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

1.4 Organization 
The dissertation reports the study of high-speed germanium-silicon electroabsorption 
modulators aiming for optical interconnects with CMOs compatible, mass-producible 
fabrication processes. Chapter 2 discusses the theoretical background for 
electroabsorption effects, as well as SiGe properties and previous SiGe 
electroabsorption approaches. Chapter 3 presents the Ge/SiGe quantum well structure 
design which utilizes the unique band structure of Ge for the electroabsorption effect. 
The effects of structural parameters are simulated by the resonant tunneling method. 
Chapter 4 discusses SiGe growth, by chemical vapor deposition, and material 
characterization. High-quality Ge quantum wells grown on silicon substrates were 
demonstrated. Chapter 5 presents the device fabrication processes and reports 
experimental measurement results. The first high-speed QCSE was observed in 
group-IV materials. Finally, Chapter 6 summarizes this dissertation and suggests 
several future directions for further scientific and engineering advances

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Chapter 2 Background 
2.1 Absorption in Semiconductors
 
2.1.1 Interband Absorption
The operation of optical devices is strongly related to upward and downward 
transitions of carriers between energy bands. These transitions result in optical 
absorption and emission of light. The absorption of a photon results in the transition 
from a lower energy state to a higher energy state, with or without the assistance of 
phonons. For the transition, the energy and the momentum conservation rules always 
have to be satisfied. 
The energy-momentum diagrams of direct and indirect transitions are shown in Fig. 
2.1 (a) and (b). In Fig. 2.1 (a), electrons and holes are at the zone center of the k-E 
band structure. At k=0, when a photon with larger energy than the band gap passes 
through the material, it will excite an electron from the valence band to the conduction 
band. The absorption coefficient can be written as: 
(2.1) 
α is the absorption coefficient, a function of the light frequency; ν is the light 
frequency; h is Planck's constant (hν is the energy of a photon with frequency ν); E
g
is 
the band gap energy, A* is a frequency-independent constant, which can be written as 
(2.2) 
where m
r
is the reduced effective mass; q is the elementary electron charge; n is 
the (real) index of refraction; ε
0
is the vacuum permittivity; x
vc
is a "matrix element", 

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with units of length and a typical value the same order of magnitude as the lattice 
constant. The formula is only valid for photons with energy larger than the band gap. 
It only includes band-to-band absorption. 
An indirect band gap transition is shown in Fig. 2.1(b). Holes are located at global 
minimum energy at the zone center of k-E band structure. However, the global 
minimum for electrons in the conduction band is not at the zone center. That means 
electrons and holes do not have the same k-momenta. When a photon with energy 
larger than the band gap passes through the material, a phonon needs to be absorbed to 
complete the absorption. This greatly reduces the transition probability and therefore 
leads to a low absorption coefficient. The coefficient can be written as: 
(2.3) 
E
p
is the energy of the phonon that assists in the transition; k is Boltzmann's 
constant; T is the thermodynamic temperature. 
Figure 2.1: (a) Direct band absorption at zone center. (b) Indirect band absorption with phonon 
assistance. 

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