From d7174ea0166db342866503d4073b7ac20cd7cb8c Mon Sep 17 00:00:00 2001
From: Iacopo Bertelli <bertelli.iacopo@gmail.com>
Date: Wed, 3 Apr 2019 09:18:04 +0000
Subject: [PATCH] fixes ex4

---
 src/14_doping_and_devices.md | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/src/14_doping_and_devices.md b/src/14_doping_and_devices.md
index 3059a7c8..1f06f6a4 100644
--- a/src/14_doping_and_devices.md
+++ b/src/14_doping_and_devices.md
@@ -249,17 +249,19 @@ For that we consider a doped semiconductor in the extrinsic regime.
 ### Exercise 3: Performance of a diode
 
 ### Exercise 4: Quantum well heterojunction 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.
+A quantum well is formed from a layer of $GaAs$ of thickness $L$, surrounded by layers of $Al_{x}Ga_{1−x}As$.
+
+![Quantum Well](https://commons.wikimedia.org/wiki/File:Quantum_well.svg#/media/File:Quantum_well.svg)
+
+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. Write down the Schrödinger's equation for electrons and holes (separating $\bf{k}$ in its three components $k_x$
-, $k_y$ and $k_z$)
+3. Write down the Schrödinger's equation for electrons and holes
 ??? hint
     It is a 2D electron gas with confined levels in the third direction
-4. Find the eigenvalues
+4. Find the eigenvalues  separating $\bf{k}$ in its three components $k_x$ , $k_y$ and $k_z$)
 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 $GaAs$?
-- 
GitLab