80
4 Structural Defects
~E i
-4
10
10
10
10
10
10
10
16
22
21
20
19
18
17
-3
0.01
0.1
1.0
(eV)
i
Si
As
P
B
Ga
Al
Li
Sb
Cu
Au
Fe
Fig. 4.11 Solubility limit for various impurities in silicon vs. their ionization energy. Adapted from [314]
Table 4.3 Maximum solubility N s of some impurities in silicon. Data for B, P, As, Sb from [313], other data from [316]
Impurity
N s (10 20 cm −3 )
B
4
P
5
As
4
Sb
0.7
Al
0.13
Cu
1.4 × 10 −2
Au
1.2 × 10 −3
Fe
3 × 10 −4
4.2.5.3 Solubility Limit
The steady-state impurity solubility can be defined as the maximum concentration of impurity atoms in
a crystal allowing thermodynamic balance between the crystal and another phase, e.g. a liquid phase,
an extended defect or a precipitate. Precipitates are small inclusions of a second phase in a crystal,
exhibiting a high concentration of ‘gathered’ impurities that cannot be solved in the crystal. Solubility
limits for impurities in silicon have been first determined in [312] with a bulk of subsequent research
[313] due to its practical relevance in device fabrication. The solubility limits for a few impurities in
silicon are listed in Table 4.3. It is related to the ionization energy of the defect (cmp. Sect. 7.4) as
shown in Fig. 4.11.
The temperature dependence of the solubility for a few dopants is depicted in Fig. 4.12a. The
solubility depends also on the present strain [315]. The simple empirical relation x s = 0.1 k (Fig. 4.12b)
between the maximum molar solubility x s and the distribution coefficient k in silicon and germanium
has been pointed out in [316].
A typical example for the formation of precipitates is Fe in InP, used for compensation of shallow
donors in order to produce semi-insulating material (Sect. 7.7.8). The solubility of Fe in InP is fairly
low, about 10
17 cm
−3 at growth temperature [317]. In Fig. 4.13 a high-resolution TEM image of a
precipitate in InP doped with 3 × 10
18 cm
−3 Fe is shown. The precipitate exhibits a lattice constant
4 Structural Defects
~E i
-4
10
10
10
10
10
10
10
16
22
21
20
19
18
17
-3
0.01
0.1
1.0
(eV)
i
Si
As
P
B
Ga
Al
Li
Sb
Cu
Au
Fe
Fig. 4.11 Solubility limit for various impurities in silicon vs. their ionization energy. Adapted from [314]
Table 4.3 Maximum solubility N s of some impurities in silicon. Data for B, P, As, Sb from [313], other data from [316]
Impurity
N s (10 20 cm −3 )
B
4
P
5
As
4
Sb
0.7
Al
0.13
Cu
1.4 × 10 −2
Au
1.2 × 10 −3
Fe
3 × 10 −4
4.2.5.3 Solubility Limit
The steady-state impurity solubility can be defined as the maximum concentration of impurity atoms in
a crystal allowing thermodynamic balance between the crystal and another phase, e.g. a liquid phase,
an extended defect or a precipitate. Precipitates are small inclusions of a second phase in a crystal,
exhibiting a high concentration of ‘gathered’ impurities that cannot be solved in the crystal. Solubility
limits for impurities in silicon have been first determined in [312] with a bulk of subsequent research
[313] due to its practical relevance in device fabrication. The solubility limits for a few impurities in
silicon are listed in Table 4.3. It is related to the ionization energy of the defect (cmp. Sect. 7.4) as
shown in Fig. 4.11.
The temperature dependence of the solubility for a few dopants is depicted in Fig. 4.12a. The
solubility depends also on the present strain [315]. The simple empirical relation x s = 0.1 k (Fig. 4.12b)
between the maximum molar solubility x s and the distribution coefficient k in silicon and germanium
has been pointed out in [316].
A typical example for the formation of precipitates is Fe in InP, used for compensation of shallow
donors in order to produce semi-insulating material (Sect. 7.7.8). The solubility of Fe in InP is fairly
low, about 10
17 cm
−3 at growth temperature [317]. In Fig. 4.13 a high-resolution TEM image of a
precipitate in InP doped with 3 × 10
18 cm
−3 Fe is shown. The precipitate exhibits a lattice constant