12.2 Heteroepitaxy
363
Fig. 12.18 Average film strain (measured in-situ via substrate curvature) of In 0.15 Ga 0.85 As/GaAs grown at 450 ◦ C as a
function of film thickness (determined from growth time × deposition rate). Relaxation for three different growth modes
are shown (as labeled): continuous growth, employment of several growth interruptions (GRI) and GRI with annealing
step (to 550 ◦ ). Adapted from [1155]
to accommodate part of the mismatch strain in the substrate include the use of cantilevered membranes, silicon-on-insulator, twist bonding, glass bonding or trenched substrates. In this sense also
nanowhiskers (Sect. 14.2.3) represent a compliant substrate, enabling the growth of coherent (laterally
confined) layers thicker than the critical thickness of a 2D layer (cmp. Fig. 14.8).
12.2.7 Plastic Relaxation
Above the critical thickness, a film will relax plastically by forming defects, often misfit dislocations. A
cross-hatch pattern at the surface due to misfit dislocations is shown in Fig. 12.17 (cf. also Sect. 4.3.1.4).
The strain relaxation in mismatched heteroepitaxy can be determined experimentally via the wafer
curvature of the heterostructure (Sect. 5.3.5). Data for the thickness dependent relaxation (d) of
In 0.15 Ga 0.85 As on GaAs (mismatch ≈ 1%) are shown in Fig. 12.18. Growth interruptions lead to larger
relaxation at smaller thickness. Therefore relaxation at early times or small thickness (above h c ) is
kinetically hindered, i.e., the available dislocation density and glide velocity are not sufficient to relieve
the strain. At large thickness the strain does not go to zero (saturation regime) and the film remains in
a metastable, incompletely relaxed state as discussed in more detail in [1155].
An extreme case of plastic relaxation is cracking (Sect. 4.4.1) which can occur for example in thick
films during cooling due to the mismatch of the thermal expansion coefficients of substrate and epilayer
(Fig. 12.19). Such cracking can be avoided by the introduction of suitable stress-relaxing layers and
growth on predefined mesas [1156, 1157].
12.2.8 Surfactants
The condition (12.1) allows layer-by-layer growth (cf. Sect. 12.2.3), i.e., the substrate surface free
energy is higher than the than the total of interface and film surface free energy. This makes wetting
energetically favorable. For two elements A and B, one of them must have the lower surface free
energy. If A can be grown on B in Frank-van der Merwe (or Stranski-Krastanow) growth mode, then
(12.1) does not hold for B on A and the growth will occur in Volmer-Weber mode, i.e., with islands.
363
Fig. 12.18 Average film strain (measured in-situ via substrate curvature) of In 0.15 Ga 0.85 As/GaAs grown at 450 ◦ C as a
function of film thickness (determined from growth time × deposition rate). Relaxation for three different growth modes
are shown (as labeled): continuous growth, employment of several growth interruptions (GRI) and GRI with annealing
step (to 550 ◦ ). Adapted from [1155]
to accommodate part of the mismatch strain in the substrate include the use of cantilevered membranes, silicon-on-insulator, twist bonding, glass bonding or trenched substrates. In this sense also
nanowhiskers (Sect. 14.2.3) represent a compliant substrate, enabling the growth of coherent (laterally
confined) layers thicker than the critical thickness of a 2D layer (cmp. Fig. 14.8).
12.2.7 Plastic Relaxation
Above the critical thickness, a film will relax plastically by forming defects, often misfit dislocations. A
cross-hatch pattern at the surface due to misfit dislocations is shown in Fig. 12.17 (cf. also Sect. 4.3.1.4).
The strain relaxation in mismatched heteroepitaxy can be determined experimentally via the wafer
curvature of the heterostructure (Sect. 5.3.5). Data for the thickness dependent relaxation (d) of
In 0.15 Ga 0.85 As on GaAs (mismatch ≈ 1%) are shown in Fig. 12.18. Growth interruptions lead to larger
relaxation at smaller thickness. Therefore relaxation at early times or small thickness (above h c ) is
kinetically hindered, i.e., the available dislocation density and glide velocity are not sufficient to relieve
the strain. At large thickness the strain does not go to zero (saturation regime) and the film remains in
a metastable, incompletely relaxed state as discussed in more detail in [1155].
An extreme case of plastic relaxation is cracking (Sect. 4.4.1) which can occur for example in thick
films during cooling due to the mismatch of the thermal expansion coefficients of substrate and epilayer
(Fig. 12.19). Such cracking can be avoided by the introduction of suitable stress-relaxing layers and
growth on predefined mesas [1156, 1157].
12.2.8 Surfactants
The condition (12.1) allows layer-by-layer growth (cf. Sect. 12.2.3), i.e., the substrate surface free
energy is higher than the than the total of interface and film surface free energy. This makes wetting
energetically favorable. For two elements A and B, one of them must have the lower surface free
energy. If A can be grown on B in Frank-van der Merwe (or Stranski-Krastanow) growth mode, then
(12.1) does not hold for B on A and the growth will occur in Volmer-Weber mode, i.e., with islands.