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10 Quantum Statistics
Fig. 10.8 Typical energy
occupancy level diagrams for
n-type and p-type impurity
semiconductors. Panel (a):
n-type semiconductors; panel
(b) p-type semiconductors
0
E A
Ω(ε)
(b)
0 Eg
Ω(ε)
(a)
Ω(ε)
ε
E v
E c
(a)
ε
(b)
f 0 (ε)
E v μ E c
Fig. 10.9 Density-of-states [panel (a)] and T = 0 K Fermi distribution [panel (b)] for intrinsic
semiconductors
We shall first examine intrinsic semiconductors in greater detail, after which we
shall take a brief foray into the world of impurity semiconductors.
10.5.1 Intrinsic Semiconductors
At temperature T the energy of a promoted conduction electron can often be
approximated by
(p) = E g +
1
2m ∗
e
p
2 ,
(10.5.3)
while that of the ‘hole’ left behind in the valence band may be approximated by
(p
) = −
1
2m ∗
h
p
2 ,
(10.5.4)
with m ∗
e and m ∗
h being effective masses of the electron and hole [see Appendix F.3].
We note in passing that these are the masses required for the electrons and holes
to behave like free particles; they often have values that are only fractions of the
electron rest mass. These relationships are illustrated in Fig. 10.9.