Update 14_doping_and_devices_solutions.md

src/14_doping_and_devices_solutions.md

@@ -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