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
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