Tim Frey · Simon Josef Thür
--- a/02_carrier_transport.tex
+++ b/02_carrier_transport.tex
    n_i = \sqrt{N_cN_v}e^{-(E_c-E_v)/2kT} = \sqrt{N_cN_v}e^{-E_g/2kT}
 \end{equation}

+Doing some algebra we get some interesting forms, relating n and p to the Fermi level:
+\begin{align}
+    n & = n_i e^{(E_f-E_fi)/kT} \\
+    p & = n_i e^{(E_fi-E_f)/kT}
--- a/02_carrier_transport.tex
+++ b/02_carrier_transport.tex
 \begin{equation}
-    n=N_ce^{-(E_c-E_f)/kT}
+    n = \int_{E_c}^{\infty} g_c(E)f(E)\,dE = N_ce^{-(E_c-E_f)/kT}
 \end{equation}
-Hole concentration in valence band:
+
+Same for the Hole concentration in valence band:
 \begin{equation}
-    p=N_ve^{-(E_f-E_v)/kT}
+    p=\int_{-\infty}^{E_v} g_v(E)[1-f(E)]\,dE = N_ve^{-(E_f-E_v)/kT}
 \end{equation}

+where effective densities of states are: (outside the course but it is nice to write down)
+\begin{align}
+    N_c &= 2\left(\frac{2\pi m_e^*kT}{h^2}\right)^{3/2} \prop T^{3/2}\\
+    N_v &= 2\left(\frac{2\pi m_h^*kT}{h^2}\right)^{3/2} \prop T^{3/2}