Presentation at National Center for Theoretical Sciences

& National Cheng Kung University

8/26/2006

Atomic-sized metal nanowires: novel structures, Atomic-sized metal nanowires: novel structures,

physical properties, and nanodevicesphysical properties, and nanodevices

Jijun Zhao

State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams

& College of Advanced Science and Technology

Dalian University of Technology

Outline

• Experimental background and computational methods

• Gold nanotubes and multi-shell helical nanowires

• Atomic and electronic shells in sodium nanowires

• Copper nanowires and nanocables

• Crystalline silver nanowires

• Melting behavior and thermal stability of metal wires

• Summary

Recently, atomic-sized metal nanowires have been fabricated using the following methods:

Experimental synthesis of metal nanowires

Electrochemical etching

Mechanically controllable break junction (MCBJ)

One-dimensional template-aid synthesis

Electron-beam lithograph & irradiation

STM/AFM based tip-surface contacts

Novel 1-D structures from folding 2-D slab/sheet

Single-layer sheet => nanotube Multi-layer slab => helical wires

Observation of helical nanotubes and nanowires

Takayanagi, Phys. Rev. Lett. 91, 205503(2003)

Kondo, Science 289, 606 (2000) Oshima, Phys. Rev. B 65, 121401 (2002)

Gold

Platinum

Structural optimization of nano systems

For a nano system with N atoms, the potential en

ergy is function of the atomic coordinates {xi,yi,z

i} (i=1,N): E=E(xi,yi,zi,). Optimizing the lowest-e

nergy configuration is a global minimization pro

blem in 3N dimensional potential energy surface

(PES): NP-hard problem

simulated annealing

kinetic energy

SA is hard to overcome high barriers on PES, could be very computational costly.

Genetic algorithm as a global search method

Only the fittest candidates can survive

(to mimic Darwinian evolution process)

crossover

mutation

GA can efficiently skip

from trap by local

minima and hop in

potential energy surface

Implement of GA in low-dimensional nanostructures

“cut and splice”

crossover operation

Deaven and Ho, PRL75, 288 (1995).

Successful example: C60 buckyball from scratch

For details, see our recent review: J. Comput. Theor. Nanosci. 1, 117(2004).

jiji

ii

jiij

r

FrVE

)(

)()(,

ion ion

ion

ion

ion

ion

ion ion

ionion

Electron density ρF(ρ) was usually chosen as:

Glue potential: Phys. Rev. Lett. 57, 719 (1986). Sutton-Chen potential: Philos. Mag. Lett. 61, 139 (1990). Gupta-type tight-binding potential: Phys. Rev. B 23, 6265 (1981); P

hys. Rev. B 48, 22 (1993); Phys. Rev. B 57, 15519 (1998).

Some typical many-body potentials used in our atomistic simulations

( )F

EAM-type many-body potentials used for metal nanowires

Ion i embedded in the electron den

sity ρi from other ions j

+ repulsion V between ions i and j

Phys. Rev. Lett. 86, 2046 (2001)

Helical multi-shell nanowires from GA simulation

Helical multi-shell structures were obtained in ultrathin gold nanowires,

while crystalline-like structure was found in nanowire with 3 nm.

Implement of GA into

1-D, unbiased search

from scratch (glue

potential + MD)

Structural evolution towards bulk fcc in Au nanowire

• A1-A3: noncrystalline structures

without definite bond angle. • A4-A9, three peaks at 60o, 90o,

120o (bond angle in the bulk fcc)

are gradually forming.• Atomic cross-section projection:

crystalline structure in A9 and the

transition starts from the core

region (A7, A8).

Phys. Rev. Lett. 86, 2046 (2001)

• A9 wire is similar to bulk gold.

• The first peak ~ 2.3 THz do not

sensitively change from A3-A9.

• Additional peak ~ 4.2 THz in A4

- A8 wires: the noncrystalline

curved outer surface.

• Thinnest A1 and A2 wires: many

discrete vibrational bands. The

maximal frequency are

comparable those calculated for

monatomic chains and dimer.

Phys. Rev. Lett. 86, 2046 (2001)

Vibrational properties of helical gold nanowires

Electronic density of states of gold nanowires

• Thin wire (A2): molecule-like,

sharp and discrete peaks.

• In A3, discrete levels overlap and

form continuous bands.

• The shape of DOS of A3 - A9

wires (1.0 ~ 3.0 nm) does not

sensitively depend on size. The

band width narrows as wire

become thicker.

