Environmental Engineering Reference
In-Depth Information
Figure 10.4.1
Schematic representation of semiconductor energy band levels.
where
k
is the Boltzman constant. The system is characterized by its temperature,
T
,
and its Fermi level,
E
F
, defined as the energy level at which the probability to be
occupied by an electron is 0.5.
For an intrinsic semiconductor (undoped), the Fermi Level lies at the mid-point of
the bandgap - Figure 10.4.1a - and the energy of its Fermi Level can be calculated as
follows (Nozik and Memming, 1996):
kT
ln
N
V
N
C
1
2
(E
V
1
2
E
F
=
+
E
C
)
+
(10.4.2)
where
E
V
and
E
C
are, respectively, the energy levels of the valence and the conduction
band edges and
T
is the absolute temperature.
N
C
and
N
V
are the density-of-states at
the conduction and valence bands, respectively, and given by (Memming, 2001):
2
2
πm
e
kT
h
3
3
/
2
N
C
=
(10.4.3)
2
2
πm
h
kT
h
3
3
/
2
N
V
=
(10.4.4)
where
h
is Plank's constant and
m
h
and
m
e
are the effective masses of holes and
electrons, respectively. The electron and hole densities in an intrinsic semiconductor
material in the conduction and valence bands, respectively, are given by:
N
C
exp
E
C
−
E
F
n
=
−
(10.4.5)
kT
N
V
exp
E
V
−
E
F
p
=
(10.4.6)
k
T
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