Commit e5b3580e by Isidora Araya

### 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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