@@ -276,17 +276,13 @@ Consider a a quantum well formed from a layer of $GaAs$ of thickness $L$, surrou
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Assume that the band gap of the $Al_{x}Ga_{1−x}As$ is substantially larger than that of $GaAs$.
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 $m_{e}$, the hole effective mass is 0.45 $m_{e}$ with $m_{e}$ the mass of the electron.
1. Sketch the band diagram of this quantum well.
3. Write down the Schrödinger's equation for electrons and holes
4. Find the energies of electron and holes in the quantum well
??? hint
Separating $\bf{k}$ in its components $k_z$ and $k_{\perp}$ , with $k_{\perp}^2=k_x^2+k_y^2$
2. If we want to design a quantum well with a bandgap 0.1 eV larger than that of bulk $GaAs$, what thickness $L$ do we need?
5. Calculate the density of state of electron and holes in the quantum well
6. Why could this structure be more useful as a laser than a normal pn-junction?
7. What would be the advantage of doping the $Al_{x}Ga_{1−x}As$ compared to the $GaAs$ in this quantum well?
2. Write down the Schrödinger's equation for electrons and holes
3. Find the energies of electron and holes in the quantum well as a function of $k_x, k_y$.
4. Calculate the density of states of electron and holes in this quantum well.
5. If we want to design a quantum well with a bandgap 0.1 eV larger than that of bulk $GaAs$, what thickness $L$ do we need?
6. Why is this structure more useful for making a laser than a normal pn-junction?
7. What would be the advantage of doping the Al$_{x}$Ga$_{1−x}$As compared to the $GaAs$ in this quantum well?
