76
4 Structural Defects
(a)
(b)
Fig. 4.6 (a) Relative concentration of indium along a CZ-grown germanium crystal. Absolute concentration is in the
10 16 cm −3 range. Solid line follows (4.19) with k = 1.2 × 10 −3 . Symbols are experimental data from [288]. (b) Impurity
distribution (relative concentration c(x)/c 0 ) for CZ (4.18) (solid lines) and FZ (4.20) (dashed lines, z = 0.01) silicon
crystals for B (blue), P (red), and Al (green). Distribution coefficients have been taken from Table 4.2. Note crossing of
B and P lines and possibly associated change from p-type to n-type (cmp. Fig. 1.7)
Table 4.2 Equilibrium distribution coefficients (at melting point) of various impurities in silicon, germanium and GaAs.
Data for Si from [285, 287], for Ge from [164, 288–290] and for GaAs from [164]
Impurity
Si
Ge
GaAs
C
0.07
> 1.85
0.8
Si
5.5
0.1
Ge
0.33
0.03
N
7 × 10 −4
O
≈ 1
0.3
B
0.8
12.2
Al
2.8 × 10 −3
0.1
3
Ga
8 × 10 −3
0.087
In
4 × 10 −4
1.2 × 10 −3
0.1
P
0.35
0.12
2
As
0.3
0.04
Sb
0.023
3.3 × 10 −3
< 0.02
S
10 −5
> 5 × 10 −5
0.3
Fe
6.4 × 10 −6
3 × 10 −5
2 × 10 −3
Ni
≈ 3 × 10 −5
2.3 × 10 −6
6 × 10 −4
Cu
8 × 10 −4
1.3 × 10 −5
2 × 10 −3
Ag
≈ 1 × 10 −6
10 −4
0.1
Au
2.5 × 10 −5
1.5 × 10 −5
Zn
2.5 × 10 −5
6 × 10 −4
0.1
and is then called the effective distribution coefficient. For k < 1, k eff > k eq . k eff approaches 1 for high
growth rates, i.e. all impurities at the rapidly moving interface are incorporated.
Equation (4.18) applies to Czrochalski growth where the crystal is pulled out of the melt [291].
In float-zone (FZ) growth [291] a polycrystalline rod is transformed into a crystalline one while a