Chemistry Reference
In-Depth Information
where
x
2
E
2
V
DS
e
2
n
tr
(
x, E
)
τ
T
(
x
)
S
V
1
=
)
f
T
(
E
)(1
− f
T
(
E
))
dxdE
(6)
ω
2
τ
T
(
(
WL
)
Q
n
1+
x
x
1
E
1
x
2
E
2
V
DS
e
2
)
n
tr
(
x, E
)
τ
T
(
x
)
S
V
2
=
2
µ
avg
Σ(
x
)
f
T
(
E
)(1
− f
T
(
E
))
dxdE
(
WL
)
Q
n
1+
ω
2
τ
T
(
x
x
1
E
1
(7)
x
2
E
2
S
V
3
=
V
DS
e
2
(
)
n
tr
(
x, E
)
τ
T
(
x
)
µ
avg
Σ
2
(
x
)
f
T
(
E
)(1
− f
T
(
E
))
dxdE
(8)
WL
)
1+
ω
2
τ
T
(
x
x
1
E
1
The first term arises entirely due to number fluctuation, the second term
describes the joint effect of both number and mobility fluctuation, and the
final term represents the mobility fluctuation alone.
Number fluctuation:
For a uniform trap distribution, the integral over
E
of
n
tr
f
T
(
E
)(1
−f
T
(
E
)) is approximately
k
B
Tn
tr
(
E
F
). The limits
x
1and
x
2 are such that all the traps are taken into account, in our experimental
frequency range. The first term can be calculated by integrating over
τ
as
V
DS
e
2
E
F
)
1
f
(
V
2
Hz
S
V
1
=
Q
n
α
n
T
(
)
(9)
(
WL
)
S
V
1
/V
DS
∼
10
−
30
/Hz
Using typical values of
,whichisfar
lower compared to the experimental values obtained in recent experiments.
Moreover,
n
tr
(
E
F
), we get
/n
2
, irrespective of the number of graphene layers in
the device. However, in recent noise experiments in graphene it has been
observed that the conductivity noise magnitude in single and multilayer
device behaves oppositely with gate voltage. In case of SLG devices the
noise magnitude goes down with increasing carrier density, while it increases
in case of multilayer devices. These inconsistencies indicate that the number
fluctuations to be only of minor importance in graphene.
Mobility fluctuation:
Calculating the integral exactly in (8) is not
straightforward. From (8), we find the mobility fluctuation term mainly
depends on average mobility
S
V
1
∝
1
µ
avg
and Σ. Hence,
S
V
3
V
DS
∼
Σ
2
µ
avg
(10)
