In conductors, the valence band partially overlaps the conduction band with no
forbidden energy gap between the valence and conduction bands. In semicon-
ductors the forbidden gap is less than 1.5eV. Some semiconductor materials
are silicon (Si), germanium (Ge), and gallium arsenide (GaAs). Figure 10.1
shows the energy level diagram of silicon, germanium and insulator (carbon).
10.1.2 Mobile carriers
Silicon is the most commonly used semiconductor material in the integrated
circuit industry. Silicon has four valence electrons and its atoms are bound to-
gether by covalent bonds. At absolute zero temperature the valence band is
completely filled with electrons and no current flow can take place. As the
temperature of a silicon crystal is raised, there is increased probability of
breaking covalent bonds and freeing electrons. The vacancies left by the freed
electrons are holes. The process of creating free electron-hole pairs is called
ionization. The free electrons move in the conduction band. The average
number of carriers (mobile electrons or holes) that exist in an intrinsic semi-
conductor material may be found from the mass-action law:
nATe
i
EkT
g
=
−
15.
[/()]
(10.1)
where
T
is the absolute temperature in
o
K
k
is Boltzmann’s constant (
k
= 1.38 x 10
-23
J/K or 8.62x10
-5
eV/K )
E
g
is the width of the forbidden gap in eV.
E
g
is 1.21 and
1.1eV for Si at 0
o
K and 300
o
K, respectively. It is given as
EEE
gcv
=−
(10.2)
A
is a constant dependent on a given material and it is given as
A
h
mk
m
m
m
m
n
p
o
=
2
2
30
32
0
34
()()
/
*
*
/
π
(10.3)
where
© 1999 CRC Press LLC
© 1999 CRC Press LLC
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