Fermi energy of an extrinsic semiconductor is plotted as a function of temperature. At each temperature the Fermi energy was calculated by requiring that charge neutrality be satisfied.  
 
Once the Fermi energy is known, the carrier densities $n$ and $p$ can be calculated from the formulas, $n=N_c\left(\frac{T}{300}\right)^{3/2}\exp\left(\frac{E_FE_c}{k_BT}\right)$ and $p=N_v\left(\frac{T}{300}\right)^{3/2}\exp\left(\frac{E_vE_F}{k_BT}\right)$. The intrinsic carrier density is $n_i=\sqrt{N_c\left(\frac{T}{300}\right)^{3/2}N_v\left(\frac{T}{300}\right)^{3/2}}\exp\left(\frac{E_g}{2k_BT}\right)$.  


See www.ioffe.rssi.ru/SVA/NSM/Semicond/index.html for the bandgaps and donor and acceptor states of various semiconductors.