Environmental Engineering Reference
In-Depth Information
n
=
p
(4.13)
The product of electron and hole density is called the
intrinsic carrier density
n
i
2
and depends on the absolute temperature
T
and band gap
E
g
:
(4.14)
where the Boltzmann constant
k
is given as:
k
= 1.380658
•
10
-23
J/K
(4.15)
The value for silicon is
n
i0
= 4.62
•
10
15
cm
-3
K
-3/2
. No free electrons and holes
exist at a temperature of absolute zero (
T
= 0 K = -273.15°C). With increasing
temperature their number rises rapidly.
If an electrical voltage is applied to the silicon crystal externally, negatively
charged electrons will flow to the anode. Electrons neighbouring a hole can move
into the hole created by this current. Thus, holes move in the opposite direction to
the electrons. The
mobility
µ
n
and
µ
p
of electrons and holes in the semiconductor
depends also on the temperature.
µ
n
and
µ
p
can be calculated for silicon with
µ
0n
= 1350 cm
2
/(V s) and
= 480 cm
2
/(V s) at
T
0
µ
0p
= 300 K by:
(4.16)
(4.17)
The
electrical conductivity
(4.18)
of the semiconductors is given by the sum of the electron and hole currents.
The conductivity decreases significantly at very low temperatures. This effect
is used for the production of low temperature sensors.
The influence of light also changes the electrical conductivity. This effect is
used in light sensible photoresistors. For their application, an electrical voltage
must be applied externally. However, this effect is not relevant to the
photovoltaic generation of electrical current. Therefore, another effect must be
used: the so-called extrinsic or
defect conduction
(Figure 4.6).
Atoms from group V such as phosphorus (P) and antimony (Sb) have five
valence electrons in contrast to silicon's four. If these atoms are embedded into
a silicon crystal lattice, the fifth electron cannot participate in electron pair
binding. Thus, this electron is bonded very loosely. Little energy is required to
separate this electron from the atom and thus create a free electron. The
embedding of atoms from group V is called n-doping. The impurity atoms are
called
donors
.
