Chapter 4
Structural Defects
Crystals are like people: it is the defects in them which tend to make them interesting!
C.J. Humphreys, 1979 [260]
Abstract No crystal is perfect. Various point defects and their thermodynamics, diffusion and distribution of defects are discussed. Also dislocations and extended defects such as cracks, stacking faults,
grain boundaries and antiphase domains are covered.
4.1 Introduction
In an ideal lattice each atom is at its designated position. Deviations from the ideal structure are called
defects. In the following, we will briefly discuss the most common defects. The electrical activity of
defects will be discussed in Sects. 7.5 and 7.7. For the creation (formation) of a defect a certain free
enthalpy G
f
D is necessary. At thermodynamical equilibrium a (point) defect density ∝ exp(−G
f
D /kT )
will always be present (cf. Sect. 4.2.2).
Point defects (Sect. 4.2) are deviations from the ideal structure involving essentially only one lattice
point. The formation energy for line defects (Sect. 4.3) or area defects (Sect. 4.4) scales with N
1/3
and N
2/3 , respectively, N being the number of atoms in the crystal. Therefore, these defects are not
expected in thermodynamic equilibrium. However, the path into thermodynamical equilibrium might
be so slow that these defects are metastable and must be considered quasi-frozen. There may also
exist metastable point defects. By annealing the crystal, the thermodynamic equilibrium concentration
might be re-established. The unavoidable two-dimensional defect of the bulk structure is the surface,
discussed in Chap. 11.
4.2 Point Defects
4.2.1 Point Defect Types
The simplest point defect is a vacancy V, a missing atom at a given atomic position. If an atom is at
a position that does not belong to the crystal structure an interstitial I (or Frenkel defect) is formed.
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_4
69
Structural Defects
Crystals are like people: it is the defects in them which tend to make them interesting!
C.J. Humphreys, 1979 [260]
Abstract No crystal is perfect. Various point defects and their thermodynamics, diffusion and distribution of defects are discussed. Also dislocations and extended defects such as cracks, stacking faults,
grain boundaries and antiphase domains are covered.
4.1 Introduction
In an ideal lattice each atom is at its designated position. Deviations from the ideal structure are called
defects. In the following, we will briefly discuss the most common defects. The electrical activity of
defects will be discussed in Sects. 7.5 and 7.7. For the creation (formation) of a defect a certain free
enthalpy G
f
D is necessary. At thermodynamical equilibrium a (point) defect density ∝ exp(−G
f
D /kT )
will always be present (cf. Sect. 4.2.2).
Point defects (Sect. 4.2) are deviations from the ideal structure involving essentially only one lattice
point. The formation energy for line defects (Sect. 4.3) or area defects (Sect. 4.4) scales with N
1/3
and N
2/3 , respectively, N being the number of atoms in the crystal. Therefore, these defects are not
expected in thermodynamic equilibrium. However, the path into thermodynamical equilibrium might
be so slow that these defects are metastable and must be considered quasi-frozen. There may also
exist metastable point defects. By annealing the crystal, the thermodynamic equilibrium concentration
might be re-established. The unavoidable two-dimensional defect of the bulk structure is the surface,
discussed in Chap. 11.
4.2 Point Defects
4.2.1 Point Defect Types
The simplest point defect is a vacancy V, a missing atom at a given atomic position. If an atom is at
a position that does not belong to the crystal structure an interstitial I (or Frenkel defect) is formed.
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_4
69