Low-Frequency Current Fluctuations in Graphene and van der Waals Materials

Alexander A. Balandin

Nano
-
Device Laboratory

Department of Electrical Engineering and

Materials Science and Engineering Program

University of California
–

Riverside

Low
-
Frequency Current Fluctuations in
Graphene and van der Waals Materials

FAME Talk April 2013

Balandin Group / UC Riverside

City of Riverside

UCR Botanic Gardens

Joshua Tree Park

UCR Bell Tower

UCR Engineering Building

Balandin Group / UC Riverside

Outline




Introduction


w
hy
low
-
frequency noise is important


g
raphene
device applications and noise


Graphene under Electron Beam Irradiation


m
ore defects
–

less noise


Noise in Graphene Multilayers



new insight into the century old problem



Noise in van der Waals Materials



Conclusions

Nano
-
Device Laboratory

Balandin Group / UC Riverside

Different Types of Intrinsic
Electronic Noise:


Thermal noise:

S
I
=4k
B
T/R


Shot noise:

S
I
=2e<I>


Flicker 1/f noise:

S
I

~ I
2
/f


G
-
R noise:

S
I

~ 1/(1+f
2
t
2
)

See A.A. Balandin (Ed.),
Noise and Fluctuations Control in
Electronic Devices

(ASP, 2002).

Fundamental Types
of Electronic
Noise

Electronics: noise
is a random
fluctuation in an electrical
signal
characteristic for all electronic
devices.

Balandin Group / UC Riverside

Low Frequency Noise as a “Show Stopper”



Non
-
linearity leads to 1/f noise up
-
conversion and contributions to the phase
noise of the system




Device downscaling results in a higher noise spectral density




Gate current contribution to noise may become important




1/f noise limits sensors’ sensitivity




Large device
-
to
-
device variations in noise




Graphene
and thin films of van der Waals materials can
be
more susceptible
to noise because
they are flat surfaces
exposed to traps in oxides.


USEFUL 1/f NOISE
: characterization tool to understand trap dynamics and
electron transport in a given materials system

Balandin Group / UC Riverside

6

Importance of 1/
f
Noise Reduction for
Graphene and van der Waals Materials


The 1/
f
3
phase noise
contribution comes
from 1/
f

noise


The energy of 1/f noise increases as the measurement T (~1/
f
)





One cannot improve the signal
-
to
-
noise ratio by extending T

Communication systems: noise
is an error or undesired random disturbance of a useful
information
signal
introduced before or after the detector and decoder.

Balandin Group / UC Riverside

McWhorter’s
model:

Physical Mechanism of 1/
f
Noise in
Electronic Materials and Devices

Balandin Group / UC Riverside

Low
-
Frequency Noise Measurements


The noise measurement set
-
up
is placed inside
a special room with the metal and acoustic
protection from the
environmental noises and electro
-
magnetic
fields




Low
noise batteries are used for the biasing of the
devices

Balandin Group / UC Riverside

9

Electronic Noise in Graphene Devices

S. Rumyantsev,
G. Liu, W.
Stillman, M. Shur
and A.A.
Balandin,
J.
Physics:
Condensed
Matter
, 22,
395302 (2010).


The noise level in
graphene transistors scales
with the graphene channel
area, which suggests that
the dominant noise source
is graphene channel itself.





No clear G
-
R peaks
observed in graphene
devices.

Balandin Group / UC Riverside

10

S
I
/I
2

=10
-
9

to 10
-
7

Hz
-
1

at
f
=10 Hz or
A
=
10
-
9

–

10
-
7


(
S
I
/I
2
)
L
×
W
=
10
-
8

–

10
-
7


m
2
/Hz

Specifics of Electronic Noise in Graphene

In
some graphene devices, V
-
shape
becomes M
-
shape dependence
at
lager bias range

Balandin Group / UC Riverside

11

Investigation of 1/
f

Noise in Graphene
Devices under Irradiation

Methodology


Step I: Raman of pristine graphene

Step II: IV characteristics and noise measurements

Step III: E
-
beam irradiation of the device

Step III: Raman of the irradiated device

Step IV
: IV characteristics and noise
measurements

Goal


Controlled introduction of defects by
electron beam irradiation and observation
of the evolution of 1/f noise level

Balandin Group / UC Riverside

12

Introduction of Structural Defects to
Graphene by Electron Beam Irradiation

T
he
electron energy
was set to 20
keV

in order to exclude the severe knock
-
on damage to the graphene crystal lattice, which starts at ~50
keV


Balandin Group / UC Riverside

13

Electron Beam Irradiation Effects on
Electronic Properties of Graphene

The Dirac point shift to negative side was
observed for most devices, although in a
very few cases, we recorded a positive shift
after
some irradiation steps.

