1
Homework # 9  Solution
Problem # 1
. Compute the concentration of electrons and holes in an intrinsic semiconductor
InSb at room temperature (E
g
=0.2eV,
m
e
= 0.01
m
and
m
h
= 0.018
m
).
Determine the position of
the Fermi energy.
For an intrinsic semiconductor the concentration of electrons and holes are equal and given by
(
29
3/2
3/ 4
/ 2
2
2
2
g
E
kT
e
h
kT
n
p
m m
e
π

=
=
.
Substituting
T
=300K and the given values of
E
g
,
m
e
and
m
h
, we obtain
n
=
p
≈
8.1·10
20
m
3
The Fermi energy is determined by
3
ln
2
4
v
c
h
e
E
E
m
kT
m
μ
+
=
+
.
At
T
=300K we obtain
0.011
2
v
c
E
E
eV
μ
+
≈
+
.
So the position of the Fermi energy is 0.011eV above the middle of the energy gap.
Problem # 2
. Indium antimonide has
E
g
= 0.23 eV; dielectric constant
ε
= 18; electron effective
mass
m
e
=
0.015
m
.
Calculate the donor ionization energy and the radius of the ground state
orbit. At what minimum donor concentration will appreciable overlap effects between the orbits
of adjacent impurity atoms occur? This overlap tends to produce an impurity band  a band of
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 Spring '08
 WORMER
 Energy, Work, Condensed matter physics, µe, ground state orbit, adjacent impurity atoms, minimum donor concentration

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