diff --git a/src/13_semiconductors.md b/src/13_semiconductors.md index 3d24335e1dc2fbee44f5ef54e3a99aaafc2a112e..bb0969f2f3ca8037bfb286abc8090a95c6747764 100644 --- a/src/13_semiconductors.md +++ b/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 $n_e = n_h = n_i$.