88
A. H. Seikh et al.
(iii) The isotropic parabolic energy bands
Under the condition of very large band gap, Eqs. (6a) and (6b) assume the forms
n s =
2g v
π
S
¯
B 15
E
F , n x , n y
(7a)
C g =
2g v e
2
π
S( ¯
θ 3 )
1 +
2g v e
2
πC ins
S( ¯
θ 3 )
−1
(7b)
where, ¯
B 15
E
F , n x , n y
=
2 ¯
m c
2
E
F
−
n x π
d x
2 +
n y π
d y
2
1/2
and ¯
θ 3 =
∂
∂ E
F
¯
B 15
E
F , n x , n y
.
(iv) The model of Stillman et al.
The 1D electron statistics under the condition of unity Fermi function at low
temperatures can be written following [41] as
n s =
2g v
π
S
B 17
E
F , n x , n y
(8)
Using (1) and (8) the C g can be expressed as
C g =
2g v e
2
π
S(θ 4 )
1 +
2g v e
2
πC ins
S(θ 4 )
−1
(9)
where, θ 4 =
∂
∂ E
F
B 17
E
F , n x , n y
.
(v) The model of Newson and Kurobe
The 1D electron statistics under the condition of unity Fermi function at low
temperatures can be written following [41] as
n s =
2g v
π
S
B 19
E
F , n x , n y
(10)
Using (1) and (10) the C g can be expressed as
C g =
2g v e
2
π
S(θ 5 )
1 +
2g v e
2
πC ins
S(θ 5 )
−1
(11)
where, θ 5 =
∂
∂ E
F
B 19
E
F , n x , n y
.