@@ -233,4 +233,16 @@ A $pn$-junction has a **depletion layer** in its middle with the potential in a
### Exercise 3: Performance of a diode
### Exercise 4: Quantum well in detail
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### Exercise 4: Quantum well in detail
A quantum well is formed from a layer of $GaAs$ of thickness $L$, surrounded by layers of $Al_{x}Ga_{1−x}As$
_add fig Fig. 18.2 from the book_. You may assume that the band gap of the $Al_{x}Ga_{1−x}As$ is substantially larger than that of $GaAs$.The electron effective mass in GaAs is 0.068 $m_{e}$ whereas the hole effective mass is 0.45 $m_{e}$ with $m_{e}$ the mass of the electron.
1. Sketch the shape of the potential for electrons and holes
2. If we want to design a bandgap 0.1$eV$ larger than that of bulk $GaAs$, what size of $L$ do we need?
3. Calculate the density of state of electron and holes in the quantum well
??? hint
It is a 2D electron gas with confined levels in the third direction
4. Why could this structure be more useful as a laser than a normal pn-junction?
5. What would be the advantage of doping the $Al_{x}Ga_{1−x}As$ compared to the $GaAs$?
