70
4 Structural Defects
Fig. 4.1 Images of
occupied (upper frames)
and empty (lower frames)
density of states of typical
defects on Si-doped GaAs
(110) surfaces. (a1, a2)
show a Ga vacancy, (b1,
b2) a Si Ga donor, (c1, c2) a
Si As acceptor and (d1, d2)
a Si Ga –V Ga complex.
Adapted from [261]
Depending on the position of the interstitial different types are distinguished. An interstitial atom that
has the same chemical species as the crystal is called ‘self-interstitial’.
If an atom site is populated with an atom of different order number Z , an impurity is present. An
impurity can also sit on interstitial position. If the number of valence electrons is the same as for the
original (or correct) atom, then it is an isovalent impurity and quasi fits into the bonding scheme. If the
valence is different, the impurity adds extra (negative or positive) charge to the crystal bonds, which
is compensated by the extra, locally fixed charge in the nucleus. This mechanism will be discussed in
detail in the context of doping (Chap. 7). If in an AB compound an A atom sits on the B site, the defect
is called an antisite defect A B .
A Ga vacancy, a silicon impurity atom on Ga- and As-site and a Si Ga -vacancy complex at the (110)
surface of Si doped GaAs are shown in Fig. 4.1 as observed with STM [261, 262]. Also antisite defects
in GaAs can be observed with STM [263, 264].
A point defect is typically accompanied by a relaxation of the surrounding host atoms. As an
example, we discuss the vacancy in Si (Fig. 4.2a). The missing atom leads to a lattice relaxation with
the next neighbors moving some way into the void (Fig. 4.2b). The bond lengths of the next and secondnext neighbor Si atoms around the neutral vacancy are shown in Fig. 4.2c. The lattice relaxation depends
on the charge state of the point defect (Jahn–Teller effect) which is discussed in more detail in Sect. 7.7.
In Fig. 4.2d the situation for the positively charged vacancy with one electron missing is shown. One of
the two bonds is weakened since it lacks an electron. The distortion is therefore different from that for
V
0 . Also the (self-)interstitial is accompanied with a lattice relaxation as shown in Fig. 4.3 for a silicon
interstitial at tetrahedral place. Self-interstitials in silicon and germanium are reviewed and compared
in [265] for their various charge states.
4.2.2 Thermodynamics
For a given temperature, the free enthalpy G of a crystal (a closed system with regard to particle
exchange)
G = H − T S
(4.1)
is minimum. H is the enthalpy and S the entropy. The enthalpy H = E + pV is the thermodynamic
potential for a system whose only external parameter is the volume V . It is used when the independent
variables of the system are the entropy S and pressure p. The free enthalpy is used when the independent
parameters are T and p. G 0 (H 0 ) is the free energy (enthalpy) of the perfect crystal. H
f is the formation
4 Structural Defects
Fig. 4.1 Images of
occupied (upper frames)
and empty (lower frames)
density of states of typical
defects on Si-doped GaAs
(110) surfaces. (a1, a2)
show a Ga vacancy, (b1,
b2) a Si Ga donor, (c1, c2) a
Si As acceptor and (d1, d2)
a Si Ga –V Ga complex.
Adapted from [261]
Depending on the position of the interstitial different types are distinguished. An interstitial atom that
has the same chemical species as the crystal is called ‘self-interstitial’.
If an atom site is populated with an atom of different order number Z , an impurity is present. An
impurity can also sit on interstitial position. If the number of valence electrons is the same as for the
original (or correct) atom, then it is an isovalent impurity and quasi fits into the bonding scheme. If the
valence is different, the impurity adds extra (negative or positive) charge to the crystal bonds, which
is compensated by the extra, locally fixed charge in the nucleus. This mechanism will be discussed in
detail in the context of doping (Chap. 7). If in an AB compound an A atom sits on the B site, the defect
is called an antisite defect A B .
A Ga vacancy, a silicon impurity atom on Ga- and As-site and a Si Ga -vacancy complex at the (110)
surface of Si doped GaAs are shown in Fig. 4.1 as observed with STM [261, 262]. Also antisite defects
in GaAs can be observed with STM [263, 264].
A point defect is typically accompanied by a relaxation of the surrounding host atoms. As an
example, we discuss the vacancy in Si (Fig. 4.2a). The missing atom leads to a lattice relaxation with
the next neighbors moving some way into the void (Fig. 4.2b). The bond lengths of the next and secondnext neighbor Si atoms around the neutral vacancy are shown in Fig. 4.2c. The lattice relaxation depends
on the charge state of the point defect (Jahn–Teller effect) which is discussed in more detail in Sect. 7.7.
In Fig. 4.2d the situation for the positively charged vacancy with one electron missing is shown. One of
the two bonds is weakened since it lacks an electron. The distortion is therefore different from that for
V
0 . Also the (self-)interstitial is accompanied with a lattice relaxation as shown in Fig. 4.3 for a silicon
interstitial at tetrahedral place. Self-interstitials in silicon and germanium are reviewed and compared
in [265] for their various charge states.
4.2.2 Thermodynamics
For a given temperature, the free enthalpy G of a crystal (a closed system with regard to particle
exchange)
G = H − T S
(4.1)
is minimum. H is the enthalpy and S the entropy. The enthalpy H = E + pV is the thermodynamic
potential for a system whose only external parameter is the volume V . It is used when the independent
variables of the system are the entropy S and pressure p. The free enthalpy is used when the independent
parameters are T and p. G 0 (H 0 ) is the free energy (enthalpy) of the perfect crystal. H
f is the formation