Update 13_semiconductors.md - introduced Ev for the valence band energy

src/13_semiconductors.md

@@ -182,8 +182,8 @@ $$ g(E_h) = (2m_h)^{3/2}\sqrt{E_h+E_v}/2\pi^2\hbar^3$$
 **The key algorithm of describing the state of a semiconductor:**
 
 1. Compute the density of states of all types of particles.
-2. Calculate the total amount of electrons and holes, assuming a certain value of $E_F$
-3. Write down the charge balance condition: the difference between electrons and holes should equal to the total charge of the semiconductor.
+2. Calculate the number of electrons in the conduction band and holes in the valence band, assuming a certain value of $E_F$
+3. Write down the charge balance condition: the difference between electrons and holes should equal the total charge of the semiconductor.
 4. Apply approximations to simplify the equations (this is important!).
 5. Find $E_F$ and concentrations of electrons and holes
 
@@ -229,7 +229,7 @@ Solving for $E_F$:
 
 $$E_F = \frac{E_c + E_v}{2} - \frac{3}{4}kT\log(m_e/m_h)$$
 
-An extra observation: regardless of where $E_F$ is located, $n_e n_h = N_C N_V e^{-(E_c-E_v)/kT} \equiv n_i^2$.
+An extra observation: regardless of where $E_F$ is located, $n_e n_h = N_C N_V e^{-E_g/kT} \equiv n_i^2$, where $E_g=E_c-E_v$ is the band gap of the semiconductor.
 
 $n_i$ is the **intrinsic carrier concentration**, and for a pristine semiconductor $n_e = n_h = n_i$.