• A9 wire (3 nm) is already quite

close to the bulk and like the

average of the bulk DOS.

Phys. Rev. Lett. 86, 2046 (2001)

Conductance of gold nanowire: size effect

DFT band structures of A2:two conduction channels

Phys. Rev. Lett. 86, 2046 (2001)

In general, wire conductance increases linearly

with diameters, while geometric structure has

certain influence (like A5).

Phys. Rev. B 65, 235406 (2002)

Structural growth sequences of helical nanowires

Empirical potentials +

unbiased GA search,

→complete structural

growth sequences

obtained for Au and

Zr nanowires.

Shell effects in metal clusters

Electron shell

Atomic shell

Electron shells in Na clusters:W.D.Knight, PRL52, 2141(1984).

Alkali-metal nanowires: observation of shell effects

“The quantum states of a system of particles in a finite spatial domain in general consist of a set of discrete energy eigenvalues; these are usually grouped into bunches of degenerate or closelying levels, called shells. In fermionic systems, this gives rise to a local minimum in the total energy when all the states of a given shell are occupied.” Yanson et al., Nature 400, 144 (1998).

Na wire studied by mechanically controllable break junction (MCBJ)

6

1

22

2

00

RkRkGgGG FFCorrelation between radius and conductance:

Shell structure in conductance count

Crystalline and helical structures in Na nanowires

Phys. Rev. B, submitted

Unbiased GA search

with empirical potential

+ DFT optimization of

1-D supercell length and

internal coordinates

Simultaneous observation

of helical and bulk-like bcc

structures in Na nanowires

Two formation mechanisms:

wall-by-wall and facet-based

0.2 0.4 0.6 0.8 1.0 1.2

crystalline

Eb (

eV/a

tom

)

Radius (nm)

0.5

0.6

0.7

0.8

0.9

1.0

1.1

helical

Crystalline vs. helical: binding energy of Na nanowires

Phys. Rev. B, submitted

• Binding energies of helical wires usually higher than crystalline ones, in

particular for those small wires (R<0.4 nm).

• Eb for two series of structures become closer for the thicker wires (R0.4nm).

Crystalline vs. helical: conductance of Na nanowires

0.2 0.4 0.6 0.8 1.0 1.20

2

4

6

8

10

12

14

16

18

20

crystslline

Con

duct

ance

(2e

2 /h)

Radius (nm)

helical

• Conductance is not simply proportional to area of cross section of nanowires

• Conductance sensitively depends on wire geometry. Crystalline wire typically

have more conduction channels than helical one due to higher symmetry.

• Several nanowires with different structures and radii can have identical

conductance: undistinguishable in experimental conductance histograms.

Crossover from electronic to atomic shells in Na nanowires

Phys. Rev. B, submittedYanson, Phys. Rev. Lett. 87, 216805 (2001).

C1-7 wirefrom GA

We use a sequentially numbered index to characterize

different wires according to their conductance values.

The plot of (G/G0)1/2 fall into two distinct slopes.

Approximately, nanowire radius is linearly

proportional to the square root of

conductance.

1

2

3

4

5

8G0

(G/G

0)1/

2

Numbered index0 3 6 9 12 15 18

crystalline helical

electronic shell

atomic shell

Structures and conductance of Cu nanowires: experiments

Gonzalez et al., Phys. Rev. Lett. 93, 126103 (2004).

Observation of highly stable

pentagonal copper nanowire with

a diameter of 0.45 nm and 4.5 G0.

Nanotechnology 17, 3178 (2006).

Wire D (Å) Symmetry Eb (eV/ato

m)

G (G0)

3a 2.38 D3d 2.439 3

3b 2.14 C2 2.262 2

4a 3.24 D4d 2.602 3

4b 2.86 C2 2.473 3

4c 2.74 D2d 2.563 4

5-1a 4.10 C5v 2.814 6

5-1b 3.70 C5 2.725 4

5-1c 3.52 C5v 2.735 5

6-1a 4.86 C6v 2.816 4

6-1b 4.56 C6 2.815 4

6-1c 4.24 C2 2.757 4

6-1d 4.20 C3v 2.831 4

9-3 6.78 C1 2.991 5

9-4 6.92 C2 2.997 8

12-6-1 9.36 C2 3.104 10

Atomistic simulation of Cu nanowires

Experiment: D=4.5Å, G~4.5G0

2 3 4 5 6 7 8 9 10

2

4

6

8

10

o

Qua

ntum

con

duct

ance

(G

0)Diameter (A)

