74
4 Structural Defects
Fig. 4.4 The temperature
dependent diffusion
coefficient of Si interstitials
I , vacancies V and various
impurities in silicon. Also
the self-diffusion
coefficient, labeled with
‘Si’ is shown. Based on
data from [273]
(d)
(e)
Fig. 4.5 Configurations of boron in Si: (a) Substitutional boron and Si self-interstitial at ‘T’ site (B S –Si T
i ). Interstitial
boron at (b) ‘H’ (B H
i ) and (c) ‘T’ site (B T
i ), each with the Si atoms on the Si lattice sites. The large bright ball represents
the boron atom, large and small dark balls represent Si atoms. (d) Lowest energy barrier diffusion paths for positively
charged and neutral B–Si states, total energy vs. configuration. (e) Two diffusion pathways for positively charged B–Si,
kick-out (dashed line) and pair diffusion (solid line); the activation energy is labeled. Adapted from [279]
Using the experimental value H
f
V = 2.8 ± 0.3 eV [269] from Table 4.1, for the migration enthalpy a
value around H
m
V ≈ 0.8 eV is obtained.
As an example for a dopant diffusion process that has been understood microscopically, we discuss
here boron in silicon. In Fig. 4.5a the lowest-energy configuration of a boron-related defect in silicon is
depicted, B s –Si
T
i , i.e. boron on a substitutional site and a self-interstitial Si on the ‘T’ place with highest
symmetry
2 (see Fig. 3.18). Due to its importance as an acceptor in Si, the configuration and diffusion
2 The positive charge state is stable, the neutral charge state is metastable since the defect is a negative-U center (see
Sect. 7.7.5).
4 Structural Defects
Fig. 4.4 The temperature
dependent diffusion
coefficient of Si interstitials
I , vacancies V and various
impurities in silicon. Also
the self-diffusion
coefficient, labeled with
‘Si’ is shown. Based on
data from [273]
(d)
(e)
Fig. 4.5 Configurations of boron in Si: (a) Substitutional boron and Si self-interstitial at ‘T’ site (B S –Si T
i ). Interstitial
boron at (b) ‘H’ (B H
i ) and (c) ‘T’ site (B T
i ), each with the Si atoms on the Si lattice sites. The large bright ball represents
the boron atom, large and small dark balls represent Si atoms. (d) Lowest energy barrier diffusion paths for positively
charged and neutral B–Si states, total energy vs. configuration. (e) Two diffusion pathways for positively charged B–Si,
kick-out (dashed line) and pair diffusion (solid line); the activation energy is labeled. Adapted from [279]
Using the experimental value H
f
V = 2.8 ± 0.3 eV [269] from Table 4.1, for the migration enthalpy a
value around H
m
V ≈ 0.8 eV is obtained.
As an example for a dopant diffusion process that has been understood microscopically, we discuss
here boron in silicon. In Fig. 4.5a the lowest-energy configuration of a boron-related defect in silicon is
depicted, B s –Si
T
i , i.e. boron on a substitutional site and a self-interstitial Si on the ‘T’ place with highest
symmetry
2 (see Fig. 3.18). Due to its importance as an acceptor in Si, the configuration and diffusion
2 The positive charge state is stable, the neutral charge state is metastable since the defect is a negative-U center (see
Sect. 7.7.5).