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

2.1.5 Quantum Well Structure 
A quantum well is a potential well that confines particles to two dimensional 
movement. When the quantum well thickness becomes comparable with the de 
Broglie wavelength of the particles confined, discrete energy levels will form and are 
called "energy subbands". 
Quantum wells are formed in semiconductors by having a material, like gallium 
arsenide sandwiched between two layers of a material with a wider bandgap, like 
aluminum arsenide. These structures can be grown by molecular beam epitaxy or 
chemical vapor deposition with control of the layer thickness down to monolayers. 
The ideal case is quantum well surrounded by with infinite barriers. The quantized 
momentum vectors can be written as 

---

 
 
 
18 
n
k
L


, (2.10)
L is the width of the quantum well and n is the quantum number (a positive 
integer). This implies that the allowable energy states are discrete. The quantum 
confinement makes the transition energy of electrons from the valence to the 
conduction band larger than the band gap. The energy difference shown in Fig 2.5 is 
defined as the “quantum well energy”
2
2
2
2
8
2
)
(
mL
h
n
m
k
E
n



,
(2.11) 
m is the effective carrier (electron/hole) mass and h is the Planck constant. That 
means the transition energy can be tuned by changing the quantum well width. 
Additionally, the effective mass of holes in the valence band is changed to more 
closely match that of electrons in the conduction band. These two factors made 
quantum well semiconductor a better structure for optical emission and absorption 
device applications. 
Figure 2.5: Ideal quantum well system with infinite barriers. Carriers’ wave functions are confined 
inside well with discrete energy states