E_C &= -\chi - q\psi

E_V &= E_C - E_G

At equilibrium:

n &= N_C \gamma_n \left( \eta_n \right) \exp \left( \eta_n \right)

\eta_n &= \frac{E_F - E_C}{k T}

p &= N_V \gamma_p \left( \eta_p \right) \exp \left( \eta_p \right)

\eta_p &= \frac{E_V - E_F}{k T}