a01 a2 -a02 0.68

3.27 5.39 b1 -b01 b2 -b02 0.71

1.83 5.13 c1 -c01 c2 -c02 0.69,2.12

1.71

1.45 3.14 a3 -a03 a4 -a04 0.70

3.33 5.30 b3 -b03 b4 -b04 0.79

1.69 5.22 c3 -c03 c4 -c04 0.69, 1.79

Position of peak ðE2 Þ

2.94 3.78

4.67 5.72

Transitions

a5 -a05 a6 -a06

3.29 4.22 5.32 c5 -c05 c6 -c06 d5 -d05 0.92

0.74 2.99 3.98 d3 -d03 d4 -d04

4.36

1.04

c8 -c08

d6 -d06

1.11

0.59, 1.67

Position of peak ðE2 Þ Transitions

op (eV) Linear

Position of peak (E2 ) Transitions

op (eV) Dimer

Position of peak (E2 ) Transitions

op (eV) Ladder

Zigzag

c

Ref. [63]. Ref. [64]. Ref. [62].

2.23 4.87 0 b-b a-a0 12.1, 21.0 (4.1, 7.5, 20.0)a

3.74 c-c

0

op (eV)

1.03

Position of peak ðE2 Þ

2.60 3.63 a7 -a07 a8 -a08 1.17

4.72 5.50 b7 -b07 b8 -b08 1.10

op (eV) b

Ag

b5 -b05 b6 -b06 c7 -c07 1.04

Transitions

a

Cu

d1 -d01 1.06, 2.15 1.27 d2 -d02 0.85, 1.96

1.70


Table 4 A comparison of position of observed reflectance edges (in eV) for bulk and corresponding ultrathin nanowires of different topologies. Percentage decrease in position of reflectance edges w.r.t. bulk is shown in brackets. Cu Bulk Linear Dimer Ladder Zigzag

1.77 0.68 0.70 1.03 1.17

Ag

(61) (60) (42) (34)

2.98 0.71 0.79 1.04 1.10

(76) (73) (65) (63)

Au

Pt

2.08 0.69 (67) 0.69 (67) 0.92 (56) 1.11(47)

6.00 1.06 0.85 1.70 0.59

(82) (86) (72) (90)

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