7.5 Shallow Defects
203
(a)
Ge:As
15
10
5
10
13
10
18
10
17
10
16
10
15
10
14
N -N (cm )
A
-3
D
10
12
0
E D
b
(b)
Fig. 7.26 a Donor ionization energy in n-type Ge for various doping concentrations. Dashed line is a guide to the eye.
The arrow labeled E b
D denotes the low-concentration limit (cf. Table 7.2). Experimental data from [594]. b Acceptor
ionization energy for ZnTe:Li and ZnTe:P as a function of the third root of the ionized acceptor concentration. Data
from [621]
Fig. 7.27 Electron
concentration versus
inverse temperature for
Si:P for three different
doping concentrations ((i):
1.2 × 10 17 cm −3 , (ii):
1.25 × 10 18 cm −3 , (iii):
1.8 × 10 19 cm −3 ).
Experimental data
from [622]
0
Si:P
4
1
2
1
8
0
1
6
4
2
1/T (1000/K)
10
20
10
10
10
10
10
19
18
17
16
15
-3
(ii)
(i)
(iii)
a D N
1/3
c
≈ 0.24 .
(7.54)
For GaAs with a D = 10.3 nm, the criterion yields N c = 1.2×10
16 cm
−3 , in agreement with experiment.
The achievable maximum concentration of electrically active dopants is limited by the concentration
dependence of the diffusion coefficient, Coulomb repulsion, autocompensation and the solubility limit
[575]. In Table 7.7 the maximum carrier concentrations for GaAs with various dopants are listed.
As an example we show the Ga-doping of epitaxial ZnO layers on sapphire in Fig. 7.28. Under
slightly Zn-rich (O-polar) conditions the growth mode is two-dimensional and the carrier concentration
increases linearly with the Ga concentration, n ≈ c Ga , up to high values in the 10
20 cm
−3 range
[630]. For O-rich (Zn-polar) conditions the growth mode changes to three-dimensional growth and
the activation ratio of Ga donors becomes low [631]. Above a gallium content of 2%, the octahedral
coordination of gallium and thus the partial segregation into a parasitic ZnGa 2 O 4 spinel phase is
observed for [Ga] = 4% [632].
The doping of semiconductors beyond the solubility limit is termed ‘hyperdoping’. It involves
non-equilibrium preparation methods [637, 638].
203
(a)
Ge:As
15
10
5
10
13
10
18
10
17
10
16
10
15
10
14
N -N (cm )
A
-3
D
10
12
0
E D
b
(b)
Fig. 7.26 a Donor ionization energy in n-type Ge for various doping concentrations. Dashed line is a guide to the eye.
The arrow labeled E b
D denotes the low-concentration limit (cf. Table 7.2). Experimental data from [594]. b Acceptor
ionization energy for ZnTe:Li and ZnTe:P as a function of the third root of the ionized acceptor concentration. Data
from [621]
Fig. 7.27 Electron
concentration versus
inverse temperature for
Si:P for three different
doping concentrations ((i):
1.2 × 10 17 cm −3 , (ii):
1.25 × 10 18 cm −3 , (iii):
1.8 × 10 19 cm −3 ).
Experimental data
from [622]
0
Si:P
4
1
2
1
8
0
1
6
4
2
1/T (1000/K)
10
20
10
10
10
10
10
19
18
17
16
15
-3
(ii)
(i)
(iii)
a D N
1/3
c
≈ 0.24 .
(7.54)
For GaAs with a D = 10.3 nm, the criterion yields N c = 1.2×10
16 cm
−3 , in agreement with experiment.
The achievable maximum concentration of electrically active dopants is limited by the concentration
dependence of the diffusion coefficient, Coulomb repulsion, autocompensation and the solubility limit
[575]. In Table 7.7 the maximum carrier concentrations for GaAs with various dopants are listed.
As an example we show the Ga-doping of epitaxial ZnO layers on sapphire in Fig. 7.28. Under
slightly Zn-rich (O-polar) conditions the growth mode is two-dimensional and the carrier concentration
increases linearly with the Ga concentration, n ≈ c Ga , up to high values in the 10
20 cm
−3 range
[630]. For O-rich (Zn-polar) conditions the growth mode changes to three-dimensional growth and
the activation ratio of Ga donors becomes low [631]. Above a gallium content of 2%, the octahedral
coordination of gallium and thus the partial segregation into a parasitic ZnGa 2 O 4 spinel phase is
observed for [Ga] = 4% [632].
The doping of semiconductors beyond the solubility limit is termed ‘hyperdoping’. It involves
non-equilibrium preparation methods [637, 638].