From 76399690b378ff6629095725cb9736afe16bfa9c Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Thu, 4 Apr 2019 06:32:20 +0000
Subject: [PATCH] rewording
---
src/14_doping_and_devices.md | 37 ++++++++++++++----------------------
1 file changed, 14 insertions(+), 23 deletions(-)
diff --git a/src/14_doping_and_devices.md b/src/14_doping_and_devices.md
index cca962b5..afb3c57b 100644
--- a/src/14_doping_and_devices.md
+++ b/src/14_doping_and_devices.md
@@ -256,25 +256,19 @@ Consider a pn-junction diode as follows
By Raffamaiden [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)]), [Link](https://commons.wikimedia.org/wiki/File:PN_diode_with_electrical_symbol.svg)
-The current flowing through a diode as a function of applied bias voltage is given by
+The current flowing through a diode as a function of applied bias voltage is given by the Shockley diode equation:
$$ I(V) = I_s(T)\left(e^{\frac{eV}{kT}}-1\right)$$
-where $I_s(T)$ is the current flowing through a diode termed as saturation current. $I_s(T)$ is nearly independent of the applied bias voltage (V) but varies as a function of temperature (T).
-
-<Add I-V plot of pn diode from simon's book>
-
-1. What is the significance of adding dopant atoms to an intrinsic semiconductor? Does two intrinsic semiconductors joined together in the form a p-n diode conducts current?
-
-A p-n diode can be used as a rectifier. When forward biased (positive terminal of the battery is connected to p-type semiconductor and negative terminal is connected to n-type), a p-n diode conducts current. In contrast, when the diode is reverse biased, only negligible current flow occurs which varies as a function of temperature.
-
-2. Discuss the possible scenarios by which a pn diode generates current in the reverse biased condition.
-3. How does the temperature affects saturation current $I_s(T)$?
-4. Sketch a plot of saturation current as a function of temperature T.
+where $I_s(T)$ is the saturation current.
+1. What is the significance of adding dopant atoms to an intrinsic semiconductor?
+ Can two intrinsic semiconductors joined together make a diode?
+2. Discuss the which processes carry current in a diode under reverse biase.
+3. Based on this, estimate how the saturation current $I_s$ depends on temperature.
### Exercise 4: Quantum well heterojunction in detail
-A quantum well is formed from a layer of $GaAs$ of thickness $L$, surrounded by layers of $Al_{x}Ga_{1−x}As$.
+Consider a a quantum well formed from a layer of $GaAs$ of thickness $L$, surrounded by layers of $Al_{x}Ga_{1−x}As$.
@@ -282,20 +276,17 @@ A quantum well is formed from a layer of $GaAs$ of thickness $L$, surrounded by
Vectorised by User:Sushant savla from the work by Gianderiu - [Quantum well.svg](https://commons.wikimedia.org/w/index.php?curid=73413676), [CC-BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0 "Creative Commons Attribution-Share Alike 3.0").
-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.
-
+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 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?
+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
- It is a 2D electron gas with confined levels in z
-
-??? hint
- Separating $\bf{k}$ in its components $k_z$ and $k_{\perp}$ , with $k_{\perp}^2=k_x^2+k_y^2$
+ ??? 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 $GaAs$?
+7. What would be the advantage of doping the $Al_{x}Ga_{1−x}As$ compared to the $GaAs$ in this quantum well?
--
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