Update 14_doping_and_devices_solutions.md

src/14_doping_and_devices_solutions.md

@@ -55,14 +55,35 @@ $$ I_s(T) \propto e^{-E_{gap}/k_BT}$$
 ### Subquestion 1
 
 ### Subquestion 2
+This a "particle in a box" problem.
+$$\frac{-\hbar^2}{2m_e^{\*}} \frac{\partial^2 \Phi_e(z)}{\partial z^2} = (E-U_0)\Phi_e $$
+$$\frac{-\hbar^2}{2m_h^{\*}} \frac{\partial^2 \Phi_h(z)}{\partial z^2} = (E-U_0)\Phi_h $$
+
 
 ### Subquestion 3
 
+$$E_e = E_c + \frac{\hbar^2 (k_x^2+k_y^2)}{2m_e^{\*}}$$
+$$E_h = E_v - \frac{\hbar^2 (k_x^2+k_y^2)}{2m_h^{\*}}$$
+
 ### Subquestion 4
+This is a 2D electron/hole gas. Apply 2D density of states.
+$$g_e = \frac{4\pi m^_e{\*}}{\hbar^2}$$
+$$g_h = \frac{4\pi m^_h{\*}}{\hbar^2}$$
 
 ### Subquestion 5
-
+Setting $$ E_e - E_h - E_c + E_v = 1 eV = 2\frac{\hbar^2 (k_x^2+k_y^2)}{2m_e^{\*}}$$
+L can be found here for $k_x$ and $k_y$.
 ### Subquestion 6
 
+For a laser one wants to fix the emission wavelength to a certain value. With
+this setup the band gap is "easy" to design (set by L, which is fixed).
+
 ### Subquestion 7
+If donor impurities are put outside of the well (on both sides, for example)
+the donated electrons can reduce their energies by falling into the well,
+but the ionized dopants remain behind. This gives an advanttage because an
+extremely high mobility for electrons can be obtained within the quantum well
+(there are no ionized dopants in the well to scatter off of).
+This is called modulation doping.
+