Effect of donor impurities on the density of states near the band edge in silicon

Using the effective mass approximation and assuming that the scatteirng events for the electrons and holes by the assembly of donors are independent, we have calculated the effects of heavy doping on the conduction and valence states in silicon. When no bound-electron states asocated with donors exist, the results show that: (1) the electron-donor interaction lowers the energy of the conduction and valence states, (2) band distortions occur, and (3) approeciable band-gap narrowing occurs. Our numerical results tend to support the band-gap estimates interpreted from optical measurements.