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

3.3.4 SiGe Growth Model 
The growth model for SiGe alloys with SiH
4
and GeH
4
precursors is complicated [80, 
81]. The growth of Si
1−x
Ge
x
by CVD can be divided into two regimes: a 
heterogeneous decomposition dominated regime and a homogeneous decomposition 
dominated regime.
Heterogeneous decomposition: In Si
1−x
Ge
x
CVD, there are four types of surface 
sites on the substrate: H-terminated Si sites (H-Si), H-terminated Ge sites (H-Ge), 
H-free Si sites (-Si), and H-free Ge sites (-Ge). With two precursors involved (SiH
4 
and GeH
4
), there are a total of eight most likely heterogeneous reactions on the 
substrate. 
Table 3.1: Most likely heterogeneous reactions in Si1−xGex CVD from GeH4 and SiH4 
Table 3.1 shows the eight most likely reactions in the heterogeneous decomposition 
regime. The activation energies for reactions on H-terminated Si and Ge sites are 
larger than those on H-free Si and Ge sites. As a result, reaction fluxes on 
H-terminated Si and Ge sites can be neglected compared to those on H-free Si and Ge 
sites. Therefore, we can reduce the number of expression for the Si and Ge fluxes [81]. 
Notation
Description
Reactions
J
GeH4/Ge
GeH
4
flux on Ge sites 
GeH
4
(g) + 2-Ge(s) = H
3
Ge–Ge(s) + H–Ge(s)
J
GeH4/H–Ge
GeH
4
flux on H–Ge sites 
GeH
4
(g) + H–Ge(s) = H
3
Ge–Ge(s) + H
2
(g)
J
GeH4/Si
GeH
4
flux on Si sites 
GeH
4
(g) + 2-Si(s) = H
3
Ge–Si(s) + H–Si(s)
J
GeH4/H–Si
GeH
4
flux on H–Si sites 
GeH
4
(g) + H-Si(s) = H
3
Ge–Si(s) + H
2
(g)
J
SiH4/Ge 
SiH
4
flux on Ge Sites 
SiH
4
(g) + 2-Ge(s) = H
3
Si–Ge(s) + H–Ge(s)
J
SiH4/H–Ge
SiH
4
flux on H–Ge sites 
SiH
4
(g) + H–Ge(s) = H
3
Si–Ge(s) + H
2
(g)
J
SiH4/Si 
SiH
4
flux on Si sites 
SiH
4
(g) + 2-Si(s) = H
3
Si–Si(s) + H–Si(s)
J
SiH4/H–Si
SiH
4
flux on H–Si sites 
SiH
4
(g) + H–Si(s) = H
3
Si–Si(s)+ H
2
(g)

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47 
Fig 3.11 (a) shows the schematic of all the possible heterogeneous reactions. 
Equations of fluxes can be written in relation to partial pressures of different gases and 
θ
Si
and θ
Ge
represent the ratio of H-terminated Si sites to all Si sites and the ratio of 
H-terminated Ge site to all Ge sites, respectively. Fig 3.11 (b) shows the H desorption 
from surface sites and H diffusion between Ge and Si sites. In SiH
4
CVD, the H 
coverage of Si sites; θ
Si
, decreases with increasing temperatures and increases with 
larger flow rates of SiH
4
.
(a) (b) 
Figure 3.11: (a) Most likely heterogeneous reactions in Si
1−x
Ge
x
CVD from GeH
4
and SiH
4
. (b) H 
desorption from surface sites and H diffusion between Ge and Si sites. 
Surface H coverage in Si
1−x
Ge
x
growth is complicated due to the presence of Ge. At 
lower temperatures, H desorption occurs more easily when Ge is present. This 
significantly increases the SiGe alloy deposition rate. The adsorption of SiH
4
and 
GeH
4
brings H to the surface and H desorption removes H from the surface. In 
addition, H atoms diffuse between Ge and Si sites on the surface. H desorption is 
enhanced when a H atom diffuses to a Ge site compared to desorption from a Si site. 
Homogeneous decomposition: SiH
4
homogeneously decomposes into SiH
2
and H
2
at temperatures higher than 950°C. However, the temperature for Si
1−x
Ge
x
growth by 
CVD is often between 350 and 550°C, and thus homogeneous decomposition of SiH
4
is very slow and can be neglected. GeH
4
also decomposes into GeH
2
and H
2
. At 300°C, 
heterogeneous decomposition of GeH
4
predominates when the GeH
4
flow rate is low, 

---

 
 
 
48 
and homogeneous decomposition of GeH
4
predominates at 450°C when the GeH
4
flow 
rate is high. However, a side effect of GeH
4
homogeneous decomposition is that it 
complicates the gas phase chemistry for both GeH
4
and SiH
4
, especially at high 
temperatures or high GeH
4
flow rates. 
Based on the discussions above, in order to make the growth rate more predictable 
and controllable, precise control of temperature and gas fluxes need to achieve to have 
a well controlled heterogeneous regime growth rate. Also, at 350-450°C, the growth 
rate with moderate Si and Ge fluxes must be controlled to get a predictable 
homogeneous growth rate.