-1

0

1

2

3

3a3b

-1

0

1

2

3

-1

0

1

2

3

4a

-1

0

1

2

3

En

erg

y(e

V)

4b

-1

0

1

2

4c

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

5-1a

-1

0

1

5-1b

-1

0

1

5-1c

-1

0

1

kZ

ZZZZ

6-1a

6-1b

-1

0

1

2

-1

0

1

6-1c

-1

0

1

2

6-1d

Band structures and conductance of Cu nanowires

Quadratic fitting: G=2.0+0.12D2

Number of bands crossing Fermi lever determines quantum conductance of nanowires

D=4.5Å→G=4.43G0 (experiment: ~4.5G0)

Nanotechnology 17, 3178 (2006).

Nanocable with BN tube sheaths and Cu nanowire cores

J. Phys. Chem. B 110, 2529 (2006).

Macroscopic coaxial cable

Experiment: coaxial Ag/C nanocables

Yu et al. Chem. Commun., 2704 (2005).

Cu@BN: a true nanocable with met

allic core and insulating sheath?

Tube-wire interaction mainly van der Waals

type: equilibrium distance 3.5Å, binding ene

rgy -0.04 eV per Cu atom (GGA)

Nanocable with BN tube sheaths and Cu nanowire cores

J. Phys. Chem. B 110, 2529 (2006).

Band structures for Cu@BN nanocables: clearly a

superposition of individual BN tubes and Cu wires

-3

-2

-1

0

1

2

3

EF

kkk ZZZ

E(e

V)

-3

-2

-1

0

1

2

3

-3

-2

-1

0

1

2

3

Conduction electrons local

ized on inner Cu wire;

electron transport occurs

only through Cu wires;

BN nanotubes serve as

insulating cable sheaths

Cu wire BN tubeCu@BN

Ultrathin single-crystalline silver nanowires: experiments

Hong et al., Science 294, 348 (2001). Ultrathin single-crystalline silver nanowires (0.4 nm width, m length) arrays are grown in pores of template.

Conducting wire in nanoelectonics? Effect of defect and strain?

s-orbital TB model: Phys. Stat. Sol. (b)188, 719 (1995)

Long Ag wire, 4-atoms cross section, experimentally synthesized

s electron approximation, neglecting of low-lying d electrons

Three s-bands cross Fermi level three conduction channels

Electronic states and conductance of ultrathin Ag wire

Conductance of crystalline Ag nanowires with defect

Nanotechnology 14, 501 (2003)

Infinite nanowire, 4-atom cross sectionlower coordinate

higher coordinate

Three conduction channels for perfect nanowire

One conduction channel disrupted by a single-a

tom defect, independent of defect geometry

Two-atoms vacancy Multiple single-atom vacancies

• One or two conduction channels can be disrupted by two-atoms vacancy

defect, depending on the site coordinate

• Ballistic conduction of fcc ultrathin wire is very robust (one channel at

least remains open at Fermi energy): good for nanoelectronics

Nanotechnology 14, 501 (2003)

Conductance of Ag nanowire with multiple defects

Quantum interference between two separated defects

D

G (2e2/h):

Conductance at EF

Nanotechnology 14, 501 (2003)

Quantum interference leads to strong oscillation of conductance vs. distance

between two separated single-atom defects, related to Fermi wavelength. Simi

lar effects observed in carbon nanotubes.

The original three

channels of Ag wire

remain robust under

substantial strain (up to

~5%).

Larger strain can reduce

conductance.

Conductance of silver nanowires: strain effect

Conductance of silver as function of energy and strainNanotechnology 14, 501 (2003)

Experiment: Rodrigues, Phys. Rev. B, 2002

Nanotechnology 14, 501 (2003)

Quantization of conductance for Ag nanobridge Global histogram of conductance for 500 random

ly generated finite nanowires with defects reprod

uce experimental peaks: 1 G0, 2.4 G0, 4 G0

Computational simulation on Ag nanobridge: ~2nm long, 7-atoms cross section, 5 conduction channels

Conductance of Ag nanobridge: experiment vs. theory

12.4

4

0 1 2 3 4 50.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Nor

mal

ized

num

ber

of c

ount

s

G (2e2/h)

1

2.64

Melting behavior of titanium nanowires

Phys. Rev. B 67, 193403 (2003)

