Chemistry Reference
In-Depth Information
To get the density dependence of
S
V
3
we should calculate the density de-
pendence of Σ and
µ
avg
. Within the semiclassical model of conductivity
Σ(
x
) can be expressed as
)=
π
e
n
k
F
v
F
1
n
imp
(
τ
C
Σ(
x
)
(11)
where
τ
c
as the scattering time arising due to the Coulomb scattering only
andwehavetaken
δQ ∼ n
imp
, the density of charge impurities trapped
at the SiO
2
interface. Using the expressions for the scattering rates, cal-
culated for both single
52,53
and bilayer/multilayer graphene
54
for Coulomb
scattering, it can be shown from (9) that Σ(
) is independent of density for
both single and multilayer graphene.
55
Hence, the density dependence of
noise only arises due to that of
x
µ
avg
only. The important fact is that the
average mobility of graphene transistors comes from all scattering mech-
anisms, whereas only Coulomb scattering is responsible for the mobility
fluctuations.
So one can extract the dependence of
µ
avg
from the den-
sity dependence of the Drude conductivity
σ
=
neµ
avg
.Wefocusonthe
1. Recently,
52-54
most relevant experimental situation, where
q
TF
/
2
k
F
>
the density dependence of
has been calculated within Thomas-Fermi ap-
proximation for both single and bilayer/multilayer graphene for all possible
scattering mechanisms. In Table 1, a comparison of density dependence of
σ
σ
for various scattering mechanisms has been summarized.
Table 1. Dependence of
σ
for various scattering
mechanisms in experimentally relevant situation
where
q
TF
/
2
k
F
>
1.
SLG
BLG/MLG
2
Bare Coulomb Scattering
σ
∼
n
σ
∼
n
Screened Coulomb
σ
∼
n
σ
∼
n
0
Short-range scattering
σ
∼
n
σ
∼
n
µ
avg
∼ n
β
,where
Using Table 1, one can write
−
1
<β<
0forSLG
and 0
<β<
1 for BLG and MLG. Hence, the contribution from mobility
S
V
3
/V
DS
∼ n
2
β
, which predicts that in case of SLG the noise
magnitude always decreases with density, whereas, for BLG, the noise power
spectral density increases with increasing density. This opposite behavior is
a direct consequence of the band structures. In case of multilayer graphene
we expect noise to behave in the same way as BLG because of their similar
parabolic band structure. Noise can form an excellent probe to detect SLG
from other forms of graphene.
fluctuations
