12.2 Heteroepitaxy
355
Fig. 12.5 Growth rate of
GaAs in vapor phase
transport at 725 ◦ as a
function of crystal
orientation. The dashed
line is guide to the eye.
Adapted from [1128]
140
120
100
80
60
40
20
0
Growth rate (µm/h)
Angle (degree)
(111)A
(111)B
(001)
(110)
(110)
(113)A
(113)B
90
60
30
0
30
60
90
GaAs
A special case is the use of curved substrates which allow the study of growth on different crystal
orientations in a continuous fashion. Such experiments have been performed using cylindrical substrates
[1124] and hemispherical crystals. For the latter homoepitaxy has been reported for Si [1125, 1126],
SiC [1127] or GaAs [1128]. Also heteroepitaxy has been investigated, for example for GaP and GaAs
on Ge [1129] (cmp. Fig. 12.12). Using such curved substrates, the growth rate can be determined as a
function of crystal orientation as shown for GaAs (on GaAs) in Fig. 12.5; large differences are found
for (111)A and (111)B surfaces. For growth of silicon the variations with angle are much smaller in
the range of 10% [1124].
12.2.3 Growth Modes
The growth of a material A on a material B can occur via three fundamental growth modes (Fig. 12.6),
the layer-by-layer or Frank-van der Merwe (FvdM) growth mode [435], the island or Volmer-Weber
(VW) growth mode [1130] and the Stranski-Krastanow (SK) growth mode [1131, 1132]. In [1132] the
possibility of island formation on an initially flat heteroepitaxial surface was proposed for the growth
of lattice-matched ionic crystals that have different charges. The term SK growth is now typically used
in lattice-mismatched heteroepitaxy for the island formation (and related relaxation of strain energy,
cmp. Fig. 14.37) on an initially two-dimensional layer (wetting layer).
2 Also growth of islands relaxed
by misfit dislocations in strained heteroepitaxy has been termed SK growth [1133].
The growth mode is determined by the relation of the free energies (per area) of the surface σ s ,
interface σ i and film σ f . Wetting of the substrate and growth of a coherent film (FvdM-growth) occurs
for
σ s > σ i + σ f .
(12.1)
If the inequality has the opposite sign, Volmer-Weber or Stranski-Krastanow growth occurs. Additionally the strain energy of the film must be considered. The SK growth generally occurs when there is
wetting of the substrate but layer strain is unfavorable and leads to islanding.
Layer-by-layer growth typically involves nucleation of two-dimensional islands and ‘filling’ of
the remaining monolayer before the next one is started. Another growth mode resulting in smooth
2 This is the growth mode of self-assembled epitaxial quantum dots as discussed in Sect. 14.4.3.
355
Fig. 12.5 Growth rate of
GaAs in vapor phase
transport at 725 ◦ as a
function of crystal
orientation. The dashed
line is guide to the eye.
Adapted from [1128]
140
120
100
80
60
40
20
0
Growth rate (µm/h)
Angle (degree)
(111)A
(111)B
(001)
(110)
(110)
(113)A
(113)B
90
60
30
0
30
60
90
GaAs
A special case is the use of curved substrates which allow the study of growth on different crystal
orientations in a continuous fashion. Such experiments have been performed using cylindrical substrates
[1124] and hemispherical crystals. For the latter homoepitaxy has been reported for Si [1125, 1126],
SiC [1127] or GaAs [1128]. Also heteroepitaxy has been investigated, for example for GaP and GaAs
on Ge [1129] (cmp. Fig. 12.12). Using such curved substrates, the growth rate can be determined as a
function of crystal orientation as shown for GaAs (on GaAs) in Fig. 12.5; large differences are found
for (111)A and (111)B surfaces. For growth of silicon the variations with angle are much smaller in
the range of 10% [1124].
12.2.3 Growth Modes
The growth of a material A on a material B can occur via three fundamental growth modes (Fig. 12.6),
the layer-by-layer or Frank-van der Merwe (FvdM) growth mode [435], the island or Volmer-Weber
(VW) growth mode [1130] and the Stranski-Krastanow (SK) growth mode [1131, 1132]. In [1132] the
possibility of island formation on an initially flat heteroepitaxial surface was proposed for the growth
of lattice-matched ionic crystals that have different charges. The term SK growth is now typically used
in lattice-mismatched heteroepitaxy for the island formation (and related relaxation of strain energy,
cmp. Fig. 14.37) on an initially two-dimensional layer (wetting layer).
2 Also growth of islands relaxed
by misfit dislocations in strained heteroepitaxy has been termed SK growth [1133].
The growth mode is determined by the relation of the free energies (per area) of the surface σ s ,
interface σ i and film σ f . Wetting of the substrate and growth of a coherent film (FvdM-growth) occurs
for
σ s > σ i + σ f .
(12.1)
If the inequality has the opposite sign, Volmer-Weber or Stranski-Krastanow growth occurs. Additionally the strain energy of the film must be considered. The SK growth generally occurs when there is
wetting of the substrate but layer strain is unfavorable and leads to islanding.
Layer-by-layer growth typically involves nucleation of two-dimensional islands and ‘filling’ of
the remaining monolayer before the next one is started. Another growth mode resulting in smooth
2 This is the growth mode of self-assembled epitaxial quantum dots as discussed in Sect. 14.4.3.