Helical wire: D=1.71nm

Melting temperature: 1150 K

• Diffusion start at 950~1000K, before melting

• Transformation into bulk structure before overall melting

Size dependence of melting temperature

• Melting temperature for hexagonal nanowires (6-1, 12-6-1, 17-12-6-1) fit well to

a linear dependence of 1/D: Tm=1542K682K·nm/D

• Nanowires with 3 or 4 atomic strands in internal shell (9-3, 14-9-3, 9-4, 15-9-4) h

ave lower melting temperature than wires with one atomic strand in the center

• Melting temperature of nanowire higher than nanoclusters with comparable size

Phys. Rev. B 67, 193403 (2003)

Interior melting behavior of gold nanowires

18-12-6-1 nanowire

Starting melting temperature: 300K Overall melting temperature: 1100K

• 3501000K: core atoms begin to diffuse along wire axis and become wet; surface atoms remain solid-like.

• 10001150K: surface atoms involve in melting

• Surface melting represents the overall melting in the ultrathin multi-shell nanowires

Phys. Rev. B 66, 085408 (2002)

Mechanical properties of Ni nanowires

fcc crystalline structure helical multi-shell structure (6-1 9-3 12-6-1)

Parrinello-Rahman variable-cell MD algorithm in 1-D: constant compressive/tensile force

• Within elastic limit, elastic deformation, oscillation of 1-D supercell

• Beyond elastic limit, plastic deformation, lose initial configurations

Physica E 30, 45 (2005).

Elastic deformation under uniaxial loading

• Periodic oscillation within elastic limit• Keeping helical multi-shell structure

Compression: Physica E 30, 45 (2005).

A3 wire

Tension: Chin. Phys. Lett.22, 1195(2005).

A1 (6-1) A2 (9-3) A3 (12-6-1)

Diameter 0.76 nm 0.94 nm 1.18 nm

Tensile stress 2.85 GPa 3.38 GPa 3.48 GPa

Compressive stress 13.01 GPa 9.09 GPa 9.17 GPa

Yield strength of Ni nanowires is about one order of magnitude larger than macroscopic strength

Plastic deformation under uniaxial compression

C1, A1:

1.2 nN

(4.5GPa)

C2, A2:

2.0 nN

(4.7GPa)

C3, A3:

3.7 nN

(5.5GPa)

• Helical multi-shell structure enhance the elasticity and strength of Ni nanowires. • Mechanisms of plastic deformation different; final structures are resemblant and crystalline. • Coexistence crystalline and noncrystalline phases, related to superplasticity.

Plastic deformation under uniaxial compression

Two different kinds of deformation mechanisms:

• C1, C2, C3: crystalline amorphous crystalline (reiterative)

• A1, A2, A3: helical multi-shell distorted crystalline

Pair distribution functions g(r) of C3, A3 nanowires at different MD time steps

Physica E 30, 45 (2005).

Summary

• Helical multi-shell structures found for atomic-sized nanowires of differe

nt metals. Transition towards bulk-like crystalline structure ~ 3nm.

• For alkali-metal nanowires, atomic and electronic shells are observed.

• Wire conductance sensitively depends on size, geometry and defect.

• Ultrathin crystalline silver wires show robust conductivity, even with mul

tiple defects and can be excellent candidates in nanoelectronics.

• BN nanotube could be good sheath for constructing true nanocable.

• Interior melting behavior earlier than overall melting is found for metal

nanowires. Melting temperatures of nanowire depend on atomic geometr

y and are lower than nanoclusters of comparable size.

• Both elastic and plastic deformation observed for nanowire under uniaxi

al loading with either compression or tension. Helical multi-shell wires sh

ow enhanced yield strength than bulk solids.

Collaborators:

• Dr. B.L. Wang, Dr. J.L. Wang, Prof. G.H.Wang (Nanjing Univ.)

• Mr. J.M. Jia, Prof. D.N. Shi (Nanjing Univ. of Aeronautics & Astronautic

s)

• Dr. C. Buia, Prof. J.P. Lu (UNC-Chapel Hill)

• Prof. W. Lu, Prof. X.S. Chen (CAS, Shanghai)

• Prof. P.R. Schleyer, Prof. R. B. King, Dr. Z.F. Chen (Univ. of Georgia)

• Prof. Z. Zhou (Nankai Univ.)

Acknowledgements

Thank you for your attentions!