Lecture_13

src/13_semiconductors.md

@@ -155,13 +155,13 @@ Therefore we can approximate the dispersion relation of both bands as parabolic.
 Or in other words
 
 $$E_e = E_c + \frac{\hbar^2k^2}{2m_e},$$
-$$E_h = E_{v,h} + \frac{\hbar^2k^2}{2m_h} = -E_{v} + \frac{\hbar^2k^2}{2m_h}$$,
+$$E_h = E_{v,h} + \frac{\hbar^2k^2}{2m_h} = -E_{v} + \frac{\hbar^2k^2}{2m_h},$$
 
 with the corresponding density of states
 
-$$ E_h = -E_V + {p^2}/{2m_h}$$
+$$ g(E) = (2m_e)^{3/2}\sqrt{E-E_c}/2\pi^2\hbar^3$$
 
-$$ g(E_h) = (2m_h)^{3/2}\sqrt{E_h+E_v}/2\pi^2\hbar^3$$.
+$$ g(E_h) = (2m_h)^{3/2}\sqrt{E_h+E_v}/2\pi^2\hbar^3.$$
 
 Here $E_c$ is the energy of an electron at the bottom of the conduction band and $E_v$ is the energy of an electron at the top of the valence band.