 ### 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\$, 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 ... ...
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