Energy band diagram of an n-type semiconductor
An energy band diagram stacks the energy bands that electrons can occupy along the vertical axis. The bottom of the upper conduction band is Ec, the top of the lower valence band is Ev, and the gap between them is the band gap Eg. In an intrinsic semiconductor with no impurities, the Fermi level sits near the middle of the band gap (the intrinsic Fermi level Ei).
Adding donors such as phosphorus to silicon increases the number of electrons in the conduction band and pushes the Fermi level up toward the conduction band. Its position is given by EF − Ei = kT·ln(ND/ni): at room temperature, every tenfold increase in concentration brings it about 0.06 eV closer to the conduction band. In p-type material it moves the other way, down toward the valence band, according to the acceptor concentration.
Try it: donor concentration and Fermi level
Change the donor concentration and watch the Fermi level EF move from the intrinsic Fermi level Ei toward the conduction band edge Ec. The conditions are Si, 300 K and ni = 1.0×10¹⁰ cm⁻³, calculated with EF − Ei = kT·ln(ND/ni) (10¹⁴ to 10¹⁹ cm⁻³, the non-degenerate range).