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

2.2 SiGe Material Platform 
QCSE modulators are used widely in III-V compound alloys today. However, today’s 
semiconductor IC industry is primarily based on a Si platform. In order to integrate 
optical interconnect systems, the material, device and fabrication process have to be Si 
compatible. On the other hand, Group-IV materials like Si and Ge are widely used in 
today’s semiconductor industry. SiGe alloys have several advantages [52-54]: (1) 
Heterostructures improve the electrical properties (2) They are compatible with 
CMOS processes (3) Current material deposition technology can deposit high-quality 
SiGe thin films cost effectively. 
2.2.1 Band Structures 
Figure 2.7 : Simplified k-E band structures of bulk semiconductors: (a) GaAs (b) Ge (c) Si. 
Fig 2.7(a) shows the GaAs band E-k diagram. GaAs is a direct band gap material 
with both global minima of the conduction band and global maxima of the valence 
bands at the zone center of the band structure. The material can have radiative 
recombination and can absorb light through zone-center transitions. This is the most 
efficient optical transition process; therefore in most applications, including laser, 
LED, photodetector and QCSE modulation, direct bandgap material is used. For Si 
materials shown in Fig 2.7(b), the maxima of the valence band is at the zone center, 
however, the global minimum of its conduction band is far from the zone center [55, 
56]; thus the optical processes for absorption and emission are very inefficient. This 
E
k
E
k
E
k
E
k
E
k
E
k
(a) GaAs
(c) Ge
(b) Si
Local Minima
at zone center
Global Minima
at zone center
k
[100]
[111]
[
100
]
[111]
[111]
[
100
]
E
E
k
E
k
E
k
E
k
E
k
E
k
E
k
E
k
(a) GaAs
(c) Ge
(b) Si
Local Minima
at zone center
Global Minima
at zone center
k
[100]
[111]
[
100
]
[111]
[111]
[
100
]
E

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also indicates that Si can be very useful in optical waveguide applications. The Ge 
band structure shown in Fig 2.6 (c) appears to be of special interest. The global 
maximum for the valence band is at the zone center. Even though the global 
conduction band minimum is at L valley, there is a local minimum at the zone center 
for the conduction band, and it is very close to global minimum. At room temperature, 
the absorption edges related to the direct and indirect transitions are ~ 0.8 eV [57] and 
~0.64 eV respectively [58]. Fig. 2.8 shows the bulk absorption coefficient spectra 
versus the photon energy and wavelength for different semiconductor materials that 
are commonly used [59]. Si exhibits very typical indirect band gap absorption 
behavior; the absorption coefficient depends linear on the square root of the energy. 
For GaAs, there is almost no absorption below 1.43 eV; after that there is a very sharp 
transition. That is due to the direct bandgap. Similar behavior can be observed on InAs. 
For Ge, at 0.64eV, the absorption curve is similar to Si, however, after 0.8eV, there is 
a very sharp transition, and the absorption coefficient reaches 5000 cm
-1
. This high 
absorption efficiency of Ge comes from its Kane-shaped band structure at the zone 
center [60] similar to the direct band gap III-V compounds. 

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Figure 2.8: Bulk optical absorption coefficient spectra of major semiconductor materials. [57]