Effect of donor impurities on the conduction and valence bands of silicon

The energy shifts of valence and conduction band states in silicon due to the interaction of electrons and holes with ionized donors have been calculated by performing a partial wave analysis. The potential is modeled by the Yukawa form with the screening radius determined self-consistently by the Friedel sum rule. The results show that this effect is an important part of the optically measured band-gap narrowing. The variation of the Fermi energy due to this phenomenon is also calculated.