184
7 Electronic Defect States
Fig. 7.4 Density of states
(left column), Fermi
distribution (center
column) and carrier
concentration (right
column) for a n-type, b
intrinsic and c p-type
semiconductors in thermal
equilibrium
(b)
f(E)
E
f(E)
E
f(E)
E
D(E)
E V
E D
E
E C
D(E)
E V
E
E C
D(E)
E V
E A
E
E C
n
p
E V
E
E C
n,p
E V
E
E C
n,p
E V
E
E C
(a)
(c)
E F
E F
E F
n,p
n
p
p
n nn
The situation for an intrinsic semiconductor is schematically shown in Fig. 7.4b. In the following we
will consider doping which can shift the Fermi level away from E i . Within the Boltzmann approximation
(also n i = p i ),
n = n i exp
E F − E i
kT
(7.19)
p = p i exp
−
E F − E i
kT
.
(7.20)
7.4 Doping
7.4.1 Concept
The modification of the conductivity of a semiconductor using point defects is termed doping. In
1930 electrical conduction of semiconductors was attributed solely to impurities [566, 567]. However
‘chemically pure’ substances become conductive upon deviation from stoichiometry, e.g. historically