194
7 Electronic Defect States
Table 7.4 Binding energies E b
A of group-III acceptors in elemental semiconductors. Data for diamond from [596, 597].
All values in meV
B
Al
Ga
In
C
369
Si
45
57
65
16
Ge
10.4
10.2
10.8
11.2
Table 7.5 Binding energies E b
A of acceptors in GaAs, GaP and GaN (low concentration values, data from [598, 599]).
All values in meV
V site
III site
GaAs
C
27
Be
28
Si
34.8
Mg
28.8
Ge
40.4
Zn
30.7
Sn
167
Cd
34.7
GaP
C
54
Be
57
Si
210
Mg
60
Ge
265
Zn
70
Cd
102
GaN
C
230
Mg
220
Si
224
Zn
340
Cd
550
conductivity type is fixed, while the same semiconductor can be made n- or p-type with the appropriate
doping.
The acceptor concentration is denoted by N A . The concentration of neutral acceptors is N
0
A , the
concentration of charged acceptors is N
−
A . Of course
N A = N
0
A + N
−
A .
(7.37)
The ratio of the degeneracy of the (singly) filled and empty acceptor level is ˆ
g A . In Ge ˆ
g A = 4 since
the localized hole wave function may be formed in EMA with four Bloch wave functions (heavy and
light holes) [600]. For Si with its small split-off energy (Table 6.6) ˆ
g A = 6 according to [601]. For
doubly ionized acceptors, e.g. Zn in Si and Ge (see Sect. 7.7.3), the more shallow level (Zn
−
→ Zn
0 )
has ˆ
g A = 6/4 = 1.5 in Ge [601]. A more general discussion of the degeneracy factor for multiply
charged acceptors can be found in [585, 602]. Similar to the considerations for electrons and donors
we have
N
0
A
N
−
A
= ˆ
g A exp
−
E F − E A
kT
.
(7.38)
The population of the acceptor levels is given by
N
−
A =
N A
1 + ˆ
g A exp
−
E F −E A
kT
.
(7.39)
The formulas for the position of the Fermi level and the hole density are analogous to those obtained
for electrons and donors and will not be explicitly given here. The analogue to Fig. 7.11b is shown for
data on p-doped Ge [603, 604] in Fig. 7.15. The acceptor activation energy is 11 meV which could be
7 Electronic Defect States
Table 7.4 Binding energies E b
A of group-III acceptors in elemental semiconductors. Data for diamond from [596, 597].
All values in meV
B
Al
Ga
In
C
369
Si
45
57
65
16
Ge
10.4
10.2
10.8
11.2
Table 7.5 Binding energies E b
A of acceptors in GaAs, GaP and GaN (low concentration values, data from [598, 599]).
All values in meV
V site
III site
GaAs
C
27
Be
28
Si
34.8
Mg
28.8
Ge
40.4
Zn
30.7
Sn
167
Cd
34.7
GaP
C
54
Be
57
Si
210
Mg
60
Ge
265
Zn
70
Cd
102
GaN
C
230
Mg
220
Si
224
Zn
340
Cd
550
conductivity type is fixed, while the same semiconductor can be made n- or p-type with the appropriate
doping.
The acceptor concentration is denoted by N A . The concentration of neutral acceptors is N
0
A , the
concentration of charged acceptors is N
−
A . Of course
N A = N
0
A + N
−
A .
(7.37)
The ratio of the degeneracy of the (singly) filled and empty acceptor level is ˆ
g A . In Ge ˆ
g A = 4 since
the localized hole wave function may be formed in EMA with four Bloch wave functions (heavy and
light holes) [600]. For Si with its small split-off energy (Table 6.6) ˆ
g A = 6 according to [601]. For
doubly ionized acceptors, e.g. Zn in Si and Ge (see Sect. 7.7.3), the more shallow level (Zn
−
→ Zn
0 )
has ˆ
g A = 6/4 = 1.5 in Ge [601]. A more general discussion of the degeneracy factor for multiply
charged acceptors can be found in [585, 602]. Similar to the considerations for electrons and donors
we have
N
0
A
N
−
A
= ˆ
g A exp
−
E F − E A
kT
.
(7.38)
The population of the acceptor levels is given by
N
−
A =
N A
1 + ˆ
g A exp
−
E F −E A
kT
.
(7.39)
The formulas for the position of the Fermi level and the hole density are analogous to those obtained
for electrons and donors and will not be explicitly given here. The analogue to Fig. 7.11b is shown for
data on p-doped Ge [603, 604] in Fig. 7.15. The acceptor activation energy is 11 meV which could be