Terahertz Conductivity of Silver Nanoparticles

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Nov 16, 2013 (3 years and 8 months ago)

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Terahertz Conductivity
of Silver Nanoparticles

Abstract:

The

electrical

conductivity

for

bulk

metal

is

described

by

the

well
-
known

Drude

model
.

As

the

size

of

the

metal

is

reduced

to

the

nanometer

scale

however,

the

energy

levels

become

discrete,

rather

than

continuous
.

The

average

spacing

between

adjacent

energy

levels

in

a

metal

nanoparticle

is

called

the

Kubo

gap,

and

is

related

to

the

Fermi

energy

of

the

metal

and

the

size

of

the

nanoparticle
.

For

instance,

in

a

silver

nanoparticle

of

3
-
nm

diameter

containing

~
10
3

atoms,

the

Kubo

gap

is

around

5
-
10

meV
.

Therefore,

at

room

temperature

when

the

thermal

energy

is

greater

than

this

gap,

the

electrical

conductivity

will

be

the

same

as

in

bulk

metal
.

As

the

temperature

is

lowered

however,

the

Kubo

gap

becomes

significant

and

the

nanoparticle

becomes

an

insulator
.

Although

the

DC

properties

of

this

metal
-
to
-
insulator

transition

are

well

understood,

the

experimental

observations

and

theoretical

description

for

AC

conductivity

are

much

less

comprehensive
.

The

AC

conductivity

of

silver

nanoparticles

will

be

measured

in

an

interesting

frequency

range

that

corresponds

with

the

Kubo

gap

of

the

nanoparticles
.

Conductivity

will

be

measured

using

terahertz

time
-
domain

spectroscopy

based

on

a

mode
-
locked

laser
.


Aaron Shojinaga with
Jie

Shan

Department of Physics, Case Western Reserve University

Introduction
:


Metal

nanoparticles

are

small

clusters

of

metal,

less

than

100

nm

in

size
.

Although

metal

nanoparticles

have

been

used

in

various

scientific

and

other

fields

for

some

time,

their

physical

and

electronic

properties

are

still

not

fully

understood
.

The

potential

applications

for

metal

nanoparticles

include

use

in

nanoelectronics
,

electronics

with

components

of

nanometer

scale
.

Detailed

understanding

of

the

electrical

properties

of

these

nanoparticles

is

crucial

in

developing

nanoelectronics
.



If

the

size

of

a

metal

cluster

is

less

than

the

de

Broglie

wavelength

of

an

electron,

conduction

electrons

will

be

confined

to

certain

allowed

energy

levels
.

The

average

spacing

between

allowed

energy

levels

is

called

the

Kubo

gap
.

The

effect

of

the

Kubo

gap

will

not

be

apparent

at

room

temperature,

because

the

thermal

energy

is

greater

than

this

energy

gap
.

In

this

case,

the

nanoparticles

have

metallic

conductivity
.

If

the

thermal

energy

is

less

than

the

Kubo

gap,

however,

the

nanoparticle

conductivity

should

be

like

an

insulator
.



The

Kubo

gap

for

a

3

nm

diameter

silver

nanoparticle

is

around

5
-
10

meV
,

which

corresponds

to

electromagnetic

radiation

with

frequencies

around

1
-
2

THz
.

Terahertz

time
-
domain

spectroscopy

can

be

used

to

study

the

conductivity

in

the

frequency

range

of

the

Kubo

gap
.

By

measuring

the

frequency
-
dependent

conductivity

as

the

temperature

is

varied,

the

transition

from

metallic

to

insulator

conductivity

and

the

effect

of

the

Kubo

gap

can

be

observed
.



Methods
:


Terahertz

time
-
domain

spectroscopy

is

used

to

measure

the

electric

field

of

terahertz

radiation

as

a

function

of

time
.

Time
-
domain

spectroscopy

allows

for

recovery

of

amplitude

and

phase

information

of

the

terahertz

signal
.

By

measuring

the

signal

after

it

has

passed

through

the

nanoparticle

sample

and

comparing

to

a

reference

signal,

the

frequency
-
dependent

optical

properties

of

the

sample

can

be

calculated
.

Ultrashort

laser

pulses

generated

from

a

mode
-
locked

Ti
:
sapphire

laser

are

used

to

generate

and

detect

terahertz

radiation
.

Terahertz

radiation

is

emitted

when

these

laser

pulses

strike

a

GaAs

semiconductor
.

The

THz

radiation

is

detected

using

a

commercially

available

photoconductive

antenna
.

The

nanoparticle

composite

sample

is

placed

between

one

set

of

parabolic

mirrors,

where

the

terahertz

radiation

is

focused

to

a

small

point
.











Figure 1: Experimental set up.



Silver

nanoparticle

composites

are

created

by

mixing

a

silver

nitrate

solution

with

polyvinyl

alcohol

and

evaporating

the

mixture

until

a

thin

film

remains
.

The

resulting

film

contains

silver

nanoparticles

suspended

in

a

polymer

matrix
.




Results
:


The

terahertz

signals

were

measured

as

a

function

of

time

and

the

FFT

was

computed

to

retrieve

the

frequency

dependence

of

the

signals
.














Figure 2: Terahertz signal in time domain.












Figure 3: FFT of terahertz signal.



The

absorption

coefficient

(k)

and

refractive

index

(n)

of

the

films

were

calculated

from

the

frequency
-
dependent

signals
.












Figures 3 and 4: Absorption coefficient and refractive index of
nanoparticle

films.


Conclusions

and

Future

Work
:


The

optical

properties

of

silver

nanoparticle

films

were

measured

in

a

range

corresponding

to

the

Kubo

gap

of

the

nanoparticles
.

Further

measurements

must

be

made

in

order

to

extract

the

conductivity

of

the

nanoparticles

themselves

from

that

of

the

films
.

The

next

step

is

repeat

the

measurements

at

different

temperatures

in

order

to

observe

a

transition

to

insulator

conductivity
.



Further

optimizations

to

the

terahertz

set
-
up

might

be

necessary

to

achieve

a

signal
-
to
-
noise

ratio

large

enough

to

observe

the

effects

of

the

Kubo

gap
.

In

particular,

there

are

several

noticeable

spikes

in

the

terahertz

spectrum

that

are

due

to

absorption

by

water

vapor

in

the

air
.

The

resolution

in

the

vicinity

of

these

absorption

peaks

can

be

increased

by

removing

water

vapor

from

the

air
.



Acknowledgements
:


I

would

like

to

thank

my

advisor,

Jie

Shan

for

guidance

in

the

concept

and

execution

of

my

project
.

I

also

thank

the

graduate

students

in

my

lab,

Brian

Kubera
,

Chris

Ryan,

and

Xia

Chen,

for

providing

assistance

and

technical

support
.



References
:

1. Kubo. J. Phys. Soc.
Jpn
.
17

(1962).

2. C.N.R.
Rao
, G.U.
Kulkarni
, P.J. Thomas, P.P. Edwards. Chem. Soc. Rev.
29
,
27
-
35 (2000).

3. L.P.
Gor’kov
, G.M.
Eliashberg
. JETP
21
, 940 (1965).

4. K.
Frahm
, B.
Mühlschlegel
, R.
Németh
.
Zeitschrift

für

Physik

B


Condensed Matter
78
, 91
-
97 (1990).

5. J. Baxter, C.
Schmuttenmaer
. J. Phys. Chem. B
110
, 25229
-
25239 (2006).

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