176
6 Band Structure
Fig. 6.54 Model density
of states in amorphous
semiconductors (solid
lines) according to Mott
[547], Cohen-FritzscheOvshinsky [548],
Davis–Mott [549] and
Marshall–Owen [550].
Dashed lines represent the
DOS of the same material
without disorder
DOS (arb. units)
Energy
E V
E C
E V
E C
Energy
E V
E C
E V
E C
DOS (arb. units)
(a)
(b)
(c)
(d)
a-Si
DOS (10 eV cm )
22
-1
-3
1.0
0.5
0
0.0
0.5
1.0
Energy (eV)
-0.5
1.5
Fig. 6.55 Theoretical calculation of the density of electronic states of amorphous silicon. The charge distribution in four
selected states at the indicated energies is shown, from right to left with decreasing localization. Adapted from [551]
E(k) =
2
2 m ∗
M
i=1
k
2
i .
(6.65)
The k i can take the values ±π n/L (in the first Brillouin zone) with n ≤ N , N being the number of unit
cells in one dimension. These values are equidistant in k-space. Each M-dimensional k-point takes a
volume of (2π/L)
M . The number of states N (E F ) up to the energy E F =
2
2m
k
2
F (later used as Fermi
energy E F and Fermi vector k F ) is
N (E F ) =
2
(2π/L) M
|k|=k F
k=0
d
M k .
(6.66)