CHEM01200604009 Sreejith Kaniyankandy - Homi Bhabha ...

16
3
8
k (1.21)
V
It can be seen that the above expression is true even when L x
L y
L z
. The total number of
filled states can be written as,
4
3 V
N 2 kf
, (1.22)
3
3 8
where k
f
is k for Fermi level. Factor of 2 come from two spin states.
Figure 1.4. Schematic of DOS in different confined systems.
Electron Density therefore is given by
4
3 V
N 2 kf
(1.23)
3
3 8
As mentioned above DOS can be given by,
1
gE ( )
V
Assuming a parabolic dispersion we arrive at,
N
E
(1.24)