Commit b735b560 authored by Isidora Araya's avatar Isidora Araya
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Update 14_doping_and_devices_solutions.md

parent e5b3580e
......@@ -9,14 +9,14 @@ from math import pi
### Subquestion 1
Law of mass action (general):
$$ n(T)p(T) = \frac{1}{2} \left(\frac{k_BT}{\pi\hbar^2}\right)^3
(m_e^{\*}m_h^{\*})^{3/2}e^{-\beta E_{gap}$$
$$ n_e n_h = \frac{1}{2} \left(\frac{k_BT}{\pi\hbar^2}\right)^3
(m_e^{\ast}m_h^{\ast})^{3/2}e^{-\beta E_{gap}$$
Doping:
$$ D = N_D - N_A$$
Charge balance condition:
$$ D = N_D - N_A$ - n_e + n_h$
### Subquestion 2
Charge balance condition:
$$ 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 $n_i=n_{e,intrinsic}=n_{h,intrinsic}$.
......@@ -27,6 +27,7 @@ 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.
Check both cases with lecture notes approximated solutions by doing a Taylor expansion.
## Exercise 2: Donor ionization
......
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