Extended donor states in doped semiconductors around the metal-insulator transition

Extended states arising from the $1s$ state and the $2s$ state of hydrogenic donors in highly doped semiconductors are discussed. The discussion is based on the Wigner-Seitz method, assuming a periodic potential in a virtual lattice with an average donor-donor separation. Then the Wigner-Seitz method is extended to include the effect of random distribution of donors. It is shown that the extended states of the band tail below the conduction-band edge arise mainly from the $1s$ state at donor concentrations exceeding that around the metal-insulator transition.