High speed, low driving voltage vertical cavity germanium-silicon modulators for optical

Chapter 3 SiGe Material 
Growth 
3.1 SiGe Alloy Surface Morphology
Studies [67-70] show that if the lattice mismatch between heterostructures is small 
and the thickness of the epilayer does not exceed the critical thickness (ref Mathews & 
Blacklee), the atoms on the two sides of the interface are in perfect registration 
in-plane and the mismatch is accommodated entirely by the elastic strain in the 
epilayer; the growth of the epilayer is then coherent, pseudomorphic or commensurate. 
This is also true for SiGe heterostructures, although the range of composition and 
thickness is certainly more constrained than in most III-V systems.
Strained SiGe layers of increasing thickness on Si tend to relax strain both by 
dislocation formation and by roughening the surface. Theis leads to local elastic 
relaxation of strain. Such roughening may be enhanced by local inhomogeneities 
caused by enhanced diffusion to dislocations, point defects or contamination. However, 
even a perfect SiGe layer on Si may have three different surface morphologies 
[71-74].

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35 
Figure 3.1: Thin film growth modes: (a) 2D growth (b) mixed growth (c) pure 3D growth [75] 
Fig 3.1 (a) shows the homogeneous 2D deposition of a SiGe layer in the 
step-flow mode on a Si substrate which has a small (inevitable) miscut. Growth on a 
miscut substrate may result in a layer of modulated thickness. Some SiGe material 
may accumulate at the intrinsic step edges, as mismatch strain can be partially relieved 
by accumulation at these locations. The local relaxation of lattice parameter of 
epitaxial SiGe in the vertical as well as the lateral direction is enabled by the modified 
boundary condition of a stepped free surface with additional free bonds compared with 
a flat layer. The elastic SiGe relaxation causes a distortion of the underlying Si 
substrate, which reduces the strain energy gained by the system. The relaxation energy 
increases with the amount of deposited SiGe material, with the Ge content and with 
the step height. This induces an instability in the strained layers on vicinal surfaces 
due to accumulation of material at step edges and enhanced bunching of surface steps 
in the strained layers.
Fig 3.1 (b) shows mixed growth of 2D and 3D features. Under this scenario, elastic 
strain is reduced by undulation of the strained layer surfaces. With waviness in certain 
directions, the lattice remains strained in that direction. The material forms 2D islands 
and allows relaxation in all directions, and the relaxation energy gained may be larger 
compared with the former case. The surface area in that situation is normally increased 
and energetically less-favourable crystal planes will be formed to lower the overall 
energy of the system. 
Fig 3.1 (c) shows the 3D growth of islands and the process, which was described 
and analyzed in Ref. [70]. If grown at higher temperatures (600-700º
C), the transition 
Si
SiGe

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36 
from uniform 2D layer growth of SiGe alloy to 3D nucleation of stable islands takes 
place rapidly like a phase transition. This requires two conditions: (1) The diffusion 
length of adatoms has to be large enough to enable effective mass transport. (2) A 
material-dependent energy barrier has to be overcome for island formation.
By understanding the difference in surface morphology, slow kinetics can be used 
to prevent approaching the energetically favored structure. 3D growth can be avoided 
by using a low substrate temperature and high growth rate to yield a high-quality and 
relatively flat surface. 
The methord to quantify strain is very important to measure the stress between 
thin-film materials. Fig 3.2 (a) schematically shows the structure of strained SiGe 
grown on a Si substrate. The lateral lattice spacing is compressed to 
which is the 
same or close to that of Si. The vertical spacing will be extended to 
. Fig 3.2 (b) 
shows the relaxed SiGe layer grown on Si. The lattice constant is the same as that of 
bulk SiGe having the same composition.
 
Figure 3.2: Atom arrangements of (a) strained (b) relaxed epi-layers on substrates. 
For Fig. 3.2 (a), the stresses on the epi-layer are
(parallel to the interface) and
(perpendicular to the interface) and can be expressed as 
a
a
a
II
II



(3.1) 
II
C
C
a
a
a


1 1
1 2
2





, 
(3.2) 
where C
11 
and C
12
are the elastic stiffness constants. C
11
and C
12
of Si (and Ge) are 
16.58 and 6.39 (and 12.85 and 4.82) respectively (all in units of 10
6
N/cm
2
) [71]. For 
a
a
a
┴
a
װ
Relaxed
Strained
Substrate
Epi-layer

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37 
certain materials, stresses in both directions can give us a very clear picture of 
information such as critical thickness, potential crystal quality, etc.