Balandin Group / UC Riverside

14

Electronic Noise Suppression via Electron
Beam Irradiation

The
noise was measured in
the linear region of the
drain bias keeping the
source at a ground
potential.


Voltage
fluctuations from
the drain load resistance of
R
L

=10
k
W

were analyzed
with
signal
analyzer.


The flicker 1/
f
noise
is
usually associated with
structural defects.


I
ntroduction
of defects by
irradiation
normally results
in increased
1/
f
noise and
reduced mobility

Balandin Group / UC Riverside

15

Low
-
Frequency Noise Suppression via
Electron Beam Irradiation

N
oise
reduces monotonically with the increasing RD for the entire range of negative
gate
-
bias voltages,
V
G
-
V
D
. The same trend was observed for the positive gate bias.

Balandin Group / UC Riverside

16

Possible Mechanisms of the 1/
f

Noise
Suppression via Irradiation

McWhorter model of the number of carriers
fluctuations:

N
t

is the concentration of the traps near the Fermi level responsible for
noise,
A

is the gate area,
n
is the carriers concentrations
and


is
the
tunneling constant.


Possible mechanism: reduction in
N
t

after irradiation

Noise spectral density of the elementary fluctuation in the mobility fluctuation model:

N
t


is concentration
of the scattering
centers
contributing to 1/
f

noise,
l
0

is
MFP
of
the charge carriers,
z

is the probability
for a scattering center to be in the state
with the cross
-
section


1

N
t



may not change much during the irradiation resulting in noise being defined by
the electron MFP:
S
I
/I
2
(~l
0
2
)
. In graphene,


is limited by the long
-
range Coulomb
scattering from charged defects even at
RT

Balandin Group / UC Riverside

17

The Old Problem of 1/
f
Noise Origin:
Surface
vs.
Volume

F
. N. Hooge, “1/f noise is no surface
effect,”
Phys
.
Lett
. A

29
, 139 (1969).


A
. Mircea, A. Roussel, A.
Mitonneau
, “1/f noise:
still

a surface
effect
,”
Phys
.
Lett
. A

41
, 345 (1972).

Inside Volume

Surface or
Interface

The direct test of whether
1/
f

noise is
dominated by contributions
from
the sample
surface or its
volume has
not been possible
because of inability to fabricate continuous
metal or semiconductor films with the
uniform thickness below ~8
nm.

For homogeneous metals and semiconductors,
S
I
(
f
) proportionality to
R
ST

or
R
ST
2

was interpreted as indication of the volume or surface noise origin,
respectively.

N. M. Zimmerman, J. H.
Scofield
, J. V.
Mantese
, W. W. Webb,
Phys. Rev. B

34
, 773 (1986).

For conventional homogeneous conductors with the volume noise: S
I
~1/N~1/H

For surface noise: S
I
~1/H
2

Balandin Group / UC Riverside

18

Current Fluctuations in Few
-
Layer Graphene

Motivations:



Practical task of
noise scaling with
the thickness



Possibility of
addressing an old
problem of origin of
noise: surface vs.
volume

The back
-
gated devices
were fabricated by the
electron
-
beam lithography
with Ti/Au (6
-
nm/60
-
nm)
electrodes.


R
ST

is sheet resistance


Balandin Group / UC Riverside

19

Electronic 1/
f
Noise in Few
-
Layer Graphene

The
S
I

proportionality to
I
2

implies
that the current does
not drive the fluctuations but
merely makes them visible as
in other homogeneous
conductors.

To minimize the influence of the
contact resistance, most of the
noise measurements were
performed close to CNP
.


Graphene channel area A varied
from 1.5 to 70

m
2

For homogeneous metals and
semiconductors,
S
I
(
f
)
proportionality to
R
ST

or
R
ST
2

was interpreted as indication of
the volume or surface noise
origin, respectively.

Balandin Group / UC Riverside

20

Interpretation of the Experimental Noise Data

Ohm’s
law:
R=ρ
×
(L/W
×
H)=R
ST
×
(L/W)
, where
ρ

is the resistivity,
L

is the length,
W

is the width and
H

is
thickness.


R
ST
~1/
H

scaling is not necessarily valid for graphene multilayers as
H

approaches a single atomic plane
–

surface.

R
ST
=R
B
×
R
S
/(R
B
+R
S
)
.







