Commit e5b3580e authored by Isidora Araya's avatar Isidora Araya
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Update 14_doping_and_devices_solutions.md

parent d8db8b7b
......@@ -71,22 +71,22 @@ $$ I_s(T) \propto e^{-E_{gap}/k_BT}$$
### Subquestion 2
This a "particle in a box" problem.
$$\frac{-\hbar^2}{2m_e^{\*}} \frac{\partial^2 \Phi_e(z)}{\partial z^2} = (E-U_0)\Phi_e $$
$$\frac{-\hbar^2}{2m_h^{\*}} \frac{\partial^2 \Phi_h(z)}{\partial z^2} = (E-U_0)\Phi_h $$
$$-\frac{\hbar^2}{2m_e^{\ast}} \frac{\partial^2 \Psi_e(z)}{\partial z^2} = (E-U_0)\Psi_e $$
$$-\frac{\hbar^2}{2m_h^{\ast}} \frac{\partial^2 \Psi_h(z)}{\partial z^2} = (E-U_0)\Psi_h $$
### Subquestion 3
$$E_e = E_c + \frac{\hbar^2 (k_x^2+k_y^2)}{2m_e^{\*}}$$
$$E_h = E_v - \frac{\hbar^2 (k_x^2+k_y^2)}{2m_h^{\*}}$$
$$E_e = E_c + \frac{\hbar^2 (k_x^2+k_y^2)}{2m_e^{\ast}}$$
$$E_h = E_v - \frac{\hbar^2 (k_x^2+k_y^2)}{2m_h^{\ast}}$$
### Subquestion 4
This is a 2D electron/hole gas. Apply 2D density of states.
$$g_e = \frac{4\pi m^_e{\*}}{\hbar^2}$$
$$g_h = \frac{4\pi m^_h{\*}}{\hbar^2}$$
$$g_e = \frac{4 \pi m_e^{\ast}}{\hbar^2}$$
$$g_h = \frac{4 \pi m_h^{\ast}}{\hbar^2}$$
### Subquestion 5
Setting $$ E_e - E_h - E_c + E_v = 1 eV = 2\frac{\hbar^2 (k_x^2+k_y^2)}{2m_e^{\*}}$$
Setting $$ E_e - E_h - E_c + E_v = 1 eV = 2\frac{\hbar^2 (k_x^2+k_y^2)}{2m_e^{\ast}}$$
L can be found here for $k_x$ and $k_y$.
### Subquestion 6
......
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