92
4 Structural Defects
Fig. 4.33 Bright-field
TEM image of pure twist
boundary with network of
pure twist dislocations
fabricated by wafer
bonding of two Si (001)
surfaces with a relative
twist. Adapted from [361]
(a)
(b)
Fig. 4.34 a Schematic of (111) twin boundary in a diamond or zincblende structure (cmp. Fig. 4.29). The grain
boundary is marked by a dashed line shown in side-view. The hexagonal and rectangular grey boxes have the same area.
The lattice points of the coincident site lattice (CSL) are shown with black circles in the lower part of the figure. The unit
cell of the CSL has three times the volume of the unit cell of the fcc lattice. b Schematic of a (001) grain boundary
in a (simple) cubic crystal shown in plane-view. The blue and the red lattice are rotated by 36.86 ◦ , the lattice points of
the CSL are shown in black. The unit cell of the CSL lattice (dark grey) has five times the volume of the cubic unit cell
(light grey)
example with (111) grain boundary is schematically shown in an example in Fig. 4.34a. A 3 (twin)
boundary in silicon with {112} grain boundary [357, 358] is depicted in Fig. 4.35 together with the
atomic arrangement of the grain boundary itself. A 5 (001) grain boundary is schematically shown
in Fig. 4.34b; the special angle is θ = arctan 3/4 ≈ 36.87
◦ .
Real grain boundaries may not be flat, contain impurities or precipitates and even consist of a thin
amorphous layer.
4 Structural Defects
Fig. 4.33 Bright-field
TEM image of pure twist
boundary with network of
pure twist dislocations
fabricated by wafer
bonding of two Si (001)
surfaces with a relative
twist. Adapted from [361]
(a)
(b)
Fig. 4.34 a Schematic of (111) twin boundary in a diamond or zincblende structure (cmp. Fig. 4.29). The grain
boundary is marked by a dashed line shown in side-view. The hexagonal and rectangular grey boxes have the same area.
The lattice points of the coincident site lattice (CSL) are shown with black circles in the lower part of the figure. The unit
cell of the CSL has three times the volume of the unit cell of the fcc lattice. b Schematic of a (001) grain boundary
in a (simple) cubic crystal shown in plane-view. The blue and the red lattice are rotated by 36.86 ◦ , the lattice points of
the CSL are shown in black. The unit cell of the CSL lattice (dark grey) has five times the volume of the cubic unit cell
(light grey)
example with (111) grain boundary is schematically shown in an example in Fig. 4.34a. A 3 (twin)
boundary in silicon with {112} grain boundary [357, 358] is depicted in Fig. 4.35 together with the
atomic arrangement of the grain boundary itself. A 5 (001) grain boundary is schematically shown
in Fig. 4.34b; the special angle is θ = arctan 3/4 ≈ 36.87
◦ .
Real grain boundaries may not be flat, contain impurities or precipitates and even consist of a thin
amorphous layer.