2
=

𝐵
2



+

𝐵
2








2
+



2



+

𝐵
2



𝐵

𝐵
2
.

R
S

i
s the sheet resistance of the first atomic plane of graphene

R
B

is the sheet resistance of (n
-
1) layers on top

R
ST
~1/n
1.4

S
RS
/R
S
2
is the area normalized surface noise


Balandin Group / UC Riverside

21

Evolution of 1/
f

Noise Behavior: Transition
from Surface to Volume

Conclusions:




The
1/
f

noise becomes
dominated by the volume
noise when the thickness
exceeds ~7 atomic layers
(~2.5 nm).




The
1/
f
noise is the
surface phenomenon
below this thickness.

G. Liu, S.
Rumyantsev
,
M.S.
Shur

and A.A.
Balandin,
“Origin of 1/f
n
oise
in graphene
multilayers: Surface vs.
volume,”
Appl
. Phys.
Lett
.,
102
, 093111 (2013)

Balandin Group / UC Riverside

Graphene Thickness
-
Graded
FETs

The SLG, GTG and BLG FETs, fabricated using the
same process, had the RT electron mobility values:
~5000
–

7000 cm
2
/
Vs
, ~4000
–

5000 cm
2
/
Vs

and
~1000
–

2000 cm
2
/
Vs
, respectively

G. Liu
,
S.
Rumyantsev
,
M.
Shur

and
A.A
.
Balandin,

Graphene
thickness
-
graded transistors with reduced
electronic noise,
Appl. Phys.
Lett
.,
100
, 033103 (2012).

Balandin Group / UC Riverside

1/
f

Noise in
Thickness Graded
Graphene
:
Comparison with SLG and
BLG

The same amount of the
charge, transferred owing to
the metal contact

doping, leads the smaller
local Fermi level shift in BLG
devices than in SLG devices.

G. Liu
,
S.
Rumyantsev
,
M.
Shur

and
A.A
.
Balandin,

Graphene
thickness
-
graded
transistors with reduced electronic noise,
Appl. Phys.
Lett
.,
100
, 033103 (2012).

L
ocal shifts
of the Fermi level
position in
graphene:

D
E
F
=
-
0.23
eV

and
D
E
F
=0.25
eV

were reported for Ti and Au
contacts to
graphene.

Balandin Group / UC Riverside

Selective Gas Sensing with Pristine
Graphene FETs

Nano Letters
(
2012
)

Collaboration with Michael
Shur

Group

Balandin Group / UC Riverside

25

Bi
2
S
e
3

The absence of scaling of the normalized
resistance with the film thickness indicates
that
the surface
transport
contribution is
substantial

Contacts
: 20 nm Ti / 180 nm Au

Resistance: 1 kW to 100 kW

M.Z.
Hossain
, S.L.
Rumyantsev
, K.M.F.
Shahil
,
M
.
Shur

and A.A.
Balandin, "Low
-
frequency current fluctuations in "graphene
-
like"
exfoliated thin
-
films of bismuth
selenide

topological insulators,"
ACS Nano
,
5
, 2657 (2011
).

Devices with the
van der Waals

Material
Channels

Balandin Group / UC Riverside

26

M.Z.
Hossain
, S.L.
Rumyantsev
, K.M.F.
Shahil
,
M
.
Shur

and A.A. Balandin, "Low
-
frequency current fluctuations in
"graphene
-
like" exfoliated thin
-
films of
bismuth
selenide

topological insulators,"
ACS Nano
,
5
, 2657 (2011
).

Noise in Devices with the Channels
Implemented with Topological Insulators

S
I
~I
a
, where
a
=1.83 (liner response
S
I
~I
2
R
2
)

Balandin Group / UC Riverside

Conclusions

Typical
graphene transistors reveal rather low level of the low
-
frequency noise: S
I
/I
2

=10
-
9

to 10
-
7

Hz
-
1

at
f
=10 Hz or A=10
-
9

–

10
-
7


The gate dependence of 1/
f

noise in graphene reveals
characteristic V
-
shape or M
-
shape
–

different from that in
conventional semiconductors and metals

It is possible to reduce 1/
f

noise via electron beam irradiation,
which introduces additional defects

Noise reduction after irradiation can be rationalized in both carrier
number and mobility fluctuation models

Noise scaling in graphene multilayers sheds light on the old
problem of noise origin: surface vs. volume

Balandin Group / UC Riverside

Acknowledgements

Nano
-
Device Laboratory (NDL)
Group,
UC Riverside, 2013

Former PhD Students:

Dr.
Zahid

Hossain

Dr.
Guanxiong

Liu