Chemistry Reference
In-Depth Information
as Fermi level E
F
shift, thereby
V
TG
=
E
F
e
+
φ
(2)
where
C
TG
and
the quantum capacitance (C
Q
) of graphene, respectively. The two capaci-
tors are in series, as shown in Fig. 8(a). In Fig. 8(b) we have shown schemat-
ically the electrostatic voltage drops in our experiment. The geometrical
capacitance is C
TG
=
0
d
TG
φ
and E
F
/e are determined by the geometrical capacitance
is the dielectric constant of the PEO
matrix and d
TG
is the Debye length is given by d
TG
=(2ce
2
/
,where
0
k
B
T)
−
1
/
2
for a monovalent electrolyte where c is the concentration of the electrolyte,
e is the electric charge, k
B
T is the thermal energy. For polymer electrolyte
gating the thickness of Debye layer is reported to be a few nanometers
(1
5nm)
48
) of PEO is 5.
53
∼
and the dielectric constant (
Assuming a
10
−
6
F
cm
−
2
, much higher than back gate capacitance. Therefore, the first term
in Eq. (2) cannot be neglected. The Fermi energy in graphene changes as
E
F
(
Debye length of 2 nm, we get a gate capacitance C
TG
=2.2
×
|v
F
|
√
πn
10
6
m/s
2,3
is the Fermi velocity,
n
)=
,where
|v
F
|
=1.1
×
hence:
V
TG
=
|v
F
|
√
πn
e
ne
C
TG
+
(3)
v
F
,
Using the values of C
TG
and
10
−
7
√
n
10
−
13
n
V
TG
(
volts
)=1
.
16
×
+0
.
723
×
(4)
is in units of cm
−
2
. Equation (4) allows us to estimate the doping
concentration at each top gate voltage (V
TG
), as shown in Fig. 8(c). The
inset in Fig. 8(c) shows that in the same voltage range the doping concen-
tration obtained in 300 nm SiO
2
back gating is two orders of magnitude
smaller compared to the present top gating. Recently, we have measured
C
TG
using back and top gate geometries and the value is 1.5
where
n
F/cm
2
.
54
We now consider the evolution of the Raman spectra. Figures 9(a)
to 9(d) show the spectra recorded during the top gate experiment.
Figure 9(a) is the PEO Raman spectrum. This has three prominent peaks
at
∼
1282 cm
−
1
(P1), 1476 cm
−
1
(P2) and 2890 cm
−
1
(P3), which corre-
spond to twisting, bending and stretching modes of the CH
2
bonds in the
polymer.
55
Luckily they do not overlap the main features of graphene (see
Figs. 9(b),(c),(d)).
µ
Furthermore these PEO Raman lines do not change
with gating.
