Analysis of nanostructural layers using low frequency impedance spectroscopy

Hans G. L. Coster

Part 1: Background Physics

Response of materials to AC currents

Sinewave signal generator

Phase shiftShift in relative magnitude

Current voltage

Electrical Circuit Equivalents

Impedance of capacitance elements

C = Q/V

Sinusoidal currents

1 jwheretjo eii

)sin( tii o

Same form as:

Impedance of a capacitance element

TT

C

dti

C

dq

00

CV

Cj

iei

CjC

ei tjo

T tjo

1

0

CC ZV iBut we have that

HenceCj

1ZC

1 jwheretjo eii

(Ohms’s Law)

Impedance of capacitance elements

C

j

Cj

1

ZC

C = Q/V

current

C

j

The voltage lags behind (phase lags) the current

Parallel Circuits

TR

Vi

21

21

21

R

1

R

1V

R

V

R

V

iii

21T R

1

R

1

R

1 Hence

i V

i2

i1 R1

R2

i V

RT

21T GGGor

Parallel impedances

ZC

ZR

ZT

RCT Z

1

Z

1

Z

1

Circuit elements to represent Layers

1C

1G

ZC

ZR

ZT

1

RCT Z

1

Z

1Z

111

1

11T GC

R

1CZ

jj

21

21

211

11 GC

CG

GC

1

j

j

Real Part

Imaginary Part

Phase relationships

222T

T

Yand

Z

1Y

GC

GCjT

We measure ZT and

ZT

Real part

Imaginary part

But it is simpler to work in terms of

Admittances (Y= 1/Z)

For a single “layer” containing parallel R and C elements :

cosYG

sinYC

T

T

YT

Real part

Imaginary part

jC

G

Detecting substructure with Impedance Spectroscopy

Homogeneous film Film with two homogeneous sub-structural layers

1C

1G

1C

1G

2C

2G

C1= 0.006 F/m2

G1 = 0.003 S/m2

C2=0.059 F/m2

G2 =4.35 S/m2

Consider an example with the following dielectric parameters:

0.1 1 10 100 1000

Frequency - Hz

100

10

1

0.1

Imp

edan

ce

Impedance Spectroscopy: Dispersion of Impedance with frequency

1C

1G

1G

C1

G2

C 2

Conclusion: The impedance as a function of frequency does not allow us to discriminate between the single and 2 layer structures.

0.1 1 10 100 1000

Frequency - Hz

Cap

acit

ance

– m

F m

-2

0.0060

0.0059

0.0058

0.0057

0.0056

0.0055

Impedance Spectroscopy: Capacitance dispersion with frequency

1C

1G

1G

C1

G2

C 2

The capacitance as a function of frequency allows the single and 2 layered structure to be readily distinguished.

0.1 1 10 100 1000

Frequency - Hz

Con

du

ctan

ce –

S m

-2

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

Impedance Spectroscopy: Conductance dispersion with frequency

1C

1G

1G

C1

G2

C 2

The conductance as a function of frequency also allows the single and 2 layered structure to be readily distinguished.

A two layer sandwich

1C

1G

2C

2G

221

2221

21

22

22

21

212

221

221

2221

212

221

22

21

2221

2

CCGG

CGCGGGGGG

CCGG

GCGCCCCCC

Whilst C1, G1, C2, G2 are frequency independent, C and G for the combination is frequency dependent

Alkane layers on silicon

Silicon Wafer

SiO2

Silicon Wafer

SiH40% NH4F

Silicon Wafer

SiH

UV

Self Assembled Organic Films

Sil

icon

[11

1]

monolayerC

solutionG

monolayerG

Decane layer attached to Si

The Born energy for ion partitioning into the alkane layer is very high. Therefore the electrical conductance of this layer will be very low.

Organic films on Silicon substartes

More info on Born Energy

The Spectrometer

Impedance range: 0.1 -1010 Frequency: < 10-2 – 106 Hz

Impedance precision: 0.002% Phase resolution: 0.001 o

Inphaze.com.au

inphaze.com.au

+ +

Ion in water Image of ion in dielectric

m ~ 2 -3

for hydrophobic films

Organic filmExternal solution

w=80

Ion Partitioning into an organic film

The Born Energy arising from image forces on the ions is:

wmo

e11

R8

22zBW

For a K+ ion in a alkane layer, WB ~ 3 eV

Ion partitioning into molecular films

Recall that kT~ 0.025 eV at room temperature

So that the partitioning goes as ~ e-120 !!

It will be a very poor electrical conductor!Return to Main