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).
<AddI-Vplotofpndiodefromsimon'sbook>
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?
