204
7 Electronic Defect States
Table 7.6 Critical doping concentration for various semiconductors (at room temperature)
Material
Type
N c (cm −3 )
References
C:B
p
2 × 10 20
[597]
Ge:As
n
1.5 × 10 17
[594]
Si:P
n
1.3 × 10 18
[622]
Si:B
p
6.2 × 10 18
[622]
GaAs
n
1.0 × 10 16
[623]
GaP:Si
n
6 × 10 19
[625]
GaP:Zn
p
2 × 10 19
[626]
GaN:Si
n
2 × 10 18
[627]
GaN:Mg
p
4 × 10 20
[598]
Al 0.23 Ga 0.77 N:Si
n
3.5 × 10 18
[628]
ZnTe:Li
p
4 × 10 18
[621]
ZnTe:P
p
6 × 10 18
[621]
ZnO:Al
n
8 × 10 18
[629]
Table 7.7 Maximum electrically active doping concentration for GaAs
Material
Type
N c (cm −3 )
References
GaAs:Te
n
2.6 × 10 19
[633]
GaAs:Si
n
1.8 × 10 19
[634]
GaAs:C
p
1.5 × 10 21
[635]
GaAs:Be
p
2 × 10 20
[636]
Fig. 7.28 Electron
concentration as a function
of gallium concentration in
MBE grown ZnO:Ga on
sapphire for the two
different polarities.
Adapted from [630, 631]
7.6 Quasi-fermi Levels
The carrier concentrations were given by (7.6) and (7.7). So far, we have only considered semiconductors in thermodynamic equilibrium for which np = n
2
i . In a nonequilibrium situation, e.g. for
external excitation or carrier injection in a diode, the electron and hole densities can each take arbitrary
values, in principle. In particular, np will no longer be equal to n
2
i and there is no Fermi level constant
throughout the structure. In this case, however, quasi-Fermi levels F n and F p for electrons and holes,
respectively, are defined via
7 Electronic Defect States
Table 7.6 Critical doping concentration for various semiconductors (at room temperature)
Material
Type
N c (cm −3 )
References
C:B
p
2 × 10 20
[597]
Ge:As
n
1.5 × 10 17
[594]
Si:P
n
1.3 × 10 18
[622]
Si:B
p
6.2 × 10 18
[622]
GaAs
n
1.0 × 10 16
[623]
GaP:Si
n
6 × 10 19
[625]
GaP:Zn
p
2 × 10 19
[626]
GaN:Si
n
2 × 10 18
[627]
GaN:Mg
p
4 × 10 20
[598]
Al 0.23 Ga 0.77 N:Si
n
3.5 × 10 18
[628]
ZnTe:Li
p
4 × 10 18
[621]
ZnTe:P
p
6 × 10 18
[621]
ZnO:Al
n
8 × 10 18
[629]
Table 7.7 Maximum electrically active doping concentration for GaAs
Material
Type
N c (cm −3 )
References
GaAs:Te
n
2.6 × 10 19
[633]
GaAs:Si
n
1.8 × 10 19
[634]
GaAs:C
p
1.5 × 10 21
[635]
GaAs:Be
p
2 × 10 20
[636]
Fig. 7.28 Electron
concentration as a function
of gallium concentration in
MBE grown ZnO:Ga on
sapphire for the two
different polarities.
Adapted from [630, 631]
7.6 Quasi-fermi Levels
The carrier concentrations were given by (7.6) and (7.7). So far, we have only considered semiconductors in thermodynamic equilibrium for which np = n
2
i . In a nonequilibrium situation, e.g. for
external excitation or carrier injection in a diode, the electron and hole densities can each take arbitrary
values, in principle. In particular, np will no longer be equal to n
2
i and there is no Fermi level constant
throughout the structure. In this case, however, quasi-Fermi levels F n and F p for electrons and holes,
respectively, are defined via