4.2 Point Defects
79
(a)
[001]
[110]
[110]
(b)
void
indium
In O
2
3
Fig. 4.9 (a) Predicted configuration of the V 5 -cluster (five vacancies) in silicon. Yellow spheres indicate more distorted
atoms than the rest of the lattice atoms (white spheres). Adapted from [307]. (b) Indium particle with adjacent void
embedded in In 2 O 3 (STEM image revealing Z -contrast in [001]). Adapted from [306]
Fig. 4.10 Minimum
energy path for the breakup
of a B 3 I 2 cluster into B 2 I
and BI. Silicon (boron)
atoms are shown as yellow
(blue) spheres. Adapted
from [310]
Typically a random distribution of dopants in the host is assumed (cmp. Sect. 3.7.1 on random
alloys). The introduction of several impurities can lead to pairing effects, e.g. described for Se and
B, Ga, Al or In in silicon [308]. A high concentration of a single impurity makes the existence of
clusters, i.e. two or more neighboring dopant atoms, more probable. This effect has been extensively
studied for B in Si [309], showing that several boron atoms with interstitials I form thermodynamically
stable clusters, e.g. B 3 I 2 . This cluster forms from B 2 I and BI with only 0.2 eV activation barrier [310]
as shown in Fig. 4.10. The formation is limited by diffusion of the smaller clusters to the same site.
The number of free carriers (here holes) released from such cluster is smaller than the number of
boron atoms since it forms a deep acceptor [309]. This autocompensation mechanism is thus limiting
the maximum achievable free carrier concentration due to doping and is technologically unfavorable.
Reactions between boron atoms and silicon self-interstitials often lead to boron clustering in the peak
region of an implantation profile and require detailed optimization of the annealing process [311].
79
(a)
[001]
[110]
[110]
(b)
void
indium
In O
2
3
Fig. 4.9 (a) Predicted configuration of the V 5 -cluster (five vacancies) in silicon. Yellow spheres indicate more distorted
atoms than the rest of the lattice atoms (white spheres). Adapted from [307]. (b) Indium particle with adjacent void
embedded in In 2 O 3 (STEM image revealing Z -contrast in [001]). Adapted from [306]
Fig. 4.10 Minimum
energy path for the breakup
of a B 3 I 2 cluster into B 2 I
and BI. Silicon (boron)
atoms are shown as yellow
(blue) spheres. Adapted
from [310]
Typically a random distribution of dopants in the host is assumed (cmp. Sect. 3.7.1 on random
alloys). The introduction of several impurities can lead to pairing effects, e.g. described for Se and
B, Ga, Al or In in silicon [308]. A high concentration of a single impurity makes the existence of
clusters, i.e. two or more neighboring dopant atoms, more probable. This effect has been extensively
studied for B in Si [309], showing that several boron atoms with interstitials I form thermodynamically
stable clusters, e.g. B 3 I 2 . This cluster forms from B 2 I and BI with only 0.2 eV activation barrier [310]
as shown in Fig. 4.10. The formation is limited by diffusion of the smaller clusters to the same site.
The number of free carriers (here holes) released from such cluster is smaller than the number of
boron atoms since it forms a deep acceptor [309]. This autocompensation mechanism is thus limiting
the maximum achievable free carrier concentration due to doping and is technologically unfavorable.
Reactions between boron atoms and silicon self-interstitials often lead to boron clustering in the peak
region of an implantation profile and require detailed optimization of the annealing process [311].