Commit d77a68b3 authored by Isidora Araya's avatar Isidora Araya
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Update 14_doping_and_devices_solutions.md

parent 16368a5d
......@@ -9,7 +9,7 @@ from math import pi
### Subquestion 1
Law of mass action (general):
$$ n_e n_h = \frac{1}{2} \left(\frac{k_BT}{\pi\hbar^2}\right)^3
$$ (n_e + N_A) (n_h + N_D) = \frac{1}{2} \left(\frac{k_BT}{\pi\hbar^2}\right)^3
(m_e^{\ast}m_h^{\ast})^{3/2}e^{-\beta E_{gap}}$$
Charge balance condition:
......@@ -17,8 +17,8 @@ $$ D = N_D - N_A - n_e + n_h = (doping)$$
### Subquestion 2
$$ n_e + n_A = \frac{1}{2}(\sqrt{D^2+4n_i^2}+D)$$
$$ n_h + n_D = \frac{1}{2}(\sqrt{D^2+4n_i^2}-D)$$
$$ n_{e} + N_A = \frac{1}{2}(\sqrt{D^2+4n_i^2}+D)$$
$$ n_{h} + N_D = \frac{1}{2}(\sqrt{D^2+4n_i^2}-D)$$
where $n_i=n_{e,intrinsic}=n_{h,intrinsic}$.
### Subquestion 3
......
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