more fixes ex4

src/14_doping_and_devices.md

@@ -285,9 +285,14 @@ You may assume that the band gap of the $Al_{x}Ga_{1−x}As$ is substantially la
 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. Write down the Schrödinger's equation for electrons and holes
+4. Find the energies of electron and holes in the quantum well
+
 ??? hint
     It is a 2D electron gas with confined levels in the third direction
-4. Find the eigenvalues  separating $\bf{k}$ in its three components $k_x$ , $k_y$ and $k_z$)
+    
+??? hint
+    Separating $\bf{k}$ in its components $k_z$ and $k_{\perp}$ , with $k_{\perp}^2=k_x^2+k_y^2$
+
 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 $GaAs$?