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
 
Search WWH ::




Custom Search