On the Quantum Capacitance of Quantum Wire Field-Effect …
87
n s =
2g v
π
S
B 11
E
F , n x , n y
(2)
where, S =
n z max
n x =1
n y max
n y =1
, E
F = [e ¯
V g − E fb −
e
2 n 0
C ins
], E fb is Fermi energy of the bulk
material, C ins =
2πε ins
ln
2t ins +t wire
t wire
, ε ins is the permittivity of the insulator layer, t ins is the
thickness of the insulator layer and t wire is the diameter of the wire. And the other
notations are given in [41].
Using (1) and (2) the C g can be expressed as
C g =
2g v e
2
π
S(θ 1 )
1 +
2g v e
2
πC ins
S(θ 1 )
−1
(3)
where, θ 1 =
∂
∂ E
F
B 11
E
F , n x , n y
.
2.2 The C g in QWFET of Kane-Type Compounds
(i) The Three-band model of Kane
Under certain constraints, Eqs. (2) and (3) get simplified as
n s =
2g v
π
S
B 13
E
F , n x , n y
(4)
C g =
2g v e
2
π
S(θ 2 )
1 +
2g v e
2
πC ins
S(θ 2 )
−1
(5)
where, θ 2 =
∂
∂ E
F
B 13 (E
F , n x , n y )
and B 13 (E
F , n x , n y ) are defined in [41].
(ii) The Two-band model of Kane
Under certain constraints, Eqs. (4) and (5) assume the forms
n s =
2g v
π
S
B 15
E
F , n x , n y
(6a)
C g =
2g v e
2
π
S(θ 3 )
1 +
2g v e
2
πC ins
S(θ 3 )
−1
(6b)
where, θ 3 =
∂
∂ E
F
B 15
E
F , n x , n y
and B 15
E
F , n x , n y
are defined in [41].