Commit d8db8b7b authored by Isidora Araya's avatar Isidora Araya
Browse files

Update 14_doping_and_devices_solutions.md

parent 42e3f98c
...@@ -8,18 +8,33 @@ from math import pi ...@@ -8,18 +8,33 @@ from math import pi
## Exercise 1: Crossover between extrinsic and intrinsic regimes ## Exercise 1: Crossover between extrinsic and intrinsic regimes
### Subquestion 1 ### Subquestion 1
Law of mass action (general):
$$ n(T)p(T) = \frac{1}{2} \left(\frac{k_BT}{\pi\hbar^2}\right)^3
(m_e^{\*}m_h^{\*})^{3/2}e^{-\beta E_{gap}$$
Doping:
$$ D = N_D - N_A$$
### Subquestion 2 ### Subquestion 2
Charge balance condition:
$$ n_e = \frac{1}{2}(\sqrt{D^2+4n_i^2}+D)$$
$$ n_h = \frac{1}{2}(\sqrt{D^2+4n_i^2}-D)$$
where $n_i=n_{e,intrinsic}=n_{h,intrinsic}$.
### Subquestion 3 ### Subquestion 3
If $D<<n_i$, then the doping is not important and results of intrinsic are
reproduced ($n_e \approx n_h$)
Contrarily, if $D>>n_i$, it's mostly the doping that determines $n_e$ and $n_h$.
The thermal factor becomes unimportant.
## Exercise 2: Donor ionization ## Exercise 2: Donor ionization
### Subquestion 1 ### Subquestion 1
### Subquestion 2 ### Subquestion 2
### Subquestion 3 ### Subquestion 3
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment