Commit b735b560 by Isidora Araya

### 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\$, 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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