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

2.3.3 Band Engineering in Ge Quantum Wells 
Extensive calculation of the energy band shift between strained Si
1-x
Ge
x
and relaxed 
Si
1-y
Ge
y
layers were performed previously [53]. Although slightly different 
approaches were used, overall agreement based on previous work has been reached. 
Only a limited number of experimental results conducted under well defined strain 
conditions are available; they basically confirm the theoretical offsets within 
negligible error margins. The valence band maximum always occurs in the layer with 
higher Ge composition. Therefore, finding a position for the right conduction band 
offset is more critical in our work. 
Fig 2.12 shows the contours of conduction band offsets (ΔE
C
) between the strained 
Si
1-x
Ge
x
and relaxed Si
1-y
Ge
y
layers. For xtensilely strained Si
1-x
Ge
x 
layer, and the band alignment is type-II. When x>y and 
y<0.6, the conduction band offset is smaller than ±20meV, which indicates a basically 
flat conduction band alignment within the accuracy of the calculations. For Ge-rich 
strained layers (x>0.8) with Ge-rich substrates (y>0.6), a type-I alignment is predicted. 
It can be seen from Fig 2.12 that previous work has been focused on Si-rich 
substrates with varying Ge composition. They all used indirect bandgap transition; 
Si-rich type-I alignment has weak absorptioin; Ge-rich alloys are type-II due to strain 
effects. All these factors lead to failure of finding strong absorption for these SiGe 
alloy systems. 

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29 
 
Figure 2.12: Conduction band offsets in SiGe heterostructures. x and y denote the Ge content in the 
strained epi-layer and relaxed buffer. Early SiGe work has been summarized (offset contours from ref. 
[51], data points from [35-40]). 
In order to have high Ge content for high absorption efficiency and also to prevent 
type-II alignment, the upper right corner of Fig. 2.12 becomes the area of choice 
investigated in recent work and continues in this work.